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i
Biomechanical Models for the Analysis of
Partial Foot Amputee Gait
Submitted by
Michael Peter Dillon
Bachelor of Prosthetics and Orthotics (Honours), La Trobe University
A thesis submitted in total fulfilment
of the requirements for the degree of
Doctor of Philosophy
School of Mechanical, Manufacturing and Medical Engineering
Faculty of Built Environment and Engineering
and
Centre for Rehabilitation Science and Engineering
Queensland University of Technology
Brisbane, Queensland, Australia
April, 2001
ii
Key words
Gait, partial foot, amputee, anthropometry, inverse dynamics, model, biomechanics
iii
Abstract
Partial foot amputation is becoming a more viable and common surgical
intervention for the treatment of advanced diabetes, vascular insufficiency and trauma.
Statistics describing the incidence of partial foot amputation are scarce. In Australia, it
is not known how many people undergo partial foot amputation annually however in the
United States upwards of 10,000 partial foot amputations are performed each year.
Many of these procedures are likely to be in preference to below-knee amputation under
the pretext of improved function associated with preserving the ankle joint and foot
length despite common failings including ulceration and equinus contracture which can
lead to more proximal amputation.
There is a substantial body of literature, which lends support to the contention
that much of clinical practice has not been based on experimental evidence describing
the gait of partial foot amputees or the influence of prosthetic and orthotic intervention.
This limited scientific underpinning of practice may contribute to the common failures
and allow misconceptions, such that preserving foot length and the ankle joint improves
function, to perpetuate.
The aim of this investigation was to develop accurate mechanical models to
analyse the effects of amputation and prosthetic/orthotic intervention on the gait of
partial foot amputees.
Anthropometric and linked-segment inverse dynamic models were developed to
accurately depict the affected lower limb and account for prosthetic/orthotic
intervention and footwear. These novel techniques enhance the accuracy of kinetic
descriptions, affecting the results obtained for terminal swing phase. These models more
accurately portray the requirements of the hamstring and gluteus maximus muscles to
decelerate the swinging limb in response to the net increase in mass and inertia of the
limb segments due to prosthetic fitting.
With an appreciation of the influence these models have on the estimation of
kinetic parameters, the gait of partial foot amputees was investigated. Kinematic
abnormalities were primarily limited to the ankle and were characterised by poor control
iv
of tibial rotation during the mid-stance phase consistent with reduced eccentric work by
the triceps surae muscles. The centre of pressure excursion and anterior progression of
the trunk outside the reduced base of support was limited until contralateral initial
contact; which could reflect triceps surae weakness and an inability to substantially load
the prosthetic forefoot. Reductions in power generation across the affected ankle were
the result of reductions in the angular excursion of the ankle and reductions in the ankle
moment. Reductions in the ankle moment were consistent with the limited excursion of
the centre of pressure commensurate with peak ground reaction forces. During early
stance, concentric activity of the hip extensor musculature was observed, bilaterally, to
advance the body forward.
Results from these investigations focus on restoring power generation across the
ankle given that the primary reason for preserving the ankle joint and calf musculature
would seem to be the ability to use it functionally. Improvements in triceps surae
strength may allow individuals to capitalise on improvements in below ankle prosthetic
design and affect significant improvements in ankle power generation. In conjunction
with improvements in muscle strength, below ankle prosthetic design needs to
incorporate a socket and toe lever capable of comfortably distributing forces caused by
loading the prosthetic forefoot. In conjunction with improvements in muscle strength,
above ankle prosthetic design needs to incorporate an ankle joint. The development of a
suitable joint poses significant design challenges for the engineer and prosthetist.
This thesis provides new insights into the gait of partial foot amputees and the
influence of prosthetic/orthotic design, which challenge common misconceptions
underpinning clinical practice, prosthetic prescription and surgery. Aside from
advancing the understanding of partial foot amputee gait and the influence of
prosthetic/orthotic fitting, these investigations challenge and aim to improve current
prosthetic and rehabilitation practice. Thus reducing the incidence of complications,
such as ulceration which have been associated with the need for more proximal below
knee amputation and allow partial foot amputees to utilise the intact ankle joint
complex.
v
Table of contents
Biomechanical Models for the Analysis of Partial Foot Amputee Gait i
Certificate of acceptance ii
Keywords ii
Abstract iii
Table of contents v
List of figures x
List of tables xv
Nomenclature xviii
Levels of partial foot amputation xix
Types of prosthetic and orthotic fittings xx
Statement of authorship xxi
Acknowledgements xxii
Chapter 1. Introduction and thesis overview 1
Chapter 2. An Anthropometric Model of the Partial Foot Residuum 7
2.1 Introduction 7
2.2 Method 11
Subjects 11
Apparatus 13
Procedure 16
Determining BSP data using the anthropometric model 16
Determining BSP data using the plaster foot replicas 17
2.3 Results 22
2.4 Discussion 31
2.5 Conclusion 38
Chapter 3. Inverse Dynamic Models for the analysis of Partial Foot Amputee
Gait 39
3.1 Introduction 39
3.2 Method 44
vi
Subjects 44
Apparatus 45
Procedure 48
Laboratory set-up 48
Equipment accuracy 49
Equipment calibration 51
Subject preparation and examination 51
Data acquisition and processing 53
3.3 Results 56
3.4 Discussion 70
3.5 Conclusion 72
Chapter 4. A Biomechanical Analysis of Partial Foot Amputee Gait 75
4.1 Introduction 75
4.2 Method 82
Subjects 82
Apparatus 84
Subject preparation 85
Data acquisition and processing 85
4.3 Results 88
Joint range of motion and muscle strength 88
Temperospatial characteristics 89
Ground reaction force and centre of pressure excursion 94
Repeatability of kinematic, kinetic and electromyographic data 101
Kinematics 102
Kinetics 111
Ankle joint moments 111
Knee joint moments 115
Hip joint moments 117
Ankle joint powers 120
Knee Joint powers 123
Hip joint powers 127
Electromyography 130
4.4 Discussion 144
vii
Range of motion and muscle strength 144
Temperospatial parameters 145
Kinematics 148
Ankle kinematics 148
Knee kinematics 158
Hip kinematics 161
Kinetics 161
Signal processing issues affecting electromyographic data 171
4.5 Conclusion 175
Chapter 5. Clinical implications affecting prosthetic design and rehabilitation
practice 178
5.1 Introduction 178
5.2 Clamshell sockets 179
5.3 Below ankle sockets, orthoses and toe fillers 185
5.4 Prosthetic prescription 188
5.5 Conclusion 188
Chapter 6. Conclusion and indications for further investigation 191
6.1 Conclusion 191
6.2 Further research 196
Appendix A. Letter for patient recruitment 199
Appendix B. An anthropometric model of the partial foot residuum 202
B.1 Introduction 202
B.2 Determining foot mass 207
B.3 Determining foot centre of mass 218
B.4 Determining mass moment of inertia of the foot 222
B.5 Determining foot volume 230
B.6 Effect of errors in anthropometric input data 230
Appendix C. Validation of the incremental immersion technique for determining
volume and centre of volume 242
viii
C.1 Introduction 242
C.2 Method 243
Subject 243
Apparatus 243
Procedure 243
C.3 Results 244
C.4 Discussion 246
C.5 Conclusion 247
Appendix D. Subject consent form 248
Appendix E. Software to process and report kinematic and kinetic data 251
E.1 Introduction 251
E.2 Processing force plate data 251
E.3 Processing kinematic data 256
E.4 Processing kinetic data 258
E.5 Processing temperospatial data 260
E.6 Reporting kinematic and kinetic data 260
Appendix F. Linked-segment inverse dynamic models for the analysis of partial
foot amputee gait: implementation 263
F.1 Introduction 263
F.2 Obtaining the necessary anthropometric descriptions 264
F.3 Combining the individual segment anthropometric descriptions 265
F.4 Transformation of the mass centroid location between the local/joint
and global coordinate systems 267
F.5 Deriving the remaining input data necessary to calculate joint moments
and powers 269
F.6 Calculating joint moments and powers 270
Appendix G. Physical assessment forms 277
Anthropometric measurement form 278
ROM assessment form 283
Muscle strength assessment form 284
ix
Appendix H. Additional results and discussion 285
Chapter 2: Additional results and discussion 285
H2.1 Bland and Altman plots for assessing agreement between
two methods of measurement 285
Chapter 3: Additional results and discussion 289
H3.1 Peak moments and powers observed during stance and
swing phase 289
H3.2 Influence of anthropometry on joint moments and powers 289
Sample-A/partial foot model-A 295
Sample-B/partial foot model-B 300
Appendix I. Gait reports 304
References 321
x
List of figures
2.1 Geometric model of a Metatarsophalangeal residuum 14
2.2 Pendulum trifilar system 16
2.3 Regression of modelled vs. experimentally derived foot mass 27
2.4 Regression of modelled vs. experimentally derived foot volume 27
2.5 Regression of modelled vs. experimentally derived CM along the x
axis
28
2.6 Regression of modelled vs. experimentally derived CM along the z
axis
28
2.7 Regression of modelled vs. experimentally derived k about the x axis 29
2.8 Regression of modelled vs. experimentally derived k about the y axis 29
2.9 Regression of modelled vs. experimentally derived k about the z axis 30
2.10 Illustration of basis vectors used to describe the position of the
centre of mass
33
3.1 Exploded view of force plate and kinematic calibration frame 49
3.2 Set up of gait laboratory 50
3.3 Points of interest examined on joint moment profiles 55
3.4 Points of interest examined on joint power profiles 56
3.5 Mean joint moments estimates using a standard linked-segment
model and the partial foot models
62
3.6 Mean joint powers estimates using a standard linked-segment model
and the partial foot models
63
3.7 Mean hip extension moment peaks during terminal swing for both
standard and partial foot linked-segment models
65
3.8 Mean knee extension moment peaks during terminal swing for both
standard and partial foot linked-segment models
66
3.9 Mean knee flexion moment peaks during terminal swing for both
standard and partial foot linked-segment models
67
3.10 Mean hip power generation/absorption during terminal swing for
both standard and partial foot linked-segment models
68
xi
3.11 Mean hip power absorption during terminal swing for both standard
and partial foot linked-segment models
69
4.1 Fore-aft ground reaction force for the affected and sound limbs of
the unilateral amputee subjects
95
4.2 Fore-aft ground reaction force for the bilateral amputee subjects 96
4.3 Vertical ground reaction force for the bilateral amputee subjects 97
4.4 Vertical ground reaction force for the affected and sound limbs of
the unilateral amputee subjects
98
4.5 Sagittal plane centre of pressure excursion for the affected and sound
limbs of the unilateral amputee subjects
100
4.6 Sagittal plane centre of pressure excursion for the bilateral amputee
subjects
101
4.7 Sagittal plane hip flexion/extension angles for the affected and sound
limbs of the unilateral amputee subjects
103
4.8 Sagittal plane hip flexion/extension angles for the bilateral amputee
subjects
104
4.9 Sagittal plane knee flexion/extension angles for the affected and
sound limbs of the unilateral amputee subjects
106
4.10 Sagittal plane knee flexion/extension angles for the bilateral amputee
subjects
107
4.11 Sagittal plane ankle dorsiflexion/plantarflexion angles for the
affected and sound limbs of the unilateral amputee subjects
109
4.12 Sagittal plane ankle dorsiflexion/plantarflexion angles for the
bilateral amputee subjects and those with Clamshell prostheses
110
4.13 Sagittal plane ankle moments for the affected and sound limbs of the
unilateral amputee subjects
112
4.14 Sagittal plane ankle moments for the bilateral amputee subjects 113
4.15 Sagittal plane ankle moments for the affected limbs of the Chopart
amputees
114
4.16 Sagittal plane knee moments for the affected and sound limbs of the
unilateral amputee subjects
116
4.17 Sagittal plane knee moments for the bilateral amputee subjects 117
xii
4.18 Sagittal plane hip moments for the affected and sound limbs of the
unilateral amputee subjects
118
4.19 Sagittal plane hip moments for the bilateral amputee subjects 119
4.20 Sagittal plane ankle power for the affected and sound limbs of the
unilateral amputee subjects
121
4.21 Sagittal plane ankle power for the bilateral amputee subjects 122
4.22 Sagittal plane ankle power for the affected limbs of Chopart
amputees
123
4.23 Sagittal plane knee power for the affected and sound limbs of the
unilateral amputee subjects
125
4.24 Sagittal plane knee power for the bilateral amputee subjects 126
4.25 Sagittal plane hip power for the affected and sound limbs of the
unilateral amputee subjects
128
4.26 Sagittal plane hip power for the bilateral amputee subjects 129
4.27 Mean EMG of tibialis anterior for the affected limb of subject 2103-
1906A
131
4.28 EMG of tibialis anterior for the affected limb of subject 2103-1906A 131
4.29 Mean EMG of tibialis anterior for both limbs of subject 2803-0410A 132
4.30 Bilateral EMG activity of tibialis anterior for subject 2803-0410A 133
4.31 EMG activity of tibialis anterior for affected limb for subject 2103-
2116A
134
4.32 Mean EMG activity of triceps surae for the affected limb of subject
2103-1906A
135
4.33 Mean EMG activity of triceps surae for the affected limb of subject
2703-1903A
136
4.34 EMG activity of soleus for the affected limb of subject 2103-1906A 136
4.35 EMG activity of biceps femoris long head for the affected limb of
subject 3004-1102A
137
4.36 Mean EMG activity of biceps femoris long head for both limbs of
subject 0904-1924A
138
4.37 EMG activity of biceps femoris long head for both limbs of subject
0904-1924A
139
xiii
4.38 EMG activity of vastus lateralis for the affected limb of subject
2103-2116A
141
4.39 EMG activity of vastus lateralis for the sound limb of subject 3004-
1102A
141
4.40 EMG data for the affected limb of subject 2803-0410A 142
4.41 Mean EMG activity of tibialis anterior for affected limb of subject
2103-1903A
143
B.1 Geometric model of the partial foot 203
B.2 Geometric model of the partial foot – exploded view 204
B.3 Basic trapezoid plate 208
B.4 Basic parabolic plate 208
B.5 Schematic diagram showing modelled and anatomical shape of the
forefoot
210
E.1 Schematic of support phase calculation using a combination of force
platform and footswitch derived event times
255
E.2 Mean joint powers for the control sample 262
F.1 Schematic illustrating derivation of anthropometric characteristics
describing the lower limb of a Chopart amputee
266
F.2 Depiction of a frame of the gait cycle shortly after heel contact for a
Chopart amputee
270
F.3 Free body diagram of a transmetatarsal amputee at mid-stance
modelled using partial foot model-A
273
F.4 Free body diagram of the “lumped” foot, leg, prosthesis and shoe of
a Chopart amputee modelled using partial foot model-B
276
H2.1 Differences between modelled and experimentally derived foot mass 286
H2.2 Differences between modelled and experimentally derived foot
volume
286
H2.3 Differences between modelled and experimentally derived foot CM
in the x-direction
287
H2.4 Differences between modelled and experimentally derived foot CM
in the z-direction
287
H2.5 Differences between modelled and experimentally derived value of k
about the x-axis
288
xiv
H2.6 Differences between modelled and experimentally derived value of k
about the y-axis
288
H2.7 Differences between modelled and experimentally derived value of k
about the z-axis
289
H3.1 Contributions to the knee joint moment equation using a standard
linked-segment model and partial foot model-A
297
H3.2 Contributions to the hip joint moment equation using a standard
linked-segment model and partial foot model-A
298
H3.3 Contributions to the knee joint moment equation using a standard
linked-segment model and partial foot model-B
301
H3.4 Contributions to the hip joint moment equation using a standard
linked-segment model and partial foot model-B
302
xv
List of tables
2.1 Anthropometric characteristics of the normal and amputee samples 12
2.2 Mean modelled and experimentally derived BSP data for the normal
sample
23
2.3 Mean modelled and experimentally derived BSP data for the
amputee sample
24
2.4 Results from regression analysis for the normal sample 25
2.5 Results from the regression analysis for the amputee sample 26
2.6 Mean difference between modelled and experimentally derived body
segment parameter data
31
2.7 Differences in the value of k between normal and amputee sample
derived using the model and experimental techniques
35
3.1 Amputee subject characteristics 44
3.2 Mean anthropometric data of the isolated foot segment for standard
linked-segment models and the partial foot models
57
3.3 Mean anthropometric data of the isolated leg segment for standard
linked-segment models and the partial foot models
58
3.4 Mean anthropometric data of the isolated thigh segment for standard
linked-segment models and the partial foot models
59
3.5 Characteristics of the combined prosthesis/orthosis and shoe for
samples A and B
59
3.6 Mean anthropometric data of the lumped segments for standard
linked-segment models and the partial foot models
60
3.7 Mean hip extension moment peaks during terminal swing for
standard linked-segment models and the partial foot models
65
3.8 Mean knee extension moment peaks during initial swing for standard
linked-segment models and the partial foot models
66
3.9 Mean knee flexion moment peaks during terminal swing for standard
linked-segment models and the partial foot models
67
3.10 Mean hip power generation/absorption during terminal swing for
standard and partial foot linked-segment models
68
xvi
3.11 Mean knee power absorption during terminal swing for standard and
partial foot linked-segment models
69
4.1 Characteristics of the amputee subjects 83
4.2 Spatial characteristics of the amputee subjects 91
4.3 Temporal characteristics of the amputee subjects 92
4.4 Single and double support phase characteristics of the amputee
subjects
93
4.5 Inter-subject variability of kinematic and kinetic patterns of the
normal population
102
4.6 Inter-subject variability of EMG patterns of the normal population 102
4.7 Periods of vastus lateralis activity observed during stance phase
including mean intensity
140
B.1 Notations 205
B.2 Anthropometric notation and measurement descriptions 206
B.3 Constants 207
B.4 Maximum errors in anthropometric input data 231
B.5 Errors in BSP data caused by errors in parameter 'b' 232
B.6 Errors in BSP data caused by errors in parameter 'c' 233
B.7 Errors in BSP data caused by errors in parameter 'l' and 'la' 234
B.8 Errors in BSP data caused by errors in parameter 'h2' 235
B.9 Errors in BSP data caused by errors in parameter 'h1' 236
B.10 Errors in BSP data caused by errors in parameter 'aml' 237
B.11 Errors in BSP data caused by errors in parameter 'aap' 238
B.12 Errors in BSP data caused by errors in parameter 'lhf' 239
B.13 Errors in BSP data caused by errors in parameter 'aaphf' 240
B.14 Errors in BSP data caused by errors in parameter 'rr' 241
C.1 Comparison of theoretical and experimentally derived V and CV of
the steel calibration block for the water only condition
244
C.2 Comparison of the theoretical and experimentally derived V and CV
of the steel calibration block for the water plus soap condition
245
C.3 Weight of liquid in the immersion container pre and post experiment
for the water only condition
245
C.4 Weight of liquid in the immersion container pre and pot experiment 246
xvii
for the water plus soap condition
F.1 Anthropometric data of the remnant foot, leg, thigh, and
prosthesis/shoe stored in cell matrix format
264
F.2 A complete set of anthropometric characteristics of the “lumped” leg,
foot, prosthesis and shoe for the affected limb of a single Chopart
amputee
267
H3.1 Mean hip joint moment peaks for both standard and partial foot
linked-segment models
290
H3.2 Mean knee joint moment peaks for both standard and partial foot
linked-segment
291
H3.3 Mean ankle joint moment peaks for both standard and partial foot
linked-segment models
292
H3.4 Mean hip joint power peaks for both standard and partial foot linked-
segment models
292
H3.5 Mean knee joint power peaks for both standard and partial foot
linked-segment models
293
H3.6 Mean ankle joint power peaks for both standard and partial foot
linked-segment models
294
xviii
Nomenclature
MTP Metatarsophalangeal BF Biceps femoris long head
TMT Transmetatarsal VL Vastus lateralis
BSP Body segment parameter SOL Soleus
M Mass RoM Range of Motion
V Volume EMG Electromyography
CM Centre of mass A/D Analogue to Digital
CV Centre of volume MMT Manual Muscle Test
k Radius of gyration Bi Bilateral
I Mass moment of inertia Uni Unilateral
CV Coefficient of variability GC Gait cycle
IFL Intact foot length AL Affected limb
RFL Residual foot length SL Sound limb
CI Confidence interval CHC Contralateral heel contact
PTB Patella Tendon bearing Fx Horizontal ground reaction force
CoP Centre of pressure Fz Vertical ground reaction force
GCS Global coordinate system SL Shoe length
LCS Local coordinate system Deg. Degrees
HM Hip moment Flex. Flexion
KM Knee moment Ext. Extension
AM Ankle moment SD Standard deviation
HP Hip power GRF Ground Reaction Force
KP Knee power R Right
AP Ankle power L Left
HA Hip angle ABS Absolute (as in error)
KA Knee angle LFP Leg/foot/prosthesis/shoe
AA Ankle angle FP Foot/prosthesis/shoe
TA Tibialis anterior CMC Coefficient of multiple
determination
GM Gastrocnemius medial head
GL Gastrocnemius lateral head
xix
Levels of partial foot amputation
Figure I Schematic of a various levels of partial foot amputation which will be referred
to throughout the thesis
A. Metatarsophalangeal (MTP)
MTP amputation is a complete
disarticulation of the MTP joint
B. Transmatatarsal (TMT)
TMT amputation is a complete
transverse amputation through part of the
metatarsal bones
C. Lisfranc
Lisfranc amputation leaves the talus,
calcaneus and some or all of the
cuniforms and navicular as remnant
bones
D. Chopart
Chopart amputation leaves the calcaneus
and talus as remnant bones
xx
Types of prosthetic and orthotic fittings
Figure II Types of prosthetic and orthotic fittings referred to throughout the thesis
Clamshell prosthesis
The clamshell prosthesis, often referred to as the clamshell
patella tendon bearing (PTB) prosthesis when the socket
extends proximally to (and loads) the patella tendon, is
typically fitted to Chopart amputees. This device encompass
the remnant foot and leg segment (or a portion there of) and
as such eliminates ankle motion. The clamshell prosthesis
often contains a carbon fibre forefoot (depicted here) or part
of a prosthetic foot bonded onto the anterior and/or inferior
portion of the socket such as used by subjects in this
investigation
Foot orthoses, shoe inserts and toe fillers
Subjects in the present investigation had polypropylene foot
orthoses, Pelite or EVA shoe inserts with or without toe
fillers made from Plastizote.
Below ankle slipper sockets
This picture depicts below ankle slipper sockets with
supramalleolar suspension. Subjects in the present
investigation used similar devices without supramalleolar
suspension. In this picture, the forefoot section was replaced
with a carbon fibre footplate. Subjects in the presented
investigation had their forefoot replaced with a portion of a
prosthetic forefoot or replaced with foams such as
EVA/pelite
xxi
Statement of authorship
The work contained in this thesis has not been previously submitted for a degree
or diploma at any other higher education institution. To the best of my knowledge and
belief, the thesis contains no material previously published or written by any other
person except where due reference is made.
Michael Dillon
April 24th, 2001
xxii
Acknowledgments
I would like to acknowledge with love and sincere gratitude the many ways my wife
and best friend, Andrea, has enriched my life with grace, patience, thoughtfulness and
most of all love. Andrea’s contributions to this thesis go back many years. I wish to
thank Andrea for the support she has demonstrated to my research which was no more
evident than by her move to Australia so that I could pursue answers to the questions I
had about partial foot amputee gait. I recognise, but cannot begin to appreciate, how
difficult a move this was for her to leave behind her family, friends and those bitterly
cold Edmonton winters. Since that time, Andrea has contributed in many ways, only a
few of which I’m sure I’ve noticed. Andrea once gave me a poem by Patrick Overton,
which has continued to be my inspiration when I felt that the challenge was beyond me.
When you come to the edge of all the light you
have, and must take a step into the darkness of
the unknown, believe that one of two things will
happen to you: either there will be something
solid for you to stand on or you will be taught
how to fly. – Patrick Overton
To my supervisor, Dr. Tim Barker, who demonstrated tremendous patience given my
lack of skills in engineering or measuring pretty much anything, but always respected
my background in prosthetics. I think Tim recognised the formidable challenge ahead of
him when as a student in one of his mathematical modelling classes to fourth year
engineering students I asked, ‘What’s a matrix?’ I would like to acknowledge the
tremendous contribution Tim has made in giving me many of the skills necessary to
begin a career in biomechanics and an appreciation of the many skills I don’t yet have.
I wish to acknowledge a debt to Professor John Evans, whose door is always open. As a
friend, John listened to my woes and gave me the advice, support and encouragement to
continue in the face of many adversities. As a mentor, John taught me by example, a
love of research and the excitement and possibilities that come with learning something
new. I thank John for the opportunity to work alongside some tremendous people and
xxiii
contribute to many of the exciting projects being undertaken by the Centre for
Rehabilitation Science and Engineering.
I wish to thank Dr Graeme Pettet, for his extensive contribution to the development of
the anthropometric model. Graeme was the first person I’ve met with a real passion for
mathematics, which was matched only be his ability to apply it. I would like to thank
Graeme for the patience he demonstrated in teaching me the skills I needed to tackle the
challenge of developing a mathematical model and for a newfound interest in
mathematics.
I would like to acknowledge my gratitude to Dr James Smeathers for the insightful
contribution he made to the initial examination of my thesis.
My initial interest in partial foot amputee gait and the prosthetic/orthotic attempts to
replace the lost foot were sparked by Les Barnes, my third year prosthetics lecturer. Les
had an obvious interest in the problems of fitting partial foot amputees, which must
have been infectious.
Dr. Tim Bach, influenced my career forever when during a second year biomechanics
lecture on how gait aids reduce joint compressive forces I recognised the tremendous
insight that could be gained into how things work using biomechanics.
To Rod Goodrick and the staff at Goodwill Orthopaedics for giving me the freedom and
space to practice in prosthetics while undertaking my PhD.
I have been fortunate enough to have the support and friendship of so many people who
have also contributed to my thesis in so many ways. I wish offer my sincere thanks and
debt to Stef, Kurt, Michelle, Ros, Laurent, Jarrod and Joan.
I wish to thank the many people who gave so generously of their time to participate in
the research. Hopefully soon your contributions will be rewarded.
xxiv
to Tim Barker.
________________________________________________________ Chapter 1. 1
Introduction and thesis overview
Partial foot amputation has long been thought of as an alternative to below knee
amputation (McKittrick et al., 1949) and is becoming a more viable and common
surgical intervention (Imler, 1985; Sobel, 1995 – cited Sobel, 2000) for the treatment of
advanced diabetes, vascular insufficiency and trauma where previously a below knee
amputation may have been the only reasonable choice. These surgical choices have
been enabled by a better understanding of diabetes and vascular disease, improvements
in surgical techniques for revascularising the arteriole structure of the foot (Habershaw
et al., 1993; Pomposelli et al., 1993) and antibiotic therapy for controlling ascending
infection (Habershaw et al., 1993; Pomoselli et al., 1993; Mueller and Sinacore, 1994)
and septicemia (Mueller and Sinacore, 1994).
Statistics describing the incidence of partial foot amputation are scarce. In
Australia it is not known how many people undergo partial foot amputation annually or
how many individuals are living in the community with partial foot amputation. The
National Centre for Disease Statistics in the United States reports that approximately
10,000 transmetatarsal amputations were performed in the USA in 1991 (Mueller and
Sinacore, 1994) and presumably, many alternate forms of partial foot amputation were
also performed. Many of these procedures are likely to have been in preference to below
knee amputation (Chrzan et al., 1993; Quigley et al., 1995; Stuck et al., 1995; Sanders,
1997).
Chapter 1
________________________________________________________ Chapter 1. 2
The preferential decision for partial foot amputation could be influenced by a
broad array of factors including the likelihood of losing the contralateral lower limb
(Sobel, 2000), the ability to weight bear on the residuum (Mc Kittrick et al., 1949;
Miller et al., 1991; Mueller and Sinacore, 1994; Boyd et al., 1999), improved cosmesis
at distal levels, psychological impact of higher amputation, lower mortality rate (Lee et
al., 1993 cited - Mueller et al., 1995), improved function associated with the
preservation of foot length (Lieberman et al., 1993; Mueller and Sinacore, 1994;
Garabolsa et al., 1996; Sanders, 1997; Mueller et al., 1998), the desire to maintain ankle
motion (Condie, 1970; Schwindt et al., 1973; Imler, 1985; Lange, 1987; Heim, 1994) or
at the patient's request for less invasive surgery.
There is little doubt that preserving a portion of the weight-bearing limb has
certain advantages. The ability to ambulate short distances without a prosthesis is easier
and safer for the partial foot amputee compared to the below knee amputee who may
hop to the toilet during the night or from a pool change room to the waters edge. In less
active individuals, the preservation of a portion of the foot may increase mobility.
Moreover, for many people unfortunate enough to loose the contralateral lower limb,
bilateral or unilateral partial foot amputation may aid transfers in and out of a
wheelchair or bed and offer enhanced mobility compared to a bilateral below knee
amputee. While there is little experimental evidence to support these views, they would
seem to be logical and clinically well accepted.
Although partial foot amputation may be preferable to more proximal
amputation for any number of these reasons, there is considerable evidence highlighting
that the procedure has a significant failure rate (Sage et al., 1989; Hodge et al., 1989;
Miller, 1991; Sanders and Dunlap, 1992; Mueller and Sinacore, 1994) and numerous
complications including ulceration (Sage et al., 1989), skin breakdown (Brand, 1983;
Sage et al., 1989; Birkie and Sims, 1988; Mueller and Sinacore, 1994) and equinus
contracture (Parzaile and Hahn, 1988; Chrzan et al., 1993; Garabolsa et al., 1996;
Sanders, 1997) which can lead to more proximal amputation. Many of these
complications have, rightly, tainted the perception of patients, surgeons, physicians and
allied health clinicians who have witnessed, first hand, these problems limit the mobility
and quality of life of many people with partial foot amputation. Complications such as
________________________________________________________ Chapter 1. 3
ulceration and delayed would healing are likely to increase length of hospital stay,
which in hindsight often serves little purpose other than to delay below knee
amputation.
Many of the complications which can result in more proximal, below knee,
amputation are likely to be influenced by the limited knowledge of partial foot amputee
gait and the effect of prosthetic/orthotic intervention. Much of the knowledge basis that
underpins clinical practice is often illogical, speculative and anecdotal, despite general
clinical acceptance.
There is a substantial body of literature, which lends weight to the contention
that current clinical practice is based largely without experimental evidence or logical
argument based on the biomechanics of partial foot amputee gait. Instead, validation for
clinical practice is drawn from an understanding of normal gait or that of other amputee
groups. The strength of this contention is evidenced in virtually any aspect of literature
concerning prescription, prosthetic/orthotic design, surgery and, to a lesser extent,
biomechanics.
For example, the literature illustrates a common belief that preserving foot
length should be a primary surgical objective, necessary to maintain function or normal
gait (Barry et al., 1993; Giurini et al., 1993; Pinzur et al., 1997; Sobel, 2000) despite
virtually no experimental evidence to support the existence of any such relationship.
Implications that foot length should be preserved because energy expenditure is
increased with more proximal amputation (Barry et al., 1993; Santi et al., 1993; Stuck
et al., 1995; Garabolsa et al., 1996; Sobel, 2000) were founded on investigations of
metabolic expenditure in transfemoral, transtibial and Symes amputees (Walters et al.,
1976) or implied from investigations of the ground reaction force in mid-foot amputees
(Pinzur et al., 1997). Moreover, authors speculate that prosthetic/orthotic devices or
footwear are able to restore the lost foot length/lever arm (Condie, 1970; Rubin, 1984;
Rubin, 1985; Pullen, 1987; Stills, 1987; Condie and Stills, 1988, Weber, 1991; Mueller
and Sinacore, 1994; Sanders, 1997; Sobel, 2000) or that full-length shoes increase the
lever arm and magnitude of the ground reaction force (Sanders, 1997). These
contentions are founded largely without experimental evidence and seem illogical given
the clinical inability of most partial foot amputees to perform a simple activity such as
________________________________________________________ Chapter 1. 4
'standing up on their toes.' Similarly, alarming contentions suggest that these devices
also aid propulsion or push-off (Rubin and Denisi, 1971; Rubin, 1984; Rubin, 1985;
Stills, 1987; Sobel, 2000) or that hallux or toe amputation results in a loss of push-off or
propulsion (Sanders, 1997; Sobel, 2000). Some authors suggest that individuals should
advance the lower limb forward using the hip flexor musculature to reduce plantar
pressures or push-off (Mueller and Sinacore, 1994; Mueller et al., 1995) as has been
advocated in diabetics with intact feet (Brand, 1983; Mueller and Sinacore, 1994). More
recent work suggests that partial foot amputees adopt a hip flexor gait to compensate for
a lack of power generation across the ankle (Mueller et al., 1998) but the experimental
evidence supporting this view is unconvincing.
Recently, many of these more common contentions have received attention as a
result of a growing awareness of the inadequacies of our understanding of partial foot
amputee gait, prescription and clinical practice. There is an increasing body of literature
examining the kinematic, ground reaction force, kinetic, temperospatial, plantar
pressure and muscle strength parameters of, primarily, the affected limb. These data
have been contributed by a small number of authors who have each, examined limited
aspects of gait, primarily at or distal to the transmetatarsal level (Dillon, 1995;
Garabolsa et al., 1996; Hirsch et al., 1996; Dorostkar et al., 1997; Burnfield et al., 1998;
Muller et al., 1998; Boyd et al., 1999). Much of this work remains ongoing with limited
details appearing in conference abstracts or research progress reports. Collectively,
these investigations raise questions about the causes and compensatory effects of
abnormal movement.
Of particular interest is the lack of power generated across the ankle (Dillon,
1995; Mueller et al., 1998) given that one important function of preserving the ankle
and calf musculature would seem to be the ability to use it. The cause of power
reduction is poorly understood and explained (Dillon, 1995; Mueller et al., 1998), as is
the influence of prosthetic/orthotic design on the ability to generate power across the
ankle. It is not yet known how partial foot amputees generate sufficient power to
advance the lower limb into swing phase and the body forward given that there appears
to be no obvious or convincing evidence (Dillon, 1995; Mueller et al., 1998) describing
compensations for reductions in ankle power generation on the affected limb. Perhaps,
as in transfemoral amputees, power is generated across the sound hip during the
________________________________________________________ Chapter 1. 5
preswing phase to advance the lower limb into swing phase and the body forward. A
thorough investigation documenting the biomechanics of partial foot amputee gait
would seem timely.
The objective of this thesis was to describe the effects of amputation and
prosthetic/orthotic fitting on gait with particular attention to why power generation
across the ankle is negligible, how sufficient power is generated to advance the lower
limb into swing phase and the influence of prosthetic/orthotic fitting.
This thesis is presented in a series of five subsequent chapters describing the
development and application of biomechanics models for the analysis of partial foot
amputee gait and prosthetic/orthotic fitting.
In Chapter 2, a geometric model is presented to provide a means for readily
estimating accurate anthropometric data of the partial foot residuum. This model may be
advantageous to investigators of partial foot amputee gait because it acknowledges the
unique anthropometry of the partial foot residuum, thus addressing one of the
limitations of previous kinetic investigations. The accuracy of the model was compared
with experimentally derived anthropometric estimates obtained using incremental
immersion and torsional table experiments.
The linked-segment inverse dynamic models presented in Chapter 3, incorporate
these improved anthropometric characteristics of the remnant foot and any
prosthetic/orthotic fitting and footwear to enhance the accuracy of biomechanical
descriptions of partial foot amputee gait. The linked-segment models describe novel and
more accurate representations of the lower limb of partial foot amputees. The effect of
these improved mechanical descriptions was contrasted against kinetic estimates
obtained from a standard linked-segment model.
Given that the primary objective of the thesis was to evaluate causes and
compensatory effects of abnormal power generation, linked-segment models were
developed for a sagittal plane analysis only, given that the major proportion of work is
performed in the plane of progression (Eng and Winter, 1995).
________________________________________________________ Chapter 1. 6
With an appreciation of the influence these models have on joint moments and
powers, they were used to document the walking patterns of a cohort of partial foot
amputees and describe the affect of amputation and prosthetic/orthotic fitting on gait in
Chapter 4. This investigation documents bilateral kinematic, kinetic, temperospatial,
ground reaction force, electromyography and joint range of motion and muscle strength
parameters of a cohort of normal and partial foot amputees.
In Chapter 5, results from the preceding investigation of partial foot amputee
gait were used to explore some of the clinical implications of these findings in relation
to the design of prosthetic/orthotic devices and rehabilitation practices for individuals
with partial foot amputation.
The major findings of these investigations are brought together in Chapter 6 and
indications for further investigation are discussed.
________________________________________________________ Chapter 2. 7
An anthropometric model of the partial foot
residuum
2.1 Introduction
Knowledge of the dimensional and inertial characteristics of the human body
are of significance to research in fields as diverse as space technology, automotive
vehicle design, physical education, gait analysis and prosthetics. As a result, a number
of researchers have devoted substantial effort toward providing these fundamental data
(Dempster, 1955; Hanavan, 1964; Clauser et al., 1969; McConville et al., 1980;
Plagenhoef, 1983; Zatsiorsky et al., 1990).
There are numerous methods of determining these data, the most accurate of
which would be to determine these measurements in vivo (Zatsiorsky and Seluyanov,
1985; Zatsiorsky et al., 1990). These methods are complex, time consuming and still
rely on assumption (McConville et al., 1980) and are, therefore, not routinely utilised.
The methods currently utilised to estimate body segment parameters (BSP) data can be
divided into two methodological groups: proportional data sets and geometric models
(Kingma et al., 1996).
Chapter 2
________________________________________________________ Chapter 2. 8
Proportional anthropometric data sets estimate body segment parameters using
regression equations, requiring minimal anthropometric measurements such as body
mass, stature and/or limb length and mid-segment circumference. Segment
characteristics are determined as a proportion of body mass or stature. Much of the data
utilised by these models were derived using small samples of cadaver specimens in an
aged population (Dempster, 1955; Clauser et al., 1969). Other studies have focused on
a specific population, such as athletes (Plagenhoef, 1983), soldiers (McConville et al.,
1980) or physical education students (Zatsiorsky et al., 1990) to determine these
measurements in vivo. While these anthropometric data sets may provide useful data
when applied within the populations the studies are based on, the uncertainty about the
data will grow as the models are applied to subjects with anthropometric characteristics
differing from the mean of that population (Kingma et al., 1996).
Geometric anthropometric models determine body segment parameters from
simple geometric shapes. Geometric representations of the human body have previously
utilised ellipses and elliptical cylinders (Hanavan, 1964) or segments divided into small
elliptical zones (Jensen, 1986). Other models utilise a variety of geometric forms to
represent the human body (Hatze, 1979; Vaughan et al., 1992). The drawbacks of these
geometric models are that they require more input measurements to derive the model
and many do not utilise the geometric form to estimate segment mass (M) (Hanavan,
1964; Vaughan et al., 1992) or centre of mass (CM) (Vaughan et al., 1992). Most of
these geometric models also assume uniform density of the limb segment. Geometric
models of human segments have the advantage that they can, in principle, be applied to
any population although the resulting accuracy is often not adequately reported (Hatze,
1979; Vaughan et al., 1992).
BSP have been used extensively for gait analysis as input data into
mathematical representations of the human body so that determinants of human
walking, such as joint moments and powers, can be estimated.
The majority of these models have limited applicability for analysis of amputee
gait because they are based on normal, non-amputee, populations and do not reflect the
unique anthropometric changes which occur due to amputation or prosthetic/orthotic
fitting.
________________________________________________________ Chapter 2. 9
When normal BSP are used to represent the partial foot residuum (Dillon, 1995;
Boyd et al., 1999) the increased M, change in the position of the CM and increased
inertial parameters relative to that of the amputee may yield inaccurate joint moment
and power estimates, especially during swing phase. In the same way, certain types of
partial foot prosthesis, such as the clamshell patella tendon bearing prosthesis, may
significantly modify the total segment M, CM and mass moment of inertia (I) and yield
inaccurate joint moment and power estimates.
Previous studies, on transfemoral and transtibial amputees, have attempted to
address these shortcomings by estimating anthropometric parameters for the residual
limb (Contini, 1970; Krouskop, 1988; Bach, 1994) and prosthesis (Capozzo et al.,
1976; Miller, 1987; Czerniecki et al., 1991; Bach, 1994). Investigations into partial foot
amputee gait have not reported addressing either of these issues (Dillon, 1995; Muller
et al., 1998; Boyd et al., 1999).
While the physical characteristics of the prosthesis/orthosis are readily
determined using standard dynamics techniques, the same characteristics of the partial
foot residuum are not so readily obtained. A number of techniques may be suitable to
determine these parameters for use with living subjects (Reid and Jensen, 1990).
Among these, incremental immersion is the most convenient and inexpensive method
of determining volume (V) and centre of volume (CV). If assumptions are made about
segment density this technique can yield estimates of M and CM. The value of I of
isolated body segments can be determined easily using the 'torsional table' or
'pendulum' method. However, this technique is not suitable for in vivo measurement.
Typically, these inertial data are obtained on cadaver specimens or plaster models of
limb segments (Contini, 1972). Mathematical modelling has the advantage that these
BSP data can be determined in a fraction of the time, once the model is developed.
Incremental immersion involves submerging a limb segment to a series of
specified depths and measuring the volume of water displaced by each successive
increment. If a constant density is assumed, M and CM (assumed equivalent to the CV
for a limb with constant density) can be estimated by summation across incremental
volumes. This method has been used with good results on normal subjects (Drillis and
________________________________________________________ Chapter 2. 10
Contini, 1966; Pagenhoef, 1971), transtibial (Fernie and Holliday, 1982) and
transfemoral amputees (Contini, 1970). Some authors have measured the volume of a
plaster cast of the residuum (Contini, 1970) or of the prosthetic socket (Bach, 1994) as
an alternate method for determining the residuum V and CV.
It is not possible to use the incremental immersion techniques to derive values
of I of the limb segment. The 'torsional table ' and 'pendulum' methods have been
widely used to determine I of isolated body segments (Nubar, 1962 -cited Drillis et al.,
1964; Drillis et al., 1964; Contini, 1972; McConville et al., 1980) and prosthetic
components (Drillis et al., 1964; Drillis and Contini, 1966; Bach, 1994; Burkett, 1998).
These techniques are most easily executed using a plaster model of the limb segment
(Contini, 1972) and are recommended over other methods of determining I such as the
'quick release method' (Drillis and Contini, 1966).
Mathematical modelling of segments through geometric representation may be
advantageous because a generic model of the partial foot residuum characterised by a
few anthropometric measurements would simplify the process of deriving the required
anthropometric data. The difficulty with selecting a suitable mathematical technique is
that many do not predict segment M (Hanavan, 1964; Vaughan et al., 1992) or CM
(Vaughan et al., 1992) using the geometric representation of the limb segment. Some,
more complex, models do predict M, CM and I using the geometric form (Hatze, 1979)
but still have limited application for certain populations due to the models' assumptions
of segment density (Schneider et al., 1990; Schneider and Zernicke, 1992). The utility
of the Hatze (1979) model is further limited by the lack of documentation describing
the input parameters necessary to execute the model and in some cases, inconsistencies
exist between the published mathematical notation and the geometric form1.
1 There appears to be some inconsistencies in the height measurements of the foot (h2,h1) between themathematical notation, the schematic figures and sample measurements in Appendix 4 (Hatze, 1979).These were confirmed by derivation of Hatze's equations from first principles. Based on the derivationfrom first principles, the sample measurements and schematic figures, h2 seems to describe the height ofthe foot from the floor to the apex of the lateral malleolus and h1 describes the height from the floor to thetop of the 1st Metatarsal head. If these deductions are true, then the height of top segment of the foot (S14)should be given by h2-h1 and not by h2, as indicated by Hatze, (1979). The schematic of the foot modeland associated measurements (Hatze, 1979) imply that the S14 segment height is equal to h2, however, thesample input data in Appendix 4 (Hatze, 1979) and the derivation of Hatze's equations from firstprinciples contradict this. Without clear descriptions of the actual measurements used to execute themodel and their relationship to the mathematical equations described by Hatze, (1979) there is no way tovalidate these equations.
________________________________________________________ Chapter 2. 11
Proportional anthropometric data sets, which predict segment M or CM as a
function of weight and height are not sensitive to the changes in BSP which occur due
to partial foot amputation. Partial foot amputation does not alter stature or significantly
alter body mass despite making large differences to the foot segment characteristics.
The differences observed in foot length, M, CM and I are not reflected by these
proportional anthropometric data sets and as such may not be suitable for this
population of amputees.
The aim of this work is to:
1. develop an anthropometric model to predict the V, M, CM and I of the partial foot
residuum and the normal foot;
2. compare the modelled predictions of M, V, CM and I to those BSP predicted from
incremental immersion and torsional table experiments using cast replicas of both
the intact and partial foot
2.2 Method
Subjects
A number of individuals were recruited, both with and without forefoot
amputation, for a number of concurrent gait investigations. Amputee subjects were
recruited through the definitive prosthetic budget holder; Queensland Amputee Limb
Service (QALS). Letters were sent to QALS for distribution to individuals currently
listed on their books with partial foot amputation (Appendix A). Subjects then
responded by telephone to acknowledge their wish to participate. Amputee subjects
were also recruited from definitive prosthetic/orthotic service providers.
QALS issued 56 letters to individuals listed as partial foot amputees. Many of
the respondents were Symes amputees or others who had been incorrectly categorised.
Fourteen individuals with partial foot amputation were identified through QALS and of
those recruited through the definitive prosthetic/orthotic service providers, all had
already received invitations from QALS. Three of the respondent's were children, all of
whom were excluded after pilot testing, due to the lengthy data collection period (4-5
hours) which made data collection difficult and unpleasant for the children. One subject
________________________________________________________ Chapter 2. 12
was excluded because of polio after presenting to the university, which was not
identified at the time the subject initially responded to acknowledge their wish to
participate. Another subject failed to attend three appointments and another became ill
and required further surgery prior to testing.
The primary cause of amputation amongst the remaining sample was trauma.
Some individuals had partial foot amputation from gangrene secondary to frostbite or
full thickness burns. No subjects in the sample had an amputation as a result of vascular
disease. Amputation level was assessed by a qualified prosthetist/orthotist (the author)
using palpation of the residual limb. Measurements of residual foot length were taken
and expressed as a percentage of intact foot length to verify amputation level (Dillon,
1995). Where possible, amputation level was also assessed using x-rays of the residual
foot.
Subjects were excluded from participation if they ambulated with the use of gait
aids, had previous limb operations or concomitant health problems such as ulcers,
which might affect gait or prevent them from undertaking all aspects of the evaluation.
Both bilateral and unilateral partial forefoot amputees were accepted as participants.
Amputation level, aetiology, age, sex and years since amputation were not included as
selection criteria because it was felt that this would place undue restriction on the
number of partial foot amputees who could be recruited. Control subjects satisfied the
same inclusion criteria as the amputee subjects. Individual control subjects were
matched for sex, age, stature and mass to one of the amputee subjects. Anthropometric
characteristics have been reported in Table 2.1 for both the normal and amputee
samples.
Modelled and experimentally derived BSP data were computed for 19 feet
including nine intact feet, two Metatarsophalangeal (MTP), one Transmetatarsal (TMT),
five Lisfranc and two Chopart residuums. Dental plaster replicas of the subjects feet
were preferable to true in vivo measurements because the I calculations were simplified,
CM estimates could be obtained for all directional axes and subjects would not have to
endure the tedious incremental immersion process to obtain V and CV data.
________________________________________________________ Chapter 2. 13
Table 2.1 Anthropometric characteristics of the normal and amputee samples.
Mean values for stature, body mass, residual foot length (RFL) and intact foot length (IFL) are presented
and the standard deviation (SD) reported in brackets. SD for mass and stature was not reported for the
MTP and TMT amputees, as there was only one amputee in each group. The MTP amputee was bilateral,
hence the SD values reported for RFL. IFL were estimated for the MTP subject as a proportion of stature
(Dempster, 1955).
Sub samples of the Amputee sampleNormal
sample
(n=9)
Amputee
Sample
(n=10)
MTP
(n=2)
TMT
(n=1)
Lisfranc
(n=5)
Chopart
(n=2)
Stature (m) 1.81
(0.07)
1.75
(0.08)
1.74
(.)
1.82
(.)
1.74
(0.11)
1.77
(0.02)
Body mass (kg) 85.49
(9.20)
73.10
(14.95)
64.85
(.)
84.50
(.)
67.74
(16.30)
89.05
(5.59)
Foot length
-IFL (m) 0.27
(0.01)
0.26
(0.01)
0.26
(0.00)
0.27
(.)
0.26
(0.01)
0.27
(0.01)
-RFL (m) 0.27
(0.01)
0.15
(0.03)
0.20
(0.00)
0.17
(.)
0.14
(0.02)
0.11
(0.00)
-RFL (% IFL) 100.00
(0.00)
52.67
(12.64)
76.72
(0.54)
62.26 55.36
(5.42)
41.15
(1.63)
Apparatus
Dimensional and inertial characteristics of the partial and normal feet were
derived using a geometric model based on work by Hatze, (1979). From first principles,
the model was derived as an assemblage of 103 plates of varying dimensions and
densities (Appendix B). Three trapezoidal plates represent the most inferior portion of
the ball of the foot (S11), the heel (S12), and the sole above these regions (S13) (Figure
2.1). The remaining 100 plates account for the middle and upper part of the foot (S14)
which were described using parabolic (S14P) and trapezoidal (S14
T) plates (Figure 2.1).
The model is symmetrical about the x-axis (Figure 2.1).
________________________________________________________ Chapter 2. 14
Figure 2.1. Geometric model of a Metatarsophalangeal residuum
Further information about the component pieces of the model including an exploded view have been
documented in Appendix B.
Anthropometric measurements of the subject's feet were taken using a set of
anthropometric callipers, with a maximum measuring range of 15cm, and a 30cm ruler.
The resolution of the measuring equipment was one millimetre. As an example of the
effect of errors in anthropometric input data, each anthropometric input parameter for a
single normal subject was independently manipulated by subtracting/adding the
maximum error associated with each input measurement and recording the BSP
calculated (Appendix B). Comparisons of the resulting BSP data to baseline values
highlighted that errors in the measurement of the lateral malleolus height (h2) and the
height of the first metatarsal (h1) had the largest affect on the prediction of BSP data
and as such should be measured with the greatest care (Appendix B). A ±3mm error
associated with the measurement of either h2 or h1 resulted in a 30ml change in foot V
(3.4%), 40g change in foot M (3.8%) and 2mm change in location of the mass centroid
along the z-axis (4.3%) (Tables B.8 and B.9). Errors in the measurement of length of
the hindfoot (lhf) of ±4mm resulted in ±3mm changes (6.3%) in the location of the
mass centroid along the z-axis (Table B.12). Errors in the measurement of other
anthropometric input data did not make significant differences to the prediction of BSP
data (Appendix B).
Z
X
YS11
S14P
S14T
S13
S12
________________________________________________________ Chapter 2. 15
The subject's feet were cast using plaster of Paris bandage and the negative
moulds were filled with dental plaster to produce the replicas. Obvious anomalies, such
as those caused by joins in the plaster negative were removed with a surform or filled
with dental plaster. The casts were then cleaned with sand screen prior to being sealed
with shellac.
Two containers were used during all immersion study experiments. The first
container was a Décor 5ltr (model 396) with an internal height of 16cm. The sides of
the container were not square. The internal dimensions of the top of the container were
30x12cm and the bottom 28.5x11cm. This container was used for immersion of the foot
model along the z-axis and will now be referred to as the z-axis immersion container.
The model axes are depicted in Figure 2.1. The second container was a ClickClack
2.1ltr canister (model 302502), with an internal height of 19.8cm and the radius at the
top of the container was 14cm. From the bottom of the container to 3cm from the top
the radius was 12.5cm. This container was used for immersion of the foot model along
the x-axis and will now be referred to as the x-axis immersion container (Figure 2.1).
An Ohanus electronic scale (model GT4100), with a resolution of 0.1g, was used to
weigh the displaced water and plaster model. A surgical steel tray with external
dimensions of 0.52×0.32×0.06m was used to catch the displaced water before decanting
into a one litre Biomex measuring beaker. A cake cooling rack was placed in the
catchment tray to keep the immersion container out of the displaced water.
Liquid soap (Bactercidal liquid soap no.563-214, RS components Pty Ltd.
Brisbane) was used to decrease the water surface tension during the incremental
immersion experiments (Appendix C). The soap was proportioned at 5g to every 2000g
of water.
A trifilar pendulum system (Figure 2.2) and an electronic, handheld, stopwatch
were used to determine the period of oscillation; a component in the calculation of the
value of I (Maltbaek, 1988). The bottom plate of the trifilar had a mass of 0.977 kg and
the value of I was theoretically determined to be 0.0168 kg.m2.
________________________________________________________ Chapter 2. 16
Figure 2.2 Pendulum Trifilar system for calculating of the inertia of isolated body
segments.
Procedure
Partial foot amputees and normal subjects presented to the university gait
laboratory for the collection of data for this investigation, as part of a comprehensive
gait analysis. Prior to the collection of data, the experimental procedures and equipment
were explained to each participant and any questions they had regarding the session
were answered prior to them consenting to participate in the experiment as required by
the University Human Research ethics committee (Appendix D). A physical
examination and medical history were documented (Appendix I) and any details about
the condition of the residuum were noted. Attempts were made to access the subject's
medical records so that details about the surgical intervention such as heel cord
lengthening, muscle reattachment or special bony modifications could be noted. These
medical records were extremely difficult to obtain, even with subject's written consent,
and the information about the surgical procedure was often sketchy and inadequate.
Determining BSP data using the anthropometric model
Physical dimensions of the partial and normal foot were recorded as described
in Table B.2 (Appendix B).
Anthropometric measurements of intact foot length (l) and the height of the 1st
metatarsal head (h1) were unable to be obtained for the bilateral MTP subject. These
measurements were estimated using regression equations. Intact foot length was
________________________________________________________ Chapter 2. 17
estimated as a proportion of stature according to Dempster (1955). The regression
equation used to estimate h1 was derived from height measurements, of the 1st
metatarsal head of a sample of intact feet and normalised for stature. The regression
coefficient was obtained by averaging these normalised data and is presented in Table
B.2 (Appendix B).
The recorded anthropometric measurements, describing the physical
characteristics of the foot, were then entered into a Matlab 5.3 (Mathworks Inc.
Englewood Cliffs, NJ) script and stored to file. Estimates of M, V, CM and I were then
derived using the geometric model described in Appendix B and stored to file for use in
the inverse dynamic model (Chapter 3).
If the density of the mathematical model was made uniform or constant, and
equivalent to that of the plaster foot being analysed, the modelled M, V, CM and I
could be compared to the experimentally derived BSP data. Density of the plaster foot
in kg/m3 was given by
(1)
where, Mpf described the mass of the plaster foot and Vpf the volume of the
plaster foot being studied.
Modelled values of I were expressed as radii of gyration, k, to account for the
reduction in M of the plaster foot replicas between the incremental immersion and
trifilar experiments; presumably as a result of the plaster feet dehydrating. These
changes in M were assumed not to affect the assumption of uniform density.
Determining BSP data using the plaster foot replicas
To obtain the negative mould, necessary to produce the plaster foot replica,
subjects were positioned prone on a treatment plinth. Prior to casting the foot in a non-
weight bearing position with the ankle at 90 degrees and the subtalar joint in neutral,
lines horizontally and vertically bisecting the lateral malleolus were marked with
indelible pencil. The foot and ankle were cast in 2 stages so that the plaster mould did
not have to be cut off the subject. The negative impression was removed once the
pf
pfpf
V
M=γ
________________________________________________________ Chapter 2. 18
plaster had cured and immediately reassembled. Subjects then participated in the gait
analysis testing session.
To create the replica plaster foot, the negative plaster mould of the subject's feet
was positioned such that the horizontal line bisecting the lateral malleolus was level.
Dental plaster was then poured into the negative cast to the horizontal line bisecting the
lateral malleolus. Once cured, the plaster bandage was removed and any obvious
anomalies, such as those caused by joins in the plaster negative were removed with a
surform or filled with dental plaster. The casts were then cleaned with sand screen prior
to being sealed with several coats of shellac.
Increments of immersion were marked on the foot along the z and x-axes. One-
centimetre increments were marked along the negative z-axis and numbered
consecutively from the top of the foot to approximately 1.5cm from the sole. The x-axis
origin was located at the line vertically bisecting the lateral malleolus. Immersion
increments were consecutively marked every 2cm along the negative and positive x-
axis from the origin to approximately 1.5cm from the heel and from the origin to
approximately 3.5cm in the intact foot - appropriately shorter for the partial feet. It was
not possible to establish more distal increments of immersion along the positive x-axis
as the volume of displaced water was too small to measure accurately. In some
instances, the origin of the foot was moved distally as only two thirds of an intact foot
was able to be immersed at any time due to the size of the immersion container
available. When calculating the CM, the origin of the plaster replica was adjusted
accordingly such that the origin of the model and plaster foot replica matched.
During the pilot investigations, it was noted that the plaster foot was able to
absorb water despite being sealed; a finding also reported by Contini (1970). If the foot
was left to soak in water for a period of 30 minutes prior to the study, the water
absorption noted was negligible as evidenced by the pre and post experiment weight of
the plaster foot replica.
Pilot investigations also demonstrated that the volume of liquid held in the tank
pre-test was an important predictor of the volume displacement during the immersion
study. Once the tank appeared full, it was possible to still add more liquid creating a
________________________________________________________ Chapter 2. 19
meniscus on the surface of the tank. During initial experiments each tank was filled
until the liquid begun to flow over the tank. The volume of liquid in the tank was
recorded and duplicated, prior to the commencement of each experiment. The weight of
liquid in the tank was noted prior to each experiment so that the error due to this
variable could be adequately assessed.
Prior to the commencement of each experimental session, the plaster foot was
left to soak in a bucket of water for 30 minutes. During this time, the stainless steel
catchment tray was placed on a level laboratory bench and the desired immersion
container placed on the cake cooling rack in the tray. The z-axis immersion container
was filled with 5.8kg of liquid and the x-axis immersion container was filled with 2.7
kg of liquid (Appendix C). The liquid decanted into each immersion container was
weighed using a Biomex 1ltr measuring beaker and this value recorded on the data
collection sheet. The plaster foot was also weighed at this time and the value recorded.
The plaster foot was immersed to each immersion increment marked on the plaster foot
and the liquid displaced in the catchment tray was decanted into the measuring beaker
and the water weight was recorded. This decanted liquid was returned to the immersion
container prior to data collection for the next immersion increment. Immediately after
the volume of the last increment was recorded the plaster foot was weighed and the
volume of liquid left in the immersion container was recorded. This experimental
procedure was repeated three times for each directional axis.
The volume of each immersion increment was determined by the change in
displaced liquid volume between immersion increments. Foot V was determined by
summation of the volume of each immersion increment. The total foot V was calculated
as the average foot V of each directional axis.
Foot CM was given by the sum of the products of the segment volumes and the
segment lever-arms, from the origin of the foot, divided by the total foot volume. Foot
CM data were derived and averaged across the trials for each directional axis.
With knowledge of the dimensional characteristics of the trifilar, the M and CM
of the plaster foot, the value of I of the plaster foot replica could be calculated. The
________________________________________________________ Chapter 2. 20
plaster foot was weighed using electronic scales and the position of the CM of the foot
had already been determined from the incremental immersion studies.
To determine the value of I, the CM of the plaster foot was located over the
centre of the bottom disc of the Trifilar. The bottom disc of the trifilar was displaced
slightly to produce a small amplitude oscillation and the time taken to produce 10
oscillations was recorded. This process was repeated five times and the period of
oscillation averaged across the trials. This process was repeated for each directional
axis.
The value of I of the plaster foot and the bottom plate combined, Ic, was
determined in a similar manner to that by Maltbaek (1988), and is given by
(2)
where Mc is the mass of the plaster foot and the bottom plate of the trifilar
combined, Rp, the distance from the centre of the bottom plate to the wire attachment
and l, the wire length. A value of 9.81m/s2 was used for the acceleration due to gravity,
g, in the calculations. The frequency of oscillation, f, was given by
(3)
where, t is the time period for 10 oscillations of the combined foot replica and
bottom plate of the trifilar.
The value of I of the plaster foot, Ipf was given by
(4)
where, Ic describes the combined I of the plaster foot and the bottom plate of the
trifilar and It describes the I of the bottom plate of the trifilar which can be theoretically
determined using the geometric equation for I of a circular plate
tf
10=
tcpf III −=
( ) lf
RpgMcIc 2
2
.2
..
π=
________________________________________________________ Chapter 2. 21
(5)
where, Mt is the mass of the bottom plate of the trifilar and R is the radius of the
plate.
The value of I was calculated for each directional axis using this process and
converted into radius of gyration to account for differences in foot mass between the
modelled and experimentally derived values of I.
Density of each subject's plaster foot replica was calculated (Eq. 1) and applied
to the model. BSP data were calculated using the mathematical model and the V, M,
CM and k data were recorded for comparison to the experimentally determined BSP
obtained from the incremental immersion and torsional table experiments using the
subject's replica plaster feet.
Paired two tailed t-tests and linear regression analyses comparing the slope of
the regression line were used to provide information about the differences between
paired observations and whether changes in BSP predicted using the geometric model
and experimental techniques were linear. The linear regression analysis compared the
95%CI of the slope of the regression line, when the y-intercept was forced through
zero, to the slope of the theoretical line of identity (Zar, 1984). The coefficient of
determination (r2) has been reported for the sake of completeness and not as a definitive
measure of the linearity of the relationship between BSP predicted using two different
techniques. While these statistical measures provide information about differences
between paired observations and describe the linearity of changes in BSP predicted
using these two techniques, the magnitude of the differences observed is not obvious.
To augment the interpretation of the paired t-test and regression analyses, the
differences between BSP data predicted using the model and experimental techniques
have been presented in Appendix H according the method described by Bland and
Altman (1986). Additional information about the mean differences between paired
observations was determined by using the basic formula (Eq 6). As an example, the
relative volume difference, v, between each experimental and modelled BSP was given,
as a percentage, by
2
.2
RMI
tt =
________________________________________________________ Chapter 2. 22
(6)
Hatze, (1979) where Vm denotes the modelled volume and Ve the experimentally
derived segment volume. By interchanging the variable, V, for other BSP data, the
relative difference for all characteristics was determined.
2.3 Results
Modelled and experimentally derived BSP data were computed for 19 feet
including nine normal (intact), two MTP, one TMT, five Lisfranc and two Chopart
residuums. These feet were categorised into a normal and amputee sample. A two tailed
t-test for sample means revealed significant differences in RFL expressed as both an
absolute difference (p<0.001) and as a percentage of IFL (p<0.001) between the normal
and amputee samples. Differences in body mass between the normal and amputee
samples approached significance (p=0.05) due to the inclusion of one male subject. If
this subject was removed from the sample there were no significant differences
observed (p=0.10). Given that each parameter tested was a paired sample (modelled vs.
experimental) the difference observed was not of concern. No significant differences in
IFL (p=0.32) or stature (p=0.15) were observed between groups.
Paired two tailed t-tests were used to determine any statistically significant
differences between the modelled and experimentally derived BSP data. The absolute
differences and percentage difference in M, V, CM and k values for the normal and
amputee samples have been presented in Tables 2.2-2.3, respectively. No significant
differences were observed between paired modelled and experimentally derived
estimates of foot M, V, CM in either the sample of intact (Table 2.2) or amputated feet
(Table 2.3). No significant differences were noted for values of k about the y and z-axes
in the sample of intact feet (Table 2.2) however, significant differences in the value of k
about the x-axes were observed (p=0.04). Estimates of k obtained for the sample of
partial feet were also significant different for all directional axes (Table 2.3).
−=
e
m
V
Vv 1.100
________________________________________________________ Chapter 2. 23
Table 2.2 Mean modelled and experimentally derived BSP data for the normal sample
γ constant denotes constant density. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Standard
deviation is reported in brackets. * denotes statistically significant differences (p<0.05).
Modelled
BSP data
Experimental
BSP data
Difference
γ constant γ constant Absolute % Significance
Mass (kg) 1.416
(0.150)
1.469
(0.155)
-0.053 3.6
p = 0.09
Volume (litres) 1.011
(0.100)
1.047
(0.069)
-0.036 3.4
p = 0.08
CMx (m) 0.063
(0.004)
0.062
(0.004)
0.001 -1.6
p = 0.33
CMy (m) - - - - -
CMz (m) -0.044
(0.004)
-0.044
(0.004)
0.000 0.0
p = 0.75
kxx (m) 0.031
(0.001)
0.045
(0.016)
-0.014 31.1 *
p = 0.04
kyy (m) 0.073
(0.003)
0.073
(0.007)
0.000 0.0
p = 0.98
kzz (m) 0.075
(0.003)
0.071
(0.008)
0.004 -5.6
p = 0.22
________________________________________________________ Chapter 2. 24
Table 2.3 Mean modelled and experimentally derived BSP data for the amputee
sample
γ constant denotes constant density. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Standard
deviation is reported in brackets. * denotes statistically significant differences (p<0.05)
Modelled
BSP data
Experimental
BSP data
Differences
γ constant γ constant Absolute % Significance
Mass (kg) 0.879
(0.223)
0.877
(0.201)
0.002 -0.2
p = 0.81
Volume (litres) 0.597
(0.170)
0.594
(0.154)
0.003 -0.5
p = 0.71
CMx (m) 0.014
(0.021)
0.014
(0.021)
0.00 0.0
p = 0.73
CMy (m) - - - - -
CMz (m) -0.037
(0.004)
-0.038
(0.004)
0.001 2.6
p = 0.43
kxx (m) 0.028
(0.003)
0.047
(0.04)
-0.019 40.4 *
p = 0.00
kyy (m) 0.045
(0.008)
0.064
(0.006)
-0.019 29.7 *
p = 0.00
kzz (m) 0.048
(0.008)
0.063
(0.006)
-0.015 23.8 *
p = 0.00
Results from the linear regression analysis have been reported for the sample of
intact and partial feet in Tables 2.4-2.5 and Figures 2.3-2.9. The regression coefficients
for M, V and CM were not significantly different from one across both the samples of
intact and partial feet. (Figures 2.3-2.6). The large confidence intervals of the
regression coefficients highlight the variability in predicting values of k compared to
other BSP data (Tables 2.4-2.5). All regression coefficients of k for the amputee sample
were different from one (Table 2.5). For the normal sample, the regression coefficients
________________________________________________________ Chapter 2. 25
of kyy and kzz were not significantly difference from one (Table 2.4). In comparison to
the experimentally derived values of kxx the model predictions were substantially biased
(Figure 2.7) across both the normal and amputee samples (Tables 2.4-2.5) and the
distribution of residuals was not bivariate (Figure 2.7). In the amputee sample,
predictions of kyy and kzz were quite variable (Figures 2.8-2.9) and the biases observed
were not as strong as for kxx (Table 2.5).
Table 2.4 Results from regression analysis for the normal sample.
Coefficient of determination (R2). Regression coefficient (ß) and 95%CI of the slope of the regression
line when the y-intercept was forced through zero. Standard error of estimate of modelled on
experimental BSP (SEme). Standard errors of the regression coefficient (ß) are reported in brackets.
Regression Coefficient
ß 95% Confidence Interval
R2 SEme
Mass (kg) 1.04
(0.02)
0.99 1.08 0.74 0.08
Volume (l) 1.03
(0.02)
0.99 1.08 0.73 0.06
CMx (m) 0.99
(0.01)
0.96 1.01 0.78 0.00
CMy (m) - - - - -
CMz (m) 0.98
(0.04)
0.88 1.08 0.04 0.01
kxx (m) 1.42
(0.17)
1.03 1.82 0.05 0.02
kyy (m) 1.0
(0.04)
0.91 1.09 0.09 0.01
kzz (m) 0.95
(0.04)
0.86 1.04 0.01 0.01
________________________________________________________ Chapter 2. 26
Table 2.5 Results from regression analysis for the amputee sample.
Coefficient of determination (R2). Regression coefficient (ß) and 95%CI of the slope of the regression
line when the y-intercept was forced through zero. Standard error of estimate of modelled on
experimental BSP (SEme). Standard errors of the regression coefficient (ß) are reported in brackets.
Regression Coefficient
ß 95% Confidence Interval
R2 SEme
Mass (kg) 0.99
(0.01)
0.97 1.02 0.99 0.03
Volume (l) 0.99
(0.01)
0.96 1.01 0.99 0.02
CMx (m) 0.98
(0.02)
0.94 1.01 1.00 0.00
CMy (m) - - - - -
CMz (m) 1.01
(0.02)
0.98 1.05 0.81 0.00
kxx (m) 1.62
(0.10)
1.40 1.84 0.21 0.01
kyy (m) 1.37
(0.09)
1.16 1.57 0.01 0.01
kzz (m) 1.27
(0.08)
1.09 1.46 0.00 0.01
Values of r2 could be said to reveal a strong linear relationship between
modelled and experimentally derived M, V and CM in the amputee sample (Tables 2.5)
however, the results are likely to be affected by the range of foot lengths and masses
observed (Figures 2.3-2.6). These relationships were not as strong in the normal sample
indicating a marginal increase in the variability and that the range of each variable was
more limited than that of the amputee sample because all the intact feet were of a
similar size (Figures 2.3-2.5). Coefficients of determination for kxx, kyy, kzz, across the
normal and amputee samples indicate the poor strength in the linear relationship
between modelled and experimentally derived parameters (Tables 2.4-2.5).
________________________________________________________ Chapter 2. 27
Figure 2.3 Modelled versus experimentally derived foot mass of both the normal and
amputee samples.
Figure 2.4 Modelled versus experimentally derived foot volume of both the normal and
amputee sample.
y = 1.0361x
R2 = 0.7362
y = 0.9912x
R2 = 0.98690
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Modelled foot mass (kg)
Exp
erim
enta
lly d
eriv
ed foot
ma
ss (
kg)
Normal sample Amputee sample
Trend line -normal sample Trend line - amputee sample
y = 1.0316x
R2 = 0.7295
y = 0.9894x
R2 = 0.98110
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Modelled foot volume (l)
Exp
erim
enta
lly d
erive
d fo
ot
volu
me
(l)
Normal sample Amputee sample
Trend line - normal sample Trend line - amputee sample
________________________________________________________ Chapter 2. 28
Figure 2.5 Modelled versus experimentally derived CM in the x direction for both the
normal and amputee samples.
Figure 2.6 Modelled versus experimentally derived CM in the z direction for both the
normal and amputee samples.
y = 0.9783x
R2 = 0.0430
y = 1.0124x
R2 = 0.8078
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
-0.06 -0.04 -0.02 0
Modelled CMz (m)
Exp
erim
enta
lly d
eriv
ed C
Mz
(m
)
Normal sample Amputee sample
Trend line - normal sample Trend line - amputee sample
y = 0.9882x
R2 = 0.7798y = 0.9767x
R2 = 0.9961
-0.02
0
0.02
0.04
0.06
0.08
-0.02 0 0.02 0.04 0.06 0.08
Modelled CMx (m)
Exp
erim
enta
lly d
eriv
ed C
Mx
(m)
Normal sample Amputee sample
Trend line - normal sample Trend line - amputee sample
________________________________________________________ Chapter 2. 29
Figure 2.7 Modelled versus experimentally derived k about the x axis through the CM
for both the normal and amputee samples.
Figure 2.8 Modelled versus experimentally derived k about the y axis through the CM
for both the normal and amputee samples.
y = 0.9983x
R2 = 0.0873
y = 1.3653x
R2 = 0.00500.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.03 0.05 0.07 0.09
Modelled kyy (m)
Exp
eri
me
nta
lly d
eri
ved
kyy
(m
)
Normal sample Amputee sample
Trend line - normal sample Trend line - amputee sample
y = 1.4236x
R2 = 0.0454y = 1.6221x
R2 = 0.2137
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.02 0.025 0.03 0.035
Modelled kxx (m)
Exp
erim
enta
lly d
eriv
ed k
xx (
m)
Normal sample Amputee sample
Trend line - normal sample Trend line - amputee sample
________________________________________________________ Chapter 2. 30
Figure 2.9 Modelled versed experimentally derived k about the z axis through the CM
for both the normal and amputee samples.
The mean absolute and percentage differences between paired observations of
BSP predicted using the geometric model and the experimental techniques have been
presented in Table 2.6 for both the normal and amputee sample.
y = 0.9469x
R2 = 0.0121
y = 1.2706x
R2 = 0.00020.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.03 0.05 0.07 0.09
Modelled kzz (m)
Exp
eri
me
nta
lly d
eri
ved
kzz
(m
)
Normal sample Amputee sample
Trend line - normal sample Trend line - amputee sample
________________________________________________________ Chapter 2. 31
Table 2.6 Mean absolute and percentage differences between modelled and
experimenterially derived body segment parameter data
Standard deviations have been reported in brackets.
Normal sample
Differences
Amputee sample
Differences
Absolute % Absolute %
Mass (kg) -0.053
(0.082)
3.5
(5.2)
0.003
(0.033)
0.4
(4.7)
Volume (litres) -0.036
(0.055)
3.5
(5.2)
0.003
(0.022)
0.4
(4.6)
CMx (m) 0.001
(0.002)
-1.2
(3.4)
0.000
(0.001)
-4.3
(11.0)
CMy (m) - - - -
CMz (m) -0.001
(0.006)
-2.4
(13.5)
0.001
(0.002)
1.2
(5.3)
kxx (m) -0.011
(0.017)
18.3
(21.1)
-0.016
(0.007)
32.7
(12.7)
kyy (m) 0.000
(0.009)
-1.4
(10.4)
-0.017
(0.008)
27.1
(10.4)
kzz (m) 0.004
(0.009)
-6.2
(11.0)
-0.014
(0.008)
21.8
(10.9)
2.4 Discussion
The geometric model provides reasonable estimates of M and V across the
sample of intact feet and excellent estimates for the sample of partial feet compared to
experimentally derived data obtained using incremental immersion. The average
absolute difference in foot M was 53g (3.5%) for the sample of intact feet (Table 2.6)
and about 3g (<1%) for the sample of partial feet. (Table 2.6). Absolute errors in the
estimation of foot M were overstated compared to previous investigations because in
the present investigation estimates of foot M were computed using the density of each
plaster foot replica which was substantially larger than that of a normal foot. If the
________________________________________________________ Chapter 2. 32
density values used in the present investigation were assumed equivalent to estimates of
normal foot density provided by Dempster (1955), the average absolute difference in
foot M for the normal sample would be 38g. Estimates of foot V are not complicated by
assumptions of density and as such provide a better basis for comparison with other
investigations. Previous investigation using comparable models and experimental
techniques have reported errors in the estimation of intact foot volume of
approximately 1.2% with maximum errors of 3.85% (Hatze, 1980). Similar differences
were observed between estimates of modelled and experimentally derived foot V in the
amputee sample (Table 2.6) however, these differences were larger for the sample of
intact feet (Table 2.6). The geometric model tended to underestimate the foot M and V
of the intact foot compared to the data derived experimentally (Table 2.4) however, the
differences observed were not statistically significant (Table 2.4)
The geometric model also provides excellent estimates of CM across both the
normal and amputee samples. The average absolute difference in foot CM for both the
normal sample and amputee sample was about 1mm (Table 2.6). The modelled
estimates of the mass centroid location along the z-axis were quite variable (Figure 2.6)
for the sample of intact feet as quantified by the large 95%CI about the regression
coefficient (Table 2.4).
It was difficult to draw direct comparison of these results with previous
mathematical modelling literature (Hatze, 1979) because the location of the mass
centroid was described relative to a rotated set of basis vectors. Vectors are represented
using the following notation; a = a1i + a2j. The main axis of the basis system (X), once
rotated by θθθθ, passes through the CM. In this way, the position of the CM can be
described by a single vector, r, assuming θθθθ is known (Figure 2.10).
________________________________________________________ Chapter 2. 33
Figure 2.10 Illustration of basis axes and rotated axes used to describe the position of
the centre of mass (CoM)
The vector r, in terms of the basis axes (X,Y), was given by
(7)
and the length of vector r was
(8)
r in terms of the rotated axes (XR,YR) was given by
(9)
Hatze, (1979) did not report values for θθθθ or the length of the vector r but instead
reported the relative CM error in percent; the basic form of which is described by
Equation 6. Hatze, (1979) expressed the computed centroid values as a ratio between
the centroid coordinate value in the direction of the main axis of the segment, and the
RXrr =
( )22bar +=
( )bar +=
________________________________________________________ Chapter 2. 34
length of the segment (R); these values were also not reported for the foot segment. The
relative CM error (in %) was, therefore, given by
(10)
where R* was obtained from comparable cadaver data of Dempster (1955) and
z bar is the mass centroid location obtained using the geometric model.
It was not possible to ascertain the exact location of the origin of Hatze's foot
model and as such it was not possible to utilise Equation 10 to provide comparison data
for the present study because values R* of would be incorrect. However, the basic form
(Eq. 6) can be utilised to provide relative CM error estimates between the modelled and
experimental CM data for the present study. In which case the length of vector r is
given by Equation 8 and the relative error between the modelled and experimental CM
data is given by Equation 6. Hatze, (1979) found the average CM error to be
approximately 1.6%. For the present study, CM error for both the normal and amputee
sample was approximately 1% which compares favourably to those errors reported by
Hatze, (1980).
Differences in the value of k, about the long axis (kxx) of the intact foot were
significant (-0.011m, 18%) compared to those observed about the kyy and kzz axes
which, were -1.4% and -6.2%, respectively. Discrepancies between the modelled and
experimentally derived estimates of k for the partial foot sample were significant with
differences in kxx -0.016m (33%), kyy -0.017m (27%) and kzz -0.014m (22%)
highlighting a systematic error quantified by the 95%CI of the regression coefficient
(Table 2.5).
It would seem logical that following forefoot amputation, differences in the
distribution of M would result in substantial decreased in the values of k about the y-
and z-axis yet have minimal influence in values of k about the x-axis (Figure 2.1).
Comparison of modelled values of k between the normal and amputee samples (Tables
2.2 and 2.3), revealed such decreases; 10% about the x-axis and ≈37% about the z- and
y-axes (Table 2.7). However, if the experimentally derived values of k are compared
−=
lR
zr
*1100
________________________________________________________ Chapter 2. 35
for the normal and amputee samples (Tables 2.2 and 2.3), the differences observed
were significantly smaller for the y- and z-axes (≈12%) and larger for the x-axis (4%)
(Table 2.7).
Table 2.7 Differences in the value of k between normal and amputee derived using the
model and the experimental technique
kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Values extracted from Tables
2.2-2.3.
Normal Sample Amputee Sample Differences
Modelled BSP data %
kxx (m) 0.031 0.028 9.7
kyy (m) 0.073 0.045 38.4
kzz (m) 0.075 0.048 36.0
Experimental BSP data
kxx (m) 0.045 0.047 -4.4
kyy (m) 0.073 0.064 12.3
kzz (m) 0.071 0.063 11.3
Discrepancies between the computed and experimentally derived values of k are
likely to reflect the inherent inaccuracy associated with orienting the plaster foot replica
on the trifilar. The accuracy of experimentally derived values of k are reliant on the CM
of the plaster replica being positioned directly over the centre of the trifilar pendulum
and the desired axis being perpendicular to the plane of oscillation. Correctly
establishing the principle x-axis would logically seem to be the most difficult and the
range of the 95% CI of the regression coefficients reflects the experimental variability
thought to be associated with orienting the replica foot on the trifilar pendulum (Tables
2.4-2.5).
Some authors have previously recognised that it is difficult to experimentally
verify computed values of I (Hanavan, 1964; Hatze, 1980) and have utilised published
________________________________________________________ Chapter 2. 36
cadaver or in vivo data to validate modelled estimates (Hanavan, 1964; Hatze, 1979)
rather than provide direct experimental verification.
Hatze (1979) drew comparisons between modelled values of I for the foot
segments of a single individual, against comparable cadaver data from Dempster,
(1955). Corresponding values of I in kg.m2 for Hatze's subject (C.P.) and Dempster's
cadaver no. 15097 (in brackets) have been presented for the foot segment: left foot
0.0051 (0.0037), right foot 0.0051 (0.0040) kg.m2 (Hatze, 1979). Direct comparison to
previous literature is difficult given the differences in methodology. However, the
errors reported by Hatze (1979) were comparable to those observed in the partial foot
sample in the present investigation.
Detailed experimental validation and statistical analyses allows the limitations
of the geometric model and experimental technique to be recognised and adequately
described so that at least potential users of such anthropometric models can be better
informed about the data they choose to utilise.
Studies such as these are affected by the assumption of constant or varying
segment density. The present model describes varying segment density which increases
linearly from proximal to distal similar to that described by Drillis and Contini, 1972 -
cited Bach, 1994) as the proportion of muscle and bone changes (Roebuck, 1975 - cited
Bach, 1994; Ackland et al., 1988). It is difficult to assess the accuracy of Hatze's
segment density values without knowledge of the derivation of these values and it
seems impossible to verify these segment density values in vivo. It appears that these
segment density values were based on tissue density values reported by Clauser et al.,
(1969). It is possible to make a limited assessment of the accuracy of the segment
density values by comparing the average foot density against previously published
literature. The average segment density can be given by
(11)
where Vi describes the volume and γγγγi describes the density of each slice of the model.
∑
∑
=
==103
1
103
1
.
i
i
i
ii
V
Vγγ
________________________________________________________ Chapter 2. 37
Using equation 11, the average density of feet in the normal sample was
approximately 1.22 kg/m2 when Hatze's (1979) segment density values were used.
Comparable values reported elsewhere (Dempster, 1955; Drillis and Contini, 1966;
Contini, 1972), found the density of the foot segment to be about 9% smaller.
This could be due to the difference in the shape of the foot between the present
model and the Hatze (1979) model. This results in an increase in foot volume
proximally, where the larger segment density values occur, thus increasing the average
modelled density value.
Previous modifications to the model of Hatze (1979) have focused on reducing
segment density coefficients such that total body mass, measured experimentally,
matched that predicted by the model in paediatric populations (Schneider et al., 1990
and Schneider and Zernicke, 1995). Both of these adaptations did not experimentally
assess the predicted segment V and CM thereby not accounting for a scenario where the
model's predicted volume may be overestimated thus causing the segment mass to be
overestimated. Reducing the segment density values may result in values which do not
match the segment tissue densities reported by Clauser et al., (1969). The sole of the
foot model, for instance, has a segment density value of 990kg/m3 (Hatze, 1979) which
seems reasonable given that the sole is comprised mostly of fat, which has an average
density of 960kg/m3 (Clauser et al., 1969). A 17.7 % reduction in the density of this
segment (Schneider and Zernicke, 1995) would result in an average density value of
815 kg/m3, which does not reflect the density of any tissue found in the foot.
The segment density values reported by Hatze (1979) might be correct for
application to his model, however the differing shape of the present model
overestimates the average foot density when Hatze's segment density coefficients are
used. Where the average tissue values reported by Clauser et al. (1969) were not
violated, the present model reduced Hatze's (1979) segment density values by
approximately 9 % (Appendix B). Globally reducing the segment density values would
seem reasonable given that the predicted V and CM, of feet in both the normal and
amputee samples, were reasonable. In this way, the average density of the foot segment
________________________________________________________ Chapter 2. 38
was reduced in line with previous work and the experimentally validated V and CM
estimates were not altered.
This model may be advantageous to investigators of partial foot amputee gait
because it addresses one of the shortcomings of previous kinetic descriptions by
acknowledging the unique anthropometry of the partial foot residuum. Linked segment
inverse dynamic models could incorporate these improved anthropometric descriptions
of the partial foot residuum to improve the accuracy of joint moments and powers over
kinetic estimates which assume that the remnant foot can be adequately described using
BSP of the intact foot.
2.5 Conclusion
The model provides an acceptable means of quickly and easily obtaining
anthropometric data of both the normal and partial foot, with an equivalent accuracy to
previously published experimental techniques, without recourse to laborious and
arguably inaccurate experimental data.
The model provides good estimates of foot mass, volume and centre of mass
across a variety of intact and amputated feet compared to experimentally derived
estimates. The average differences did not exceed 5% and were not significantly biased.
Computed values of the radius of gyration for, primarily, the partial foot sample were
significantly different compared to experimentally derived estimates. These differences
seem to reflect the difficulty associated with accurately orienting the principal axes of
the foot replica on the trifilar pendulum and were comparable to differences observed
by previous investigators, who have reported similar difficulties in experimentally
verifying computed value of inertia.
The model provides an alternative method for estimating anthropometric
characteristics of both the partial and intact foot, which is easier and less time
consuming than experimental techniques without compromising accuracy.
________________________________________________________ Chapter 3. 39
Inverse dynamic models for the analysis of partial foot
amputee gait
3.1 Introduction
In an attempt to determine the mechanical behaviour of the human body,
engineers have developed a process of modelling the human body as a simple system
whereby the body is represented as a chain of rigid segments connected by hinge or pin
joints. This model simplifies the anatomical structure, such that the body can be
mathematically represented. This mathematical model is called a linked-segment model.
Linked-segment models of the human body have proven useful in estimating those
determinates of human walking which can not be directly measured, such as joint
reaction forces or muscle moments. The process used to derive these parameters is
known as inverse dynamics, so called because it is possible to work back from these
kinematic, anthropometric and externally measured force data to derive the kinetics
thought to be responsible for the motion.
The following assumptions are made with regard to the inverse dynamic, link-
segment model (Winter, 1990).
• Each segment has a fixed mass located as a point mass at its centre of mass
Chapter 3
________________________________________________________ Chapter 3. 40
• The location of each segment's centre of mass remains fixed during the
movement
• The joints are considered to be a simple hinge
• The mass moments of inertia of each segment remains constant during the
movement
• The length of each segment remains constant during the movement
While these assumptions are certainly not always valid, such simplified
representations of the human limb provide useful approximations for parameters that
can only be mathematically estimated.
The accuracy of data derived from the mathematical model depends on how well
the system being studied has been represented and the assumptions of the system. Other
sources of error may be derived from the kinematic, anthropometric or ground reaction
force data utilised by the model. These include the estimation of joint rotation centres
(De Looze et al., 1992b; Kingma et al., 1996), movement of markers on the skin
(Capozzo et al., 1993), varying segment lengths (De Looze et al., 1992a), estimation of
body segment parameters (Capozzo and Berme, 1990; Davis, 1992), varying cadence
and stride length (White and Lage, 1993) and errors in measurement of the magnitude
and position of the ground reaction force (Davis, 1992).
Analysis of pathological gait may violate some of the basic assumptions of the
linked-segment model and/or require additional assumptions. Anthropometric data may
be derived from models of segment geometry or experimentally measured. Inadequacies
of these techniques to describe the anthropometry of pathological body segments may
affect the accuracy of net joint moment and powers.
Previous studies on Transfemoral and Transtibial amputees have attempted to
address these issues by estimating anthropometric characteristics of the prosthesis
(Capozzo et al., 1976; Miller, 1987; Czerniecki et al., 1991; Bach, 1994) and residual
limb (Contini, 1970; Krouskop, 1988; Bach, 1994) to provide more accurate input data.
However, previous studies on partial foot amputees have not acknowledged addressing
either of these issues. Instead investigators have ignored the anthropometric
________________________________________________________ Chapter 3. 41
characteristics of any prosthetic/orthotic replacement (Dillon, 1995; Muller et al., 1998)
and/or assuming that the remnant foot can be adequately described using normal body
segment parameter (BSP) data (Dillon, 1995; Burnfield et al., 1998; Muller et al., 1998;
Boyd et al., 1999).
For many researchers, providing more accurate anthropometric input data may
seem unnecessary due to the relatively small change in mass (M), centre of mass (CM)
and mass moment of inertia (I) that occurs due to partial foot amputation and most
prosthetic/orthotic fittings. Small changes in BSP data, have been shown to impact little
on the accuracy of muscle moment data (Davis, 1992) and given the considerable effort
required to provide these anthropometric input data, have probably been assumed
insignificant by most researchers.
This assumption may be reasonable for the majority of research, which has
focussed on the gait of individuals with minor amputation of the forefoot, where
conditions of barefoot walking (Burnfield et al., 1998; Boyd et al., 1999) and orthotic
intervention (Dillon, 1995; Muller et al., 1998) have been investigated. However, when
significant portions of the forefoot are compromised the efficacy of this assumption
may become questionable. Not so much because of the significant change in
anthropometry of the remnant foot, due to Chopart or Lisfranc amputation, but because
of the substantial M and I of the Clamshell patella tendon bearing (PTB) prosthesis
typically fitted to individuals with proximal forefoot amputation.
The efficacy of this assumption could be investigated using a linked-segment
inverse dynamic model, which accounted for the change in M, CM and I of the remnant
foot and included anthropometric descriptions of any prosthetic/orthotic intervention as
well as footwear
Modelling the anthropometry of orthotic/prosthetic intervention and footwear
within the constraints of a linked-segment inverse dynamic modelling approach would
be relatively simple when these devices do not compromise motion of the ankle joint.
The M, CM and I of devices, such as insoles, toe fillers or slipper sockets, could be
combined with BSP data of the remnant foot segment and not affect the assumptions of
the linked-segment model. Orthotic replacements such as ankle foot orthoses encompass
________________________________________________________ Chapter 3. 42
multiple limb segments and as such, the anthropometric characteristics of these devices
should be partitioned appropriately to those segments encompassed by the device.
Accounting for the significant change in foot anthropometry due to partial amputation
of the forefoot, and the comparatively insignificant addition of an orthotic replacement
to the inverse dynamic model are not expected to alter ankle, knee or hip moment and
power data.
Modelling prosthetic intervention in the form of a clamshell PTB prosthesis,
within the constraints of the inverse dynamic modelling approach, is rather more
challenging because the prosthesis eliminates ankle motion. The ankle kinematic pattern
has been thought to be the result of the force-deflection characteristics of the prosthetic
foot (Dillon, 1995) or movement of the leg segment within the prosthesis rather than
true joint motion.
The elimination of ankle motion, or the assumption that the ankle motion is
negligible, is quite convenient because the leg, remnant foot, prosthesis and footwear
can be modelled as a single free body segment, which acts about the knee joint. As such
the M, CM and I of the prosthesis need not be partitioned to the foot and leg segments
separately to accurately depict the anthropometry of the amputees lower limb.
Modelling the remnant limb and prosthesis/footwear as a single segment may alter the
amputee’s joint moment and power patterns because the M of the modelled lower limb
would be increased as would the value of I due to the more distal location of the mass
centroid. The altered anthropometry of the linked-segment model may increase the knee
flexion and hip extension moments during swing phase, reflecting the increased
requirement of the hamstrings muscle group and gluteus maximus to decelerate the knee
into full extension and the hip into the initial contact hip flexion angle, respectively.
Increased power absorption across the knee and power generation across the hip joint
would be expected in line with these hypothesised moment pattern changes. The
changes in muscle moment and power data would manifest during swing phase when
the contributions of inertia and angular acceleration are largest and affect the knee and
hip where the leg and thigh segment masses are large. The ankle joint moment
calculation is dominated by the magnitude of the ground reaction force and its lever arm
about the ankle and as such is not greatly subject to angular and inertial influences.
________________________________________________________ Chapter 3. 43
Net joint moment and power data obtained from the inverse dynamic approach
are routinely interpreted as being indicative of muscular response (Powers et al., 1998).
However, the accuracy of these data may be questionable when accurate mechanical
descriptions of partial foot amputee gait are dependant on the anthropometric
characteristics or the residual foot and prosthesis/orthosis being appropriately modelled.
The requirement for an inverse dynamic model for the analysis of partial foot
amputee gait is clearly evident, given the unique anthropometric and prosthetic
constraints which have been poorly modelled by pervious investigators. The accuracy of
kinetic data seems arguable when inverse dynamic models, based on normal
individuals, are used to describe the gait of partial foot amputees wearing prosthetic
devices such as Clamshell PTB prostheses. At the very least, quantifiable data is
required to support the efficacy of disregarding the anthropometry of orthotic devices
and below ankle prosthetic sockets within the inverse dynamic model. The addition of a
clamshell PTB prosthesis to the linked-segment model is expected to alter knee and hip
moments and powers during swing phase reflecting a more accurately portrayal of the
demand on the hamstring and gluteus maximums muscles to moderate the increased
inertia and angular acceleration of the limb segment.
The aim of this work is to:
1. develop inverse dynamic models for the analysis of normal and partial foot
amputee gait, which address the inadequacies of current kinetic analysis by
adequately depicting M, CM and I of the remnant foot, proximal limb segments
and prosthesis/orthosis/shoe;
2. compare ankle, knee and hip muscle moment and power data derived using the
partial foot inverse dynamic models and a standard inverse dynamic model, such
as that used by previous investigators of partial foot amputee gait;
3. determine the accuracy of previous kinetic descriptions of partial foot amputee
gait and highlight how more accurate anthropometric descriptions affect the net
muscle moment and power estimates.
________________________________________________________ Chapter 3. 44
3.2 Method
Subjects
Subject recruitment and the provision of informed consent has previously been
described in Chapter 2.
Subjects with unilateral partial foot amputation were categorised into one of two
samples according to whether prosthetic/orthotic fitting eliminated ankle motion. Based
on this criterion, one of two linked-segment inverse dynamic models was used to
estimate net joint moments and powers for ‘Sample A - with ankle motion’ and
‘Sample B - without ankle motion’. Bilateral subjects were not included in this
investigation because body segment parameter data from the sound limb was needed to
describe comparatively 'normal' segment dimensional and inertia characteristics.
Characteristics of individuals comprising the two samples including age, stature,
mass, cause of amputation and descriptions of the prosthetic/orthotic devices fitted are
given in Table 3.1.
Table 3.1 Amputee subject characteristics
TMT is an abbreviation for Transmetatarsal. Standard deviations (SD) are reported in brackets.
Subject ID Amputation
Level
Aetiology Age
(years)
Stature
(m)
Mass
(kg)
Type of fitting
Sample A - with ankle motion
2103-2116A TMT Trauma 54 1.82 84.5 Toe filler
2103-1906A Lisfranc Trauma 55 1.80 80.7 Toe filler
2703-1903A Lisfranc Trauma 53 1.82 76.6 Slipper socket
0704-0403A Lisfranc Trauma 22 1.84 81.5 Slipper socket
Mean
SD
46
(16)
1.82
(0.02)
80.8
(2.8)
Sample B - without ankle motion
3004-1102A Chopart Trauma 19 1.79 93.0 Clamshell socket
________________________________________________________ Chapter 3. 45
Apparatus
Anthropometric characteristics of the partial and intact foot were determined
using the anthropometric model described in Chapter 2. Anthropometric characteristics
of the thigh and leg segments were determined using the anthropometric models
described by Hatze (1979). A water-soluble marker was used to identify the necessary
anatomical landmarks and a set of anthropometric callipers, 30cm ruler and tape
measure were used to record the necessary input data. A stadiometer and a set of
electronic scales were used to determine stature and body mass. The callipers, tape
measure and ruler had a resolution of 1mm and the scales had a resolution of 1g.
The M of the prosthesis/orthosis and shoe was determined using a 2kg electronic
scale with a resolution of 1g. The CM was determined using a plumb-bob and the value
of I was determined using a Trifilar pendulum system and an electronic, handheld,
stopwatch with a resolution of 1ms as described in Chapter 2.
Kinematic data were collected using a Peak 3D-motion analysis system and
Motus version 4.3.0 software (Peak Performance Technologies. Englewood CO, USA).
Six Burle TC354AX cameras (Burle Security. Ireland), with a resolution of 720x526-
PAL, were fitted with Cosmicar, 6mm, 1:1.2 TV lenses and Tiffen 40.5mm infra red
filters (Peak Performance Technologies. Englewood CO, USA). This camera set-up
sampled the location of 20mm Scotchlite reflective markers at a rate of 50Hz.
An A.M.T.I. OR6-5, six channel, strain gauge force platform and amplifier
(Advanced Mechanical Technology Inc. Waterton Mass., USA) was used to sample
ground reaction force and moment data at a rate of 1000Hz. The force platform
amplifier had a bridge excitation of 5V and a gain of 2000. The amplifier output range
was ±10V. The force platform amplifier automatically low-pass filtered data using one
of two default settings. Data were low-pass filtered at a cut-off frequency of 1050Hz
rather than at 10Hz so that the data would not be attenuated at this point. Data were
recorded using a multiplexing, 16 channel, 12 bit, analogue-to-digital (A/D) conversion
card with a ±10V range and a resolution of 4.8mV/bit (Data Translation. Marlboro
Mass., USA. Model DT 2821 ).
________________________________________________________ Chapter 3. 46
The Peak-Motus software controlled kinematic and kinetic data synchronisation.
A transistor-to-transistor logic (TTL) pulse of approximately 5V was recorded in the
analogue data in response to an increase in the voltage signal recorded on the vertical
force channel of the force platform. An event marker was also recorded in the kinematic
data at this time. Data were then synchronised by matching the event marker in the
kinematic data with the analogue pulse recorded.
Kinematic and kinetic data were derived using software coded in Matlab 5.3
(Mathworks Inc. Englewood Cliffs, NJ USA) and detailed information on data
reduction, processing and reporting has been presented in Appendix E.
Using one of two linked-segment inverse dynamic models, based on the type of
prosthetic/orthotic intervention, net joint moments and powers were estimated for the
three lower limb segments of each leg (Appendix F).
The first linked-segment model (Partial foot model-A) was based on a standard
set of inverse dynamic assumptions (Winter, 1990) and was used to describe the kinetic
patterns of partial foot amputees wearing insoles, toe fillers and slipper sockets
(Appendix F). These types of prosthetic/orthotic devices do not compromise the ankle
joint and as such the M, CM, and I of these devices could be combined with the BSP of
the remnant foot without affecting the basic assumptions of the linked-segment model.
However, in order to describe the prosthesis/orthosis and shoe within the constraints of
a standard linked-segment model it was necessary to assume that:
• the prosthesis/orthosis did not eliminate ankle motion
• the prosthesis/orthosis encompassed only the foot segment
• the residual foot, prosthesis/orthosis and shoe could be considered as a
'lumped' free body segment which rotated about the ankle joint
• the 'lumped' segment could be described by a single set of BSP data such
that the M, CM and I of the residual foot, prosthesis/orthosis and shoe were
combined
A standard linked-segment inverse dynamic model (Winter, 1990) such as that
utilised by Dillon (1995) and presumably by other investigators of partial foot amputee
________________________________________________________ Chapter 3. 47
gait (Muller et al., 1998; Burnfield et al., 1998; Boyd et al., 1999) could be easily
replicated using partial foot model-A. Utilising anthropometric descriptions of the
sound foot, leg and thigh (assumed equivalent to normal) and ignoring any
prosthesis/orthosis and footwear, partial foot model-A could be used to estimate net
joint moments and powers comparable to those determined by previous investigators of
partial foot amputee gait.
The second, linked-segment inverse dynamic model (partial foot model-B) was
used to describe kinetic parameters of amputees wearing Clamshell PTB prostheses
(Appendix F). These types of prosthetic intervention eliminate ankle motion, which for
modelling purposes was quite convenient because the leg, remnant foot, prosthesis and
shoe could be considered as a single 'lumped' free body segment about the knee joint.
As such, the M, CM and I of the prosthesis and shoe need not be partitioned to the foot
and leg segment separately to accurately depict the amputee's lower limb, assuming
that:
• the Clamshell PTB prosthesis eliminated ankle motion
• the Clamshell PTB prosthesis encompassed the remnant foot and the leg
segment or a portion there of
• the residual foot, leg, prosthesis and shoe could be considered as a 'lumped'
free body segment which rotated about the knee joint
• the 'lumped' segment could be described by a single set of BSP data such
that the M, CM and I of the residual foot, leg, prosthesis and shoe were
combined
These assumptions allow the anthropometry of the residual foot, leg and
prosthesis/shoe to be represented as a single free body segment about the knee joint.
The location of the mass centroid was described relative to the knee joint and the value
of I of the 'lumped' segment was taken through the CM of the 'lumped' segment
(Appendix F).
________________________________________________________ Chapter 3. 48
Procedure
Laboratory set-up
The force platform was embedded midway along an elevated 10m walkway. The
true origin of the force plate coordinate system was located at offsets of XO,YO, ZO from
the geometric centre, of the top surface, of the force plate (AMTI, 1999). The geometric
centre of the force plate was used to define the force plate coordinate system in X and Y
given that the true origin differed from the geometric origin by less than one millimetre
(AMTI, 1999). The offset ZO was appreciable (38mm) and was accounted for when
calculating centre of pressure (CP).
An 'L' shaped calibration frame, consisting of four markers was used to
determine the origin of the kinematic coordinate system (Figure 3.1). One arm of the
calibration frame comprised three co-linear markers and was aligned, with one edge of
the force platform, such that this arm was parallel to the direction of walking (Figure
3.1). The second arm of the calibration frame comprised two markers and was aligned
with the perpendicular edge of the force platform (Figure 3.1). Vectors connecting the
centroids of markers C and A and markers C and D defined the X and Y-axes,
respectively (Figure 3.1). The Z-axis was orthogonal to the XY plane. The kinematic
coordinate system was located at floor level.
A Scotchlite reflective marker was located on the edge of the walkway at a
known position from the force plate coordinate system (Figure 3.1). The position of this
marker was recorded in the kinematic data and allowed force data collected relative to
the force plate coordinate system to be transformed relative to the kinematic coordinate
system.
Cameras were positioned in a semicircular arrangement with three cameras
located each side of the walkway (Figure 3.2). Camera locations were based on work
examining the optimal camera locations such that the largest percentage of marker
displacement data could be tracked and the number of potential marker identifications
was minimised (Frossard and Dillon, 1999A).
________________________________________________________ Chapter 3. 49
Figure 3.1 An exploded view of the force plate and kinematic calibration frame.
The force plate coordinate system was assumed equivalent to the geometric centre of the force plate and
was identified by the orthogonal axes set (Fx, Fy, Fz). The kinematic coordinate system was identified by
the orthogonal axes set (X, Y, Z) and also identified the laboratory or global coordinate system.
Equipment accuracy
It was necessary to thoroughly examine the accuracy of the Peak-Motus system
and AMTI force platform given that the facility had previously not been commissioned.
The kinematic system was able to determine the location of a single marker in
3D space to within 0.5cm across the entire data collection area (Frossard and Dillon,
1999B). The data collection area was 5.3m (X), 1.6m (Y) and 2.2m (Z) (Figure 3.2) and
commensurate with the calibrated volume. The expected accuracy was calculated
according the system manufacturer, where the root mean square (RMS) error was
expressed relative to the distance from the base of each camera to the object observed.
The expected RMS errors were 1.78%, 1.13% and 0.89% along the X, Y and Z-axes.
________________________________________________________ Chapter 3. 50
The actual RMS errors along the X, Y and Z-axes were 0.19%, 0.34% and 0.20%,
respectively (Frossard and Dillon, 1999B). Small errors in the systems ability to
accurately predict the location of a single marker were not compounded when
reconstructing a limb segment defined by a marker at either end. Using a 92cm
calibration wand to represent an individual limb segment, the RMS error associated
with reconstructing the length of a static wand was 0.012cm (Frossard and Dillon,
1999B). During dynamic situations, the length of the wand could be reconstructed with
less accuracy as evidenced by the increased RMS error (0.105cm) (Frossard and Dillon,
1999B).
Figure 3.2 Set up of the gait laboratory.
Cameras are numbered from 1-6 with numerals at floor level next to each camera. The global coordinate
system, calibration frame and force platform are depicted in the middle of the walkway.
________________________________________________________ Chapter 3. 51
The magnitude of forces recorded in shear (Fx, Fy) and compression (Fz) were
quite accurate with differences between the applied and measured forces, expressed as a
percentage of the force applied, were 3.24±0.68%, 3.15±0.19% and 1.21±0.56%,
respectively (Frossard and Dillon, 1999B). As the magnitude of vertical force increased
to approximately body weight, the error observed along Fz reduced to 0.5% of the
applied force (Frossard and Dillon, 1999B). The mean error associated with the location
of the centre of pressure was 1.5±0.7mm and 2.2±1.7mm along the x and y-axes,
respectively (Frossard and Dillon, 1999B). These results were far superior to those
previously reported by Bobbert and Schamhardt, (1990) and simular to those reported
more recently by Middleton et al., (1999).
Equipment calibration
Prior to each testing session the laboratory was set-up as illustrated in Figures
3.1-3.2. The Peak-Motus software controlled calibration of the kinematic system.
During the calibration procedure a wand, of known dimensions, was swept through the
data collection area. The data collection area was compliant with the calibrated area. If
the calibration was unsuccessful the equipment was checked and the process repeated.
Subject preparation and examination
Subjects presented to the university biomechanics laboratory. Participants were
interviewed to obtain a medical history and standard anthropometric measurements of
stature and weight were recorded. Anthropometric characteristics of the normal and
partial foot were determined using the anthropometric model, and measurement
techniques described in Chapter 2. Anthropometric characteristics of the leg and thigh
segments were determined using the anthropometric models described by Hatze (1979).
The coordinate systems of the leg and thigh segments were altered to reflect the global
coordinate system (GCS) of the laboratory used in the present investigation. No
principal axes transformations were undertaken as described by Hatze (1979). Instead
the position of the segments CM was described relative to the joint local coordinate
system (LCS) and transformations were undertaken between the local and global
coordinate systems (Appendix F). The anthropometric input data required to execute
these models were not reported by Hatze (1979) or in other literature utilising these
models (Schneider et al., 1990; Schneider and Zernicke, 1992). These anthropometric
________________________________________________________ Chapter 3. 52
input measurements were, therefore, determined by deriving Hatze's (1979)
mathematical notation from first principles.
The leg model has been described as an assemblage of ten horizontal elliptical
cylinders and two paraboloids of revolution, which represent the medial and lateral
malleoli (Hatze, 1979). The length of the leg segment was defined as the distance
between the tibial plateau and the apex of the lateral malleolus. By dividing the leg
length into ten equal segments and taking both circumference and medio-lateral
measurements at the centre of each elliptical segment, the measurements required to
describe the M, CM and I of each elliptical cylinder were obtained (Appendix G). The
width of the lateral malleolus defined the radius and height of the two paraboloids of
revolution (Appendix G).
The thigh model has been described as an assemblage of ten elliptical cylinders
and an ellipto-parabolic hoof (Hatze, 1979). The height of each elliptical cylinder of the
thigh model was described as a tenth of the length measurement from the ramus to the
tibial plateau. Circumference and mediolateral measurements taken at the centre of each
elliptical cylinder completed the complement of input data required to describe this
portion of the thigh model. A second thigh length measurement, from the tibial plateau
to the apex of the greater trochanter of the femur, less the distance from the tibial
plateau to the ramus, describes the height of the ellipto-parabolic hoof. The diameter
across the greater trochanters, firstly including any soft tissue without compression, and
secondly a bone-to-bone diameter was used to describe the soft tissue mass around the
pelvis (Hatze, 1979). The anthropometric measurement form used to record the
necessary input data forms part of Appendix G.
The anthropometric characteristics of the prosthesis/orthosis and shoe were
determined using standard techniques describing the dynamics of a rigid body. The M
of the prosthesis/orthosis and shoe was determined using an electronic scale. The
location of the mass centroid of the prosthesis/orthosis and shoe was given by the
intersection of three plumb lines marked on the prostheses when suspended from three
different points. With the prosthesis/orthosis and shoe on the patient, the vertical and
horizontal distances from the CM to the proximal joint centre were recorded. The value
________________________________________________________ Chapter 3. 53
of I about each orthogonal axis was determined using a Trifilar pendulum system using
the techniques described in Chapter 2.
20mm Scotchlite retroflective markers were located on the following anatomical
landmarks: Spinous process of the fifth lumber vertebra, anterior superior iliac spine,
greater trochanter of the femur, knee joint space inferior to the lateral epicondyle of the
femur, lateral malleolus, posterior calcaneus at the level of the fifth metatarsal head,
fifth metatarsal head or its estimated location. Markers were also located mid-thigh and
mid-leg just anterior to a line connecting the proximal and distal segment markers.
The location of the absent 5th metatarsal head was duplicated from the sound
foot by placing a ruler posterior to the shoed foot and measuring the distance from the
ruler to the centre of the marker.
Data acquisition and processing
Subjects were allowed to practise traversing the walkway with the reflective
markers in place. The subjects were instructed to practise contacting the force platform
so that their walking velocity remained the same and they did not change their step
length or coordination to contact the platform. The subjects were allowed to practise and
adjust their starting position on the walkway until they felt confident that they could
perform the task.
Kinematic data describing the neutral segment angles were collected with the
subject standing with their arms crossed over their chest. Dynamic data were then
collected, at the subject's self-selected walking speed, until seven successful trials were
obtained for each limb.
Kinematic data were initially processed using the Peak-Motus software. Three
dimensional marker coordinates, for approximately four gait cycles, were obtained and
tracked so that any change in walking velocity or coordination to target the force
platform could be evidenced and those trials rejected. The 3D marker coordinates were
then reconstructed and any missing data interpolated using spline routines standard to
the Motus software. The unfiltered marker coordinate data were then exported for
further processing.
________________________________________________________ Chapter 3. 54
Raw marker displacement data were filtered using a fourth order low pass
Butterworth filter with a cut-off frequency of 6Hz (Appendix E). Segment angles
describing the orientation of the pelvis, thigh, leg and foot relative to the horizontal axis
of the GCS were determined using an arc tangent function. Joint angles were then
determined as the difference between adjacent segment angles (Winter, 1990).
Force platform voltage data were then filtered using a fourth order Butterworth
digital filter with a cut-off frequency of 125Hz to remove the unwanted electrical noise
affecting the signal (Appendix E). Force platform data were converted to Newtons
(Appendix E). Differences in force and moment data, from absolute zero, were
accounted for by offsetting the force and moment data by the mean of a one-second
sample of data collected before heel contact for each force plate measurement
(Appendix E). Force platform data were then sub-sampled from 1000Hz to match the
kinematic sampling rate of 50Hz (Appendix E). Centre of pressure excursion was
calculated and accounted for the offset between the true and geometric origin of the
force plate in the vertical direction (Appendix E).
To reflect kinetic estimates provided by previous investigators, net joint
moments were estimated for both samples A and B using a standard inverse dynamic
model. Anthropometric characteristics of the sound foot, leg and thigh were used and
characteristics of any prosthesis/orthosis and shoe were disregarded. Net joint moments
were also estimated for sample A using 'partial foot model-A' and for sample B using
'partial foot model-B'. Anthropometric descriptions of the affected limb including the
residual foot were used and any prosthetic/orthotic replacement and footwear were also
accounted for (Appendix F).
Joint powers were calculated as the scalar product of moment and angular
velocity and accounted for power transfer across joints (Winter, 1990). The resultant
components of the joint moments and powers were normalised by body mass (Winter,
1990; Allard et al., 1997; Craik and Oatis, 1995) in preference to alternate techniques
which as an example, normalise joint moments by body mass and limb length (Perry,
1992). Normalisation of kinetic parameters by body mass alone seems to be the
standard convention and little evidence could be found to support the use of, non-
________________________________________________________ Chapter 3. 55
dimensional, techniques which also results in kinetic parameters that are less readily
interpreted by clinicians and biomechanists.
The magnitude and timing of peak joint moments and powers were extracted
from each subject's ensembled average using a set of mouse driven crosshairs
(Appendix E). Figures 3.3 and 3.4 illustrate the points analysed. The crosshairs
displayed the x-y coordinates of each point (Appendix E) and those data points selected
were averaged within each sample. Absolute and percentage differences were calculated
using the technique described by Hatze (1979) which was presented in Chapter 2.
Figure 3.3 Points of interest examined on joint moment profiles.
H, K and A denote hip, knee and ankle, respectively. M denotes moment. Positive values along the y-axis
indicate extension moments. Encircled values describe the data points examined and are numbered
consecutively. The solid line delineates swing and stance phase.
0 20 40 60 80 100-1
0
1
2
Hip Moment (-)
(Nm
/kg)
Ext
. >
0 20 40 60 80 100
-1
0
1
Knee Moment (-)
(Nm
/kg)
Ext
. >
0 20 40 60 80 100
0
1
2
Ankle Moment ()
Gait Cycle [%]
(Nm
/kg)
Ext
. >
HM1
HM2
HM3
KM1
KM2
KM3
KM4
KM5
AM1
AM2
________________________________________________________ Chapter 3. 56
Figure 3.4 Points of interest examined on joint power profiles.
H, K and A denote hip, knee and ankle respectively. P denotes power. Positive values along the y-axis
indicate power generation. Encircled values describe the data points examined. These data points were
numbered consecutively. The solid line delineates swing and stance phase.
3.3 Results
Anthropometric characteristics were computed for each subject in samples A
and B. Mean M, CM and I of the isolated foot, leg and thigh segments are presented in
Tables 3.2-3.4, respectively. Anthropometric characteristics of the prosthesis/orthosis
and shoe for each sample are presented in Table 3.5 and the characteristics of the
'lumped' segments are reported in Table 3.6.
0 20 40 60 80 100-1
0
1
2
Hip Power (-)(W
/kg)
Gen
. >
0 20 40 60 80 100
-2
-1
0
1
2Knee Power (-)
(W/k
g) G
en.
>
0 20 40 60 80 100-2
0
2
4
6Ankle Power ()
(W/k
g) G
en.
>
Gait Cycle [%]
AP1
AP2
KP1
KP2
KP3KP4
HP1
HP2
HP3
HP4
________________________________________________________ Chapter 3. 57
Although no formal statistical analyses were undertaken, data presented in Table
3.2 highlights a reduction in the M and I of the isolated foot segment and the more
proximal location of the CM when the partial foot models were used compared to the
standard inverse dynamic model. There were no differences of note in the
anthropometry of the leg and thigh segments, between modelling approaches, for
subjects in sample-A (Tables 3.3 and 3.4). However, for the subject in sample-B, the M
and I of the leg segment was substantially less than that observed using a standard
model (Table 3.3). There were no differences in the anthropometry of the thigh segment
for this subject between the affected and sound/normal limb (Table 3.4).
Table 3.2 Mean anthropometric data of the isolated foot segment for a standard linked-
segment model and the partial foot models
Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial Foot absolute %
Sample A - with ankle motion
Mass (kg) 1.065
(0.030)
0.793
(0.036)
-0.272 25.5
CMx (m) 0.060
(0.001)
0.019
(0.005)
-0.041 68.3
CMz (m) -0.042
(0.002)
-0.038
(0.001)
0.004 9.5
Iyy (kg.m2) 0.006
(0.002)
0.002
(0.000)
-0.004 66.7
Sample B - without ankle motion
Mass (kg) 1.064 0.443 -0.621 58.4
CMx (m) 0.054 -0.013 -0.067 106.7
CMz (m) -0.041 -0.036 0.005 12.2
Iyy (kg.m2) 0.005 0.001 -0.004 80.0
________________________________________________________ Chapter 3. 58
Table 3.3 Mean anthropometric data of the lower leg segment generated for a standard
linked-segment model and the partial foot models
Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial Foot absolute %
Sample A - with ankle motion
Mass (kg) 3.365
(0.059)
3.178
(0.084)
-0.187 5.6
CMx (m) 0.000 0.000 0.000 0.0
CMz (m) -0.173
(0.002)
-0.173
(0.001)
0.000 0.0
Iyy (kg.m2) 0.046
(0.001)
0.045
(0.002)
-0.001 2.2
Sample B - without ankle motion
Mass (kg) 3.992 2.673 -1.319 33.0
CMx (m) 0.000 0.000 0.000 0.0
CMz (m) -0.171 -0.158 0.013 7.6
Iyy (kg.m2) 0.053 0.040 -0.013 24.5
The anthropometric characteristics of the prosthesis/orthosis and shoe rivalled
that of the isolated foot segment in sample-A (Table 3.5). The addition of a
prosthesis/orthosis and shoe to the linked-linked segment model (partial foot model-A)
resulted in a net increase in the M and I of the 'lumped' segment of about 30% compared
to the standard model (Table 3.6). The position of the CM of the 'lumped' segment was
significantly closer to the ankle joint along the long axis (x-axis) and more distally
along the z-axis, compared to a standard linked-segment model (Table 3.6).
________________________________________________________ Chapter 3. 59
Table 3.4 Mean anthropometric data of the thigh segment for a standard linked-
segment model and the partial foot models.
Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial Foot absolute %
Sample A - with ankle motion
Mass (kg) 8.205
(0.629)
8.417
(0.719)
0.212 -2.6
CMx (m) 0.000 0.000 0.000 0.0
CMz (m) -0.193
(0.003)
-0.192
(0.003)
0.001 0.5
Iyy (kg.m2) 0.131
(0.010)
0.134
(0.011)
0.003 -2.3
Sample B - without ankle motion
Mass (kg) 11.000 10.654 -0.346 3.1
CMx (m) 0.000 0.000 0.000 0.0
CMz (m) -0.181 -0.180 0.001 0.6
Iyy (kg.m2) 0.164 0.158 -0.006 3.7
Table 3.5 Characteristics of the combined prosthesis/orthosis/shoe for samples A and B
For sample - B the position of the CM was described relative to the knee joint and the value of I, through
the CM of the lumped segment. Standard deviation reported in brackets.
Sample A -
with ankle motion
Sample B -
without ankle motion
Mass (kg) 0.731
(0.261)
1.589
CMx (m) 0.052
(0.013)
0.028
CMz (m) -0.058
(0.020)
-0.375
Iyy (kg.m2) 0.006
(0.001)
0.034
________________________________________________________ Chapter 3. 60
Table 3.6 Mean anthropometric data of the lumped segments for a standard linked-
segment model and the partial foot models
For sample - B the position of the CM was described relative to the knee joint and the value of I, through
the CM of the lumped segment. Due to the differences in the way the segments have been modelled it was
not possible to draw comparisons between anthropometric data of the lumped segment for partial foot
model-B and a standard linked-segment model. Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial Foot absolute %
Sample A - with ankle motion
Mass (kg) 1.066
(0.060)
1.524
(0.203)
0.458 -43.0
CMx (m) 0.060
(0.002)
0.034
(0.01)
-0.026 43.3
CMz (m) -0.042
(0.004)
-0.048
(0.004)
-0.006 -14.3
Iyy (kg.m2) 0.006
(0.000)
0.008
(0.001)
0.002 -33.3
Sample B - without ankle motion
Mass (kg) - 4.705 - -
CMx (m) - 0.008 - -
CMz (m) - -0.259 - -
Iyy (kg.m2) - 0.161 - -
Due to the differences in the way the segments were modelled it was not
possible to draw direct numeric comparisons between anthropometric data of the
'lumped' segment for partial foot model-B and a standard linked-segment model. As
such, the characteristics of the lumped segment have been presented in isolation (Table
3.6). For partial foot model-B the position of the CM of the lumped segment was given
relative to the knee axis and the value of I was taken through the CM of the lumped
segment.
________________________________________________________ Chapter 3. 61
The M of the clamshell prosthesis in sample-B was about half of the combined
M of the remnant foot and leg (Tables 3.2, 3.3 and 3.5). The position of the CM of the
'lumped' segment in sample-B was anteriorly displaced relative to the sagittal mid-line
of the leg and significantly closer to the ankle (Table 3.6) primarily due to the anterior
and distal location of the CM of the prosthesis (Table 3.5). The value of I of the
'lumped' segment (Table 3.5) was comparable to that observed for the thigh (Table 3.4),
again due to the distal location of the CM of the 'lumped' segment relative to the knee
joint (Table 3.6).
Data comparing the timing of these peak moments and powers (as a percentage
of the gait cycle) have not been presented because, on the whole, only the magnitudes of
the peaks were affected by differences in the linked-segment models. The small
differences in timing of these moment or power peaks did not exceed 2% of the gait
cycle and were limited to periods when the data points were identical to several decimal
places. Figures 3.5 and 3.6 illustrates that the timing of peak joint moments and powers
were unaffected by differences in the linked-segment models.
________________________________________________________ Chapter 3. 62
Figure 3.5 Mean joint moments estimated using a standard linked-segment model and
partial foot model - A for subject 2103-2116A (n=3).
Positive figures on the y-axis indicate an extension moment. Negative figures on the y-axis indicate a
flexion moment. Toe-off occurred at 61%of the gait cycle.
0 20 40 60 80 100-0.5
0
0.5
1Hip Moment
(Nm
/kg)
Ext
. >
0 20 40 60 80 100-0.4
-0.2
0
0.2
0.4Knee Moment
(Nm
/kg)
Ext
. >
0 20 40 60 80 100-0.5
0
0.5
1Ankle Moment
Gait Cycle [%]
(Nm
/kg)
Ext
. >
Standard model Partial foot model A
________________________________________________________ Chapter 3. 63
Figure 3.6 Mean joint powers estimated using a standard linked-segment model and
partial foot model - A for subject 2103-2116A (n=3).
Positive figures on the y-axis indicate power generation. Negative figures on the y-axis indicate power
absorption. Toe-off occurred at 61%of the gait cycle.
0 20 40 60 80 100-0.5
0
0.5
1Hip Power
(W/k
g) G
en.
>
0 20 40 60 80 100-1
-0.5
0
0.5Knee Power
(W/k
g) G
en.
>
0 20 40 60 80 100-1
-0.5
0
0.5
1Ankle Power
(W/k
g) G
en.
>
Gait Cycle [%] Standard Partial foot model AStandard model
________________________________________________________ Chapter 3. 64
Differences in peak joint moments and powers, between the standard and partial
foot linked-segment models, were limited to the hip and knee and almost exclusively
affected terminal swing. There were no differences of note between modelling
approaches during stance phase and as such only differences during swing phase have
been presented. A complete set of results including peak moments and powers observed
during stance phase has been presented in Appendix H. Peak joint moments and powers
selected from the each subject's ensembled average have presented in Tables 3.7-3.11
and Figures 3.7-3.11.
Compared to a standard linked-segment model, partial foot models increased the
mean hip extension moment (HM3) and knee flexion moment (KM5) peaks during
terminal swing (Tables/Figures 3.7 and 3.9). An increase in the knee extension moment
during initial swing (KM4) was observed in sample-B only (Table/Figure 3.8). No
differences in the peak ankle joint moments were observed between models for sample-
A (Appendix H). For sample-B the ankle joint was irrelevant due to the 'lumped'
segment created with partial foot model-B and therefore, the ankle moment was not
calculated.
Compared to a standard linked-segment model, partial foot model-A increased
the power generated across the hip joint during terminal swing (HP4) (Table/Figure
3.10). A negligible increase in power absorption was observed across the hip joint with
the use of partial foot model-B (Table/Figure 3.10). Increased power absorption was
observed at the knee during terminal swing (KP4) with the use of the partial foot models
compared to a standard linked-segment model (Table/Figure 3.11). No difference in
ankle power absorption or generation peaks (AP1 and AP2) were observed as a result of
the application of the different inverse dynamic models (Appendix H).
________________________________________________________ Chapter 3. 65
Table/Figure 3.7 Mean hip joint extension moment peaks during terminal swing
(HM3) for both the standard and partial foot linked-segment models.
HM denotes hip moment. Positive values indicate a hip extension moment. Standard deviation reported in
brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
HM3 (Nm/kg) 0.208
(0.041)
0.301
(0.032)
0.093 -44.7
Sample B - without ankle motion
HM3 (Nm/kg) 0.188 0.242 0.054 -28.7
Sam
ple
-B
Sam
ple
-A
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
HM
3 E
xt.>
(N
m/k
g)
Sta
ndard
m
od
el
Part
ial f
oot
mo
de
l
Ab
solu
tediff
ere
nce
________________________________________________________ Chapter 3. 66
Table/Figure 3.8 Mean knee joint extension moment peaks during initial swing (KM4)
for both the standard and partial foot linked-segment models.
KM denotes knee moment. Positive values indicate a knee extension moment. Standard deviation
reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
KM4 (Nm/kg) 0.116
(0.034)
0.120
(0.034)
0.004 -3.5
Sample B - without ankle motion
KM4 (Nm/kg) 0.040 0.066 0.026 -65.0
Sam
ple
-B
Sam
ple
-A
0.00
0.02
0.04
0.06
0.08
0.10
0.12
KM
4 E
xt.>
(N
m/k
g)
Sta
nd
ard
mo
de
l
Part
ial f
oo
tm
od
el
Ab
solu
ted
iffe
ren
ce
________________________________________________________ Chapter 3. 67
Table/Figure 3.9 Mean knee joint flexion moment peaks during terminal swing (KM5)
for both the standard and partial foot linked-segment models.
KM denotes knee moment. Negative values indicate a knee flexion moment. Standard deviation reported
in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
KM5 (Nm/kg) -0.195
(0.024)
-0.256
(0.026)
-0.061 -31.3
Sample B - without ankle motion
KM5 (Nm/kg) -0.181 -0.222 -0.041 -22.7
Sam
ple
-B
Sam
ple
-A
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
KM
5 F
lex.
< (N
m/k
g)
Sta
nd
ard
mo
de
l
Pa
rtia
l fo
ot
mo
de
l
Ab
solu
ted
iffe
ren
ce
________________________________________________________ Chapter 3. 68
Table/Figure 3.10 Mean hip joint power generation/absorption during terminal swing
(HP4) for both the standard and partial foot linked-segment models.
HP denotes hip power. Positive values indicate power generation. Negative values indicate power
absorption. Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
HP4 (W/kg) 0.079
(0.080)
0.132
(0.160)
0.053 -67.1
Sample B - without ankle motion
HP4 (W/kg) -0.013 -0.016 -0.003 -23.1
Sa
mp
le-B
Sa
mp
le-A
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
HP
4 G
en.>
(W
atts/
kg)
Sta
nd
ard
mo
de
l
Pa
rtia
l fo
ot
mo
de
l
Abso
lute
diff
ere
nce
________________________________________________________ Chapter 3. 69
Table/Figure 3.11 Mean knee joint power absorption during terminal swing (KP4) for
both the standard and partial foot linked-segment models.
KP denoted knee power. Negative values indicate power absorption. Standard deviation reported in
brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
KP4 (W/kg) -0.831
(0.176)
-1.070
(0.280)
-0.239 -28.8
Sample B - without ankle motion
KP4 (W/kg) -0.665 -0.797 -0.132 -19.8
Sa
mp
le-B
Sa
mp
le-A
-1.20
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
KP
4 A
bs.
< (
Wa
tts/
kg)
Sta
ndard
model
Part
ial f
oot
model
Ab
solu
tediff
ere
nce
________________________________________________________ Chapter 3. 70
3.4 Discussion
Researchers of partial foot amputee gait have investigated conditions of barefoot
walking and prosthetic/orthotic intervention. However the unique anthropometry of the
partial foot residuum and any prosthetic/orthotic intervention (including footwear) have
not previously been acknowledged.
For conditions of barefoot walking where the partial foot would be considered in
isolation, the M and I of the isolated/modelled foot segment would be substantially
reduced and the location of the mass centroid closer to the ankle joint when the partial
foot model was used (Table 3.2).
There were significant anthropometric differences between the modelled limb
segments with the use of a standard linked-segment model and the partial foot models.
These anthropometric differences were due, in part, to amputation of the foot and the
addition of a prosthesis/orthosis and shoe (Table 3.2). In the case of individuals with
clamshell prostheses, these anthropometric differences were also due to how the limb
segments were modelled within the constraints of the inverse dynamic modelling
approach and the reduction in the M of the leg segment (Table 3.3), reflecting atrophy
of the triceps surae musculature. It is difficult to separate whether the differences in
joint moments and powers were due to anthropometry or the assumptions of partial foot
model-B because the two were linked. Without the basic assumptions used to describe
the clamshell prosthesis within the constraints of the linked-segment model, the
prosthesis would have to be dissected and the anthropometric characteristics of each
piece uniquely assigned to the foot and leg segment separately.
The net joint moment profiles for the knee and hip, obtained using the partial
foot models, illustrate a systematic percentage increase in the knee flexion and hip
extension moments during swing phase compared to a standard model (Tables 3.7-
3.11). Estimates of work at the knee and hip joints reflect differences in the moment
profiles observed. These differences are indicative of a more accurate portrayal of the
activity of the hamstring and hip extensor muscle groups to decelerate the knee into full
extension and the hip joint into its initial contact hip flexion angle and prevent further
hip flexion prior to initial contact.
________________________________________________________ Chapter 3. 71
While such clinical interpretations of the joint moment profiles provide useful
information about the causes of movement, their usefulness for observing how
anthropometric changes affect the net joint moments are limited because only changes
caused by differences in anthropometric data as a whole can be observed.
By dissecting the joint moment equations into their components it was possible
to gather more information about how the moment equations were affected by changes
in segment anthropometry (Appendix H). To better illustrate the mass-acceleration
terms of the moment equation, joint moments were subsequently taken about the
proximal end of the free body segments rather than about the mass centroid. The value
of I was transposed using the parallel axis theorem.
The joint moment profiles calculated using partial foot model-A, were
dominated by the additional M of the modelled foot segment (Appendix H). In terms of
the ankle joint moment equation, the additional M was reflected in the mass-
acceleration products (Appendix H). In turn, these ankle joint reaction forces affected
the knee and hip joint moment calculations. The small differences in the location of the
mass centroid and value of I between modelling approaches seemed to be of little
consequence. Hence, only the M of the modelled segment would be of major concern
with this modelling approach (partial foot model-A).
The knee joint moment patterns, observed with partial foot model-B compared
to the standard linked-segment model, reflected not only changes in the M of the
modelled segments but the influence of I proved dominant during both initial and
terminal swing (Appendix H). Differences in the location of the segment's mass centroid
were also evident (Appendix H). Differences in the hip extension moments observed
during terminal swing were exclusively due to the carry over knee joint moments
(Appendix H). With this modelling approach it seems imperative that not only the M,
but also the location of the mass centroid and the value of I be adequately depicted.
Future investigations considering incorporating anthropometric characteristics of
the Clamshell prosthesis without accurate anthropometric modelling of the
anthropometry of the residuum and lower leg segments would be likely to overestimate
________________________________________________________ Chapter 3. 72
the swing phase moments and powers. For the Chopart amputee subjects, substantial
differences in the joint moments and powers were not observed because the additional
mass and inertia of the prosthesis and shoe were offset by reductions in the mass and
inertia of the affected leg and remnant foot segments due to muscle atrophy and
amputation. During the pilot investigation, when the mass and inertia of the clamshell
prosthesis was combined with these characteristics of the normal leg and intact foot,
derived using regression equations based on stature and body mass, significantly
differences in the swing phase moments were observed. As such, future investigations
should accurately depict the anthropometry of the remnant foot and lower leg segment if
the anthropometry of the clamshell prosthesis is being incorporated into the model.
Alternatively, investigators could ignore the anthropometry of the clamshell prosthesis
and assume that the anthropometry of the free body segments can be adequately
approximated using anthropometric descriptions of the intact foot and sound leg
segment. The efficacy of this alternative approach can be verified by comparing the
anthropometric characteristics of the combined leg, foot and prosthesis/shoe of the
Chopart amputee with the same characteristics of the sound leg and intact foot segment.
For example, the mass of the combined prosthesis/shoe, lower leg and remnant foot
segment of the Chopart amputee was equal to 4.7kg (Table 3.6) compared to 5.0kg for
the combined intact foot (Table 3.2) and leg segment (Table 3.3) of the same individual.
3.5 Conclusion
Linked-segment inverse dynamic models have been developed to incorporate
improved anthropometric descriptions of the partial foot residuum as well as account for
any prosthetic/orthotic intervention and footwear with a view to providing more
accurate kinetic estimates. This addresses the shortcoming of previous kinetic
descriptions of partial foot amputee gait, which have not acknowledged the
anthropometric contributions of the prosthesis/orthosis/shoe and have assumed that the
residuum can be adequately described using body segment parameter data of the intact
foot.
The partial foot models significantly modified the anthropometry of the free
body segments compared to the standard model. These differences were due to
amputation of the foot and the addition of a prosthesis/orthosis and shoe. However, in
________________________________________________________ Chapter 3. 73
the case of individuals with clamshell prostheses, these anthropometric differences were
linked to how the limb segments were modelled within the constraints of the inverse
dynamic modelling approach. These anthropometric differences manifested in the joint
moments during swing phase and depending on the partial foot model used, the
influence of mass, centre of mass location and mass moment of inertia differ. For partial
foot model-A, the mass of the modelled segment dominated the moment patterns
observed however, for partial foot model-B not only was the mass of the modelled
segment important, but the value of the mass moment of inertia was the primary
influence on the swing phase joint moments.
The joint moment profiles obtained with these partial foot models increased the
knee flexion and hip extension moments during terminal swing phase compared to a
standard model. These findings are indicative of a more accurate portrayal of the
requirement of the hamstrings muscle group and gluteus maximum to decelerate the
knee into full extension and the hip joint into its initial contact hip flexion angle and
prevent further hip flexion prior to heel contact, respectively. Increased power
absorption was observed across the knee and hip joints in line with the changes
observed in the moment profiles.
Previous investigators of partial foot amputee gait are likely to have
underestimated the magnitude of these peak joint moments and powers by not
accurately describing the anthropometry of the free body segments. In relative terms the
differences observed were significant. However, in absolute terms these differences
were negligible. For comparison, these differences were within the range of values
typically reflected by the 95% confidence interval of a normal population. Such small
difference would not affect clinical interpretation or treatment planning.
Many investigators of partial foot amputee gait may feel that the additional work
required to generate these improved anthropometric input data and additional
complexity of the linked-segment models were not warranted by the small, absolute,
differences observed in the swing phase moments and powers. While the partial foot
models are not likely to be used routinely given the small absolute differences in joint
moments and powers, these models do demonstrate the influence of accurate
anthropometric modelling which is advantageous to all investigators of partial foot
________________________________________________________ Chapter 3. 74
amputee gait. Results from this study indicate that a conventional linked-segment model
would yield kinetic data of sufficient accuracy for the study of partial foot amputee gait,
particularly given that stance phase seems to be of particular concern for this
population. Studies specifically interested in swing phase kinetics of high inertial
activities, such as kicking, may benefit from the modelling techniques developed.
________________________________________________________ Chapter 4. 75
A Biomechanical Analysis of Partial Foot Amputee Gait
4.1 Introduction
Partial foot amputation has become a more viable surgical intervention for the
treatment of advanced diabetes, vascular insufficiency and trauma where previously a
below knee amputation may have been required (Boyd et al., 1999; Burnfield et al.,
1998; Dorostkar et al., 1997). This is due largely to improvements in surgical
techniques for revascularising the micro arteriole structure of the foot and antibiotic
therapy for controlling ascending infection and septicemia (Muller and Sinacore, 1994).
Despite these medical advances, the perception of patients, surgeons, physicians
and allied health clinicians, toward partial amputation of the foot, has been tainted by a
long and chequered history of ongoing complications often resulting in surgical
revision. Questions about the efficacy of partial foot amputation as a viable long-term
alternative to more proximal amputation have been raised (Hirsch et al., 1996). The
occurrence of many ongoing complications such as ulceration (Sage et al., 1989), skin
breakdown (Brand, 1983; Sage et al., 1989; Birke and Sims, 1988; Muller and Sinacore,
1994) and equinus deformity (Chrzan et al., 1993; Parzaile and Hahn, 1988) could be
reduced given a better understanding of the gait of partial foot amputees and how
prosthetic/orthotic intervention influences the mechanics of locomotion.
Chapter 4
________________________________________________________ Chapter 4. 76
Until recently, our understanding of the biomechanics of partial foot amputee
gait was based largely on that of normal individuals with authors speculating about the
effect of amputation and socket design on gait (Condie, 1970; Condie and Stills, 1988;
Chrzan et al., 1993). Condie (1970) provided some biomechanical merit to the
speculation by analysing the forces acting on the residuum and socket in conventional
below and above ankle socket designs.
The crux of this work (Condie, 1970) demonstrated that the forces experienced
by the Tarso-Metatarsal or Chopart residuum, to resist the external moments generated
during initial contact and toe-off, were alarmingly large when below ankle fitting
concepts were employed. Extending the socket proximally could reduce the magnitude
of forces experienced by the residual foot and the majority of force could be transmitted
away from the sensitive distal residuum to the naturally adapted fatty pad of tissue
covering the heel (Condie, 1970).
While these findings were exciting, their validity seemed questionable. For to
undertake such a static force analysis, whereby a series of forces are resolved for
equilibrium, the magnitude, point of application and line of action of each force must be
known. While some of this information can be measured, such as the magnitude, point
of application and line of application of the ground reaction force (GRF), much of the
required information cannot be obtained easily. Without these data, assumptions about
these forces must be made. It may be reasonable to make assumptions about the line of
action of forces (for example, the forces acting on the stump are normal to the stump
surface). However, unless the point of application of each force is known an infinite
number of solutions for force and moment equilibrium exist.
Condie's (1970) static force analyses depicting toe-off in Transmetatarsal and
Tarso-Metatarsal amputees, using below ankle fitting concepts, demonstrates how by
varying the point of application of the superincumbent weight force it is possible to
reach an alternate solution for force and moment equilibrium. While this was probably
not Condie's original intention, inconsistencies such as this cast doubt on the efficacy of
comments about transmitting the majority of force away form the distal residuum to the
heel pad. Such conclusions could be explained by the limitations of determining the
point of application of the forces analysed.
________________________________________________________ Chapter 4. 77
Despite the over simplicity of Condie's (1970) work, this original contribution
formed the foundation underpinning our biomechanical understanding of partial foot
amputee gait for more than two decades. Comparable static force analyses have been
presented by a number of authors (Condie and Stills, 1988; Weber, 1991; Muller and
Sinacore, 1994) without addressing the potential limitations of such analyses. Despite
the limitations of these works, the collective contribution raises questions and
misconceptions about prosthetic prescription, ankle range of motion (ROM), socket
design and the excursion of the centre of pressure and its affect on joint moments.
Many of the questions and misconceptions have recently received attention as a
result of a growing awareness of the inadequacies of laying a foundation of knowledge
about partial foot amputee gait and prosthetic design based on speculative and anecdotal
evidence. There is an increasing body of literature examining the kinematics (Dillon,
1995; Garabolsa et al., 1996; Hirsch et al., 1996; Dorostkar et al., 1997; Muller et al.,
1998), ground reaction forces (Dillon, 1995; Boyd et al., 1999; Burnfield et al., 1998;
Muller et al., 1998), kinetics (Dillon, 1995; Boyd et al., 1999; Muller et al., 1998),
temperospatial (Dillon, 1995; Dorostkar et al., 1997; Burnfield et al., 1998; Muller et
al., 1998), plantar pressure (Garabolsa et al., 1996) and muscle strength (Burnfield et
al., 1998; Dorostkar et al., 1997) parameters of, primarily, the affected limb. However,
much of this work remains unpublished, appearing as conference abstracts or research
progress reports where detailed discussion is usually not permitted.
Empirical studies have focused primarily on the gait of individuals with
amputation distal to and including the Transmetatarsal (TMT) level (Garabolsa et al.,
1996; Burnfield et al., 1998; Boyd et al., 1999; Dorostkar et al., 1997; Dillon, 1995;
Muller et al., 1998) with a limited number of studies examining more proximal
amputation levels (Dillon, 1995). Studies have examined conditions of bare-foot
walking (Garabolsa et al., 1996; Burnfield et al., 1998; Boyd et al., 1999; Dorostkar et
al., 1997) or prosthetic/orthotic intervention (Dillon, 1995; Hirsch et al., 1996; Muller et
al., 1998).
As a result of these empirical studies, it has been demonstrated that unilateral
partial foot amputees walk at about two-thirds the velocity of normal individuals with
________________________________________________________ Chapter 4. 78
little difference evident between groups based on amputation level (Boyd et al., 1999;
Burnfield et al., 1998; Dorostkar et al., 1997; Dillon, 1995; Muller et al., 1998).
Significant reductions in stride length, cadence (Burnfield et al., 1998; Boyd et al.,
1999; Dorostkar et al., 1997; Dillon, 1995) and step length (Muller et al., 1998) were
observed, with reductions in stride length being implicated as the primary reason for
reduced walking velocity (Dorostkar et al., 1997). There were no differences evident in
stride length (Dillon, 1995; Dorostkar et al., 1997) or cadence (Dorostkar et al., 1997)
between amputee groups. The duration of the gait cycle and proportions of swing and
stance phase were comparable to normal on the affected limb irrespective of residual
foot length (Dillon, 1995).
Joint angular kinematic patterns have focused, primarily, on the ankle joint
(Boyd et al., 1999; Dorostkar et al., 1997; Garabolsa et al., 1996) with limited work
examining more proximal joints (Dillon, 1995; Muller et al., 1998) or reporting swing
phase kinematics (Dillon, 1995). At the ankle, static range of motion was not
statistically different from normal (Garabolsa et al., 1996; Dillon, 1995). During gait, it
appears that TMT amputees utilise a much smaller proportion of the available range
than do their normal counter parts (Garabolsa et al., 1996). Dillon (1995) also identified
this trend across both Metatarsophalangeal (MTP) and TMT groups however, a
statistically significant difference was not observed. Some authors have observed a
number of kinematic abnormalities at the ankle joint once amputation compromises the
Metatarsal heads. Boyd et al., (1999), Dorostkar et al., (1997) and Garabolsa et al.,
(1996) all reported a reduction in ankle dorsiflexion peak in TMT amputees. Dillon
(1995) observed an increase in the peak ankle dorsiflexion in the same group and Muller
et al. (1998) observed no difference. Irrespective of the peak dorsiflexion angle, most
authors agree that there is a significant delay in the timing of this angle peak compared
to normal or MTP groups (Boyd et al., 1999; Dorostkar et al., 1997; Dillon, 1995). Peak
ankle plantarflexion was significantly reduced in TMT amputees relative to normal
(Dillon, 1995; Muller et al., 1998) and the MTP group (Dillon, 1995). Kinematic
profiles of a single Chopart amputee identified that the ankle motion observed was the
result of the force/deflection characteristics of the prosthetic foot because the Clamshell
patella tendon bearing (PTB) prosthesis eliminated true ankle motion (Dillon, 1995).
The kinematic patterns observed at the knee and hip joint appear to be relatively normal
across the MTP and TMT groups. However, small variations in maximum knee flexion
________________________________________________________ Chapter 4. 79
and initial contact hip flexion angles were observed (Dillon, 1995; Muller et al., 1998)
and found to be significantly different from normal by Muller et al., (1998). The
initiation of knee flexion into swing phase was delayed by about 10% of the gait cycle
in TMT amputees (Dillon, 1995).
A number of differences in the GRF data have been reported. Some authors have
found that there was no difference in the vertical GRF irrespective of amputation level
compared to the normal population (Dillon, 1995; Boyd et al., 1999; Burnfield et al.,
1998). However, when adjusted for velocity, the normalised peak magnitudes were
significantly reduced in the toe and TMT groups relative to normal and each other
(Burnfield et al., 1988). Boyd et al., (1999) found that the rise toward the second
vertical GRF peak was significantly delayed in TMT amputees and those with
Metatarsal ray resections. Hirsch et al., (1996) also observed a similar trend however no
statistical analyses were performed. During loading response, the magnitude of the
vertical GRF was increased on the sound limb compared to the residual limb (Burnfield
et al., 1998). A reduction in the magnitude of the horizontal GRF peaks was observed
by Hirsch et al., (1996) and Dillon (1995), which approached statistical significance in
the MTP and TMT groups, compared to normal (Dillon, 1995). Centre of pressure
(CoP) excursion was significantly reduced in TMT amputees relative to normal and the
MTP amputee group (Dillon, 1995). A strong correlation was observed between
residual foot length and CoP excursion irrespective of orthotic fitting (Dillon, 1995).
The ankle foot orthoses and insoles fitted to these amputees were unable to restore the
normal excursion of the CoP past the distal residuum (Dillon, 1995). It appears that
prosthetic fitting was able to restore normal CoP excursion in a single Chopart amputee
(Dillon, 1995). Replacing the lost lever arm with a suitably rigid material in conjunction
with a socket capable of distributing forces caused by loading the toe lever may be
responsible for restoring normal CoP excursion in this Chopart amputee (Dillon, 1995).
This theory may also explain why similar findings were not evident in the MTP and
TMT amputee groups fitted with orthotic devices as neither a socket nor a rigid forefoot
lever was incorporated into the prosthetic replacement (Dillon, 1995).
Kinetic anomalies were prevalent particularly once amputation compromised the
metatarsal heads. Small decreases in the maximum ankle plantarflexion moment were
observed with small reductions in residual foot length (Dillon, 1995). A significant
________________________________________________________ Chapter 4. 80
reduction in the ankle plantarflexion moment peak was observed in the MTP and TMT
amputees compared to normal (Dillon, 1995; Boyd et al., 1999; Muller et al., 1998).
Similar results have also been reported for toe amputees and those with metatarsal ray
resection (Boyd et al., 1999). The peak ankle plantarflexion moment was delayed in
TMT amputees (Boyd et al., 1999) as it was in a single Chopart amputee (Dillon, 1995).
Amputation proximal to the TMT level did not appear to greatly reduce the peak
dorsiflexion moment from that observed in the TMT group (Dillon, 1995). Ankle power
generation in the MTP group was significantly reduced compared to normal as a result
of reductions in the excursion of the CoP given that no differences in the dynamic ankle
range were observed (Dillon, 1995). Once the metatarsal heads had been compromised,
ankle power generation was reduced to the point of being negligible (Dillon, 1995;
Muller et al., 1998). Questions about the ability of TMT amputees to utilise the
available ankle motion, as measured by plantarflexor power generation, have been
raised (Dillon, 1995).
An extension moment was observed about the knee joint from foot-flat to toe-off
in both the MTP (Dillon, 1995) and TMT amputee groups (Dillon, 1995; Muller et al.,
1998). In the MTP group, the normal knee moment pattern was maintained (Dillon,
1995), however it was completely absent in the TMT amputees (Dillon, 1995; Muller et
al., 1998). Dillon (1995) observed little power absorption immediately before toe-off in
the TMT amputee group. In contrast, Muller et al., (1998) observed a period of
relatively normal power absorption across the knee at this time. In both studies, the
absence of the normal power exchange, between 25-50%GC was notable.
The hip moment and power patterns observed in the MTP cohort, closely
resemble that of the normal population (Dillon, 1995). Muller et al., (1998) reported the
early onset of a flexion moment about the hip joint. In contrast, Dillon (1995) reported a
delay in the hip extension moment peak and the maintenance of an extension moment
about the hip in the TMT amputee group until about 45%GC. The hip flexion moment
peak was considerably delayed and substantially smaller than normal in the TMT
amputees (Dillon, 1995). In the TMT amputee group, hip power generation during
initial stance was comparable to that observed in the normal population however, the
power peak was delayed (Dillon, 1995). Mueller et al., (1998), however, observed very
little concentric muscle activity at this time. Power generation at the hip during the
________________________________________________________ Chapter 4. 81
propulsive phase was comparable to that observed in the normal population (Dillon,
1995; Mueller et al., 1998). However, Mueller et al., (1998) reported that the small
differences were indicative of a hip flexor gait strategy.
Substantial reductions in both sound and residual limb strength have been
observed in toe (Dorostkar et al., 1997) and TMT (Dorostkar et al., 1997; Burnfield et
al., 1998) amputees compared to normal with the most pronounced deficits occurring in
the residual limb ankle plantarflexors (Dorostkar et al., 1997). Burnfield et al., (1998)
identified that there were no differences in plantarflexor strength between the sound and
residual limbs in TMT amputees.
There is little doubt that a substantial number of empirical contributions have
been made over the last five years, particularly given the relatively small population of
partial foot amputees whom may benefit from such work. These empirical studies have
advanced our understanding of partial foot amputee gait from the theoretical static force
analyses presented some 30 years ago. For the most part, authors have tended to
document the mechanical abnormalities without substantial explanation or insightful
comment illustrating the underlying causes for the mechanical behaviours observed.
Perhaps this is merely a reflection of reviewing very recent and ongoing works, which
have been presented largely as conference abstracts or research progress reports where
sufficient detail is usually not permitted.
To date, research has tended to focus on limited aspects of partial foot amputee
gait such as ankle kinematics, stance phase or the affected limb. The existing body of
knowledge raises questions about the causes and compensatory effects of abnormal
movement.
For example, there appears to be some fundamental issue surrounding the
inability of partial foot amputees to load the distal residuum. This poorly understood
problem seems to manifest itself in a number of gait parameters including: reductions in
the excursion of the CoP; reductions in the ankle plantarflexion range utilised during
gait; and reductions in the horizontal GRF associated with push-off. The inability to
load the distal residuum, at least in part, limits the ability of the amputee to generate
power across the ankle.
________________________________________________________ Chapter 4. 82
Given that TMT amputees generate negligible power across the affected ankle,
and that power generation across the affected hip appears to be comparable to normal,
how is power generated to advance the body forward? Perhaps, as in transtibial and
transfemoral amputees, the sound hip extensor musculature work concentrically during
the propulsive phase of the affected limb to push the body forward from the rear.
It would be prudent not to speculate too much about the potential causes of
abnormal movement and what compensatory adaptations may occur but instead to
provide a thorough biomechanical description of partial foot amputee gait.
The purpose of this investigation was to document bilateral ankle, knee and hip
kinematic, kinetic, electromyographic and temperospatial parameters on a cohort of
normal and partial foot amputees to more fully describe the effects of amputation and
prosthetic/orthotic fitting on gait.
4.2 Method
Subjects
The method by which amputee subjects were recruited (including exclusion
criteria and assessment of amputation level) has previously been described in Chapter 2.
Of the amputee subjects recruited for these studies, bilateral gait data were obtained
from a cohort of eight partial foot amputees. Of the eight amputee subjects, five
unilateral partial foot amputees including one Transmetatarsal (TMT), three Lisfranc
and one Chopart amputee were studied. The three remaining subjects had bilateral
amputation including one Metatarsophalangeal amputation (MTP), one Lisfranc
amputation and one subject had bilateral Chopart amputation with partial resection of
the posterioinferior portion of the calcaneus. This individual was not a true forefoot
amputee however the gait patterns observed were dominated by the Clamshell patella
tendon bearing (PTB) prosthesis and were comparable to those observed in the other
Chopart amputee with similar prosthetic fitting. Given the limited number of individuals
with Clamshell PTB prostheses, data from this subject were also considered. Amputee
subjects had a variety of orthotic/prosthetic replacements including toe fillers, custom
________________________________________________________ Chapter 4. 83
orthoses, slipper sockets or Clamshell PTB prostheses. Due to the limited sample and
the variability of individuals in terms of amputation level, number of limbs affected and
prosthetic/orthotic fitting, each subject was considered in isolation relative to a normal,
non-amputee control sample. Characteristics of the amputee subjects have been
presented in Table 4.1.
Table 4.1 Characteristics of the amputee subjects
Bi denotes bilateral; uni denotes unilateral; *Gangrene secondary to frostbite; ‡ Gangrene secondary to
water burns. Standard deviation (SD).
Subject Level Aetiology Age
(years)
Stature
(m)
Mass
(kg)
Device
Amputee subjects
1004-1307A Bi MTP Gangrene* 40 1.74 64.92 Custom orthosis
2103-2116A Uni TMT Trauma 54 1.84 84.50 Toe filler
2703-1903A Uni Lisfranc Trauma 53 1.82 76.60 Slipper socket
0704-0403A Uni Lisfranc Trauma 22 1.84 81.45 Slipper socket
2103-1906A Uni Lisfranc Trauma 55 1.82 80.65 Stuffed shoe
2803-0410A Bi Lisfranc Gangrene 63 1.61 50.00 Toe filler
0904-1924A Bi Chopart Gangrene‡ 31 1.73 82.24 Clamshell PTB
3004-1102A Uni Chopart Trauma 19 1.79 93.00 Clamshell PTB
Mean 42.13 1.77 76.67
SD 16.60 0.08 13.35
Eight non-amputee control subjects were also recruited. Control subjects
satisfied the same inclusion criteria as the amputee subjects. Each control subject was
age, weight, height and sex matched to an amputee subject. Control subjects were
grouped to provide a description of a 'normal' population. In this way, the gait of any
amputee subject could be compared to the mean and 95% confidence interval (CI) of a
normal population rather than to the idiosyncratic pattern of locomotion of a single
control subject with similar anthropometric characteristics. Any given able body subject
may exhibit large variations from the mean control group data, making comparison
either difficult or misleading (Allard et al., 1997). The mean age, stature and mass of
________________________________________________________ Chapter 4. 84
the control sample, including standard deviations in parentheses, were 41.13 years
(±14.81), 1.74m (±0.08) and 77.11kg (±6.83), respectively.
Apparatus
Joint ROM measurements were undertaken using a plastic goniometer with
angles marked in 2-degree increments and muscle strength was rated using the Oxford
Manual muscle test scale. A treatment plinth was used during all measurements, which
were conducted according to the techniques described by Clarkson and Gilewich
(1989). The subject assessment forms used to record the results of the joint ROM and
muscle strength tests are part of Appendix G.
Anthropometric models for the description of the thigh and leg segments as well
as the intact and partial foot have previously been described in Chapters 2 and 3.
Anthropometric descriptions of any prosthetic/orthotic replacement and footwear were
obtained using standard dynamics techniques described in Chapter 3. One of two
linked-segment inverse dynamic models, based on the type of prosthetic/orthotic
intervention (if any), was used to calculate net joint moments and powers as described
in Chapter 3.
In addition to the equipment used to collect the kinematic and kinetic data
described in Chapter 3, EMG signals were detected using 22mm wide bipolar,
silver/silver chloride, pregelled electrodes (Biotabs - MIE Medical Research Ltd. Leeds
UK). The electrodes were attached to the preamplifier at the skin surface. EMG
preamplifiers had a gain of 1000. Footswitch signals were obtained using compression
closing, individual heel and toe switches and voltage dividers (MIE Medical Research
Ltd. Leeds UK). EMG and footswitch signals were obtained at a rate of 1000Hz, using a
waist belt transmitter and FM receiver as part of the MT8 Biological Telemetry System
(MIE Medical Research Ltd. Leeds UK). Analogue footswitch and EMG signals were then
passed to the A/D conversion card. Characteristics of the A/D card have been described
in Chapter 3.
________________________________________________________ Chapter 4. 85
Subject preparation
The preparation of subjects including the provision of informed consent,
documentation of a medical history and anthropometric measurements as well as
kinematic marker placement have previously been described in Chapter 3.
For the collection of joint ROM data and muscle strength testing, subjects were
positioned on a treatment plinth (Clarkson and Gilewich, 1989). Each test manoeuvre
was explained to the subject and instruction provided until the subject could perform the
required task. Measurements were compared bilaterally and against normative data
(Kendall and McCreary, 1993) so that mismeasurements could be identified.
Subsequent measurements were taken where necessary to verify measurements that
were questionable.
Preparation of the skin before the application of the EMG electrodes was
accomplished by shaving and lightly abrading the skin surface with fine grit sand paper
and cleaning with alcohol wipes. Electrodes were then placed on vastus lateralis, biceps
femoris long head, gastrocnemius medial and lateral heads, soleus and tibialis anterior
(Perotto, 1994) with a centre to centre interelectrode distance of 25mm. Foot switches
were placed bilaterally on both the heel and toe. With the electrodes and footswitches in
place, the subject was asked to perform a number of test manoeuvres (Kendall and
McCreary 1993) to assess the placement of the electrode and the efficacy of the EMG
signal.
Data acquisition and processing
The acquisition and processing of force platform and kinematic data have
previously been described in Chapter 3. Kinetic data were calculated using the linked-
segment inverse dynamic models described in Chapter 3 and included anthropometric
descriptions of the remnant foot, leg and thigh segment as well as any
prosthesis/orthosis and footwear. EMG data were collected simultaneously with the
force and kinematic data and synchronisation was controlled by the Peak-Motus
software as described in Chapter 3.
________________________________________________________ Chapter 4. 86
For the normal and amputee subjects, kinetic and kinematic data obtained from
multiple trials were averaged for each limb (Appendix E). A time dependent 95%CI was
created from the ensembled averages to reflect the range of values observed in the
normal population. For each amputee subject, data from both limbs were depicted
relative to the 95% CI of the normal population to facilitate comparison.
The timing and magnitude of certain peak angles, moments, powers and ground
reaction forces were obtained and analysed in more detail (Appendix E). For the normal
population, the timing and magnitude of these points of interest were obtained from the
ensembled averages of each individual. The timing and magnitude of these points of
interest for the normal population were represented by a 95%CI for each parameter.
Similarly, the range of temperospatial, joint ROM values observed in the normal
population were also represented by a 95%CI to facilitate comparison of data from each
limb of the amputee subjects. Views on the presentation of particularly stride length
vary considerably because of attempts to account differences in stature or limb length
between individuals. Stature (or limb length) has been demonstrated to influence stride
length (Dean, 1965; Greive and Gear 1966 -both cited; Inman et al., 1981; Perry, 1992;
Craik and Dutterer, 1995) hence the recommendation that stride length routinely be
defined as a ratio of stature (Winter et al., 1974; Greive and Gear, 1966 - all cited Perry,
1992). The normalisation of stride parameters by stature has become common place as
illustrated by Craik and Dutterer (1995) despite reports that only a weak relationship
exists between these parameters at normal walking speeds (Perry, 1992). In adults only
4-28% of the variability in stride length can be explained by differences in stature
(Perry, 1992). Some authors oppose such normalisation on the basis that the relative
values do not present a clear picture of the distances covered (Das and Ganguli, 1979 -
cited Perry, 1992). In the present investigation stride length has been presented in basic
units of meters as well as normalised by stature given the lack of clear consensus
regarding how this parameter should be reported.
Raw EMG data were initially inspected across multiple strides to ensure a
synchronous pattern of EMG activity that was free from artefact and unsuitable data
were rejected at this stage. EMG data were then filtered using a 4th order high pass
Butterworth filter with 6Hz cut-off (Solomonow, 1990; Nilsson et al., 1993; Acierno et
________________________________________________________ Chapter 4. 87
al., 1998) to eliminate movement artefact and stabilise the baseline signal. Data were
then low pass filtered using a 4th order Butterworth filter with 500Hz cut-off (Yang and
Winter, 1984; Nilsson et al., 1993; Acierno et al., 1998). The effective bandwidth was
therefore 6-500Hz. Data were full wave rectified and integrated over 10ms intervals
(Powers et al., 1998; Perry, 1992). EMG data were amplitude normalised using the
manual muscle test (MMT) method (Perry, 1992; Powers et al., 1998) and MMT data
were collected using the standard test positions described by Kendall and McCreary
(1993). Subjects were given encouragement during the MMT data collection.
Much of the EMG signal characteristic of the noise observed in the present
investigation was well in excess of the 5%MMT threshold utilised by Powers et al.,
(1998) to distinguish meaningful muscle activity from the background noise. The 5%
MMT threshold reflects the equivalent to the clinically effective grade 2 level of muscle
activity (Beasley, 1961 - cited Perry, 1992) and is a means by which meaningful muscle
activity can be identified from the occasional spike, small burst or extremely small
signal which are functionally insignificant (Perry, 1992).
The maximum MMT voltage, representing 100% activity, was determined to be
the mean voltage of a stable sample of MMT data (Powers et al., 1998; Perry, 1992).
Perry (1992) describes utilising the peak one-second sample of the isometric manual
muscle test. In the present study, the maximum MMT values were given by determining
the peak voltage of each 10ms interval of the integrated MMT signal over a stable one-
second sample of MMT data. The 100% MMT value was given by the average of all of
the peak MMT values from the one-second sample of integrated MMT data. This signal
processing technique increased the maximum MMT voltage to a value approximately
midway between the mean and peak MMT voltage. This technique also overcame the
inadequacies associated with normalisation to a single peak (Yang and Winter, 1984).
Determining the maximum MMT voltage in this manner reduced the overall magnitude
of the gait EMG (as a percentage of MMT) and the noise observed was typically below
the 5%MMT threshold.
An ensembled average was created from the multiple trials of EMG data
recorded for each subject. From the ensembled average of each individual limb, the
periods of muscle activity were determined as EMG data exceeding the 5% threshold
________________________________________________________ Chapter 4. 88
level (Powers et al., 1998; Perry, 1992). Packets of EMG activity separated by less than
5% of the gait cycle were combined and any packets of EMG smaller than 5% of the
gait cycle were removed (Powers et al., 1998; Perry, 1992). The mean intensity of EMG
packets together with the time of muscle onset and offset, as a percentage of the gait
cycle, were determined (Powers et al., 1998).
Good approximations of the onset and cessation of packets of EMG activity,
relative to those expected from visual observation of the filtered and rectified signal,
were obtained when this technique was applied to a group of individuals, such as the
ensembled average of the normal cohort. However, when applied to an individual,
rather than to a group ensembled average, the onset and cessation times of packets of
EMG activity were sensitive to small changes in the 5%MMT threshold. As such, the
packets of EMG activity obtained were checked to ensure that the packets of EMG
activity reflected the onset and cessation times expected from visual inspection of the
filtered and rectified signal. Where necessary, the threshold level was adjusted from
5%MMT until the packets of EMG activity of each muscle reflected those expected
from observation of the filtered and rectified signal. When the threshold level was not
5%MMT, the figures were marked with the threshold level used.
4.3 Results
Joint range of motion and muscle strength
A number of differences in hip and knee joint ranges of motion (ROM) were
observed between the normal population and individual amputee subjects. Differences
in many amputee subjects were very close the 95%CI of the normal population.
Differences in joint ROM that did not exceed the 95%CI of the normal population by
more the 5° were not considered clinically significant given that the resolution of the
technique which was about 5°, depending on the joint assessed.
Ankle plantarflexion ROM was significantly reduced in the bilateral Lisfranc
(21°±1°), unilateral Chopart (20°) and bilateral Chopart amputee (30° ± 3°) compared to
the 95%CI of the normal population (32° to 60°). Reductions in plantarflexion range
________________________________________________________ Chapter 4. 89
approached significance on the affected limbs of the unilateral TMT (36°) and Lisfranc
cohort (35°±10°) however were not considered to be functional gait limitations.
Reductions in the available dorsiflexion range approached functional
significance in the affected limbs of the unilateral TMT (10°), Lisfranc cohort (12±5°)
and Chopart amputees (8°) compared to the normal population (95%CI, 6° to 18°).
Dorsiflexion range on the sound limb was also reduced in the TMT (5°), Lisfranc
(12±8°) and Chopart amputees (8°).
Ankle inversion range was significantly compromised in the bilateral Lisfranc
(6±2°) and Chopart (2±0°) amputee compared to normal (95%CI, 12° to 31°). Ankle
inversion was also significantly reduced on the affected limb of the unilateral Chopart
amputee (8°) compared to normal. Compared to the ankle eversion ROM observed in
the normal population (95%CI, 7° to 15°), the eversion ROM observed in the bilateral
Lisfranc (2±0°) and Chopart amputees (2±0°) was significantly compromised. Similar
reductions in ankle eversion ROM were also observed on the affected limb of the TMT
(5°), Lisfranc (2°±2°) and Chopart amputees (2°).
Using the Oxford Manual Muscle Test scale, strength of hip, knee and ankle
musculature on both the sound and affected limb was typically grade 5, as for the
normal population. Reductions in muscle strength were observed in the hip adductors
(grade 4) of subject 2103-1906A. Reductions in muscle strength were also observed
across the hip extensors, adductors and abductors in subject 2803-0410A. Grade 2 ankle
inversion and eversion strength was also observed in this subject.
Temperospatial characteristics
A number of temporal and spatial anomalies were observed among the amputee
cohort. Spatial parameters of stride length, walking velocity and cadence are presented
in Table 4.2. Temporal components including gait cycle duration and proportions of
swing and stance time are presented in Table 4.3. Single and double support phase data
as well as timing of contralateral initial contact are presented in Table 4.4.
________________________________________________________ Chapter 4. 90
Walking velocity was significantly reduced in the unilateral TMT
(1.18±0.04m/s) and Chopart (1.18±0.03m/s) amputees as well as in the bilateral
Lisfranc amputee (0.92±0.02m/s) compared to the 95%CI of the normal population
(1.41-1.71m/s) (Table 4.2). Reductions in walking velocity were commensurate with
reductions in stride length in the unilateral TMT (1.40±0.05m) and the bilateral Lisfranc
amputees (0.99±0.02m) compared to the normal population (95%CI, 1.41 to 1.71m)
(Table 4.2). In the unilateral Chopart amputee, reductions in stride length approached
significance (1.45±0.05m) as did reductions in cadence (97.3±0.6 steps/minute) (Table
4.2). For the cohort of unilateral Lisfranc amputees reductions in stride length
(1.49±0.04m) approached significance however, walking velocity was comparable to
that observed in the normal population (1.32±0.05m/s) as was cadence (106
steps/minute) (Table 4.2). No significant differences in cadence were observed in the
amputee subjects compared to the normal population (95%CI, 91.9 steps/min to 119.7
steps/min).
No significant differences in the duration of the gait cycle were observed in the
amputee subjects compared normal population (95%CI, 0.99s to 1.29s) (Table 4.3). In
the normal population, stance and swing occupied an average of 60±1%GC and 40±1
%GC, respectively (Table 4.3). The proportion of the gait cycle occupied by sound limb
stance phase was significantly larger than that spent in affected limb stance for the
unilateral TMT, Chopart and several of the Lisfranc amputees (Table 4.3). The duration
of sound limb stance, as a percentage of the gait cycle, was significantly larger than that
the normal population (95%CI, 59%GC to 62%GC) for several of these individuals
(Table 4.3). For subject 2803-0410A, the duration of stance phase, as a percentage of
the gait cycle, was increased bilaterally (Table 4.3). Proportionate reductions in the
duration of swing phase, as a percentage of the gait cycle, were observed.
The proportion of the gait cycle spent in affected limb single support was
decreased for the unilateral TMT (38%GC) and Chopart (37%GC) amputees compared
to the normal population (95%CI, 38%GC to 41%GC) (Table 4.4). A similar decrease
was seen for the bilateral Lisfranc amputee (37±0%GC) and the unilateral Lisfranc
amputee subject 0704-0403A (Table 4.4). The duration of affected limb single support,
as a percentage of the gait cycle, was shorter than that of the sound limb in all the TMT
________________________________________________________ Chapter 4. 91
and Lisfranc amputees except subject 2103-1906A (Table 4.4). The statistical
significance of these results (ie: values outside the 95%CI of the normal population)
were varied when compared to the normal population (Table 4.4). For subject 2103-
1906A, affected limb single support was comparable to normal however, the proportion
of the gait cycle spent in sound limb single support was significantly reduced (Table
4.4).
Table 4.2 Spatial characteristics of the amputee subjects.
Standard deviations reported in brackets.* denotes parameter outside the 95% confidence interval of
normal population. 'norm' indicates parameters normalised by stature in meters.
Stride length Walking velocitySubject Cadence
(step/min) (m) norm (m/s) norm (s-1)
Control 105.8
(6.93)
1.56
(0.08)
0.90
(0.05)
1.37
(0.07)
0.80
(0.06)
1004-1304A Bi MTP 103.9
(0.42)
1.57
(0.02)
0.90
(0.01)
1.36
(0.01)
0.78
(0.01)
2103-2116A Uni TMT 100.9
(0.70)
1.40*
(0.05)
0.77*
(0.03)
1.18*
(0.04)
0.64*
(0.02)
2703-1903A Uni Lisfranc 103.9
(3.25)
1.56
(0.08)
0.85
(0.04)
1.35
(0.11)
0.74
(0.06)
0704-0403A Uni Lisfranc 106.2
(2.14)
1.44
(0.02)
0.78*
(0.01)
1.28
(0.01)
0.69
(0.01)
2103-1906A Uni Lisfranc 109.7
(1.21)
1.48
(0.01)
0.82
(0.00)
1.35
(0.02)
0.75
(0.01)
2803-0410A Bi Lisfranc 111.2
(0.84)
0.99*
(0.02)
0.61*
(0.01)
0.92*
(0.02)
0.57*
(0.01)
0904-1924A Bi Chopart 103.8
(2.89)
1.44
(0.05)
0.83
(0.03)
1.25
(0.08)
0.72
(0.05)
3004-1102A Uni Chopart 97.34
(0.61)
1.45
(0.05)
0.81
(0.03)
1.18*
(0.03)
0.66*
(0.02)
________________________________________________________ Chapter 4. 92
For the unilateral Chopart amputee, the duration of double support following
affected limb initial contact was increased (13%GC) compared to the normal population
(95%CI, 9%GC to 12%GC). For the unilateral TMT amputee and subject 0704-0403A
the proportion of the gait cycle spent in double support following sound limb initial
contact was significantly increased. The duration of double support, as a percentage of
the gait cycle, was 14±1%GC for the bilateral Lisfranc amputee.
Table 4.3 Temporal characteristics of the amputee subjects.
Standard deviations reported in brackets.* denotes parameter outside the 95% confidence interval of
normal population. AL denotes affected limb. SL denotes sound limb.
Stance time Swing timeSubject Gait
cycle
(sec) (sec) (%GC) (sec) (%GC)
Control 1.176
(0.074)
0.688
(0.048)
60.4
(0.8)
0.451
(0.029)
39.6
(0.8)
1004-1304A Bi MTP 1.156
(0.005)
0.688
(0.007)
59.6
(0.9)
0.467
(0.012)
40.4
(0.9)
2103-2116A Uni TMT AL
SL
1.183
1.195
0.720
0.750
60.9
62.8*
0.463
0.445
39.1
37.2*
2703-1903A Uni Lisfranc AL
SL
1.130
1.181
0.663
0.731
58.7
61.9
0.467
0.450
41.3
38.1
0704-0403A Uni Lisfranc AL
SL
1.147
1.114
0.703
0.697
61.3
62.6*
0.443
0.417
38.7
37.4*
2103-1906A Uni Lisfranc AL
SL
1.105
1.086
0.680
0.644
61.7
59.3
0.423
0.442
38.3
40.7
2803-0410A Bi Lisfranc 1.080
(0.007)
0.690
(0.015)
63.9*
(1.1)
0.3900
(0.014)
36.1*
(0.1)
0904-1924A Bi Chopart 1.158
(0.032)
0.694
(0.015)
59.9
(0.4)
0.464
(0.017)
40.1
(0.4)
3004-1102A Uni Chopart AL
SL
1.228
1.238
0.750
0.777
61.1
62.7*
0.478
0.462
38.9
37.3*
________________________________________________________ Chapter 4. 93
Table 4.4 Single and double support phase characteristics of the amputee subjects.
Standard deviations reported in brackets.* denotes parameter outside the 95% confidence interval of
normal population. AL denotes affected limb. SL denotes sound limb. CHC denotes time of contralateral
heel contact as a percentage of the gait cycle. Double support phase AL, indicates the double support
phase after affected limb heel contact. Similarly, double support SL, indicates the double support phase
after sound limb heel contact.
Single support Double SupportSubject CHC
(%GC) (sec) (%GC) (sec) (%GC)
Control 49.8
(0.2)
0.452
(0.029)
39.7
(0.8)
0.120
(0.014)
10.5
(0.9)
1004-1304A Bi MTP 49.7
(0.3)
0.467
(0.013)
40.2
(1.1)
0.114
(0.006)
9.9
(0.6)
2103-2116A Uni TMT AL
SL
47.8*
52.8*
0.444
0.460
38.0*
39.4
0.119
0.156
10.2
13.4*
2703-1903A Uni Lisfranc AL
SL
49.2*
50.6*
0.452
0.466
38.5
40.8
0.133
0.108
11.3
9.5
0704-0403A Uni Lisfranc AL
SL
48.9*
50.7*
0.416
0.443
36.5*
38.4
0.133
0.144
11.7
12.4*
2103-1906A Uni Lisfranc AL
SL
51.6*
48.5*
0.443
0.419
40.5
37.8*
0.116
0.113
10.6
10.2
2803-0410A Bi Lisfranc 50.4*
(0.1)
0.388
(0.014)
36.8*
(0.4)
0.147
(0.011)
14.0*
(1.4)
0904-1924A Bi Chopart 49.3*
(0.9)
0.464
(0.015)
39.9
(0.1)
0.123
(0.010)
10.6
(1.2)
3004-1102A Uni Chopart AL
SL
50.6*
49.5
0.461
0.478
37.0*
38.32
0.165
0.129
13.2*
10.3
________________________________________________________ Chapter 4. 94
Contralateral heel contact occurred at 49.8±0.2%GC for the normal population
and the 95%CI was very tight (49.4%GC to 50.2%GC). For the majority of unilateral
amputee subjects, affected limb contralateral initial contact occurred prematurely and
sound limb initial contact was delayed compared to normal population (Table 4.4).
However, for subject 2103-1906A the opposite affect was observed (Table 4.4). For the
bilateral Lisfranc amputee, contralateral heel contact was also delayed (50.4±0.1%GC).
Contralateral initial contact was more variable for the bilateral Chopart amputee with
significant differences observed on only one limb but on average, was premature
(49.3±0.9%GC).
Ground reaction force and centre of pressure excursion
The ground reaction force (GRF) and centre of pressure (CoP) excursion
patterns observed for the partial foot amputees were similar to those observed in the
normal population.
Figures 4.1 to 4.4 describe the body-mass-normalised, fore-aft and horizontal
GRF patterns for the bilateral amputees and both limbs of the unilateral amputees
compared to the 95% CI of the normal population. The timing of the first horizontal
shear force (Fx1) was delayed in the bilateral Lisfranc amputee (14±1%GC) as well as
on the affected limb of the unilateral Chopart (16%GC) amputee (Figure 4.1) compared
to the normal population (95%CI, 9%GC to 12%GC).
The magnitude of Fx1 was significantly smaller in the bilateral Lisfranc amputee
(-1.36±0.12N/kg) (Figure 4.2) compared to the normal population (95%CI, -1.56N/kg to
-2.63N/kg). In the bilateral Chopart amputee, the magnitude of the breaking force was
substantially smaller than normal for the left limb (-0.80N/kg) however, no clear peak
was observed for the right limb. Of particular interest is the small impulse in the
horizontal GRF observed between initial contact and mid-stance compared to that
observed from mid-stance until toe-off in the bilateral Chopart amputee (Figure 4.2). In
the normal population and the remaining amputee subjects, the impulses of these two
periods were relatively similar (Figure 4.1-4.2).
________________________________________________________ Chapter 4. 95
Figure 4.1 Fore-aft ground reaction force for the affected and sound limbs of the
unilateral amputee subjects relative to the normal population
10 20 30 40 50 60 70 80 90 100-3
-2
-1
0
1
2
3Fore-aft ground reaction force for affected limbs(-)
Fx
(N/k
g)
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-3
-2
-1
0
1
2
3Fore-aft ground reaction force for sound limbs (-)
Fx
(N/k
g)
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 96
Figure 4.2 Fore-aft ground reaction force for the bilateral amputee subjects relative to
the 95% confidence interval of the normal population.
The letters R and L before the subject codes denote right and left limbs.
The timing of the second horizontal GRF peak (Fx2) was premature on the
affected limbs of the unilateral TMT (48%GC) and Lisfranc cohort (48±3%GC)
compared to the normal population (95%CI, 50%GC to 54%GC) (Figure 4.1). The
magnitude of Fx2 was substantially smaller in the bilateral Lisfranc amputee
(1.21±0.03N/kg) compared to the normal population (95%CI, 1.65N/kg to 2.66N/kg)
(Figure 4.2).
The magnitude of the first vertical GRF peak (Fz1) was larger on the sound limb
of the Lisfranc cohort (12.92±0.60N/kg) compared to the normal population (95%CI,
10.20N/kg to 12.02N/kg) (Figure 4.3). The timing of Fz2 was delayed on both limbs of
the unilateral Chopart amputee (35±1%GC) (Figure 4.3) as well as in the bilateral
Chopart amputee (33±1%GC) compared to the normal population (95%CI, 23%GC to
31%GC) (Figure 4.4). Delays in the timing of Fz2 approached significance in the
bilateral Lisfranc amputee (31±2%GC) as did differences on the sound limb of the
unilateral TMT amputee (31%GC). Differences in the magnitude of Fz3 were
10 20 30 40 50 60 70 80 90 100-3
-2
-1
0
1
2
3Fore-aft ground reaction force for Bilateral amputees(-)
Fx
(N/k
g)
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 97
significant on the affected limbs of the unilateral TMT subjects 2703-1903A (9.95N/kg)
and 2103-1906A (9.51N/kg) (Figure 4.3) compared to the normal population (95%CI,
10.04N/kg to 11.96N/kg). Reductions in the magnitude of Fz3 approached significance
on the affected limb of the unilateral TMT amputee (10.20N/kg). On the right limb of
the bilateral Lisfranc amputee, reductions in the magnitude of Fz3 were significant only
on the right limb (9.44N/kg) and approached significance on the left limb (10.30N/kg)
(Figure 4.4).
Figure 4.3 Vertical ground reaction force for the bilateral amputee subjects relative to
the normal population.
The letters R and L prefixing the subject codes denotes right and left limb for each of the bilateral
amputees.
10 20 30 40 50 60 70 80 90 100
0
5
10
15Vertical ground reaction force for Bilateral amputees(-)
Fz
(N/k
g)
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 98
Figure 4.4 Vertical ground reaction force for the affected and sound limbs of the
unilateral amputee subjects relative to the normal population
10 20 30 40 50 60 70 80 90 100
0
5
10
15Vertical ground reaction force for affected limbs(-)
Fz
(N/k
g)
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100
0
5
10
15Vertical ground reaction force for sound limbs (-)
Fz
(N/k
g)
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 99
No significant reductions in the total excursion of the centre of pressure,
normalised by shoe length (SL), were observed compared to the normal population
(95%CI, 95.02%SL to 103.24%SL). On the sound limbs of the unilateral amputees, a
relatively normal, linear excursion of the CoP was observed, except in the unilateral
Chopart amputee (Figure 4.5). On the sound limb of the unilateral Chopart amputee the
GRF progressed very rapidly until about mid-stance where it remained at a relatively
constant lever-arm until approximately 50%GC (Figure 4.5).
On the affected limbs of the unilateral TMT and Lisfranc amputees, the CoP
progressed relatively normally until foot-flat when the excursion of the CoP was at
about 30-40%SL (Figure 4.5-4.6). The GRF then remained at a relatively fixed lever-
arm until about 45%GC (Figures 4.5 and 4.6). The CoP progressed rapidly during the
propulsive phase as evidenced clearly on the affected limb of the unilateral TMT
amputee (Figure 4.5) and the bilateral Lisfranc amputee (Figure 4.6). The profiles
observed in the bilateral MTP amputee, were similar to those of the normal population
(Figure 4.6). The CoP excursion profiles observed on the affected limbs of the Chopart
amputees were distinctly different from those observed in the TMT and Lisfranc
amputees (Figures 4.5-4.6). On the affected limb of the unilateral Chopart amputee, the
progression of the CoP was relatively linear, as in the normal population. However in
the bilateral Chopart amputee, an extraordinary progression of the CoP was observed.
Irrespective of the profiles observed in these individuals, the excursion of the CoP
commensurate with the peak GRF, were similar to normal.
________________________________________________________ Chapter 4. 100
Figure 4.5 Sagittal plane centre of pressure excursion (as a percentage of shoe length,
SL) for the affected and sound limbs of the unilateral amputee subjects relative to the
normal population.
10 20 30 40 50 60 70 80 90 100-20
0
20
40
60
80
100
120
Centre of pressure excursion for affected limbs(-)
CoP
(%S
L)
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-20
0
20
40
60
80
100
120
Centre of pressure excursion for sound limbs (-)
CoP
(%
SL)
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 101
Figure 4.6 Sagittal plane centre of pressure excursion profile (as a percentage of shoe
length, SL) for the bilateral amputee subjects relative to the normal population.
The letters R and L prefixing the subject codes denote the right and left limb, respectively.
Repeatability of kinematic, kinetic and electromyographic data
The repeatability of kinematic, kinetic and electromyographic data was assessed
using the coefficient of variation (CV) (Winter, 1991; Winter, 1984) and the coefficient
of multiple determination (CMC) (Kadaba et al., 1989). The CV is expressed as a
percentage of the mean value of the signal. In effect, it is a measure of the variability-to-
signal ratio (Winter, 1991). The CV was found to be inadequate when the mean of the
signal was close to zero and gave abnormally large values. The fore-aft GRF or hip joint
moment profiles are typical examples of data that is symmetrical about zero. The CMC
is an alternate technique for describing the variability of waveforms that is not affected,
like the CV, by waveforms with a mean close to zero. The CMC is expressed as a ratio
where one indicates a perfect match between waveforms. For the normal population, the
CV and CMC measured of variability have been presented in Tables 4.5 and 4.6. Due to
the extensive measures of intra-subject variability for the amputee subjects, these data
have been presented as part of the individual gait reports (Appendix I).
10 20 30 40 50 60 70 80 90 100-20
0
20
40
60
80
100
120
Centre of pressure excusrion for Bilateral amputees(-)
CoP
(%
SL)
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 102
Table 4.5 Inter-subject variability of the kinematic and kinetic patterns of the normal
population.
Angle Moment Power
CV(%) CMC CV(%) CMC CV(%) CMC
Ankle 81 0.85 24 0.96 166 0.88
Knee 20 0.95 168 0.83 161 0.74
Hip 34 0.91 1037 0.82 134 0.71
Table 4.6 Inter-subject variability of the EMG patterns of the normal population.
CV(%) CMC
Soleus 76 0.47
Gastrocnemius Lateral Head 97 0.43
Gastrocnemius Medial Head 87 0.47
Tibialis Anterior 53 0.69
Biceps Femoris Long Head 115 0.25
Vastus Lateralis 87 0.43
Kinematic
While the majority of kinematic abnormalities observed occurred at the ankle,
many individuals displayed idiosyncrasies affecting the hip and knee joints.
The kinematic pattern of hip motion for both the sound and affected limbs of the
unilateral, and both limbs of the bilateral, amputees closely resembled that observed for
the normal population (Figures 4.7 and 4.8). For the affected limbs in all but the
bilateral MTP amputee (Figure 4.8) and the unilateral Chopart amputee (Figure 4.7), the
hip extended immediately after heel contact.
________________________________________________________ Chapter 4. 103
Figure 4.7 Sagittal plane hip flexion and extension angles for the affected and sound
limbs of the amputee subjects relative to the normal population
Positive values along the y-axis indicate hip flexion. Negative values on the y-axis indicate hip extension.
10 20 30 40 50 60 70 80 90 100-40
-20
0
20
40
Hip Angle Affected limbs (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-40
-20
0
20
40
Hip Angle Sound Limb (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 104
Figure 4.8 Sagittal plane hip flexion and extension angles for the bilateral amputee
subjects relative to the normal population
Positive values along the y-axis indicate hip flexion. Negative values on the y-axis indicate hip extension.
Premature maximum hip extension was observed on the affected limbs of the
combined unilateral Lisfranc cohort (49±0%GC) (Figure 4.7) and the bilateral Chopart
amputee (49±1%GC) (Figure 4.8) with respect to the normal population (95%CI,
50%GC to 52%GC). In contrast, maximum hip extension was delayed on the sound
limb of the TMT amputee (54%GC), the Lisfranc cohort (53±1%GC), the bilateral
Lisfranc amputee (54±1%GC) and the affected limb of the unilateral Chopart amputee
(53±0%GC) with respect to the normal population (Figure 4.7). The magnitude of
maximum hip extension was significantly larger on the affected limb of the unilateral
Chopart amputee (-21.27± 0.71°) compared to the normal population (95%CI, -4.03° to
–18.16°). In the bilateral Lisfranc amputee, reductions in maximum hip extension (-
2.72± 2.02°) approached significance.
The hip flexion/extension angle at toe-off was substantially less than the 95% CI
of the normal population (-10.63° to 4.39°) on the affected limb of the unilateral
10 20 30 40 50 60 70 80 90 100-40
-20
0
20
40
Hip Angle Bilateral limbs (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 105
Chopart amputee (-14.42±0°) (Figure 4.7) and substantially larger in the bilateral
Lisfranc amputee (7.07±1.85°) (Figure 4.8).
The patterns of knee motion observed on the sound and affected limbs were very
similar to that of the normal population. For the bilateral MTP subject, substantial knee
flexion at initial contact (9.27±2.29°) was observed compared to the normal population
(95%CI, -4.56° to 5.57°) (Figure 4.10). Excessive stance phase knee flexion was also
observed in the bilateral MTP amputee (26.37±1.85°) compared to the normal
population (95%CI, 10.82° to 22.71°).
Substantial reductions in stance phase knee flexion were observed on the
affected limb of the TMT amputee (6.55°) (Figure 4.9) and the bilateral Chopart
amputee (8.00±2.42°) (Figure 4.10). In contrast, excessive stance phase knee flexion
was observed on the sound and affected limbs of a single unilateral Lisfranc amputee
(2703-1903A) (29.19° and 24.62°, respectively) (Figure 4.9). The timing of stance
phase knee flexion was substantially delayed in the bilateral Chopart amputee
(19±1%GC) (Figure 4.10) compared to the normal population (95%CI, 13%GC to
17%GC).
Knee hyperextension was observed on the affected limb of the unilateral
Chopart (Figure 4.9) and the bilateral Chopart amputees (Figure 4.10), which seemed to
delay the initiation of knee flexion into swing phase to varying degrees (Figure 4.9).
The knee flexion angle at toe-off on the affected limb of the unilateral Chopart amputee
(23.11°) and in the bilateral Chopart amputee (25.75 ±1.92°) were marginally less than
the normal population (95%CI, 26.20° to 46.97°).
Maximum knee flexion was delayed in the bilateral Lisfranc amputee
(75±0%GC) and difference on the sound limb of the unilateral TMT amputee (74%GC)
approached significance in comparison to the normal population (95%CI, 70%GC to
74%GC).
________________________________________________________ Chapter 4. 106
Figure 4.9 Sagittal plane knee flexion/extension angles for the affected and sound
limbs of the unilateral amputee subjects relative to the normal population
Positive values along the y-axis indicate knee flexion. Negative values on the y-axis indicate knee
extension.
10 20 30 40 50 60 70 80 90 100-20
0
20
40
60
80Knee Angle Affected Limb (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-20
0
20
40
60
80Knee Angle Sound Limb (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 107
Figure 4.10 Sagittal plane knee flexion angles for the bilateral amputee subjects
relative to the normal population
Positive values along the y-axis indicate knee flexion. Negative values on the y-axis indicate knee
extension.
At initial contact, substantial dorsiflexion was observed in the bilateral MTP
amputee (5.38±1.00°) (Figure 4.12) and on the affected limbs of a number of Lisfranc
amputees (Figure 4.11) compared to the normal population (95%CI, -13.15° to 3.67°).
The mean dorsiflexion angle at initial contact for the cohort of Lisfranc amputees
(5.85±3.39°) was substantially larger than normal due to the excessive dorsiflexion
observed in subjects 2103-1906A (9.53°) and 2703-1903A (5.18°).
The timing of initial plantarflexion was substantially delayed on the affected
limb of the unilateral Chopart amputee (12%GC) and on both limbs of the bilateral
Chopart amputee (12±1%GC) compared to the normal population (95%CI, 5%GC to
9%GC) (Figure 4.12). For the bilateral Chopart amputee, the mean plantarflexion angle
obtained (-5.06±1.45°) was marginally less than that observed in the normal population
(95%CI, -16.74° to -5.53°). For the bilateral MTP amputee similar reductions in the
mean initial plantarflexion peak were observed (-3.28± 3.14°).
10 20 30 40 50 60 70 80 90 100-20
0
20
40
60
80
Knee Angle Bilateral Amputees(-)
(Deg
.) F
lex.
>
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 108
Peak dorsiflexion was substantially delayed on the affected limbs of all subjects
except the bilateral MTP amputee. In comparison to the normal population (95%CI,
40%GC to 49%GC) peak dorsiflexion was delayed on the affected limb of the unilateral
TMT (51±0%GC) and Lisfranc (51±2%GC) amputees. Differences in the unilateral
Chopart amputee also bordered significance (50±0%GC). Peak dorsiflexion was also
delayed in the bilateral Lisfranc (55±5%GC) and Chopart (54±0%GC) amputees
compared to the normal population (Figure 4.12). The magnitude of peak dorsiflexion
was substantially larger than the normal (95%CI, 4.17° to 12.17°) in the bilateral MTP
amputee (17.27±2.43°) and the affected limbs of the unilateral TMT (13.91°) and
Lisfranc group (14.00±2.93°). Peak dorsiflexion was substantially reduced in the
unilateral Chopart amputee on both the sound (2.41°) and affected limbs (0.26°)
compared to the normal population (Figure 4.11-4.12).
Significant reductions in the plantarflexion angle at toe-off were observed on the
affected limbs of the unilateral TMT (-4.20°), Lisfranc (-0.93±3.60°) and Chopart (-
4.89°) amputees as well as the bilateral MTP (-2.27±2.14°), Lisfranc (1.28±8.42°) and
Chopart (1.76±1.17°) amputees (Figures 4.11-4.12).
Substantial reductions in maximum plantarflexion were also observed on the
affected limb of the unilateral Chopart amputee (-9.25°) and the Lisfranc cohort (-
9.22±4.59°) compared to the normal population (95%CI, -15.95° to -32.35°). Maximum
plantarflexion was also substantially reduced in the bilateral MTP (-9.65±1.88°),
Lisfranc (-11.53±1.28°) and Chopart amputees (-4.00±1.67°).
________________________________________________________ Chapter 4. 109
Figure 4.11 Sagittal plane ankle dorsiflexion/plantarflexion angles for the sound and
affected limbs of the unilateral amputee sample
Positive values along the y-axis indicate ankle dorsiflexion or flexion. Negative values on the y-axis
indicate ankle plantarflexion or extension.
10 20 30 40 50 60 70 80 90 100-40
-30
-20
-10
0
10
20Ankle Angle Affected Limbs (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-40
-30
-20
-10
0
10
20Ankle Angle Sound Limbs (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 110
Figure 4.12 Sagittal plane ankle dorsiflexion/plantarflexion angles for the bilateral
amputees and those with Clamshell PTB prostheses
Positive values along the y-axis indicate ankle dorsiflexion or flexion. Negative values on the y-axis
indicate ankle plantarflexion or extension.
10 20 30 40 50 60 70 80 90 100-40
-30
-20
-10
0
10
20
30Ankle Angle Bilateral amputees (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancControl ±2SD
10 20 30 40 50 60 70 80 90 100-40
-30
-20
-10
0
10
20
30Ankle Angle Chopart amputees with Clamshell PTB prostheses (-)
(Deg
.) F
lex.
>
Gait Cycle [%]
R0904-1924A - ChopartL0904-1924A - Chopart3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 111
Maximum plantarflexion was substantially delayed in the bilateral Lisfranc
(72±1%GC) and Chopart (69±1%GC) amputees compared to normal population
(95%CI, 62%GC to 66%GC). Similar delays were also observed on both limbs of the
TMT amputee (67±0%GC) and the affected limb of the unilateral Chopart amputee
(69.0%GC). Delays in the timing of maximum plantarflexion were commensurate with
delays in the timing of toe-off on the sound limb of the unilateral TMT and bilateral
Lisfranc amputees.
Two distinct kinematic profiles were observed during swing phase on the
affected limb of the unilateral amputees (Figure 4.11) which, appear to be related to the
maximum plantarflexion angle and initial contact angle.
Kinetic
Ankle joint moments
Ankle moment data has been presented in Figures 4.13 and 4.14. Following
initial contact, a dorsiflexion moment was observed in the partial foot amputees as in
the normal population. The peak dorsiflexion moment was delayed in the bilateral
Lisfranc amputee (7±1%GC) and was premature on the sound limb of the TMT
amputee (4%GC). Compared to the normal population (95%CI, 4%GC to 7%GC)
delays in the peak dorsiflexion moment approached significance in the bilateral Lisfranc
amputee (7±1%GC) and on the affected limb of the Lisfranc cohort (7±2%GC) due to
differences in subjects 0704-0403A (8%GC) and 2103-1906A (7%GC). The magnitude
of the dorsiflexion moment was significantly increased on the affected limb of subject
2103-1906A (-0.45Nm/kg) compared to the normal population (95%CI, -0.22Nm/kg to
–0.05Nm/kg).
The ankle moment patterns on the sound limbs of subjects 3004-1102A and
2103-2116A were distinctly different, during the loading and mid-stance phases, from
those observed in the normal population (Figure 4.13).
________________________________________________________ Chapter 4. 112
Figure 4.13 Sagittal plane ankle moments for the affected and sound limbs of the
unilateral amputee sample.
Positive values along the y-axis indicate an ankle extension moment. Negative values on the y-axis
indicate an ankle flexion moment.
10 20 30 40 50 60 70 80 90 100-0.5
0
0.5
1
1.5
2
2.5Ankle Moment Affected Limbs (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - LisfrancControl ±2SD
10 20 30 40 50 60 70 80 90 100-0.5
0
0.5
1
1.5
2
2.5Ankle Moment Sound Limbs (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 113
Figure 4.14 Sagittal plane ankle moments for the bilateral amputee sample.
Positive values along the y-axis indicate an ankle extension or plantarflexion moment. Negative values on
the y-axis indicate an ankle flexion or dorsiflexion moment.
One of the most startling differences about the gait of partial foot amputees was
the reduction in the magnitude of the plantarflexion moment peak (Figures 4.13 and
4.14). In comparison to the normal population (95%CI, 1.49Nm/kg to 1.95Nm/kg),
significant reductions in the peak plantarflexion moments were observed on the affected
limbs of the Lisfranc cohort (0.85±0.30Nm/kg), the TMT amputee (0.85Nm/kg) and
both limbs of the bilateral Lisfranc amputee (0.59±0.22Nm/kg).
The ankle moment data for the affected limbs of the Chopart amputees were
calculated using a standard linked-segment model because these data could not be
calculated given the basic assumptions governing partial foot model-B. Given that the
ankle joint moment equation is dominated by the magnitude and lever-arm of the
vertical GRF and, therefore, robust to errors in the anthropometric, angular and linear
input data the joint moment data were considered to be accurate. For the unilateral
10 20 30 40 50 60 70 80 90 100-0.5
0
0.5
1
1.5
2
2.5Ankle Moment Bilateral Amputees(-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancControl ±2SD
________________________________________________________ Chapter 4. 114
Chopart amputee, anthropometric characteristics of the sound limb were used. For the
bilateral Chopart amputee, the anthropometric characteristics for each affected limb
were maintained, however the prosthesis and footwear were not considered.
The dorsiflexion moment peak observed on the left limb of the bilateral Chopart
amputee was absent and on the right, the dorsiflexion moment was relatively prolonged
(Figure 4.15). The relatively linear moment pattern observed in the normal population
was not observed in the unilateral Chopart amputee or on the right limb of the bilateral
Chopart amputee (Figure 4.15).
Figure 4.15 Sagittal plane ankle moments for the affected limbs of the Chopart
amputees
Positive values along the y-axis indicate an ankle extension or plantarflexion moment. Negative values on
the y-axis indicate an ankle flexion or dorsiflexion moment.
10 20 30 40 50 60 70 80 90 100-0.5
0
0.5
1
1.5
2
2.5Ankle Moment Chopart Amputees (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
3004-1102A - Chopart R0904-1924A - ChopartL0904-1924A - ChopartControl ±2SD
________________________________________________________ Chapter 4. 115
The ankle plantarflexion moment peak observed on the affected limb of the
unilateral Chopart amputee (1.72N/kg) was comparable to that observed in the normal
population (Figure 4.15). For the bilateral Chopart amputee, the peak plantarflexion
moments were reduced on the right limb (1.39Nm/kg) and bordered the 95%CI on the
left (1.52Nm/kg) (Figure 4.15). The timing of the plantarflexion moment peak observed
on the affected limb of the unilateral Chopart amputee (50%GC) bordered the 95%CI of
the normal population (45.12%GC to 49.63%GC) (Figure 4.15).
Knee joint moments
A normal knee moment pattern was observed on the sound limb of all unilateral
partial foot amputees and the timing and magnitude of the moment peaks were
comparable to the range of values observed in the normal population (Figure 4.16).
The maximum extension moment (KM2), associated with stance phase knee
flexion, was delayed in the bilateral Lisfranc (16±1%GC) and Chopart amputees
(18±0%GC) compared to the normal population (95%CI, 12%GC to 15%GC) (Figure
4.17). The magnitude of the KM2 peak was increased in the bilateral MTP amputee
(0.95±0.10Nm/kg) and decreased the bilateral Chopart amputee (0.16±0.15Nm/kg)
compared to the normal cohort (95%CI, 0.31Nm/kg to 0.86Nm/kg) (Figure 4.17).
Reductions in the magnitude of the KM2 peak approached significance on the affected
limb of the unilateral TMT (0.32Nm/kg) and Chopart amputees (0.33Nm/kg) (Figure
4.16).
The timing of the knee flexion moment associated with knee flexion into swing
phase (KM3) was significantly delayed on the affected limb of the unilateral Chopart
amputee (47%GC) compared to the 95%CI of the normal cohort (40%GC to 46%GC).
The KM3 moment peak was absent on the affected limb of the unilateral TMT (Figure
4.16) and bilateral Lisfranc amputees (Figure 4.17) and therefore, the timing and the
magnitude of this moment peak were unable to be identified.
________________________________________________________ Chapter 4. 116
Figure 4.16. Sagittal plane knee moment for the affected and sound limbs of the
unilateral amputee sample
Positive values along the y-axis indicate a knee extension moment. Negative values on the y-axis indicate
a knee flexion moment.
10 20 30 40 50 60 70 80 90 100-1.5
-1
-0.5
0
0.5
1
1.5
2Knee Moment Affected limbs (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-1.5
-1
-0.5
0
0.5
1
1.5
2Knee Moment Sound Limbs (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 117
Figure 4.17 Sagittal plane knee moment for the bilateral amputees
Positive values along the y-axis indicate a knee extension moment. Negative values on the y-axis indicate
a knee flexion moment.
The knee flexion moment peak was significantly decreased on the affected limb
of the unilateral TMT amputee and Lisfranc amputees 2103-1906A (-0.05Nm/kg) and
0704-0403A (-0.04Nm/kg) as well as in the bilateral Lisfranc amputee compared to
normal population (95%CI, -0.76Nm/kg to -0.27Nm/kg). The magnitude of the KM3
peak observed in subject 2703-1903A (-0.39Nm/kg) was comparable to normal (Figure
4.16). The knee flexion moment peaks observed on the affected limbs of the unilateral
Chopart (-0.75Nm/kg) and bilateral Chopart amputees (-0.63Nm/kg ±0.24Nm/kg) were
quite substantial and bordered the 95%CI of the normal population (Figures 4.16-4.17).
The swing phase knee moments observed in the amputee subjects were
comparable to those of the normal population.
Hip joint moments
The hip joint moments have been presented in Figures 4.18 and 4.19.
10 20 30 40 50 60 70 80 90 100-1.5
-1
-0.5
0
0.5
1
1.5
2
Knee Moment Bilateral Amputees(-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 118
Figure 4.18 Sagittal plane hip moment for the affected and sound limbs of the unilateral
amputee sample
Positive values along the y-axis indicate a hip extension moment. Negative values on the y-axis indicate a
hip flexion moment.
10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
1.5
2Hip Moment Affected limbs (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
1.5
2Hip Moment Sound Limbs (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 119
Figure 4.19 Sagittal plane hip moment for the bilateral amputees
Positive values along the y-axis indicate a hip extension moment. Negative values on the y-axis indicate a
hip flexion moment.
The basic pattern of the hip moment profile was relatively normal for the
amputee subjects although the patterns observed were variable reflecting the
heterogeneous nature of the sample. Many individuals maintained an extension moment
about the hip joint well into stance phase and in some cases until the propulsive phase of
gait (Figures 4.18-4.19). The stance phase hip extension moment peaks (HM1) were
relatively poorly defined in both the normal and amputee populations. The HM1 peaks
occurred bilaterally at about 10-15% of the gait cycle commensurate with contralateral
initial contact. Substantial HM1 peaks were observed on the affected limb in subject
2703-1903A and on the sound limbs of subjects 2103-2116A and 2103-1906A
compared to those observed in the normal population (Figure 4.18). In the bilateral
Lisfranc and Chopart amputees, the hip extension moments observed on the left limb
were substantially larger than that observed on the right limb (Figure 4.19).
The hip flexion moment peak (HM2) was well defined in both the normal
population and the amputee subjects. Compared to the 95%CI of the normal population
(47%GC to 56%GC) the HM2 peak was substantially delayed on both the sound
10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
1.5
2Hip Moment Bilateral Amputees(-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 120
(63%GC) and affected limbs (60%GC) of the unilateral TMT amputee (Figure 4.18).
Similar delays were observed unilaterally in the bilateral Lisfranc (63.0%GC) and
Chopart (61.0%GC) amputees (Figure 4.19) and on the affected limbs of subjects 2703-
1903A and 2103-1906 (Figure 4.18).
During swing phase, no differences in the hip moment patterns or extension
moment peaks were observed between the amputee subjects and the normal population
(Figure 4.18 and 4.19).
Ankle joint powers
Ankle power data have been presented in Figures 4.20-4.22. A relatively normal
pattern of power absorption then generation was observed on the sound limb of the
unilateral amputees as well as all affected limbs.
Substantial power absorption was observed following initial contact on the
affected limb of subject 2103-1906A (Figure 4.20). Peak power absorption (AP1) was
not well defined in either the normal or amputee subjects however, the AP1 peak
seemed to be delayed on the affected limbs of the TMT and Lisfranc amputees
compared to the normal population (Figures 4.20-4.21). The magnitude of peak power
absorption seemed to be largely unaffected except for the affected limb of subject 2703-
1903A (Figure 4.20).
The ankle power generation peak associated with push-off (AP2), was delayed
on the sound limb of the TMT amputee (57%GC) and both limbs of the bilateral
Lisfranc amputee (59±4%GC) compared to the normal population (95%CI, 52%GC to
55%GC) (Figure 4.20-4.21). Delays in the timing of the AP2 peak approached
significance on the sound limb of the Lisfranc cohort (55±0%GC) and the unilateral
Chopart amputee (55%GC) (Figure 4.20-4.21).
________________________________________________________ Chapter 4. 121
Figure 4.20 Sagittal plane ankle power for the affected and sound limbs of the
unilateral amputee sample
Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power
absorption.
10 20 30 40 50 60 70 80 90 100-2
0
2
4
6Ankle Power Affected Limbs(-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - LisfrancControl ±2SD
10 20 30 40 50 60 70 80 90 100-2
0
2
4
6Ankle Power Sound Limbs (-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 122
Figure 4.21 Sagittal plane ankle power for the bilateral amputees
Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power
absorption.
Once the metatarsal heads were compromised, the magnitude of the AP2 peak
was significantly reduced on the affected limbs of the unilateral TMT amputee
(0.72W/kg) and the Lisfranc cohort (0.91±0.39W/kg) as well as in the bilateral Lisfranc
amputee (0.41±0.41W/kg) compared to normal cohort (95%CI, 2.56W/kg to 5.06W/kg)
(Figures 4.21-4.22). Power generation observed in the bilateral MTP amputee flanked
the lower boundary of the 95%CI but was not significantly different from the normal
population (Figure 4.22). Power generation on the sound limb of the unilateral amputee
subjects was comparable to that observed in the normal population (Figure 4.21).
Figure 4.22 illustrates the power generation observed in the Chopart amputees
using a conventional linked-segment model. The data was derived using the
assumptions previously described for the ankle moment calculation for these amputees.
10 20 30 40 50 60 70 80 90 100-2
0
2
4
6Ankle Power Bilateral Amputees(-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
1004-1307A - MTP 2803-0410A - Lisfranc Control ±2SD
________________________________________________________ Chapter 4. 123
Figure 4.22 Sagittal plane ankle power for the affected limbs of the Chopart amputees
Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power
absorption.
The timing of the AP1 peaks appeared to be delayed in the bilateral Chopart
amputee. Similarly, the timing of the AP2 peak was significantly delayed in both the
bilateral Chopart (57±0%GC) and unilateral Chopart amputees (56%GC) compared to
the normal population (Figure 4.22). Reductions in work across the ankle joint during
push-off were similar to those observed in the Lisfranc and TMT amputees. The
unilateral Chopart and bilateral Chopart amputees generated 0.78W/kg and
0.32±0.17W/kg, respectively (Figure 4.22).
Knee joint powers
Figures 4.23 and 4.24 illustrate the work observed across the knee joint.
Following initial contact, a period of power absorption describes eccentric activity of
the knee extensor musculature to control stance phase knee flexion (KP1). Normal
power absorption (KP1) was observed on the sound limb of the amputee subjects except
in subject 2703-1903A where excessive eccentric activity was observed (-1.84W/kg)
compared to the normal population (95%CI, -1.48W/kg to -0.24W/kg). Normal power
10 20 30 40 50 60 70 80 90 100-2
0
2
4
6Ankle Power Chopart Amputees (-)
(Wat
ts/k
g) E
xt.
>
Gait Cycle [%]
3004-1102A - Chopart R0904-1924A - ChopartL0904-1924A - ChopartControl ±2SD
________________________________________________________ Chapter 4. 124
absorption was observed on the affected limbs of the unilateral Lisfranc cohort (-
1.03±0.26W/kg) and bilateral MTP amputee (1.46±0.21W/kg). In contrast, significantly
less power absorption was observed on the affected limbs of the unilateral TMT (-
0.18W/kg) and Chopart amputees (-0.21W/kg) compared to the normal population.
Reductions in the KP1 peak approached significance in the bilateral Lisfranc (-
0.38±0.08W.kg) and Chopart amputees (-0.27W/kg). The KP1 peak was normally timed
(95%CI, 9%GC to 11%GC) except in the bilateral Chopart amputee where delays
appeared to be significant bilaterally, but only a true peak existed for the right limb
(14%GC).
The knee extensor musculature contract concentrically to extend the knee into
mid-stance following the relatively flexed position attained during stance phase knee
flexion (KP2). Typically, changes in KP2 are commensurate with changes in KP1. For
example, the bilateral MTP amputee (0.86±0.11W/kg) and Lisfranc subject 2703-1903A
(0.69W/kg) displayed greater power generation (KP2) than that observed in the normal
population (95%CI, 0.02W/kg to 0.67W/kg). This exaggerated power generation would
be required to extend the knee from the relatively large flexion angle attained during
stance phase compared to the normal population (Figure 4.9 and 4.10).
Power generation across the knee during the propulsive phase of gait was
comparable to normal on the sound limbs of the unilateral amputee subjects and the
bilateral MTP amputee (Figures 4.23-4.24). Normal power generation was also
observed across the knee joint on the affected limb of subject 2703-1903A, which was
in stark contrast to the negligible work observed in the other Lisfranc and TMT
amputees. In comparison to the normal population, significantly more power was
generated across the knee during the propulsive phase on the affected limb of the
unilateral Chopart amputee. Substantial power generation was also observed in the
bilateral Chopart amputee at this time however, these differences were not significantly
different from the normal population (Figure 4.24).
________________________________________________________ Chapter 4. 125
Figure 4.23. Sagittal plane knee power for the affected and sound limbs of the unilateral
amputee sample
Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power
absorption.
10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
3Knee Power Affected limbs (-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
3Knee Power Sound Limbs (-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 126
As the knee continues to flex, power was absorbed by the knee extensors during
push off (KP3). Peak power absorption at this time was delayed on the sound limb of
the unilateral TMT (66%GC) and Lisfranc subject 2103-1906A (65%GC) compared to
normal (Figure 4.24). KP3 appeared to be comparably delayed on the affected limb of
the unilateral Chopart amputee (66%GC) however, this peak was not well defined
(Figure 4.24). The magnitude of KP3 was comparable to normal except on the affected
limb of subject 2103-1906A (Figure 4.23).
No significant differences in the swing phase powers or the timing and
magnitude of KP4 were observed indicating relatively normal power absorption by the
hamstrings to decelerate the leg segment into full extension.
Figure 4.24 Sagittal plane knee power for the bilateral amputees
Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power
absorption.
10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
3
Knee Power Bilateral Amputees(-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 127
Hip joint powers
Substantial differences in work across the hip joint were observed on both the
sound and affected limbs of the amputee subjects compared to normal (Figures 4.25 and
4.26). The mechanical power patterns observed at the hip were extremely variable,
especially during the beginning of stance phase where a brief period of power
generation describes work done by the hip extensors as the hip joint extends as the knee
flexes (HP1). The HP1 peak was not well defined in the normal population or among
the amputee subjects. In the normal population, 95% of the HP1 peaks occurred within
the ranged of 0.38W/kg to 0.70W/kg. The power generated on the sound limb during
HP1 was substantially larger than normal for the unilateral TMT (1.21W/kg) and
Chopart amputees (0.86W/kg) as well as Lisfranc subject 2103-1906A (1.14W/kg)
(Figure 4.25). Substantial power generation was also observed on the sound limb of
subject 2703-1903A (0.65W/kg) but was not significantly greater than normal.
Similarly, substantial power was also generated on the affected limbs of the unilateral
Chopart amputee (0.86W/kg), Lisfranc subject 2703-1903A (1.66W/kg) and 2103-
1906A (0.76W/kg) (Figure 4.25). For the bilateral amputee subjects, HP1 was
significantly larger than normal on the left limb of subject 2803-0410A (1.26W/kg)
however, these differences were not observed bilaterally (Figure 4.26). Relatively
substantial power generation was also observed during this time on both limbs of the
bilateral Chopart amputee (Figure 4.26). HP1 occurred at about 15%GC in the entire
amputee population except on the affected limb of the unilateral Chopart amputee
(20%GC). The normal timing of HP1 was difficult to establish given the poorly defined
power generation peak, but the timing of this peak does not seem to be abnormal in the
amputee population.
Relatively normal power absorption was observed by the hip flexors to
decelerate the backward rotating thigh during the middle of the gait cycle (HP2).
However, HP2 was delayed on the sound limb of the TMT subject (55%GC) and on the
affected limb of the unilateral Chopart amputee (49%GC) compared to normal (95%CI,
43%GC to 48%GC) (Figure 4.25). Similar delays were also observed in isolation on the
left limbs of the bilateral Lisfranc and Chopart amputees, which approached
significance (Figure 4.26).
________________________________________________________ Chapter 4. 128
Figure 4.25 Sagittal plane hip power for the affected and sound limbs of the unilateral
amputee sample
Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power
absorption.
10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
1.5
2
2.5Hip Power Affected limbs (-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
1.5
2
2.5Hip Power Sound Limbs (-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 129
Figure 4.26 Sagittal plane hip power for the bilateral amputees
Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power
absorption.
Good power generation was observed on both the sound and affected limbs by
the hip flexor muscles to advance the lower limb forward during the terminal stages of
the propulsive phase (HP3). Delays in the timing of HP3 approached significance on the
sound limbs of the unilateral TMT (65%GC) and Lisfranc amputees (65±2%GC) and
both limbs of the bilateral Lisfranc amputee (66±2%GC) compared to normal (95%CI,
58%GC to 64%GC). HP3 was normally timed on the affected limb of the unilateral
amputee subjects (Figure 4.25).
The magnitude of HP3 was marginally larger than that of the normal population
(95%CI, 0.46W/kg to 1.27W/kg) on the affected limb of subject 2103-1906A
(1.34W/kg). The magnitude of HP3 was comparable to normal on both the sound and
affected limbs of the other amputee subjects (Figures 4.25-4.26).
No significant differences in power generation across the hip joint were
observed during terminal swing (HP4) except in subject 0704-0403A. In this subject,
10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
1.5
2
2.5
Hip Power Bilateral Amputees(-)
(Wat
ts/k
g) G
en.
>
Gait Cycle [%]
R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD
________________________________________________________ Chapter 4. 130
power generation across the hip joint was 0.38W/kg and 0.56W/kg for the affected and
sound limbs, respectively (Figure 4.25).
Electromyography
Electromyography is a useful means of identifying abnormal muscle activity and
provides useful information, which aids the interpretation of joint moments and powers.
As a means of identifying abnormal muscle activity, 'normal' muscle function has been
described as the intensity and timing of EMG activity, which is within one standard
deviation from the mean EMG activity of the normal cohort. While this standard
excludes 33% of the data observed in the 'normal' population, correlations with gait
motion indicate EMG activity outside this range represents inefficient muscle action and
should not be a standard for normal function (Perry, 1992). In the present investigation,
the 'significance' of any given period of muscle activity was assessed using the mean
intensity of the EMG activity (as a percentage MMT) and periods of activation (as a
percentage of the gait cycle). However, without considering the profile of muscle
activation in relation to the functional phases of the gait cycle this is a relatively
arbitrary and inaccurate process. EMG data presented in Figure 4.27 provides an
excellent illustration in that it is difficult to compare the mean amplitude of tibialis
anterior (TA) during loading response given that the mean intensity of EMG activity of
the amputee was spread over 30% of the gait cycle. In considering loading response
alone, it would be reasonable to conclude that there was an increase in EMG activity
observed in the amputee subjects compared to normal. It is possible to make
interpretations about the significance of these differences when the mean and standard
deviation values are considered. For the normal population, the mean intensity of EMG
activity during loading response was 16%MMT and varied between 13%MMT and
21%MMT (mean ±1SD). For the amputee subject, the intensity of EMG during loading
response peaked at about 25-30%MMT. The mean intensity of TA in the amputee
during loading response is likely to be only marginally above the confidence interval of
the normal population and not outside a 95%CI.
In the normal population, TA was active during loading response from initial
contact through until between 5-9%GC. Mean intensity of normal TA varied between
13%MMT and 21%MMT. For the majority of amputee subjects, the timing, duration
________________________________________________________ Chapter 4. 131
and intensity of TA activity during loading response was comparable to that observed in
the normal population. However, for the affected limbs of subjects 2103-1906A, 2103-
2116A and 2803-0410A EMG activity was prolonged well into stance phase and was
characterised by significant variability. EMG activity was unable to be recorded for the
affected limbs of the Chopart amputees because the preamplifier and electrode units
could not fit inside the socket.
Figure 4.27 Mean EMG activity of tibialis anterior for the affected limb of subject
2103-1906A compared to the mean of the normal population
Figure 4.28 EMG activity of tibialis anterior for the affected limb of subject 2103-
1906A (n=5).
0 20 40 60 80 1000
10
20
30
40
50Tibialis Anterior (-)
EM
G -
Nor
mal
ised
to
100%
MM
T
Gait Cycle [%]
________________________________________________________ Chapter 4. 132
For the affected limb of subject 2103-1906A, TA activity seemed to be
marginally increased during loading response compared to that observed in the normal
population (Figure 4.27). Following loading response, the activity of TA was more
variable and as such the mean EMG signal between 10-30%GC does not reflect the
actual EMG activity observed in a number of trials (Figure 4.28). The variability of the
EMG pattern was characterised by CV and CMC measures, which were 69% and 0.34,
respectively. EMG activity was observed until mid-stance (Figure 4.27-4.28).
The activity of tibialis anterior was also prolonged in the bilateral Lisfranc
amputee (2803-0410A) on the right (1-71%GC) and the left (1-35%GC) limbs
compared to the normal population (Figure 4.29). However, the reliability of these
periods of muscle activity could certainly be questioned given that the patterns of
activity were very erratic, except during terminal swing phase (Figure 4.30). The
usefulness of this EMG data is certainly questionable due to the large variability. The
CV and CMC measures of variability for the right limb were 59% and 0.31,
respectively. For the left limb, the CV was 72% and the CMC was 0.35.
Figure 4.29 Mean EMG activity of tibialis anterior for the right and left limbs of subject
2803-0410A compared to the mean of the normal population
________________________________________________________ Chapter 4. 133
Figure 4.30 EMG activity of tibialis anterior for the right (n=5) and left (n=4) limbs of
subject 2803-0410A.
For the affected limb of subject 2130-2116A, excessive EMG activity of tibialis
anterior was observed during stance phase (Figure 4.31). Determining the periods of
muscle activity was difficult and probably unreliable given the variability observed
during stance phase. The stance phase periods of muscle activity were determined to be
1-14%GC and 28-43%MMT. The mean intensity of these periods of activity were both
6%MMT (Figure 4.31).
In the normal population, gastrocnemius medial head (GM) activity commenced
between 8-17%GC and terminated between 45-50%GC (95%CI). The CI of GM
intensity was 9-25%MMT. The initiation of gastrocnemius lateral head activity (GL)
was more varied with muscle activation commencing between 14-29%GC and
concluding between 44-51%GC. The mean intensity of GL activity varied between 7-
0 20 40 60 80 1000
10
20
30Tibialis Anterior (-)
EM
G -
Nor
mal
ised
to
100%
MM
T
0 20 40 60 80 1000
10
20
30
40
50Tibialis Anterior (-)
EM
G -
Nor
mal
ised
to
100%
MM
T
Gait Cycle [%]
Gait Cycle [%]
Right
Left
________________________________________________________ Chapter 4. 134
17%MMT. Soleus activity commenced between initial contact and 18%GC and
concluded between 46-54%GC. The CI of soleus intensity was 9-19%MMT.
Figure 4.31 EMG of tibialis anterior for the affected limb of subject 2103-2116A (n=7).
In many amputee subjects, the activity of one or more calf muscles on the
affected limb was substantially delayed relative to the normal population. These delays
were most evident on the affected limb GM and GL in both subjects 2103-1906A and
2703-1903A and soleus only in subject 2703-1903A (Figures 4.32-4.33). In these cases,
EMG activity was not observed until about mid-stance (Figures 4.32 and 4.33). Similar
delays in the initiation of GL activity were observed in subject 2103-2116A (40%GC)
and soleus activity in subject 0704-0403A (32%GC).
Figure 4.32 depicts a period of soleus inactivity between ≈20-30%GC, which
may not be an accurate reflection given the EMG data from each trial (Figure 4.34). No
EMG data were recorded for the triceps surae muscles on the affected limbs of the
Chopart amputees because the electrodes were unable to be placed inside the socket. No
meaningful EMG data could be obtained for the triceps surae group in subject 2803-
0410A. Sound limb triceps surae activity was comparable to that of the normal
population. Mean intensity of soleus, GM and GL observed in the amputee subjects
were comparable to that of the normal population.
0 20 40 60 80 1000
10
20
30
40Tibialis Anterior (-)
EM
G -
Nor
mal
ised
to
100%
MM
T
Gait Cycle [%]
________________________________________________________ Chapter 4. 135
Figure 4.32 Mean EMG activity of triceps surae for the affected limb of subject 2103-
1906A compared to the mean of the normal population
________________________________________________________ Chapter 4. 136
Figure 4.33 Mean EMG activity of triceps surae for the affected limb of subject 2703-
1903A compared to the mean of the normal population
Figure 4.34 EMG activity of soleus for the affected limb of subject 2103-1906A (n=5).
0 20 40 60 80 1000
10
20
30Soleus (-)
Gait Cycle [%]EM
G -
Nor
mal
ised
to
100%
MM
T
________________________________________________________ Chapter 4. 137
The normal pattern of biceps femoris (BF) activity was maintained following
partial foot amputation except for the affected limbs of the Chopart amputees.
Abnormal EMG activity was not limited to just the affected limb. On the sound limb of
the unilateral amputee subjects, BF activity was prolonged in subjects 3004-1102A (1-
18%GC), 2103-2116A (1-22%GC), 2703-1903A (1-24%GC) and 2103-1906A (1-
21%GC) compared to the CI of the normal population (1-12%GC). The mean intensity
of BF activity was comparable to the CI of the normal population (2-14%MMT).
For the affected limbs of the Chopart amputees, BF activity was observed from
initial contact until mid-stance for the right limb of subject 0904-1924A and until about
45%GC for the left limb (Figure 4.36-4.37) as well as for subject 3004-1102A (Figure
4.35). For subject 3004-1102A and the left limb of subject 0904-1924A, substantial
aphasic activity was observed during the later portions of the mid-stance period.
Figure 4.35 EMG activity of biceps femoris long head for the affected limb of subject
3004-1102A (n=3)
0 20 40 60 80 1000
10
20
30
40Biceps Femoris (-)
EM
G -
Nor
mal
ised
to
100%
MM
T
Gait Cycle [%]
________________________________________________________ Chapter 4. 138
Figure 4.36 Mean EMG activity of biceps femoris long head for the right and left limbs
of subject 0904-1924A compared to the mean of the normal population.
________________________________________________________ Chapter 4. 139
Figure 4.37 EMG activity of biceps femoris long head for the right (n=6) and left (n=6)
limbs of subject 0904-1924A.
Mean intensity of vastus lateralis activity in the normal population was 6-
13%MMT. For many amputee subjects, the mean intensity of packets of VL activity
were reduced (Table 4.7). The reduction in mean intensity did not seem to be the cause
for prolonged activity following initial contact.
( )
0 20 40 60 80 1000
10
20
30
40
50Biceps Femoris (-)
EM
G -
Nor
mal
ised
to
100%
MM
T
Gait Cycle [%]
Right
0 20 40 60 80 1000
10
20
30
40Biceps Femoris (-)
EM
G -
Nor
mal
ised
to
100%
MM
T
Gait Cycle [%]
Left
________________________________________________________ Chapter 4. 140
Table 4.7 Periods of vastus lateralis activity observed during stance phase including
mean intensity.
R = right. L = left. AL denotes affected limb. SL denotes sound limb. * denotes significant differences
greater then mean ±2SD. ‡ denotes differences greater then mean ±1SD but less then mean ±2SD.
Active period Mean intensitySubject Comments
%GC %GC %MMT
Control 1 11-16 6.3:12.6
1004-1304A Bi MTP R
L
1
1
19*
14
4.7‡
10.2
2103-2116A Uni TMT AL
SL
1
1
40*
17‡
11.3
8.3
2703-1903A Uni Lisfranc AL
SL
1
1
26*
15
10.15
12.1
0704-0403A Uni Lisfranc AL
SL
1
1
16
13
3.6‡
5.8‡
2103-1906A Uni Lisfranc AL
SL
1
1
27*
20*
10.2
11.9
2803-0410A Bi Lisfranc R
L
Erratic
Erratic
1
1
28*
48*
15.3
3.7‡
0904-1924A Bi Chopart R
L
1
1
15
17‡
4.1‡
5.7‡
3004-1102A Uni Chopart AL
SL
1
39*
1
23*
49*
13
5.2‡
5.9‡
5.9‡
________________________________________________________ Chapter 4. 141
Figure 4.38 EMG activity of vastus lateralis for the affected limb of subject 2103-
2116A (n=7).
Figure 4.39 EMG activity of vastus lateralis for the sound limb of subject 3004-1102A
G i l l h d ( )
0 20 40 60 80 1000
10
20
30Vastus Lateralis (-)
EMGE
MG
- N
orm
alis
ed t
o 10
0% M
MT
Gait Cycle [%]
0 20 40 60 80 1000
5
10
15Vastus Lateralis (-)
EMG
EM
G -
Nor
mal
ised
to
100%
MM
T
Gait Cycle [%]
________________________________
Figure 4.40 EMG data for the affected limbs of subject 2803-0410A
During swing phase, the activit
and tibialis anterior were very similar
population.
The initiation of vastus lateralis
85%GC and 89%GC for the normal p
normal population, the intensity of V
duration of VL activity during swing
amputee subjects. The mean intensity o
minus one standard deviation and not
number of amputee subjects.
t
0 20 40
5
10
15Vastus Lateralis (-)
EMG
0 20 40 60 80 1000
10
20
30
40Vastus Lateralis (-)
EMG
EM
G -
Nor
mal
ised
to
100%
MM
T
G
Right
eft
LefL________________________ Chapter 4. 142
ies of vastus lateralis, biceps femoris long head
between the amputee subjects and the normal
activity during swing phase occurred between
opulation and continued until 100%GC. In the
L activity occurred between 4-12%MMT. The
phase was comparable to normal in all the
f vastus lateralis was marginally below the mean
below, the two standard deviation mark for a
0 60 80 100
ait Cycle [%]
________________________________________________________ Chapter 4. 143
The initiation of biceps femoris activity during swing phase commenced
between 75-86%GC and terminated between 97-100%GC. A large range of muscle
intensities were observed with the CI being 3-17%MMT. The 95%CI of muscle
intensity was 0-24%MMT. The duration and intensity of BF activity was comparable to
normal in the partial foot amputees.
The initiation of tibialis anterior activity observed in the normal population
during swing phase (54-57%GC) was comparable to that observed in most of the
amputee subjects. However, the initiation of tibialis anterior activity occurred
prematurely on the affected limb of subject 2103-1906A (49%GC) (Figure 4.27-4.28)
and was delayed on the affected limb of subject 2703-1903A (86%GC) (Figure 4.41).
The initiation of tibialis anterior activity during swing phase was also delayed on the left
limb of subject 2803-0410A (Figure 4.29-4.30). On the right limb of this subject, tibialis
anterior was active from initial contact through until mid-swing (Figure 4.29) and was
active again between 83%GC and 100%GC (Figure 4.29). No differences were
observed between the intensity of TA in the normal population during swing phase (7-
13%MMT) and the amputee subjects.
Figure 4.41 Mean EMG activity of tibialis anterior for the affected limb of subject
2103-1903A compared to the mean of the normal population
________________________________________________________ Chapter 4. 144
4.4 Discussion
The aim of this investigation was to provide a thorough bilateral description of
the gait of a cohort of partial foot amputees to better describe the effects of amputation
and prosthetic/orthotic fitting on gait. The temperospatial, kinematic, kinetic and
electromyographic characteristics showed changes in many partial foot amputees
compared with those of the normal, able-bodied population studied.
The joint ranges of motion and muscle strength, temperospatial, kinematic and
kinetic parameters have been presented as individual discussions. A brief discussion of
the EMG signal processing technique follows the discussion of the results. EMG and
force platform data have not been presented in isolation, but rather as part of the
kinematic and kinetic analysis to augment interpretation of the gait data. Where
possible, the discussion of each topic follows the following basic phases of the gait
cycle: initial contact, loading response, the mid-stance phase, pre-swing, initial swing,
mid-swing and terminal swing phases (Perry, 1992).
Range of motion and muscle strength
The available static range of motion observed at the hips, knees and ankles of
the normal population were comparable to previous reports (Kendall and McCreary,
1993; Clarkson and Gilewich, 1989). Static ankle range was substantially compromised
on the affected residua of primarily the Lisfranc and Chopart amputees. Reductions in
plantarflexion/dorsiflexion and inversion/eversion range were characteristic of the
equinus deformity observed in many amputees. Equinus deformity is often a long-term
consequence of, primarily, Lisfranc and Chopart amputation because tibialis anterior is
often reattached more proximally, where the effective lever-arm is reduced and the
tendons of extensor digitorum longus and extensor hallucis longus are often not
reattached at all. Reductions in the available ankle range are likely to make functional
differences particularly during stance phase dorsiflexion where the available range was
roughly equivalent to the range utilised by these amputees during gait (Figures 4.11-
4.12). Reductions in ankle range of the Chopart residuums may also be a long-term
consequence of the elimination of ankle range within the clamshell prosthesis. Previous
investigations have studied TMT, MTP amputees or individuals with metatarsal ray
resection have found static ankle ROM to be comparable to normal (Garabolsa et al.,
________________________________________________________ Chapter 4. 145
1996; Dillon, 1995). However, these same data have not previously been reported for
individuals with Lisfranc and Chopart amputation.
The Oxford Manual Muscle test provided a basis for documenting 'significant'
areas of muscle weakness, particularly with reference to the sound limb. Significant
weakness, as evidenced through the muscle test, was generally not observed in the
amputee population despite the fact that the ankle kinematic patterns were indicative of
triceps surae weakness. Such discrepancies were not surprising, given that the amputee
subjects were able to ambulate independently with, arguably, minor variations on the
basic pattern of normal locomotion. Clinically, individuals can often perform well on
the test despite obvious limitations in performing functional activities such as walking
or descending stairs for a number of reasons.
The Oxford test measures an individual's isometric muscle strength through the
available joint range, which is not indicative of an individuals ability to perform an
eccentric activity. The ability to control the angular joint range, such as is necessary to
moderate tibial rotation over the stance foot or control the knee when descending stairs,
is not necessarily a measure related to isometric muscle strength. Moreover, individuals
can often perform well on the Oxford test because the influence of fatigue is minimal
unlike repetitious activities such as walking. Results from the muscle strength test can
be relatively subjective when differentiating between grades 4 and 5 where the test
activity is performed against gravity with varying degrees of resistance. When both
limbs demonstrate similar isometric strength is difficult to distinguish between grades 4
and 5 because the strength of an individual is a relatively subjective measure. For
example, a 60-year-old will likely produce more muscle force to achieve a grade 4 than
a 90-year-old. When the affected limb can be compared to the sound limb, a more
accurate grade 4 can be established if the affected limb is weaker than the sound limb.
In essence, the utility of the technique is limited for distinguishing relatively minor
areas of muscle weakness, such as those evident in this population.
Temperospatial
In the present investigation, temperospatial parameters for the normal population
were comparable to previously published investigations of normal gait (Allard et al.,
1997; Craik, 1995; Sadeghi et al., 1997; Murry et al., 1964; Winter, 1991; Perry, 1992).
________________________________________________________ Chapter 4. 146
In comparison to previous investigations (Boyd et al., 1999; Burnfield et al.,
1998; Dorostkar et al., 1997; Dillon, 1995; Muller et al., 1998), very few amputee
subjects displayed abnormal stride length and walking velocity. However, substantial
reductions in walking velocity were observed in the unilateral TMT and Chopart
amputees as well as in the bilateral Lisfranc amputee (Table 4.2). Significant reductions
in stride length appeared to be the reason for reduced walking velocity in the unilateral
TMT and Lisfranc amputees, as no differences in cadence were evident. For the
unilateral Chopart amputee, significant reductions in walking velocity seemed to be the
result of reductions in both stride length and cadence.
The chronological age of the bilateral Lisfranc amputee (63) is unlikely to have
resulted in the substantial reductions in walking velocity observed given that the
influence of age to 60 has little effect (Grabiner et al., 1997) and that mean decreases in
walking velocity between 60-65 are just 3% (Murry et al., 1969 - cited Perry, 1992).
However, the biological age seemed to be a primary influence in this subject who
almost appeared 'frail.' The influence of arthritis or other health pathologies not detected
during the subject evaluation may have confounded the results.
Reductions in walking velocity and contralateral step length are common
mechanisms to control tibial rotation (Sutherland et al., 1980; Lehmann et al., 1985;
Simon et al., 1978) but do not explain the differences observed across the wider
population. Reductions in power generation across the ankle (Winter, 1990) also do not
seem to explain the differences in stride length and walking velocity in these individuals
given reductions in ankle power generation observed across the entire group. It is
questionable whether reductions in stride length are a result of reductions ankle power
generation or whether the reduced plantarflexor work simply reflects the mechanical
requirement of the reduced stride length (Grabiner et al., 1997). Stability may be a
primary concern in these individuals or the altered stride length and velocity may
optimise energy expenditure. Neither of these characteristics were assessed.
In comparison to previous investigations (Boyd et al., 1999; Burnfield et al.,
1998; Dorostkar et al., 1997; Dillon, 1995; Muller et al., 1998) amputees in the present
study tended to walked faster (≈85% of normal vs. ≈65% of normal). Individuals in the
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present investigation had forefoot amputation due to trauma or gangrene secondary to
non-systemic vascular diseases such as frostbite rather than vascular disease secondary
to diabetes. Previous investigations have found consistent differences in both stride
length and cadence (Burnfield et al., 1998; Boyd et al., 1999; Dorostkar et al., 1997;
Dillon, 1995) which were not observed in the present study. Reductions in stride length
have previously been implicated as the primary reason for reductions in walking
velocity over differences in cadence (Dorostkar et al. 1997). As in the present
investigation no clear differences were evident between levels of amputation (Dillon,
1995; Dorostkar et al., 1997).
The duration and phasing of swing and stance has received little attention in
published literature presumably because, as in the present study, there were no
differences from normal on the affected limb. Studies have not previously examined the
sound limb where the proportion of stance phase was increased and swing phase
decreased, relative to the normal population in the unilateral TMT, Chopart and bilateral
Lisfranc amputees (Table 4.3).
Reductions in the proportion of the gait cycle spent in single support on the
affected limb were commensurate with reductions in swing time on the sound limb of
the unilateral TMT, Chopart and bilateral Lisfranc amputees. The proportion of the gait
cycle spent in double limb support following sound limb initial contact was increased
for the unilateral TMT as it was for the unilateral Chopart amputee following affected
limb initial contact. For the bilateral Lisfranc amputee, increases in double support
proportions were relatively symmetrical. Identifying the cause of prolonged double
support is difficult to ascertain given the variability observed in the small number of
individuals who exhibited abnormal double support time (as a percentage of the gait
cycle). Previous investigations have not reported support phase data for either the sound
or affected limbs.
In the present study, no differences in the total excursion of the CoP were
observed between the amputee subjects and the normal population. In comparison,
previous investigation has reported a significant correlation between reductions in total
CoP excursion and residual foot length (Dillon, 1995). Differences in the total excursion
of the CoP are likely to reflect differences in the force threshold criteria between these
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investigations. In the present study, CoP data were calculated once the magnitude of the
vertical GRF exceeded 10N which was substantially less than the 200N threshold
utilised by Dillon (1995).
Kinematics
Mean kinematic patterns of motion observed at the hip, knee and ankle of the
normal population were comparable to published analyses of normal gait, in terms of
both timing and peak magnitudes (Perry, 1992; Winter, 1983). The variability of these
kinematic patterns was also comparable to previous reports of normal gait (Winter,
1983; Winter, 1991). Intra-subject kinematic variability of individuals in the normal
cohort were similar to those reported by Kadaba et al., (1989).
Previous investigations reporting joint angular kinematics of partial foot
amputee gait have focused primarily on the affected ankle joint (Boyd et al., 1999;
Dorostkar et al., 1997; Garabolsa et al., 1996) with limited work examining proximal
joints (Dillon, 1995; Mueller et al., 1998) or reporting swing phase kinematics (Dillon,
1995). Kinematic patterns of the sound limb have not previously been reported. Very
few kinematic anomalies were observed at the hip and knee joints however, substantial
differences from the normal population were observed, primarily, at the affected ankle.
Ankle kinematics
Affected limb ankle kinematic data have been discussed, firstly, for the bilateral
MTP amputee where no functionally significant differences were observed from the
normal population. Secondly, ankle kinematic data for the TMT and Lisfranc amputees
have been presented and could be characterised by excessive ankle dorsiflexion during
terminal stance and reduced peak plantarflexion. There were no clear differences
between TMT and Lisfranc amputees based on the type of prosthetic fitting which
included insoles, toe fillers or slipper sockets. Finally, ankle kinematic data for the
Chopart amputees have been presented. For the Chopart amputees, the kinematic
patterns observed at the ankle were dominated by the clamshell prosthesis.
For a bilateral MTP amputee, the ankle kinematic patterns were very similar to
those of the normal population (Figure 4.12). The timing of peak joint angles and the
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dynamic range were also comparable to the normal population. However, the ankle
motion pattern was biased toward dorsiflexion. There was no evidence to suggest errors
in marker placement based on the neutral segment angles. Functionally, there were no
significant differences in the kinetic patterns describing the causes of movement and as
such, the unexplained dorsiflexion bias was not of particular concern.
During initial contact, substantial dorsiflexion was observed on the affected limb
of the Lisfranc cohort. Increased dorsiflexion at initial contact is likely to cause an
exaggerated heel rocker given the large angle between the foot segment and the floor.
The foot will be driven to the floor more rapidly. The exact purpose of this dynamic
response is difficult to explain. However, it is likely to draw the tibia more rapidly
forward as the foot plantarflexes and increase the heel only time given the exaggerated
height of the toe from the floor an additional time to it would take to reach foot-flat.
Both of these actions contribute to forward limb progression and roll the body weight
forward on the heel (Perry, 1992) and may be required to keep the tibial advancement in
line with that of the thigh and trunk segments. The rapid change in ankle angle would
necessitate some compensatory mechanism, such as additional eccentric work by the
pre-tibial muscles or increased stance phase knee flexion and eccentric quadriceps
activity. In subject 2103-1906A substantial power absorption was observed across the
ankle (Figure 4.20) to resist the large external torque (Figure 4.13). Prolonged and
marginally increased eccentric activity of tibialis anterior controlled the kinematic
pattern (Figure 4.27). An alternate mechanism may be to increase knee flexion during
stance phase such as was observed in subject 2703-1903A. This kinematic pattern
would reduce the activity level of tibialis anterior to a more normal level (Figure 4.41).
However, it would tend to increase the demand on the quadriceps musculature, as was
observed in this subject (Table 4.5). For the affected limb of many amputee subjects, the
activity of vastus lateralis was prolonged, presumably in an attempt to control the
trajectory of the knee (Table 4.5). The relatively normal plantarflexion angle during
loading response actually reduces the heel rocker effect so the tibia will not advance too
rapidly (Perry, 1992).
Following loading response, the progressive increase into ankle dorsiflexion on
the affected limbs of the TMT and Lisfranc amputees (Figures 4.11-4.12) reflects
increasing anterior tilt of the tibia as the contralateral limb swings through and the upper
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body moves anteriorly over the fixed foot (Perry, 1992). Eccentric activity of, primarily,
soleus (augmented by the gastrocnemius muscles when the trunk is anterior to the knee
axis) typically moderates tibial progression and helps control forward movement of the
trunk over the stance foot (Meinders et al., 1998; Perry, 1992; Sutherland et al., 1980;
Simon et al., 1978). However, the ankle moment profiles of the affected limbs show
substantial reductions in the resistance to ankle dorsiflexion from loading response
through to heel-off (Figures 4.13-4.14). Reductions in the external moment, and
therefore, the internal muscle requirements, are the result of the relatively fixed lever-
arm of the GRF about the ankle (Figures 4.5-4.6). The CoP remained relatively fixed at
about 40% of shoe length, just proximal to the distal residuum.
It would not be possible for the CoP to move substantially beyond the remnant
foot as the position of the trunk is unlikely to be modulated by the weak soleus and
gastrocnemii muscles unless alternate gait strategies, such as increased knee flexion and
eccentric quadriceps activity, were engaged. It is difficult to ascertain whether the
primary purpose of modulating the position of the CoP was to reduce the requirement of
the soleus muscle and maintain trunk stability or to avoid substantial force on the
sensitive distal residuum, which will be examined later in the discussion. Perhaps both
of these gait strategies are of equal importance and the adoption of the observed gait
pattern enhances stability and protects the distal residuum.
Control of tibial rotation during the initial portion of the mid-stance period
seems to be largely a reflection of the moderated trunk position to minimise the
muscular requirement. Anterior progression of the tibia does not seem to have been
controlled by soleus activity in subjects 2703-1903A (Figure 4.33) and 0704-0403A
where muscle activity was absent until mid-stance on the affected limbs. For the
remaining subjects, the timing of soleus activity was comparable to that observed in the
normal population. Despite the mean electrical activity of soleus being similar to that of
the normal population, the accompanying force generation is likely to be substantially
less given the atrophy of triceps surae muscles observed. Atrophied muscle has the same
number of motor units as normal muscle; hence, the electrical activity recorded is
similar. However, each muscle fibre is substantially smaller and can only produce a
fraction of the force of normal muscle. The normal function of soleus may have been
augmented by concentric activity of vastus lateralis following the KP2 power generation
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associated with knee extension following stance phase knee flexion. EMG activity of
Vastus lateralis was prolonged on the affected limbs of the TMT and most Lisfranc
amputees until about mid-stance, which may help moderate progression of the tibia over
the stance foot.
Terminal stance could be characterised as the most demanding period of the gait
cycle for the TMT and Lisfranc amputees and a period when the amputee 'fell over' the
end of the remnant foot. The CoP progressed anterior to the distal residuum presumably
as the CM of the trunk progressed substantially forward of the reduced base of support
(the remnant foot). The ankle dorsiflexed rapidly during terminal stance compared to
the mid-stance phase (Figures 4.11-4.12). The resulting dorsiflexion angle was
excessive (Figure 4.11) and the peak delayed (Figures 4.11-4.12) compared to the
normal population, which is likely to reflect substantial anterior tibial tilt resulting from
the relatively unrestrained forward fall of the trunk.
It is difficult to substantiate the anterior position of the trunk in relationship to
the reduced base of support without kinematic data however, a number of parameters
would indicate the relatively anterior position of the trunk. Firstly, the anterior
orientation of the tibia over the fixed foot with the knee (Figure 4.9) and hip extended
(Figure 4.7) would imply that the trunk must be positioned anteriorly over the base of
support by virtue of the alignment of the rest of the limb. With the limb in this
orientation, the only mechanism by which the trunk could be brought back over the foot
would be to extend the lumbar spine substantially. Secondly, the absence of a knee
flexion moment during the mid-stance phase on the affected limbs of the TMT and
Lisfranc amputees (Figures 4.16-4.17) would suggest that the tibial angle, and therefore
knee position, moved in unison with the line of action of the GRF presumably in an
attempt to reduce the requirement of the weak gastrocnemius musculature. The effect of
muscle activity on the knee moment is likely to be negligible given the atrophied soleus
and gastrocnemius and the absence of other muscle activity and that no co-contraction
with tibialis anterior was evidenced. Thirdly, the fore-aft GRF peaks typically
associated with the forward thrust of push-off (Figure 4.1-4.2) occurred prematurely
before the ankle had reached peak dorsiflexion and the commencement of push-off
(Figure 4.11-4.12). These horizontal GRF peaks are therefore likely to be a reflection of
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the leverage produced by body alignment (Murry et al., 1978; Sutherland et al., 1980;
Perry, 1974; Simon et al., 1978).
Peak eccentric activity of soleus and the gastrocnemii muscle was observed
during terminal stance phase in an attempt to decelerate and arrest the rapid rotation of
the tibia and reverse the dorsiflexion angle (Sutherland et al., 1980) as illustrated in
Figures 4.32 and 4.33. However, the muscle activity observed seemed to be ineffective
given that the ever-increasing dorsiflexion angle was eventually checked by the
premature contralateral heel contact (Sutherland et al., 1980) marking the end of
terminal stance phase (Table 4.4). This mechanism was observed on all the TMT and
Lisfranc residuums except the right leg of subject 2803-0410A (Figure 4.12) where
contralateral heel contact preceded peak dorsiflexion by nearly 10% of the gait cycle.
During pre-swing, the CoP progressed rapidly from approximately 40% of shoe
length to the end of the foot on the affected limbs of the Lisfranc and TMT amputees
(Figure 4.5). Immediately after contralateral initial contact, a substantial proportion of
body weight was redistributed from the sensitive distal residuum to the sound limb as
evidenced by the increased magnitude of the vertical GRF peak (FZ1) above that
normally associated with loading response (Figure 4.4). The GRF did not progress
substantially beyond the remnant foot until the magnitude of the vertical GRF was
rapidly diminishing (Figure 4.4) which would seem to be a useful method of protecting
the distal end of the remnant foot from undesirable forces and moments. As mentioned
earlier, it is difficult to establish whether the primary aim of limiting substantial
excursion of the CoP until double support was an attempt to protect the distal residuum
or control the position of the trunk.
During double support, as the sound limb accepted weight and the CoP moved
anterior to the distal residuum, the affected ankle began to plantarflex rapidly (Figure
4.11). Plantarflexion of the partial foot during the pre-swing phase seemed to be a
relatively passive activity as the trunk, being well forward of the remnant foot, drew the
tibia forward once the ankle's passive range had been reached. Similar gait patterns have
been observed in individuals with plantarflexor weakness (Perry, 1992; Perry, 1974)
and temporary tibial nerve paralysis (Simon et al., 1978; Sutherland et al., 1980).
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In the present investigation there seems to be little evidence suggesting that
ankle plantarflexion was not a passive activity given the negligible work observed
across the affected ankle of the TMT and Lisfranc amputees (Figure 4.20-4.21). The
premature timing of the fore-aft GRF did not seem to support the concept of active
plantarflexion nor did the premature timing and reduced magnitude of the vertical GRF
peak (FZ3) (Figures 4.3). EMG activity of the triceps surae muscle group was absent
during this time but is likely to be a reflection of the lag between electrical activity and
force production (Winter, 1990; Meinders et al., 1998).
Reductions in the magnitude of peak plantarflexion from normal are difficult to
explain but are likely to be related to triceps surae weakness. Weakness of the triceps
surae muscle group may result in an inability to lock the ankle so that the tibia and foot
act together (Perry, 1974). Loss of metatarsal length and reduced inversion/eversion
range would likely result in such instability. Metatarsal length is typically required to
create eversion moments about the oblique axis of the midtarsal joint. The coordinated
actions between the midtarsal joint and the subtalar joint are likely to be lost. An
inability to lock the midtarsal joint onto the subtalar joint may result in additional
synchronous movements of adduction, abduction, dorsiflexion and plantarflexion about
the oblique axis and eversion and inversion movements about the longitudinal axis of
the midtarsal joint (Norkin and Levangie, 1992). Flexor stabilisation provided by
intrinsic foot muscles, such as flexor digitorum brevis, is also likely to be compromised
due to fore foot amputation. It is unlikely that difficulties associated with weight bearing
on the sensitive distal residuum are an issue during pre-swing given that the CoP has
progressed substantially past the distal residuum and that the majority of body weight
has been transferred to the contralateral limb.
During the terminal stages of pre-swing and the early stages of initial swing, two
distinct peak plantarflexion angles were observed on the affected limbs of the unilateral
TMT and Lisfranc amputees (Figure 4.11). In subjects 2703-1903A and 2103-1906A,
the peak plantarflexion angle was normally timed but substantially reduced in
magnitude (Pattern-A) compared to that observed in subjects 2103-2116A and 0704-
0403A (Pattern-B). Differences in these kinematic profiles may be a reflection of the
necessity to achieve adequate stability during double support phase before progressing
to single support. Subjects who exhibited pattern B, seemed to take longer to transfer
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weight off the affected limb to the sound limb than subjects who exhibited pattern A
(Figure 4.3). It is difficult to ascertain whether these weight transfer delays were simply
a reflection of reduced walking velocity (Table 4.2) and increased time spent in double
support (Table 4.4) and sound limb stance (Table 4.3) compared to subjects who
exhibited Pattern-A or the primary cause. The increased plantarflexion angles
characterised by Pattern-B are likely to reflect how the foot continued to freely rotate
until sufficient sound limb stability had been achieved to lift the foot off the ground and
conclude double support phase. The kinematic patterns observed in the bilateral
Lisfranc amputee (Figure 4.12) were characteristic of Pattern-B and reflect the increased
proportion of the gait cycle spent in stance and double support and reductions in
walking velocity (Tables 4.2-4.4).
Differences in maximum plantarflexion and swing phase kinematics were not
likely to be of clinical significance, given the trailing position of the limb during initial
swing and that the foot seemed to have adequately cleared the ground during mid-swing
(Figure 4.11). However, these functional abnormalities do have implications for the
ankle position at initial contact.
During terminal pre-swing and initial swing, the initiation and intensity of
tibialis anterior activity exhibited by the majority of the unilateral Lisfranc and TMT
amputees was comparable to that observed in the normal population. However, the
initiation of tibialis anterior activity was delayed until 85% of the gait cycle in subject
2703-1903A (Figure 4.41). Despite these delays in the onset of tibialis anterior activity,
there appeared to be substantial toe clearance during mid-swing evidenced by the
excessive dorsiflexion angle observed (Figure 4.11). There did not appear to be any
compensatory increases in knee or hip flexion or sound limb plantarflexion, which may
indicate some coronal plane compensation.
For the Chopart amputees, the kinematic patterns at the ankle were dominated
by the Clamshell prosthesis (Figure 4.12). The dynamic ankle range was limited to
approximately 10° which was about half that observed in below knee amputees with
various fixed ankle feet (Torburn et al., 1990). The ankle kinematic patterns have
previously been thought to reflect the force/deflection characteristics of the prosthetic
foot (Dillon, 1995). During swing phase, the kinematic patterns of the Chopart
amputees are likely to be the result of movement of the leg segment within the
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prosthetic socket given that the prosthetic foot was not loaded. This measurement error
will also affect the kinematic data observed during stance phase.
Measurement of this unwanted motion between the socket and leg reflects
limitations in the kinematic marker set. The accuracy of measuring displacement of the
leg and prosthetic socket could be improved with individual marker triads located on the
socket and leg segments. Future investigation could look at utilising the small space
between the proximal portion of the socket and the knee joint axis to locate a suitable
marker triad however, this is likely to be difficult.
During loading response, the Chopart amputees exhibited a loss of normal
plantarflexion (Figure 4.12) because the prosthetic socket eliminated ankle motion. It
was expected that the fixed 90° angle between the tibia and foot would progress the
tibia forward at the same rate that the foot moves toward the ground (Perry, 1992).
However, the heel of the prosthetic foot seemed to effectively modulate the transition
from initial contact to foot flat (Figure 4.12). This transition seemed somewhat slower
than normal given the relatively delayed initial plantarflexion peak (Figure 4.12). The
kinematic pattern and timing of peak plantarflexion was comparable to that observed in
below knee amputees using various fixed ankle prosthetic feet (Torburn et al., 1990).
The kinematic pattern observed during loading response seems to be due to the type of
prosthetic heel incorporated into the prosthesis.
During the mid-stance phase, tibial progression appears to have been moderated
more normally than in the TMT and Lisfranc amputees (Figure 4.15). Tibial progression
is likely to be resisted by a counterforce generated across the anterior wall of the socket
in response to the increasing external torque, as the GRF continues to move toward the
toe. Soleus and gastrocnemius are not likely to contribute effectively given the restricted
range and clinically observed atrophy of the calf musculature. The ankle moment
profiles of the affected limbs of the Chopart amputees show substantial reductions in the
resistance to ankle dorsiflexion from 25-40%GC (Figures 4.15). In subjects 3004-
1102A and on the right limb of subject 0904-1924A, the ankle moment plateaus were
commensurate with periods when the CoP remained at a relatively fixed lever-arm from
the ankle (Figure 4.5-4.6). The CoP and joint moment patterns seem to describe a lack
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of resistance to the external torque which could be the result of how the leg segment
moves within the socket, just prior to, and following mid-stance.
As the limb approaches mid-stance, a reaction force has been generated on the
posterior surface of the calf to resist the plantarflexion movement into foot-flat. From
this period through to just after mid-stance, the prosthesis is flat on the floor and the leg
segment may rotate anteriorly within the socket. Resistance to the external torque, and
progression of the CoP, could not occur until a sufficient counterforce was generated
between the anterior socket wall and the leg segment to overcome the external
plantarflexion moment caused by the anterior position of the GRF relative to the ankle.
During terminal stance, tibial progression appears to have been restrained in the
Chopart amputees by knee recurvatum causing posterior alignment of the tibia relative
to the femur (Figure 4.9-4.10). In subject 3004-1102A and on the left limb of subject
0904-1924A where knee hyperextension was significantly larger than normal, EMG
activity of biceps femoris long head was observed (Figures 4.35-4.37). Activity of
biceps femoris is likely to play a role in protecting the knee joint from uncontrolled
hyperextension. Increased power absorption was observed across the knee joint in these
amputees (Figure 4.23-4.24) commensurate with a protective function.
During pre and initial swing phases, there was a substantial lag between toe-off
and the peak plantarflexion angle (Figure 4.12). This pattern of ankle motion has not
been observed in transtibial amputees with fixed ankle feet (Torburn et al., 1990) where
following toe-off, foot deformation recovers promptly with negligible angular changes
during swing phase. The delayed peak plantarflexion and swing phase kinematic
patterns observed in the Chopart amputees are likely to reflect movement of the leg
segment within the prosthetic socket. During initial swing, the posterior wall of the
prosthetic socket is likely to rotate until supported against the compressed tissue of the
posterior calf. The angulation between the markers located on the knee and prosthetic
socket over the lateral malleolus, when reconstructed, would have created a leg segment
at an angle larger then 90° to the foot segment. Thus, the orientation of the leg segment
relative to the foot segment would create a plantarflexion angle.
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The majority of previous investigations report a reduction in peak ankle
dorsiflexion in TMT amputees (Boyd et al., 1999; Garabolsa et al., 1996; Dorostkar et
al., 1997). These studies have investigated conditions of barefoot ambulation (Boyd et
al., 1999; Garabolsa et al., 1996) or have reported utilising footwear in addition to
barefoot examination but have not reported which condition resulted in the data reported
(Dorostkar et al., 1997). Other investigations have studied orthotic intervention with
footwear and have reported an increase in peak dorsiflexion in the same group (Dillon,
1995) or that there was no real difference (Muller et al., 1998). Studies investigating the
effects of prosthetic/orthotic intervention may be complicated by errors associated with
motion of the residuum within the footwear or movement of the remnant limb inside the
prosthesis/orthosis. Some of the kinematic patterns observations in the present
investigation and by other investigators (Dillon ,1995; Mueller et al., 1998), may be
complicated by limitations imposed by using reflective marker triads utilising one or
more markers located on the shoe. Other marker sets have utilised a marker triad located
exclusively on the rear foot for barefoot ambulation studies (Garabolsa et al., 1996) and
are likely have been used by other investigators (Boyd et al., 1999; Dorostkar et al.,
1997). Substantial reductions in maximum plantarflexion (Dillon, 1995) and the
plantarflexion angle at toe off (Mueller et al., 1998) have previously been reported at
the TMT level.
Kinematic patterns of the sound ankle were similar to the basic motion pattern
observed in the normal population (Figure 4.11). At initial contact, a variety of
responses were observed from substantial dorsiflexion in the Lisfranc cohort to
plantarflexion in the TMT amputee (Figure 4.11). Irrespective of the differences
observed, these responses were not significantly different from the normal population.
During loading response, the initial plantarflexion peak was comparable to that
observed in the normal population however, significant variability was observed (Figure
4.11).
During the initial stages of the mid-stance phase, excessive dorsiflexion was
observed on the sound ankle of subject 2703-1903A which is likely to reflect rapid tibial
rotation following loading response (Figure 4.11). It is difficult to explain the
requirement for this gait pattern. Excessive knee flexion (Figure 4.9) was commensurate
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with increased power absorption across the knee joint (Figure 4.23) which would seem
to be a typical mechanism to control the position of the trunk given the rapid tibial
rotation.
On the sound ankle of the unilateral Chopart amputee the ankle remained at
virtually neutral from 20% of the gait cycle to maximum dorsiflexion (Figure 4.11).
Restricting and maintaining the dorsiflexion range may be a mechanism to control the
substantial progression of the CoP that occurred from initial contact to mid-stance
(Figure 4.5). By mid-stance the CoP had progressed to about 70% of shoe length and
remained at this position until maximum dorsiflexion (Figure 4.5).
During pre and initial swing phases, peak ankle plantarflexion was comparable
to normal on the sound limb of all unilateral amputee subjects except subject 2703-
1906A (Figure 4.11). Reductions in peak plantarflexion in this subject are difficult to
explain but appear to be a functional choice rather than due to limitations in the
available joint range.
During swing phase, the ankle kinematic patterns were quite variable (Figure
4.11). Excessive ankle dorsiflexion dominated the swing phase kinematic profile
observed in subject 2703-1903A and excessive plantarflexion was observed during mid
and terminal swing phases in subject 2103-2116A (Figure 4.11). The swing phase
kinematic pattern observed in subject 2703-1903A is not likely to be of clinical
significance given the adequate foot clearance evidenced by the ankle dorsiflexion angle
(Figure 4.11). However for subject 2103-2116A, foot clearance may be more of an issue
but deviant plantarflexion did not commence until just after mid-swing (Figure 4.11).
The functional significance of these swing phase kinematic profiles is difficult to
explain.
Knee kinematics
At the knee joint, the kinematic patterns observed in the amputee subjects were
very similar to those of the normal population (Figures 4.9-4.10).
For the affected limbs of the bilateral MTP amputee and subject 2703-1906A
increased stance phase knee flexion was observed (Figures 4.9-4.10). Increases in stance
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phase knee flexion were commensurate with increases in the knee extension moments
(Figure 4.17) and power absorption across the knee in the bilateral MTP amputee
(Figure 4.24) but not subject 2703-1906A (Figure 4.23). For the bilateral MTP amputee
the increased knee flexion is likely to be a mechanism to control the trunk position in
lieu of the dorsiflexion range through which the ankle operates (Figure 4.12). In subject
2703-1903A this pattern of knee motion may be a mechanism to control rapid tibial
progression. However, there was no substantial increases in the knee extension moment
(Figure 4.16) and power absorption across the knee (Figure 4.23) which would typically
be commensurate with this type of gait pattern.
Reductions in stance phase knee flexion were observed in the bilateral Chopart
amputee and on the affected limb of the unilateral TMT amputee (Figures 4.9-4.10).
Reductions in the knee extension moment (Figures 4.16-4.17), power absorption (KP1)
and power generation (KP2) across the knee joint were commensurate with reductions
in the angular excursion of the knee. Reductions in stance phase knee flexion may be
the result of reductions in walking velocity in the TMT amputee however, such
reductions in walking speed were not observed in the bilateral Chopart amputee.
Reductions in stance phase knee flexion may be employed to reduce the demand of the
quadriceps musculature and preserve walking velocity (Perry, 1992).
On the affected limb of the unilateral Chopart amputee, the magnitude of stance
phase knee flexion was comparable to that observed in the normal population (Figure
4.9). It is difficult to explain how this gait pattern was controlled given that the kinetic
descriptions more closely resemble that observed in individuals with compromised
stance phase knee flexion. Reductions in the knee extension moment (KM2) approached
significance (Figure 4.16) as did reductions in power absorption (KP1) and power
generation (KP2) across the knee joint (Figure 4.23).
In the bilateral Chopart amputee, the stance phase knee flexion peak was
significantly delayed compared to normal (Figure 4.10) and commensurate delays in the
knee extension moment peak (KM1) (Figure 4.17), power absorption (KP1) and power
generation (KP2) were observed. These anomalies seem to reflect delays in the
progression of weight onto the limb, particularly given the delayed vertical GRF peak
(FZ1) (Figure 4.4).
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During terminal stance, knee recurvatum was observed on the affected limbs of
the Chopart amputees, presumably to control tibial rotation by posteriorly aligning the
tibia relative to the femur (Figure 4.9-4.10). A consequence of this movement pattern is
the relatively delayed initiation of knee flexion into swing phase such as that observed
in subject 3004-1102A (Figure 4.9) which has also previously been observed in TMT
amputees (Dillon, 1995). Despite the delayed initiation of knee flexion, the joint angle
at toe off for subject 3004-1102A was only marginally outside the 95%CI of the normal
population and maximum knee flexion was normally timed (Figure 4.9). This rapid knee
flexion is likely to be aided by concentric activity of biceps femoris long head in a role
similar to that normally associated with the short head of biceps femoris muscle.
Substantial power generation was observed across the knee joint at this time (Figures
4.23-4.24). This power generation peak is typically associated with power generation
across the knee joint due to concentric gastrocnemius activity. However, the atrophy of
the triceps surae and the minimal or absent KP3 power absorption peak typically
associated with controlling the rate of knee rotation due to acceleration of the leg
segment by the triceps surae, would seem to indicate a marginal contribution by the calf
musculature.
Knee flexion into swing phase was delayed in the bilateral Lisfranc amputee
(Figure 4.10). This delay is likely to reflect the increased proportion of stance phase.
For the sound limb, the kinematic patterns observed were virtually identical to
the normal population except increased stance phase knee flexion was observed in
subject 2703-1903A. As previously described, this kinematic pattern modulated the
position of the trunk due to rapid tibial rotation following loading response (Figure
4.11). Although not significant, increased stance phase knee flexion was observed on
the sound limb of many of the Lisfranc and TMT amputee subjects. As previously
described with regard to the pre-swing ankle kinematics of the affected limb, this
pattern of knee motion may be due to the unrestrained fall of the trunk checked by
sound limb initial contact. Increased stance phase knee flexion is likely to absorb the
increased impact and smooth the transfer of weight to the sound limb (Sutherland et al.,
1980; Simon et al., 1978).
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Hip kinematics
At the hip joint, the kinematic pattern of motion was virtually comparable to that
observed in the normal population. Small differences in the timing of maximum hip
extension were observed but these were quite variable and only marginally outside the
tight 95%CI of the normal population and not likely to be of functional significance.
Excessive hip extension was observed on the affected limb of the unilateral
Chopart amputee (Figure 4.7) which, may be an attempt to maintain normal stride
length.
Reductions in static hip extensor range approached significance (13°) in the
bilateral Lisfranc amputee. There seems to be little reason for the reductions in dynamic
hip extension given that gait did not tax the extremes of hip extension (Figure 4.8).
However, given that the majority of power generation causing advancement of the limb
occurred at the hip joint, limiting the available extensor range may put the hip extensor
musculature into at a more advantageous position to generate power during contralateral
toe off.
No significant differences in the swing phase kinematics were evident on the
sound or affected limbs of the amputee subjects compared to the normal population.
Previous investigations into hip kinematics have not reported substantial
differences from normal (Dillon, 1995; Mueller et al., 1998).
Kinetics
Mean kinetic patterns observed at the hip, knee and ankle of the normal
population were comparable to published analyses of normal gait, in terms of both
timing and peak magnitudes (Allard et al., 1997; Winter, 1983). The variability of these
kinetic patterns were also comparable to previous reports of normal gait (Allard et al.,
1997; Winter, 1983; Winter, 1991) except the hip moment CV. The hip moment CV
was exaggerated, reflecting the limitations of the CV technique when the mean of the
signal is close to zero. No differences in the hip moment CMC were observed. Intra-
subject kinematic variability of individuals in the normal cohort were similar to those
reported by Kadaba et al., (1989).
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Interpretation of kinetic parameters are complicated in investigations such as this
where cadence and stride length (the two determinates of walking speed) were not
controlled. Changes in cadence, stride length and thus walking velocity have been
demonstrated to influence the gain of peak joint moments (Winter 1983; Winter 1984;
Winter 1989; White and Lage 1993).
In the present investigation, changes in the gain of peak hip and knee joint
moments were inconsistent with changes expected as a result of decreased walking
speed (Winter 1983; Winter 1984; Winter 1989; White and Lage 1993). The reduced
peak ankle plantarflexor moments observed in the TMT and Lisfranc amputee subjects
(Figures 4.13-4.14) were akin to those changes expected as a result of reductions in
walking velocity. However, reductions in the peak ankle extension moments, observed
uniformly across the TMT and Lisfranc amputee subjects (Figures 4.13-4.14), can not
adequately be explained by the reductions in walking velocity observed in only a few
individuals (Table 4.2).
For example, subjects 2130-2116A and 2803-0410A walked significantly slower
than normal (Table 4.2) but exhibited reductions in the ankle extension moment peak
(Figures 4.13-4.14), comparable to other amputees who walked at the same speed as the
normal population. Moreover, the ankle extension moments were reduced by
approximately 1Nm/kg (Figures 4.13-4.14), which is about five times greater than that
consistent with slow walking (Winter 1983; Winter 1984; Winter 1989; White and Lage
1993). The unilateral Chopart amputee (3004-1102A) who also walked significantly
slower than the normal population (Table 4.2) exhibited an ankle extension moment
peak comparable to the normal population (Figure 4.15).
During loading response, a relatively normal ankle dorsiflexion moment was
observed on both the sound and affected limbs of the amputee subjects except subject
2103-1906A (Figures 4.13-4.14). For this subject, the ankle moved rapidly through a
20° range during loading response from ≈10° dorsiflexion at initial contact to ≈10°
plantarflexion at the initial plantarflexion peak (Figure 4.11). The ankle moment (Figure
4.13) and power (Figure 4.20) profiles reflect the additional eccentric activity of tibialis
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anterior (Figure 4.27) to control the rapid rate of ankle rotation during loading response
(Figure 4.11).
In the preceding discussion on ankle kinematics, the ankle moment profiles of
the affected limbs highlighted reductions in the resistance to ankle dorsiflexion from
loading response through to heel-off (Figures 4.13-4.14). Reductions in the external
moment, and therefore, the internal muscle requirements, are the result of the relatively
fixed lever-arm of the GRF about the ankle (Figures 4.5-4.6). As previously discussed,
it is difficult to ascertain whether the CoP did not progress to avoid substantial force on
the distal residuum or to moderate the trunk position.
During the mid-stance phase, the ankle moment observed on the sound limb of
subject 3004-1102A reflects the varying contributions of the CoP and vertical GRF.
Following loading response, the rapid progression of the CoP dominated the ankle
moment pattern until about 25% of the gait cycle when the progression of the CoP
plateaued (Figure 4.5). At this time, the GRF was located at about 70% of shoe length
(Figure 4.5). The plateau in the ankle moment between 20-40% of the gait cycle reflects
the relatively fixed lever-arm of the GRF about the ankle. The rapid increase in the
ankle moment between 38%GC and 50%GC reflects the increasing magnitude of the
vertical GRF toward the FZ3 peak (Figure 4.3) given that the CoP did not progress
anteriorly during this time (Figure 4.5). Identical variations in the ankle moment pattern
were also observed on the affected limb of subject 3004-1102A and on the right limb of
subject 0904-1924A (Figure 4.15).
A similar plateau in the ankle moment pattern was observed on the sound limb
of subject 2103-2116A. This moment pattern does not seem to be the result of changes
in the external moment given that the magnitude of the vertical GRF was comparable to
normal (Figure 4.3) as was the progression of the CoP (Figure 4.5). As such, the
moment profile is likely to reflect the excessive muscle contributions of, most likely, the
triceps surae however, no substantial increases in EMG activity were observed.
Substantial reductions in the ankle plantarflexion moment were observed across
the TMT and Lisfranc amputees (Figures 4.13-4.14) reflecting the limited progression
of the CoP when the largest vertical GRFs occurred. The CoP had progressed to only
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about 40-50% of its total excursion (Figure 4.5-4.6) when the peak vertical GRFs were
observed (Figure 4.3-4.4). Hence, the negligible peak plantarflexion moments (Figure
4.13-4.14). Substantial progression of the CoP did not occur until double support when
the increasing lever-arm of the GRF was coincident with the rapidly diminishing
vertical force given that the FZ3 peaks occurred prematurely (Figure 4.3). In the
Chopart residuums, the bilateral MTP amputee and the sound limbs of the TMT and
Lisfranc amputees, the timings of the FZ3 peaks were commensurate with substantial
anterior excursion of the CoP. This would explain the normal magnitudes of the
plantarflexion moment peaks observed.
Arguably, these mechanical differences could highlight a limitation of some
prosthetic/orthotic designs to comfortably distribute forces such that maximum forefoot
loading could occur simultaneous to substantial anterior progression of the GRF.
However, as previously discussed, the limited anterior excursion of the CoP may also
serve a role in moderating trunk position due to weak calf musculature. Irrespective of
the prosthetic/orthotic device fitted, the external moments would still need to be
moderated for the CoP to progress substantially forward in unison with increases in the
vertical GRF. It would be difficult for the TMT and Lisfranc amputees to generate
significant internal muscle moments from the calf musculature. Alternatively, the
external moments could be resisted, as in the Chopart amputees, by the
prosthesis/orthosis.
Previous investigations have reported similar reductions in the peak ankle
plantarflexor moments in MTP and TMT amputees (Dillon, 1995; Boyd et al., 1999;
Mueller et al., 1998) and those with metatarsal ray resection or toe amputation (Boyd et
al., 1999).
The ankle power absorption peak (AP1) was substantially delayed on the
affected limbs of the TMT and Lisfranc amputees (Figure 4.20-4.21) commensurate
with the delayed and rapid increase in ankle dorsiflexion observed during terminal
stance (Figure 4.11-4.12).
Significant reductions in power generation across the ankle joint were observed
on the affected limbs of all the amputee subjects except the bilateral MTP amputee
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(Figures 4.20-4.22). For the MTP amputee, reductions in power generation approached
significance and were consistent with reductions in the excursion of the CoP that also
bordered the 95%CI of the normal population (Figure 4.6). No significant reductions in
the joint angular velocity were observed given the normal angular excursion from peak
dorsiflexion to peak plantarflexion during pre-swing (Figure 4.12); confirming that
reductions in power generation were due to changes in the excursion of the CoP.
The generation of work across the ankle was virtually negligible in the TMT and
Lisfranc residuums due to the diminished ankle moment coupled with reductions in the
joint angular velocity. These angular velocity data have not been presented, but such
interpretation may be based on the limited angular excursion of the ankle from
maximum dorsiflexion to maximum plantarflexion (Figures 4.11-4.12). For the Chopart
amputees, where the peak plantarflexion moments were comparable to those observed
in the normal population, reductions in power generation across the ankle reflect the
elimination of ankle motion by the prosthetic socket.
Clinically, reductions in power generation across the ankle reflect the limited
work by ankle plantarflexors to accelerate the leg segment into swing phase (Meinders
et al., 1998; Capozzo et al., 1976; Dillingham et al., 1992), contribute to the forward
kinetic energy of the trunk and maintain the vertical height of the CM of the upper body
(Meinders et al., 1998).
Despite the long-standing controversy in the literature regarding the role of
ankle plantarflexors (Meinders et al., 1998; Sutherland et al., 1980; Simon et al., 1978;
Perry, 1974), more recent and comprehensive evidence suggests that the primary role of
plantarflexor musculature is to accelerate the leg into swing phase and not to contribute
to raising the trunk against gravity (Meinders et al., 1998; Dillingham et al., 1992).
These recent works add new evidence to previous suggestions that the ankle
plantarflexors do not contribute to push-off (Perry, 1974; Mann et al., 1974; Simon et
al., 1978; Sutherland et al., 1980).
Previous investigations have reported similar reductions in power generation
across the ankle in TMT (Mueller et al., 1998, Dillon 1995) and MTP amputees (Dillon,
1995). These findings have been attributed to the shortened plantarflexor lever arm
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(Mueller et al., 1998) and reductions in the total excursion of the CoP (Dillon, 1995) but
have not acknowledged the role of joint angular velocity.
Partial foot amputation affected the knee joint moment profiles during loading
response and the latter portion of the mid-stance phase (Figures 4.16-4.17). In the
bilateral MTP amputee, the knee extension moment during loading response was
significantly larger than normal (Figure 4.17) as was the power absorbed across the
knee (Figure 4.24). These kinetic abnormalities reflect the increased requirement of the
quadriceps musculature to eccentrically control the increased stance phase knee flexion
(Figure 4.10). During the proceeding discussion of knee kinematics, the increased knee
flexion was thought to be a mechanism to control the trunk position in lieu of the
dorsiflexion range through which the ankle operated (Figure 4.12).
On the affected limbs of the unilateral TMT and Chopart amputees reductions in
the knee extension moment (KM2) approached significance (Figure 4.16) and
reductions in the power absorption across the knee (KP1) were significantly different
from normal (Figure 4.23). In the TMT amputee, reductions in power absorption across
the knee reflect reductions in the extension moment about the knee (Figure 4.16) and
the angular velocity of the knee joint given the reduced stance phase knee flexion
(Figure 4.9). Similar findings were also observed in the bilateral Chopart and Lisfranc
amputees that would explain the reductions in work across the knee joint. For the
Chopart amputee, the knee extension moment peak (KM2) was comparable to that
observed in the TMT amputee as was the power absorption peak (KP1) despite a normal
angular excursion of the knee joint (Figure 4.9) which is difficult to explain. The lack of
power absorption (KP1) expected may indicate some energy transfer to another limb
segment. Delays in the timing of the KM2 and KP1 peaks observed in the bilateral
Chopart amputee reflect delays in the peak stance phase knee flexion as previously
discussed (Figure 4.10).
During the latter half of the mid-stance phase, the normal knee flexion moment
was absent on the affected limbs of the TMT and Lisfranc amputees, except subject
2703-1903A (Figure 4.16-4.17). Mechanically, the absence of the normal knee flexion
moment typically reflects the limited carry over ankle plantarflexion moment (Figures
4.13-4.14) that is a primary influence on the knee moment equation during this time.
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Clinically, it is likely that that the tibial angle, and therefore knee position, moved in
unison with the line of action of the GRF in an attempt to reduce the external moment
and the muscular requirement of the weak gastrocnemius musculature. The affect of
muscle activity on the knee moment is likely to be negligible given the atrophied soleus
and gastrocnemius and the absence of other muscle activity and no co-contraction was
observed about the knee joint. The normal power absorption observed across the knee
joint at this time (40%GC) and subsequent power generation prior to the KP3 peak were
equally as puzzling (Figure 4.23) but are the product of the moment profile observed.
For subject 2703-1903A the normal knee flexion moment observed (Figure
4.16) is difficult to explain given that the plantarflexion moment was relatively small
and comparable to the other TMT and Lisfranc amputees (Figure 4.13). It would seem
unlikely that there is substantial triceps surae force in this individual given the atrophy
observed and the subsequent concentric activity of these muscles that would be
indicative of normal function. It is also difficult to explain the normal exchange of
power across the knee between mid-stance and the pre-swing phase (Figure 4.23).
The relatively normal knee flexion moments observed on the affected limbs of
the Chopart amputees were in stark contrast to those of the TMT and Lisfranc amputees.
A substantial external moment is likely to have been observed about the knee joint in
these individuals given the normal magnitude and lever-arm of the GRF (Figure 4.15).
The external moments could be resisted by the clamshell PTB socket assuming
sufficient resistance could be tolerated between the anterior surface of the leg and the
anterior wall of the socket. The external moments seem to have been significantly larger
than normal in subject 3004-1102A and on the left limb of subject 0904-1924A (Figures
4.16-4.17) driving the knee into hyperextension (Figures 4.9-4.10). Resistance to the
external joint moment is likely to have been augmented by the eccentric activity of
biceps femoris long head (Figures 4.23-4.24) in subject 3004-1102A (Figure 4.35) and
on the left limb of subject 0904-1924A (Figure 4.36-4.37). On the right limb of subject
0904-1924A, the knee flexion moment pattern (Figure 4.17) and exchange of work
across the knee (Figure 4.24) were comparable to normal despite the absence of biceps
femoris activity (Figure 4.37). These results may indicate that equilibrium could be
reached without additional muscle activity.
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The kinematic pattern of knee hyperextension observed in the Chopart subjects
3004-1102A and on the left limb of subject 0904-1924A tended to delay knee flexion
into swing phase (Figures 4.9-4.10). This kinematic anomaly seems to have been
resolved by rapid knee flexion into swing phase (Figure 4.9-4.10) and is likely to be due
to concentric activity of biceps femoris (Figures 4.23-4.24) working in a similar manner
to the short head of biceps femoris which is likely to be active at this time. On the right
limb of subject 0904-1924, the same kinematic pattern appears to have been controlled
using more substantial power generation by the hip flexor muscles than observed on the
contralateral limb (Figure 4.26).
Knee joint moment patterns observed in the majority of TMT and Lisfranc
amputees concur with previous reports that a small extension moment was maintained
from foot-flat through to toe-off in TMT amputees (Dillon, 1995; Mueller et al., 1998).
Very little power exchange was observed across the knee during this time (Dillon, 1995;
Mueller et al., 1998), which corroborates findings from the present investigation. The
absorption of power across the knee joint during pre-swing (KP3) was comparable to
previous reports (Muller et al., 1998) however, Dillon (1995) reported substantially less
power absorption at this time. Kinetic patterns for Chopart amputees and the sound limb
have not previously been reported.
The kinetic patterns at the hip were extremely variable across the amputee
subjects compared to those observed at the ankle and knee joints. Unlike the kinetic
patterns observed at the ankle and knee joints, the joint moment and power patterns
observed at the hip were inconsistent with the level of amputation or prosthetic fitting.
A multiplicity of moment and power generation patterns were consistent with
the need to compensate for the lack of power generated across the ankle during terminal
stance (Figures 4.18-4.19). Two basic patterns of power generation across the hip joints
were observed. The first pattern of power generation occurred on the affected hip during
early stance to propel the body forward from the rear. The second pattern also occurred
during early stance, but on the sound limb to provide forward impulse for the pelvis
coincident with the 'push-off' phase on the affected limb.
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The first pattern was observed on the affected limbs of primarily subjects 2703-
1903A, 3004-102A and on the left limbs of the bilateral subjects 2803-0410A and 0904-
1924A where an extension moment was maintained about the hip until just after mid-
stance (Figures 4.18-4.19). Increases in HP1 approached significance in the amputee
subjects except 0704-0403A (Figure 4.25). These hip extension moments were
consistent with significant increases in power generation across the hip during early
stance (HP1) (Figures 4.25-4.26). Prolonged activity of biceps femoris was observed in
several of these individuals, but without EMG of the primary hip extensors like gluteus
maximus it is difficult to establish a concrete relationship. This gait pattern has been
widely reported in both below knee amputees (Winter and Sienko, 1988; Winter, 1991;
Gritter et al., 1991) as well as in above knee amputees (Winter, 1991) to propel the
body forward from the rear.
The second pattern of hip power generation was observed on the sound limb
during early stance (Figure 4.25). This power generation period was coincident with the
pre and initial swing phases on the affected limb. Increased concentric hip extensor
activity was observed in all subjects except subject 0704-0403A (Figure 4.25) and
biceps femoris EMG was also prolonged in many individuals consistent with this type
of gait pattern. This pattern of sound limb power generation has also been observed in
above knee amputees (Seroussi et al., 1996) and provides forward momentum for the
pelvis.
During pre and initial swing phase, the normal power generation associated with
concentric hip flexor activity (HP3) was comparable to normal in all the amputee
subjects (Figures 4.25-4.26). On the sound limbs of the TMT and Lisfranc amputees and
the bilateral Lisfranc amputee, delays in HP3 seemed to coincide with affected limb
HP1 power generation perhaps to drive the body forward in a coordinated bilateral
fashion (Figure 4.25).
A number of interesting relations seem to exist between the hip power
generation peaks HP1 and HP3 which identify a number of different mechanisms to
generate 'sufficient' power to propel the body forward. For example, a substantial power
generation peak (HP1) was observed during early stance on the affected limb of subject
2703-1903A to propel the body forward from the rear (Figure 4.25). The magnitude of
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HP1 must have provided 'sufficient' forward propulsion given that the HP1 peak
observed on the sound limb was substantially smaller than the other TMT and Lisfranc
amputees (Figure 4.25). An alternate pattern of power generation was observed in
subject 3004-1102A where power generation was observed bilaterally during early
stance (HP1) presumably to compensate for the minimal power generated bilaterally
during the HP3 phase (Figure 4.25).
Given the normal power generation observed across the ankle joint of the
bilateral MTP amputee (Figure 4.21) it was not surprising that there were no significant
changes to the hip joint moment (Figure 4.19) and power (Figure 4.26) profiles
compared to the normal population.
For subject 0704-0403A the power generation profiles observed across the hip
joints were comparable to the normal population (Figure 4.25) despite reductions in
power generation across the affected ankle. For the other Lisfranc and TMT amputees,
additional power generation was observed across either the sound or affected hips
during early stance to augment the normal power generation across the sound ankle.
A similarly puzzling scenario was observed for the bilateral Chopart amputee,
where power generation across the ankle was negligible (Figure 4.15) and power
generation across the hip was not commensurately increased above that observed in the
normal population (Figure 4.26). For example, power generation was prolonged until
pre-swing on the left limb of the bilateral Chopart amputee, but the magnitude of this
power generation was relatively small, as was the magnitude of the HP3 peak on both
limbs (Figure 4.26). For the right limb the exchange of work across the hip joint was
comparable to that observed in the normal population (Figure 4.26). This lack of power
generation across the hips and ankles may be explained by the reduced impulse of the
first horizontal GRF peak (FX1) compared to the second (FX2) (Figure 4.2). This
imbalance may tend to cause the limb segment to continually accelerate. Previous
investigators have reported similar reductions in the magnitude of the first horizontal
GRF peak (Dillon, 1995; Hirsch et al., 1996).
For the bilateral Lisfranc and Chopart amputees an extension moment was
dominant across the left hip (Figure 4.19) commensurate with prolonged power
________________________________________________________ Chapter 4. 171
generation and the absence of the normal, HP2 power absorption peak (Figure 4.26). In
these individuals, it appears that only the left limb was responsible for the bulk of power
generation from initial contact through to pre-swing. Similar asymmetries in sagittal
plane energetics have previously been reported for normal individuals (Allard et al.,
1996). Perhaps this gait pattern provided much needed power generation. Reductions in
power generation to advance the body forward with limited compensations in these two
individuals, may be the primary cause of reductions in stride length and walking
velocity (Tables 4.2-4.4).
Previous investigations reporting kinetic patterns for the hip support the variety
of responses observed in the present investigation. Dillon (1995) reported the
maintenance of an extension moment about the hip until after mid stance and a
reduction in the hip flexion moment peak. Similar gait patterns were observed in many
individuals in the present investigation. In contrast, Mueller et al., (1998) reported the
early onset of a flexion moment about the hip which was not corroborated by findings
of the present investigation. Similar variability in the power generation patterns were
also observed, with Dillon (1995) reporting no significant increased in early stance
phase power generation, while Mueller et al., (1998) observed little concentric activity.
Results from the present investigation identified relatively normal power generation
across the hip during early stance in a number of individuals, which would support the
results of Dillon (1995). However, substantial increases in power generation on the
affected limb during early stance were also observed which have not previously been
reported. Previous investigations have not found significant differences in the
magnitude of power generation across the sound hip during pre and initial swing phased
(Dillon, 1995; Mueller et al., 1998). However, Mueller et al., (1998) reported that these
small differences from normal were indicative of a hip flexor gait pattern. Kinetic
patterns for the sound hip or Chopart amputees have not previously been reported with
limited work examining bilateral amputee gait (Dillon, 1995).
Signal processing issues affecting electromyographic data
From the outset of this investigation, the aim of collecting EMG data was,
primarily, to provide quantifiable information about the timing of muscle activity to
augment the interpretation of joint moments and powers. Information about the relative
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intensity of muscle activation was of lesser importance given that many of the muscles
to be analysed in the partial foot population were significantly atrophied. Such
quantifiable information is typically not available using conventional signal processing
techniques, which report either the rectified EMG data or a linear envelope thought to
reflect the pattern of force generation across time.
The simplest technique, which seemed to satisfy the original aim, reported
amplitude normalised EMG using the manual muscle test method (Perry, 1992; Powers
et al., 1998). Periods of muscle activation were determined using a simple threshold
based criteria centred about the 5%MMT level which reflects the equivalent to the
clinically effective grade 2 level of muscle activity (Beasley, 1961 - cited Perry, 1992).
In hindsight, the primary problem with results of the MMT technique proved to
be the level of background noise affecting the quality of the signal and that the level
changed with each electrode placement and person. Much of the EMG signal
characteristic of the noise observed in the present investigation was well in excess of the
5%MMT threshold used to distinguish meaningful muscle activity from the background
noise when the mean of the stable isometric contraction was used (Powers et al., 1998;
Perry, 1992). This lead to the necessity to reduce the level of background noise such
that the clinically meaningful level of 5%MMT could be maintained.
In this investigation, raw EMG data were high-pass filtered at 6Hz to stabilise
the base line signal. Previous investigations have typically utilised a variety of high-pass
cut-off frequencies varying between 10Hz and 40Hz (Hodges and Bui, 1996; Winter,
1991; Basmajian et al., 1985; Murry et al., 1985; Kadaba et al., 1989; Pierotti et al.,
1991; Perry, 1992; Shiavi et al., 1987) to accomplish this goal. However, recent work
suggests that the cut-off frequency should be somewhat less (Nilsson et al., 1993;
Acierno et al., 1998). In the present investigation, high-pass filtering at 6Hz (Acierno et
al., 1998) resulted in marked stabilisation of the baseline signal which was not
improved dramatically with higher cut-off frequencies up to about 20Hz. Cut-off
frequencies above 20Hz, such as the 40Hz utilised by Perry (1992) and Shiavi et al.,
(1987) resulted in a better baseline signal at the expense of affecting the power of the
signal.
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The very stable baseline achieved by Perry (1992) and Powers et al., (1998) was
due to the use of fine-wire electrodes and the high-pass filter cut-off frequency of
150Hz. The choice of cut-off frequency while providing a stable base-line signal would
seem to compromise the power of the EMG frequency. The bulk of the power of the
EMG signal lies between 75-102Hz for surface electrodes (Acierno et al., 1998) with a
slightly higher range for indwelling electrodes (Winter, 1990).
Filtering the signal to the point of affecting the power of the signal did not seem
to be a suitable method of resolving the large baseline signal. In order to bring the
baseline signal back within the range needed to utilise the 5%MMT threshold, the
maximum MMT voltage describing 100% muscle activation was determined in a novel
way. Using a stable one-second isometric contraction, the 100% MMT value was given
by the average of the peak voltages of each 10ms interval of the integrated MMT signal.
Determining the maximum MMT voltage in this manner reduced the overall magnitude
of the gait EMG (as a percentage of MMT) and that part of the signal characteristic of
the noise observed was typically below the 5%MMT threshold. The need to modify the
threshold level from 5%MMT suggests that the signal processing technique was not
robust to changes in the level of baseline noise. The variability of the baseline noise was
not well controlled by the signal processing technique used. In some instances, the
baseline noise may have only been 2%MMT, while other times it was above 10%MMT
necessitating that the threshold level be adjusted to give reasonable muscle on/off times.
These variations are likely to reflect factors such as electrode placement and skin
impedance which affected walking EMG as well as the voltage determined to be
100%MMT.
In hindsight, a superior technique would have been to remove the baseline level
of noise. This would have been possible with the collection of a baseline measure of
noise for each electrode placement and offsetting the walking and MMT data by that
level of noise. Determining the 100% MMT value could then utilise the mean of a stable
one-second isometric contraction as described by Powers et al., (1998) and Perry (1992)
without the problems associated with excessive baseline noise. The baseline measure of
noise could have also been used to establish a variable threshold criterion using the
mean and several standard deviations above the baseline signal (Hodges and Bui, 1996;
________________________________________________________ Chapter 4. 174
Studenski et al., 1991; Di Fabio, 1987) to determine an acceptable threshold criteria that
would vary according to the data recorded.
Irrespective of the threshold level used or how the 100%MMT value was
determined, the MMT technique still provided reasonable estimates of muscle on/off
times assuming that the threshold level was adjusted accordingly for each individual
electrode placement. Provided the threshold level utilised was recorded, the results
obtained are reproducible and open for individual interpretation alongside the raw,
filtered and rectified or uncut MMT normalised gait data. The tedious process of
adjusting the threshold level for each muscle of each individual ensured reasonable
muscle on/off times in comparison to previous investigations.
In comparison to previous investigations reporting MMT normalised EMG data
(Perry, 1992) results from the normal population compared favourably in terms of
periods of muscle activation indicating that the estimates of periods of muscle activity
were reasonable. The magnitude of the signals recorded, as a %MMT, were
substantially smaller compared to previous investigation (Perry, 1992). In the present
investigation, peak EMG activity was about one-third that reported elsewhere (Perry,
1992) reflecting differences in the signal processing technique. The mean intensity of
periods of muscle activity proved to be somewhat useless due to fluctuations in the
profile of EMG during lengthy contractions that encompassed more than one phase or
function such as that described in the results section. Moreover, the amplitude
normalisation technique determines each EMG profile relative to the individuals
maximum ability, which does not describe the relative force produced. The relationship
of force production to EMG recorded is further complicated when analysing atrophied
muscle.
In retrospect, a simple linear envelope EMG signal would have provided
sufficient information to identify abnormal periods of muscle activity or gross changes
in amplitude without many of the complications and downfalls of the technique used in
the present investigation.
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4.5 Conclusion
During the last five years, our understanding of the way partial foot amputees
walk has progressed substantially from the static force analysis theories that have
dominated our clinical understanding and treatment practices for some 30 years. Recent
research quantifying the gait of partial foot amputees has highlighted a number of
temperospatial and biomechanical abnormalities. These abnormalities required further
research to identify the causes underpinning the abnormal movement patterns described
in the literature. This study provides new insights into the gait of partial foot amputees
by documenting previously unpublished information such as bilateral electromyography
and mechanical descriptions of the sound limb. These contributions provide much
needed data, which has allowed many of the abnormal movement patterns to be
identified and better understood. Our understanding of the gait of these amputees could
be further enhanced with information documenting kinematic movement of the trunk,
the rise and fall of the centre of mass of the trunk relative to power generation across the
ankle, step length and EMG of the major hip extensors and flexors.
The major findings from this investigation include:
1. Reductions in ankle range of motion in the Lisfranc and Chopart
amputees were consistent with equinus deformity. Reductions in ankle range were
functionally significant for the Lisfranc amputees but not for the Chopart amputees
fitted with clamshell sockets.
2. Temperospatial abnormalities in a few individuals were observed but
were inconsistent with amputation level, age or prosthetic/orthotic fitting.
Reductions in walking velocity were primarily due to reductions in stride length, not
cadence. The proportion of the gait cycle spent in sound limb stance was increased
in these individuals and commensurate reductions in contralateral single support
were observed. The duration of double support (as a percentage of the gait cycle)
was increased in these individuals but differences were inconsistent.
3. No significant reductions in the total excursion of the centre of pressure
were observed, however, substantial progression of the centre of pressure past the
distal residuum did not occur until contralateral heel contact in the TMT and
Lisfranc amputees. These differences seem to reflect requirements to keep the centre
________________________________________________________ Chapter 4. 176
of mass of the trunk within the base of support and have the benefit of protecting the
distal residuum from extreme forces.
4. Ankle kinematic patterns observed in the TMT and Lisfranc amputees
could be characterised by rapid limb loading, poor control of tibial rotation during
the mid-stance and pre-swing phases, reductions in maximum plantarflexion and
variable swing phase trajectories. The ankle kinematic patterns were consistent with
reductions in the effectiveness of soleus and gastrocnemius. During the mid-stance
phase, the tibia seemed to rotate freely over the stance foot and this rotation was
checked by contralateral initial contact. The peak plantarflexion angles observed on
the affected limbs of the TMT and Lisfranc seemed to be related to the ability to
transfer weight to the sound limb and achieve double support stability.
5. Ankle kinematic patterns observed on the affected limb of the Chopart
amputees reflect relative movement of the leg segment within the socket and the
force deflection characteristics of the prosthetic foot. Tibial rotation seemed to be
controlled by an internal moment generated against the anterior wall of the socket,
which was augmented by knee hyperextension during the latter part of the mid-
stance phase.
6. The effects of amputation on stance phase knee flexion were variable and
inconsistent with kinematic patterns commonly seen in individuals with soleus
weakness. In the Chopart amputee, knee flexion into swing phase was delayed as a
result of the knee hyperextension previous described. Concentric activity of biceps
femoris long head was associated with rapid knee flexion, ensuring that the swing
phase knee trajectory was normal.
7. Kinematic patterns of the hip were comparable to normal except in two
individuals where changes in maximum hip extension angle were observed. These
abnormalities may be a mechanism to obtain normal stride length or put the hip
extensor musculature in a more advantageous force/length relationship.
8. Significant reductions in the ankle plantarflexion moment were observed
only in TMT and Lisfranc amputees reflecting changes in both the excursion of the
centre of pressure and premature timing of the terminal vertical force. Reductions in
ankle power generation were consistent with reductions in the external torque in the
TMT and Lisfranc amputee subjects. For the Chopart amputee, reductions in power
generation across the ankle were the result of the elimination of ankle motion.
________________________________________________________ Chapter 4. 177
9. Reductions in ankle power generation were compensated for by
increased concentric activity on both the sound and affected hip joints during early
stance. Increased power generation across both the hip joints provided the missing
work necessary to advance the body forward. Sound limb power generation during
early stance was commensurate with the generation of power across the hip joint
during the pre- and initial swing phases. No significant increases in power
generation were observed during the pre- and initial swing phase. Some individuals
did not seem to generate additional power to compensate for reductions in power
generation across the ankle. Reductions in the impulse of the horizontal ground
reaction force may add acceleration to the limb system as observed in a single
Chopart amputee.
The clinical implications of these results have not been discussed as part of this
chapter. The subsequent chapter focuses on the significant findings of this investigation
and addresses the clinical implications for rehabilitation, prosthetic/orthotic design and
prescription.
_______________________________________________________ Chapter 5. 178
Clinical implications affecting prosthetic design and
rehabilitation practice
5.1 Introduction
Results from the preceding investigation (Chapter 4) highlight that partial foot
amputation results in a number of adaptations to the basic pattern of locomotion
characteristic of triceps surae weakness and the influence of prosthetic and orthotic
design. The purpose of this discussion is to explore some of the clinical implications of
these findings in relation to the design of prosthetic/orthotic devices, rehabilitation
practices for individuals with partial foot amputation and the basis of prescription.
The initial part of this discussion focuses on the gait patterns of Chopart
amputees, describing how prosthetic design and rehabilitation could be altered to reduce
the requirement of the hip extensor musculature to compensate for the lack of power
generated across the affected ankle during early stance. The second part of this
discussion examines the gait patterns of TMT and Lisfranc amputees and demonstrates
how little prosthetic/orthotic design influences the mechanics of locomotion when the
triceps surae musculature is weak. A brief discussion on the merit of current
prescription practices is the final contribution to this discussion chapter.
Chapter 5
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5.2 Clamshell sockets
In light of the gait patterns observed on the affected limb of the Chopart
amputees, a number of novel ideas regarding the design of prostheses, incorporating
clamshell sockets, have come to the fore. These ideas focus on restoring power
generation across the ankle joint to reduce the requirement placed on both sound and
contralateral limb hip extensors during early stance phase and generally improve gait.
Results from the preceding investigation highlighted that power generation
across the ankle was significantly compromised in the Chopart amputees, to the point of
being negligible (Figure 4.22). Reductions in ankle power generation were due to the
effective elimination of ankle motion by the clamshell socket design (Figure 4.12).
Biomechanically, reductions in power generation across the ankle joint were the result
of the restricted joint angular velocity and not the reduced ankle joint moment. The peak
'passive' plantarflexion moments were normally timed and of similar magnitude to those
observed in the normal population (Figure 4.15). These moments are termed 'passive'
because the fixed ankle joint allows the prosthesis to carry the moment without muscle
activity. The abnormal ankle moment pattern observed during the mid-stance phase
would not influence the power generation peak given that by 40% of the gait cycle,
when power generation commenced, the moment patterns were similar to normal
(Figure 4.15).
These gait observations highlight that without a suitable joint in the clamshell
socket it would not be possible to generate power across the ankle. These data also
highlight that prostheses with clamshell sockets enabled the individual to apply body
weight loads (Figures 4.3-4.4) when the GRF was at a substantial lever-arm from the
ankle (Figures 4.5-4.6 and 4.15). Given these observations, if an external ankle joint
could be incorporated into the prosthetic design, would Chopart amputees be able to
generate power across the ankle comparable to that observed in a normal population?
If incorporating an ankle joint into the Clamshell prosthesis did not substantially
alter the ankle kinematic pattern or joint moment from that observed in the normal
population, then it would seem mechanically possible to restore power generation across
the ankle. It would be difficult to demonstrate this clinically given that it is not possible
_______________________________________________________ Chapter 5. 180
to predict how an individual would respond to such radically different prosthetic fitting
given the potential limitations of muscle weakness, difficulties with adequately coupling
the remnant foot and prosthesis to transmit the muscle force develop to the prosthesis.
However, this mechanical principal could be demonstrated mathematically or using a
simple model where the normal ankle kinematic pattern, or joint angular velocity, could
be modelled using a polynomial function. The modelled or 'normal' joint angular
velocity could replace that measured in an amputee subject prior to determining joint
powers using the inverse-dynamic approach. Given that the joint moment and angular
velocity data fed into the joint power calculation would be comparable to normal, then
the calculated ankle power generation would also be comparable to normal.
The inferences able to be gathered from such a model are extremely limited
given the assumptions made with regard to the ankle kinematic pattern and joint
moment profile. While it may be beneficial for an individual to display a 'normal' ankle
kinematic pattern simply by incorporating a joint into the prosthesis, the reality is that
this is an unlikely occurrence given the significant muscle weakness observed in these
amputees and the potential limitation of coupling muscle force to the prosthesis.
Moreover, the 'normal' joint moment could only be carried by the prosthesis because the
ankle joint was fixed and without this mechanism it may not be possible for the weak
calf musculature alone to moderate the external torque. There is little evidence to
suggest that such modifications to the clamshell prosthesis would enable individuals to
adopt a gait pattern commensurate with the ability to moderate the magnitude of the
external torque such that substantial anterior progression of the GRF was commensurate
the peak vertical GRFs during late stance.
The preceding investigation highlights that the 'normal' ankle kinematic pattern
was very much dependant on a number of factors. These factors are likely to include the
strength of the ankle plantarflexor musculature and the ability of these muscles to
generate sufficient internal torque to produce the desired kinematic pattern of motion
against the external torque. Both of these factors, in turn, influence the position of the
trunk over the stance foot. The relationship between the ankle kinematic pattern and
these other factors is worthy of further discussion in the context of designing an ankle
joint for Chopart amputees.
_______________________________________________________ Chapter 5. 181
The weakness of soleus and gastrocnemius would seem to be one limitation to
providing an ankle joint for Chopart amputees. In normal gait, the ankle plantarflexor
musculature not only contribute to the generation of power across the ankle joint during
the pre and initial swing phases, but the role of these muscles during the mid-stance
phase is arguably more important in terms of controlling the kinematic trajectories of
the ankle, knee and trunk.
Throughout the mid-stance phase of normal gait, eccentric activity of soleus
(later augmented by gastrocnemius) contributes to stability of the knee and ankle and
restrains the rate that the tibia rotates over the stance foot. The controlled movement of
the ankle into increasing dorsiflexion is the result of the balance between the intrinsic
muscle and extrinsic joint torques. During the mid-stance phase, the magnitude of the
external joint torque increased linearly and by the end of single limb support is
substantially larger than the internal torque produced by contraction of the ankle
plantarflexors. As such, the ankle dorsiflexion angle increases in a controlled manner.
These actions help control forward movement of the trunk over the stance foot and
prevent excessive ankle dorsiflexion. During the later portion of the mid-stance phase,
the increasing dorsiflexion angle is halted and reversed. These kinematic changes are
affected by substantial activity of the ankle plantarflexors, which increase the magnitude
of the internal torque to match and then exceed the external torque, consequently
moving the ankle toward plantarflexion. In the Chopart amputees where soleus and
gastrocnemius have little effect, the external torque and tibial progression appear to
have been moderated by a counterforce generated across the anterior wall of the
clamshell socket. The ability of the socket alone, to resist the largest external torques
seems unlikely given that hyperextension of the knee (Figures 4.9-4.10) was necessary
to moderate the external torque and the rotation of the leg and foot segment (Figures
4.16-4.17).
If a freely rotating ankle joint were incorporated into a clamshell socket, the
prosthesis would not enable the individual to adopt a gait pattern, which would allow
normal magnitude external torques to be generated. Essentially, the prosthesis would
not be able to resist the external torque and control tibial rotation. Neither would the
weak calf musculature. In all likelihood, the external torque would have to be
substantially reduced to a point where the magnitude of this torque could be managed
_______________________________________________________ Chapter 5. 182
by a combination of the torque developed by the weak ankle plantarflexor musculature
and gait adaptations. The resulting gait pattern could be very similar to that observed in
the TMT and Lisfranc amputees.
In the TMT and Lisfranc amputees, eccentric activity of the triceps surae
seemed unable to control the rate of tibial rotation or halt and reverse the increasing
dorsiflexion angle. Rapid and excessive ankle dorsiflexion was observed during the later
half of the mid-stance phase, which was eventually checked by contralateral heel
contact. The magnitude of the external torque was reduced by limiting the excursion of
the CoP, thus reducing the lever-arm of the GRF about the ankle. The magnitude of the
external torque is likely to have been reduced to a point where it could be controlled by
a combination of muscle activity and gait adaptations. These actions also moderated the
excursion of the CM of the trunk in relation to the base of support until such time that
the trunk could progress outside the base of support in an, arguably, controlled manner.
The resulting gait pattern was described in the preceding investigation as ‘falling over’
the end of the remnant foot.
Many of these potential gait anomalies, which may result by incorporating a
freely rotating ankle joint into the Clamshell prosthesis, could be addressed by
prosthetic design and physical therapy.
Rather than by incorporating a freely rotating ankle joint into the clamshell
prosthesis some mechanism could be incorporated which could moderated tibial rotation
and the increasing ankle dorsiflexion angle during the mid-stance phase. Such an ankle
joint would also allow a portion of the external torque to be carried by the leg shell
given that there would be some degree of controlled coupling, or motion restriction,
between the leg and foot segments. The prosthetic ankle joint may be similar to the
dorsiflex assist ankle joint used in ankle foot orthoses. Ankle dorsiflexion could be
resisted by a tension spring incorporated posterior, or a compression spring anterior, to
the joint axis. The resistance to ankle dorsiflexion would increase linearly with joint
angle in a similar fashion to the external torque if such a spring mechanism were
utilised. The amount of mechanical resistance should be inversely proportional to the
strength of the calf musculature. With physical therapy to strengthen the calf
musculature, the elastic resistance could be reduced as muscle strength increased. The
_______________________________________________________ Chapter 5. 183
device would then augment the remaining muscle activity rather than be the primary
control. However, this relies on research identifying the initial cause of soleus weakness
and thus the muscles potential for rehabilitation.
In the Chopart amputee, soleus weakness and disuse atrophy may be the result of
the elimination of ankle motion due to prosthetic fitting or the result of not developing
force across the ankle joint regularly. Given this scenario, a suitable physical therapy
program in combination with prosthetic fitting that incorporates an ankle joint, could
address the muscular and gait related problems. A suitable physical therapy program
may need to focus on restoring triceps surae strength, ankle joint range of motion in
combination with gait rehabilitation. If the primary cause of triceps surae atrophy is not
disuse, then this type of prosthetic and rehabilitation intervention may fail. However,
alternate explanations for soleus weakness, such as a reluctance or inability to load the
distal residuum or control the position of the trunk seem unconvincing, with
conventional clamshell prosthetic sockets, given that the magnitude and timing of the
external torque was comparable to normal (Figures 4.13,4.15). The normal magnitude
of the net ankle joint torque is a reasonable indicator that the individual could
comfortably apply substantial load the prosthetic forefoot and that the sensitive tissues
are well protected by this socket/prosthetic design.
The transition from peak dorsiflexion to plantarflexion, in the absence of
sufficient muscle strength, would be difficult to achieve using a mechanical joint given
the magnitude of the force required to overcome the substantial external torque during
terminal stance. At best, the stored energy in the ankle joint's spring mechanism would
be returned as the contralateral limb is loaded and the external torque on the affected
limb reduces, forcing the ankle toward a neutral position. However, the timing of rapid
ankle rotation is likely to be delayed if the ankle can not actively halt and reverse the
increasing ankle dorsiflexion until contralateral initial contact. This kinematic pattern
assumes that the torque generated using such a spring mechanism would exceed the
magnitude of the external torque and drive the foot toward plantarflexion. The
continued movement of the ankle into substantial plantarflexion angles, as in normals, is
likely to be a passive occurrence as the magnitude of the external torque is relatively
small, plantarflexor muscle activity has diminished and the vertical and fore-aft forces
are rapidly declining (Sutherland et al., 1980).
_______________________________________________________ Chapter 5. 184
The trailing posture of the limb segment into initial swing relieves concerns
about toe clearance until mid-swing when the effective length of the limb is greatest. In
the Chopart amputees, tibialis anterior is significantly atrophied which would
complicate issues of toe clearance during swing phase. Moreover, the dorsum of the
remnant foot is almost non-existent, almost vertical, and is likely to limit the ability to
gain sufficient purchase of the prosthesis to actively dorsiflex the prosthetic forefoot. A
prosthetic ankle joint would also be required to resolve issues of swing phase toe
clearance. Attaining normal plantarflexion angles during pre and initial swing and rapid
dorsiflexion after toe-off would be difficult to achieve with a simple spring arrangement
such as that described earlier. The likelihood is that any torque designed to move the
foot into neutral during swing phase would also restrict the maximum plantarflexion
angles able to be obtained. A simple, but less than ideal, solution would be for the
spring mechanism to be balanced at a neutral joint angle similar to the position of a
current clamshell socket or ankle foot orthosis. The plantarflexion angles obtained
during pre and initial swing would probably be less than normal in order to obtain
sufficient toe clearance. The simple 'spring-loading' mechanism described here may be
less than ideal, but the number of more complex alternatives are virtually endless.
It is difficult to assess the likely impact an ankle joint would have on the gait
patterns of Chopart amputees described in the preceding chapter. Any such description
would be speculative. Only by understanding how an individual responds to the altered
prosthetic mechanism could mathematical modelling or clinical intervention be used to
improve the design of a suitable ankle joint. Modelling the gait patterns of these
Chopart amputees with a view to designing a suitable joint would require substantial
kinematic and kinetic inputs utilising prototype ankle joints. This type of prosthetic
intervention would rely heavily on physical therapy intervention to improved joint
range, muscle strength and provide gait retraining. Ideally, it would be beneficial to fit
amputees with this style of prosthesis as a primary interim during early rehabilitation.
Thereby, minimising the atrophy of the calf and pre-tibial muscles, minimise muscle
contracture which limits joint range and avoiding extensive physical therapy/gait
retraining.
_______________________________________________________ Chapter 5. 185
It is difficult to know whether these changes would make functionally
significant differences to the power generation observed across the hip joints or merely
alter the ankle kinematic profile to better reflect those observed in non-amputee
populations. Without significant improvement in power generation across the ankle,
striving for kinematic resemblance to normal seems unwarranted. The concept of fitting
Chopart amputees with a functional ankle joint, so that they may benefit from having an
intact ankle and triceps musculature seems worthy of further investigation.
5.3 Below ankle sockets, orthoses and toe fillers
The gait patterns of the TMT and Lisfranc amputee subjects are likely to be
dominated more by the influence of muscle weakness than by prosthetic/orthotic design;
although this was not formally assessed. Given that some subjects were fitted with
below ankle slipper sockets, others with orthoses and toe fillers or had their shoe stuffed
with a sock, it was surprising that the basic pattern of locomotion varied so little once
the metatarsal heads were compromised. This observation was quite surprising given the
author's expectation that below ankle sockets would substantially modify the gait
pattern compared to orthotic interventions or toe fillers given that these devices had a
socket and 'substantial' forefoot replacement.
The basis for this expectation was founded largely on the observations of a
single Chopart amputee (Dillon, 1995) where, as in the Chapter 4, the effective locus of
the CoP was extended and substantial force was applied to the prosthetic forefoot during
terminal stance. The ability of Chopart amputees to demonstrate this loading pattern
during gait reflects the ability of the clamshell socket to comfortably distribute forces
caused by loading the toe lever and the ability to moderate the external torque using the
prosthesis. Of course, without a 'substantial' forefoot lever capable of transmitting these
forces to the socket, the system would not function as observed. The Chopart amputees
moderate the external torque using the anterior leg segment of the clamshell socket in
conjunction with adaptations to the orientation of the leg or thigh segments as evidenced
by the knee hyperextension observed during the mid-stance phase.
The toe fillers and orthoses fitted to some of the Lisfranc and TMT amputees
were unable to function in a similar manner to the Chopart prostheses because orthotic
_______________________________________________________ Chapter 5. 186
management does not incorporate a socket or effective/'substantial' toe lever. An
ineffective toe-lever could be thought of as a material which is unable, or unlikely, to be
able to transmit force to a socket such as plastizote or even polypropylene of a thickness
used in AFOs. The below ankle sockets fitted to some of the Lisfranc amputees did
incorporate a socket and a 'substantial' toe lever. So why were the observed gait patterns
not different from those of other Lisfranc or TMT amputees who were not fitted with
prosthetic style devices?
The gait patterns observed for all the TMT and Lisfranc amputees were limited,
in part, due to soleus and gastrocnemius weakness. For all intents and purposes it would
probably not matter how the orthosis or below ankle socket was designed unless there
was sufficient muscle force to control tibial rotation and trunk position which would
allow individuals to adopt a gait pattern where substantial external torques could be
resisted. Without the ability to match the ‘normal’ magnitude of the external torque, the
individual would adopt an alternate gait pattern to reduce the external torque and
therefore the muscular requirements. If there was sufficient muscle force to resist an
external torque of ‘normal’ magnitude, then a device incorporating a socket and suitable
toe lever would seem to be the most appropriate. For without these two fundamental
aspects of the prosthetic design such torques could not be achieved.
Perhaps the most fundamental question concerning prosthetic/orthotic design for
individuals who do not utilise clamshell style prostheses is what mechanisms cause
weakness of the triceps surae musculature?
Unlike in the Chopart amputees, the initial cause of triceps surae muscle
weakness does not seem to be the result of disuse atrophy due to the elimination of the
available joint range of motion. The preceding investigation highlighted that soleus
weakness may be the result of adopting a gait pattern that reduced the forces applied to
the distal residuum. This seems to have been accomplished, as described in Chapter 4,
by limiting the excursion of the CoP until double support is achieved, when a significant
portion of the superincumbent load could be transferred to the sound limb and
progression of the GRF could then occur with significantly less force transmitted across
the distal residuum. In effect, triceps surae weakness may be the result of inadequacies
in the prosthetic/orthotic design.
_______________________________________________________ Chapter 5. 187
If the devices initially prescribed to people during rehabilitation are unable to
comfortably distribute forces caused by proper loading of the prosthetic forefoot,
individuals may adopt a gait pattern to reduce pain on the distal residuum such as that
just described. Limiting the excursion of the CoP until initial contact of the contralateral
foot, while minimising the force applied to the distal residuum, would decrease the
external torque and forward progression of the CM of the upper body. The long-term
consequence of adopting this gait pattern would be the reduced requirement of the
triceps surae muscles resulting in disuse atrophy. Even if later prosthetic/orthotic
intervention was able to restore the mechanical lever arm of the foot effectively and
distribute forces caused by loading the toe lever in a comfortable fashion, the triceps
surae muscles would be so weak that adopting a more advantageous gait pattern would
not be possible; at least not without prior physical therapy. This hypothesis would seem
to explain the gait patterns of the Lisfranc amputees fitted with below ankle style
prostheses.
Further research needs to identify the initial cause of soleus weakness. If, as
hypothesised here, triceps surae weakness is the result of adopting a gait pattern to
reduce undesirable force on the distal residuum, then primary or interim
prosthetic/orthotic intervention needs to provide devices with suitable forefoot levers
and sockets capable of comfortably distributing forces caused by loading the prosthetic
forefoot. If the devices initially fitted to amputees are not capable of this, then weakness
of the triceps surae is an almost inevitable result. The resulting or long term gait pattern
would then be dominated by muscle weakness even in spite of subsequent prosthetic
fitting which may well have been designed to comfortably distribute forces caused by
loading the forefoot lever.
Reductions in the abnormally high power generated across the hip joint during
early stance phase, on both the sound and affected limbs, are only likely if substantial
power can be produced across the ankle during terminal stance. Again, further research
is warranted to try to provide partial foot amputees with the ability utilise the intact
ankle and triceps surae musculature given that the primary benefit of preserving the
ankle joint is likely to be the ability to use it.
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5.4 Prosthetic prescription
It was surprising that the basic pattern locomotion observed across the TMT and
Lisfranc amputees varied so little, particularly given that subjects were fitted with a
wide variety of devices including below ankle slipper sockets, foot orthoses, toe fillers
or had their shoe stuffed with a sock. This finding is, in its self, a remarkable discovery.
To think that the aforementioned prosthetic and orthotic devices fitted to the TMT and
Lisfranc offered no substantial biomechanical benefit above that which was be achieved
by stuffing a sock in a shoe. So much for prescription criteria based on mechanical
function!
For many decades rehabilitation specialists, podiatrists and prosthetists/orthotists
have prescribed devices such as toe fillers and slipper sockets based largely on clinical
experience in the absence of numerical information describing the biomechanics of
partial foot amputee gait and the influence of prosthetic/orthotic fitting. In light of this
new information, common conceptions about how various prosthetic and orthotic
devices function, such that these devices restore foot length, are brought into question.
So is the mechanical basis upon which each of these devices is prescribed. While there
appears to be little mechanical evidence to support the prescription of toe fillers, slipper
sockets or foot orthoses for the restoration of lost foot length, to aid propulsion or
protect the distal residuum from extreme forces there may be measurable benefits not
identified by this research such as reductions in plantar pressure.
It would be premature to provide an evidence-based approach to the prescription
of prosthetic and orthotic devices given that quantifiable literature is available for only a
small number of amputee subjects and that the insights into the biomechanics of partial
foot amputee gait and the influence of prosthetic/orthotic fittings are theoretical.
5.5 Conclusion
Results from the preceding investigation highlighted that partial foot amputees
typically generate abnormally large power across either or both the sound and affected
hip joints during early stance as a mechanism to compensate for reductions in power
generation across the affected ankle.
_______________________________________________________ Chapter 5. 189
This discussion highlighted the cause of reductions in ankle power generation
and proposed changes to prosthetic/orthotic design and rehabilitation practices aimed at
restoring power generation across the ankle so as to reduce the requirements of the hip
extensor musculature and improve gait in general.
For the Chopart amputee, reductions in affected limb ankle power generation
were due to the elimination of ankle motion resulting from prosthetic fitting. Providing
an ankle joint for the prosthesis would seem to be a simple solution to this problem.
However, the fixed ankle and the clamshell socket design allows the amputee to adopt a
gait pattern commensurate with the ability to moderate the magnitude of the external
torque. Significant improvements in ankle power generation would not be possible
without the inclusion of a custom design ankle joint and the ability to control it. Any
ankle joint would need to augment the available muscle activity and afford the amputee
the ability moderate the external torque in addition to:
1. providing the necessary resistance to control the rate of tibial progression as the
limb rotates over the stance foot;
2. decelerate the rapid anterior rotation of the tibia and allow the individual the
ability to use the existing musculature to drive the foot toward plantarflexion
commensurate the largest ankle joint moments;
3. providing adequate toe clearance during mid-swing given that there is likely to
be an inability to dorsiflex the prosthesis as a result of the shape of the distal
residuum and the poor coupling of the remnant foot and the prosthesis.
For the TMT and Lisfranc amputees, improving strength of the triceps surae
muscles would seem to be the only way of restoring power generation across the ankle.
Sufficient triceps surae strength may allow individuals to adopt a gait pattern that would
capitalise on prosthetic design that incorporates an effective replacement foot lever. The
toe lever would have to be able to transmit forces caused by loading to the prosthetic
socket. The prosthetic socket must be able to comfortably distribute forces caused by
loading the toe lever. A simple clinical test to determine if the prosthesis functions in
this manner may be to see if individuals can 'stand up on their toes'. Individuals with
TMT and Lisfranc amputation who took part in the preceding investigations were
unable to perform this simple test with the prosthesis on. With the prosthesis off, these
_______________________________________________________ Chapter 5. 190
individuals could achieve a reasonable joint range with good muscle strength, which
may have been limited compared to the normal population with the prosthesis on due to
pain or ankle plantarflexor weakness. This test is more limited for Chopart amputees
given the limited range of ankle motion resulting from prosthetic fitting.
Developing a prototype ankle joint for clamshell prostheses would seem like a
logical next stage. Assessment of the resulting gait patterns will provide much
information to guide further development and provide answers or insights to many of
the fundamental questions concerning the efficacy of this concept.
Further research is needed to identify whether the insights discussed regarding
prosthetic design and rehabilitation will result in improved power generation across the
ankle and reductions in the demand on the hip extensor musculature during early stance
and generally improved gait.
________________________________________________________ Chapter 6. 191
Conclusion and indications for further investigation
6.1 Conclusion
This thesis presented a number of discrete investigations, which developed the
central theme of providing accurate mechanical models that could subsequently be
applied to study the effect of amputation and prosthetic/orthotic intervention on gait.
In Chapter 2, a geometric model based on work by Hatze (1979) was developed
to improve the accuracy of anthropometric input data utilised by linked-segment models
used to estimate kinetic parameters of partial foot amputee gait. The model provided
reasonable estimates of foot mass, volume and centre of mass across a wide variety of
intact and partially amputated feet compared to experimentally derived estimates
obtained using incremental immersion. Modelled values of the radius of gyration were
compared to experimental data derived using a trifilar torsional pendulum and the
discrepancies observed, primarily in the amputee population, seem to reflect difficulties
associated with accurately orienting the principle axes of the foot replica on the trifilar.
The discrepancies observed were comparable to those reported for similar models. The
model may be advantageous to investigators of partial foot amputee gait wishing to
acknowledge the unique anthropometry of the remnant foot and improve the accuracy of
kinetic descriptions obtained using linked-segment inverse dynamic models.
Chapter 6
________________________________________________________ Chapter 6. 192
Linked-segment inverse dynamic models were developed in Chapter 3, which
incorporating improved anthropometric descriptions of the remnant foot as well as
accounted for changes in anthropometry of the proximal limb segments and
prosthesis/orthosis and footwear. These modifications to a standard linked segment
model more accurately depicted the amputee’s lower limb, enhancing the kinetic
estimates obtained from these models. These improved linked-segment models
significantly modified the anthropometry of the modelled free body segments and the
influence of changes in segment mass, centre of mass and mass moment of inertia
differed depending on the type of model used. The partial foot models increased the
knee flexion and hip extension moments observed during terminal swing compared to a
standard linked-segment model. These kinetic differences were indicative of a more
accurate portrayal of the activity of the hamstring and gluteus maximums muscles to
decelerate the knee into full extension and the hip into it's initial contact hip flexion
angle. Changes in power generation/absorption across the knee and hip were
commensurate with changes in the joint moments. Previous investigators are likely to
have underestimated the magnitude of moments and powers during terminal swing
phase. Given the substantial work necessary to generate these models and improved
anthropometric input data, many investigators may feel that the additional work is not
warranted by the small absolute differences observed.
Having established an appreciation of the influence these improved
anthropometric and linked-segment models have on the kinetic parameters estimated,
the effect of amputation and prosthetic/orthotic fitting on the gait of a cohort of partial
foot amputees was investigated.
The investigation presented in Chapter 4, reported temperospatial abnormalities
in only a handful of individuals, inconsistent with age, prosthetic/orthotic fitting or level
of amputation. These results indicate that temperospatial abnormalities, such as reduced
walking velocity and stride length or increased proportion of the gait cycle spent in
sound limb stance, were not a direct result of forefoot amputation but could be related to
other measures of function, which were not examined, such as balance. Ankle kinematic
patterns in the transmetatarsal (TMT) and Lisfranc amputees were characterised by poor
control of tibial rotation during the mid-stance phase resulting in an ever increasing
dorsiflexion angle which was eventually checked by contralateral initial contact.
________________________________________________________ Chapter 6. 193
Maximum plantarflexion was substantially reduced in many individuals which seemed
to be related to the ability to transfer weight onto the sound limb and achieve double
support stability. For the Chopart amputee, the ankle kinematic pattern was a reflection
of the force/deflection characteristics of the prosthetic foot and movement of the leg
within the clamshell prosthesis. The centre of pressure did not progress substantially
past the distal residuum until contralateral heel contact in the TMT and Lisfranc
amputees reflecting the requirement to keep the trunk positioned within the base of
support. This gait pattern also has the advantage of protecting the distal residuum from
the peak ground reaction forces. The peak plantarflexion moment observed in the TMT
and Lisfranc amputees was substantially reduced due to the limited anterior excursion of
the centre of pressure commensurate with the peak vertical ground reaction force. This
finding indicates that although the total excursion of the centre of pressure was
comparable to normal, the ability to substantially load the replacement forefoot was
compromised. The inability to load the prosthetic forefoot could reflect inadequacies in
prosthetic design and the inability to control the position of the centre of mass of the
trunk if it progressed outside the base of support. Reductions in power generation
across the ankle of the TMT and Lisfranc amputees were commensurate with reductions
in the joint moment and angular excursion of the ankle. For the Chopart amputees,
reductions in power generation across the ankle were due to the elimination of the ankle
range and not the inability to load the prosthetic forefoot as evidenced by the peak
plantarflexion moment. Reductions in power generation across the ankle resulted in
compensatory increases in concentric hip extensor activity on both the sound and
affected hip joints during early stance. Increased power generation on the affected limb
propelled the body forward from the rear. While power generation across the sound hip
during early stance was commensurate with power generation across affected hip joint
during the pre and initial swing phases associated with concentric work of the hip flexor
musculature.
The substantial work observed across the hip joint could be moderated by
restoring power generation across the affected ankle as discussed in Chapter 5. For the
TMT and Lisfranc amputees, improvements in triceps surae strength may allow
individuals to capitalise on prosthetic design that includes a toe lever and socket capable
of transmitting, and comfortably distributing, forces caused by loading the forefoot.
Shoe inserts or toe fillers do not incorporate a substantial toe lever capable of
________________________________________________________ Chapter 6. 194
transmitting the forces developed by loading the forefoot to the socket nor a socket
capable of comfortably distributing these forces. The ability to load the remnant
forefoot relies on suitable prosthetic design and sufficient calf muscle strength to
moderate the external torque generated by adopting a gait pattern consistent with the
ability to load the replacement forefoot. While the clamshell prosthesis fitted to the
affected limb of the Chopart amputees allowed individuals to generate substantial
external ankle joint torques, improvements in power generation would not be possible
without the ability to utilise the available ankle range. Significant improvements in
power generation across the ankle would not be possible without a suitable ankle joint
and improvements in joint range and muscle strength to control the angular excursion
and moderate the external joint torque. The development of an ankle joint for clamshell
prostheses would pose a substantial design challenge. While mathematically, the merit
of the proposal can be demonstrated, the likelihood is that the internal torques needed to
be generated either by the remnant musculature or a mechanical joint would be too
large.
In conclusion, this thesis provided novel anthropometric and linked-segment
inverse dynamic models that enabled more accurate mechanical descriptions of the
swing phase of partial foot amputee gait. While these models are not likely to be used
routinely, given the small absolute differences in swing phase moments and powers,
they demonstrate the influence of accurate anthropometric modelling on kinetic
descriptions of partial foot amputee gait which may be advantageous to future
investigators.
Results from this thesis also provided exciting new insights into the mechanics
of partial foot amputee gait, which highlighted a number of abnormal movement
patterns and compensatory effects. Previous investigations have not documented kinetic
descriptions of the sound limb or electromyography, which in hindsight proved to be the
keystones explaining how reductions in power generation across the affected ankle were
compensated for. Although previous investigations have documented reductions in
power generation across the affected ankle (Dillon, 1995; Mueller et al., 1998) neither
of these investigations provided substantial insight describing the causes of this
abnormality or the influence of prosthetic and orthotic intervention. This thesis
________________________________________________________ Chapter 6. 195
provided substantial insight into changes in work, satisfying the original objectives of
the thesis.
Results from these investigations challenge common misconceptions about the
gait of partial foot amputees and how prosthetic/orthotic devices function, which have
underpinned our clinical and prescription practices as well as design principles for many
decades. Views concerning the ability of prosthetic/orthotic devices and footwear to
restore the lost lever arm or foot length (Condie, 1970; Rubin, 1984; Rubin, 1985;
Pullen, 1987; Stills, 1987; Condie and Stills, 1988, Weber, 1991; Mueller and Sinacore,
1994; Sanders, 1997; Sobel, 2000) are by and large, not supported by findings from this
research because only Clamshell prostheses were able to restore the 'effective' lever-arm
of the forefoot. Results from this investigation also refute contentions that
prosthetic/orthotic devices aid propulsion or push-off (Rubin and Denisi, 1971; Rubin,
1984; Rubin, 1985; Stills, 1987; Sobel, 2000) or that hallux or toe amputation results in
a loss of push-off or propulsion (Sanders, 1997; Sobel, 2000). Only once the metatarsal
heads were affected was power generation across the ankle negligible irrespective of
foot length. Thus if surgery compromises the metatarsal heads, then more proximal
level selection should be based on criteria (ie: quality of skin coverage) other than trying
to preserve the ability to generate power across the ankle joint by preserving foot length.
This finding also challenges the common belief that preserving foot length should be a
surgical objective necessary to maintain normal gait (Barry et al., 1993; Giurini et al.,
1993; Pinzur et al., 1997; Sobel, 2000). Recent work concluding that partial foot
amputees adopt a hip flexor gait to compensate for a lack of power generation across the
ankle (Mueller et al., 1998) were not supported by results from this work. Results from
this investigation found that the primary compensation for the lack of power generation
across the ankle was an increase in hip extensor work during early stance on both the
sound and affected limb.
While results from this thesis provide substantial insight advancing the
understanding of the gait of partial foot amputees and the influence of
prosthetic/orthotic fitting, it would be beyond the scope of these results to use this data
to provide much needed biomechanical merit to the prescription of prosthetic/orthotic
intervention. A number of subsequent investigations, such as those currently in progress
in the United States (Boyd et al., 1999; Burnfield et al., 1998) may be in a better
________________________________________________________ Chapter 6. 196
position to overcome the limitations of sample size. However, it will be a number of
years before a concrete understanding of partial foot amputee gait can be developed
from studies such as this which offer theoretical insights into causes of abnormal
movement and the influence of prosthetic/orthotic fittings. Only then, can an evidence-
based prescription principle developed.
6.2 Further research
While analysing results from the present investigation, additional information
describing step length, trunk kinematics and displacement of the centre of mass of the
combined head, arms and trunk would have been of tremendous benefit in drawing
more conclusive descriptions of the underlying causes of the abnormal movement
patterns observed. The electromyographic (EMG) patterns of only a small number of
muscles were collected for the hip and knee, which were not sufficient to lead to
conclusive results about the muscles which actually contributed internal work to the
kinetic patterns observed. The major hip extensor muscles should be examined to
provide additional insight supporting kinetic descriptions of power generation across the
hip during early stance phase. Similarly, the EMG profiles of additional knee flexor
muscles should be examined to aid explanation of knee flexion moments which were
largely unexplained in a single Lisfranc amputee and the Chopart amputee subjects.
EMG analysis could also estimate force production through calibrating EMG activity
with muscle activity using a dynamometer.
One aspect of the linked-segment model, which was not exploited in this thesis,
was the ability to extract the measured centre of pressure excursion and replace it with a
modelled norm. The modelled centre of pressure excursion was derived mathematically
using a polynomial function where the coefficients for the function were derived from
normalised centre of pressure excursion measurements of intact feet/normal gait. In this
way the abnormal centre of pressure excursion profile, measured for each amputee
subject, could be replaced with a modelled norm and the influence of restorations of
foot length on kinetic parameters could be assessed. This modelling concept was not
pursued given the unreliability introduced by the assumptions about the timing of peak
ground reaction forces and kinematic profiles, which were necessary. For example, it
would be possible using the centre of pressure excursion model to depict a more normal
________________________________________________________ Chapter 6. 197
progression of the ground reaction force such as would ideally be reconstituted with any
prosthetic design. However, if a prosthetic device, which could restore the effective
centre of pressure was fitted, the amputee would likely adopt an alternate kinematic
pattern. Hence, the joint powers generated would be relatively meaningless unless it was
possible to predict how the kinematic pattern and ground reaction forces would adapt to
improvements in centre of pressure excursion. The centre of pressure excursion model
may provide useful information about prosthetic design and optimal foot length once a
better understanding of how the kinematic profiles vary with changes in the effective
locus of the centre of pressure.
In terms of effecting significant changes to prosthetic/orthotic design, research
needs to focus on determining the mechanisms leading to reductions in ankle power
generation in TMT and Lisfranc amputees. Perhaps, during rehabilitation individuals
learn to adopt a gait pattern, which avoids excessive plantar pressures resulting from the
prosthetic/orthotic device. If subsequent prosthetic/orthotic fitting incorporates a socket
and toe lever suitably designed to effect forefoot loading, these individuals may still not
have sufficient muscle strength to adopt a gait pattern characteristic of the ability to
moderate the external joint torque and ankle kinematic pattern. Alternatively, sockets
and toe levers may not provide the necessary relief of forces as expected thus not permit
the individual to walk in a manner that would maintaining muscle strength. Further
research needs to identify the primary cause of calf atrophy in these amputees so that
suitable rehabilitation programs and prosthetic devices can be designed.
For the Chopart amputee, the inability to generate power across the affected
ankle is the result of the elimination of ankle motion due to prosthetic fitting. The
development of an ankle joint for the clamshell prosthesis poses substantial design
challenges for the engineer and prosthetist given the complexities associated with
maintaining the ability to moderate the external torque and produce a desirable ankle
kinematic pattern. Any ankle joint would need to augment the available muscle strength
to produce a desirable kinematic pattern. A desirable kinematic pattern could be
described as controlled tibial rotation during the mid-stance phase, rapid ankle rotation
from peak dorsiflexion to peak plantarflexion commensurate with the largest joint
moments and safe clearance of the prosthetic foot during swing phase. The development
________________________________________________________ Chapter 6. 198
of such an ankle joint would ideally see Chopart amputees benefit from the intact ankle
joint musculature.
Further research will undoubtedly focus on providing new principles for the
prescription of various prosthetic and orthotic replacements based on biomechanical
merit rather than anecdotal evidence and clinical experience. It will be some time before
the provision of evidenced-based prescription principles becomes a reality given that
our understanding of partial foot amputee gait and the influence of prosthetic and
orthotic design is very much in its infancy. It would be premature for studies such as
this one to provide principles for the prescription of prosthetic/orthotic devices for two
reasons. Firstly, like many studies of amputee gait, the present investigation was based
on a limited sample which will require a number of similar investigations by a number
of investigators to reach a conclusive understanding about the gait of partial foot
amputees and the influence of prosthetic and orthotic fitting. Secondly, many of the
insights into prosthetic design and function highlighted in this thesis are theoretical and
will require ongoing research to either support or refute the understanding attained by
this research.
______________________________________________________ Appendix A. 199
Letter for patient recruitment
This appendix contains a copy of the letter sent to the Queensland Amputee
Limb Service (QALS), definitive prosthetic/orthotic service providers, acute care and
rehabilitation hospitals which these institutions distributed to clients whom were partial
foot amputees.
Appendix A
______________________________________________________ Appendix A. 200
To whom it may concern,
The Queensland Amputee Limb Service has been kind enough to offer me this
opportunity to contact you regarding current research being conducted at Queensland
University of Technology. A PhD study titled “The Biomechanics of Partial Foot
Amputee Gait” is about to commence, however, we need your help to make this
research possible.
Currently there is little data available on the gait or walking patterns of partial foot
amputees. Current literature remains speculative and evidence anecdotal. The purpose
of this study is to gather and document information on the way that partial foot
amputees walk so that prosthetists may have a better understanding of how forefoot
amputation effects the way partial foot amputees walk. The data collected will also be
used to develop a biomechanical model with the view to basing prosthetic design on
biomechanical data rather than anecdotal evidence.
Participants in the study will be required to attend a single testing session of 4-5 hours
duration at a time convenient to them. Queensland University of Technology will
arrange transport for you to attend the testing session and for your return home.
Participants will incur no expense from their involvement.
During the session, I will take your medical history and record some measurements
such as weight, height and foot length. Participants will be required to wear shorts or
bathers during the session so that reflective markers can be placed on the joints of your
leg and foot. Video cameras will record the motion of these markers as you traverse a
10-metre walkway. A platform will be mounted in the floor midway down the walkway
and will collect information about forces during walking. Electromyography (EMG)
______________________________________________________ Appendix A. 201
data, information about the timing and intensity of muscle activation, will also be
collected. All measurements will be taken while you wear your current
prosthetic/orthotic device.
As a participant in the study, you may withdraw your consent to participate at any time.
The information collected during the session will remain confidential, and your name
and personal details will not be associated with the data collected.
If you are interested in participating, or would like further information about the project
or what your involvement would entail, before making a decision please contact me on
3864 -2451.
I thankyou in anticipation for your support.
Kindest regards,
Michael Dillon.
B. Prosthetics and Orthotics (Hons.), PhD Student
Queensland University of Technology
Centre for Rehabilitation Science and Engineering
School of Mechanical, Manufacturing and Medical Engineering
Po Box 2434
Brisbane 4001
______________________________________________________ Appendix B. 202
An Anthropometric Model of the Partial Foot Residuum
B.1 Introduction
Dimensional and inertial characteristics of the partial and normal feet were
derived using a geometric model based on work by Hatze (1979). From first principles,
the model was derived as an assemblage of 103 plates of varying dimensions and
densities. Three trapezoidal plates represent the most inferior portion of the ball of the
foot (S11), the heel (S12), and the sole above these regions (S13) (Figure B.2). The
remaining 100 plates account for the middle and upper part of the foot (S14) which were
described using parabolic (S14P) and trapezoidal (S14
T) plates (Figure B.1-B.2). The
model is symmetrical about the x-axis (Figure B.1).
An exploded view of the foot illustrates the component plates comprising the
model (Figure B.2).
Equations describing the mass (M), volume (V), centre of mass (CM) and mass
moments of inertia about the CM (I) of the model use notations described in Table B.1,
anthropometric measurements described in Table B.2 and constants in Table B.3.
Appendix B
______________________________________________________ Appendix B. 203
Figure B.1 Geometric model of the Metatarsophalangeal residuum of subject 1004-
1307A; including a schematic representation of the input measurements.
See Tables B.1-B.3 for details of the nomenclature and input measurements pictured here.
c
har
b
la
lhf
h2
ha
h1-har
aml
aap
aaphf
½rr
X
Y
Z
S11
S12
S13
S14T
S14P
lk
OS14P
______________________________________________________ Appendix B. 204
Figure B.2 Geometric model of the Metatarsophalangeal residuum of subject 1004-
1307A. Exploded view illustrating the various components comprising the model.
S14T
S13
S11
S12
S14P
S14P
______________________________________________________ Appendix B. 205
Table B.1 Notations
Notation Explanation
S11..14 Numerical depiction of each segment (S) from 11 to 14
according to Hatze, (1979)
M11..14 Mass of each segment of the foot model [kg]
Mfoot Total mass of the foot [kg]
V11..14 Volume of each segment of the foot model [l]
Vfoot Total volume of the foot [l]
X'11..14, Y'11..14, Z'11..14 Coordinates of the mass centroid in the X,Y,Z direction
for each segment of the model [m]
X'foot, Y'foot, Z'foot Coordinates of the mass centroid of the foot in the X,Y,Z
direction [m]
Ixx11..14, Iyy11..14, Izz11..14 Mass moment of inertia about the X,Y,Z axes taken
through the mass centroid for each segment of the model
[kg.m2]
Ixxfoot, Iyyfoot, Izzfoot Mass moment of inertia of the foot about the X,Y,Z axes
taken through the mass centroid of the foot [kg.m2]
kxx11..14, kyy11..14, kzz11..14 Radii of gyration about the X,Y,Z axes taken through the
mass centroid for each segment of the model [m]
kxxfoot, kyyfoot, kzzfoot Radii of gyration of the foot about the X,Y,Z axes taken
through the mass centroid of the foot [m]
γγγγ(i)
γγγγ11..14
Density of the i-th segment; unit kg/m3
Density of each segment of the model [kg/m3]
______________________________________________________ Appendix B. 206
Table B.2 Anthropometric notation and measurement descriptions
Notation Description Measurement
l Intact foot
length
Distance between the most posterior part of the foot
and the end of the hallux taken parallel to the long axis
of the foot. For amputees use sound foot or estimate
using l = stature(m) * 0.15 (Dempster, 1955)
la Amputated foot
length
Distance between the most posterior part of the foot
and the end of the residuum taken parallel to the long
axis of the foot. Is equal to l for normal subjects
lhf Length of the
hind foot
Distance from the most posterior part of the foot, to a
line vertically bisecting the lateral malleolus
b Width across the
distal foot
Width across the 1st to 5th Metatarsal head
perpendicular to the long axis of the foot. If absent,
measure this dimension across the widest portion of the
distal residuum
c Width across the
proximal foot
Width across the calcaneus, perpendicular to the long
axis of the foot in non-weight bearing
h1 Toe height Distance between the floor and superior aspect of the
first phalanx. If absent use contralateral foot or
estimate using h1 = stature(m) * 0.0203 (Chapter 2)
h2 Foot height Distance between the floor and the apex of the lateral
malleolus
ha Amputated foot
height
Distance from the floor to the superior aspect of the
distal end of the residual foot
aap Ankle A-P Anterior-posterior dimension. With one arm of an
anthropometric calliper nestled into the anterior of the
subtalar joint, slide the other arm onto the posterior
surface of the Achilles tendon.
aaphf Ankle A-P of
hind foot only
Distance from the most posterior part of the foot, at the
level of the apex of the lateral malleolus, to a line
vertically bisecting the lateral malleolus
______________________________________________________ Appendix B. 207
aml Ankle M-L Medio-lateral dimension taken across the malleoli
perpendicular to the long axis of the foot
rr Width of the
lateral malleolus
Width of the lateral malleolus at the level of its apex
Table B.3 Constants
Notation Constant value
γγγγ11, γγγγ12 960 kg/m3
γγγγ13, γγγγ100 1001 kg/m3
γγγγ1 1347 kg/m3
har h1/2 when la > 3l/4 [m]
h1/3 when la > 3l/5 and la< 3l/4 [m]
h1/4 when la < 3l/5 [m]
B.2 Determining foot mass
The M of the foot can be determined by calculating and summing the M of each
component plate comprising the foot model. The basic equation describing the M of a
trapezoidal plate was given by
(1)
Hatze, (1979) and is illustrated in Figure B.3.
2
)( cblhM
+= γ
______________________________________________________ Ap
Figure B.3 Basic trapezoid plate
The basic equation describing the M of a parabolic plate was given by
Hatze, (1979) and is illustrated in Figure B.4
Figure B.4 Basic parabolic plate
3
4 abhM
γ=
Z
h a
b
Z
Y X
2
c 2
bThickness, h
l
pendix B.
Y
X
208
(2)
______________________________________________________ Appendix B. 209
The M of the ball of the foot (M11) was given by
(3)
where l11 describes the segment length and the remaining equation notations have been
described in Tables (B.1. and B.3). The derivation of l11 will now be explained in detail.
Modelling the distal foot as an assemblage of trapezoids (S11 and S13) was
mathematically, relatively simple although not anatomically correct. As such, the V of
the distal foot was overestimated relative to a plaster foot replica, which was used to
validate the model. The area of the plaster foot, corresponding to S11, and the area of the
geometric shape of S11, were estimated by tracing these forms on graph paper (Figure
B.4). Using Figure B.4 the area of the plaster foot corresponding to S11 was
approximately 56 cm2 compared to the modelled area of 70.5cm2. The poor anatomical
match between the trapezoid model and the natural arc formed between the hallux and
smaller toes accounted for the bulk of the difference. This could be more accurately
modelled as a separate geometric segment consisting of a parabola or more simply, the
length of the segment could be reduced until the appropriate area was achieved.
Reducing the segment length reduces the V of the modelled foot, which needs to be
balanced against the actual area of the foot depiction and was only possible because the
model was symmetrical about the x-axis.
( )6
5111111
cbhlM
ar += γ
______________________________________________________ Appendix B. 210
Figure B.5 Schematic diagram showing the modelled and anatomical shape of S11
The solid lines represent the modelled shape and the dotted lines the anatomical shape of the distal foot.
The difference between the area of the plaster foot and the model was
approximately 3.5cm2, when the segment length (l11) was given by
(4)
which represents ¾ of the original segment length. When the amputated foot length, la,
was less than ¾ intact foot length, the length of S11 was no longer affected by the shape
of the toes, and could be determined by
(5)
S11 was affected by forefoot amputation such that when the amputated foot length (la)
was less than two thirds of the intact foot length (l), the M of this segment (M11) will
equal zero as amputation has occurred proximal to this segment.
Equation (3) will only be valid when
3
2lla >
4
2311
llal
−=
3
211
llal −=
______________________________________________________ Appendix B. 211
Otherwise equation (3) will yield a negative M. If the M of this segment (M11) is zero
the corresponding CM and I will also be zero hence this simple equation can be used to
govern the dimensional and inertial contributions of S11.
The M of S12 (M12) was given by
(6)
The M of S13 (M13) was given by
(7)
where l13 is also affected, like l11, by the shape of the toes. When
l13 was given by
(8)
Otherwise,
(9)
The M of the top of the foot (M14) was given by summing the M of each of the
100 slices comprising S14. Two parabolic plates were used to independently represent
the hind foot and the fore foot portions of each slice of the proximal section of S14. The
proximal section of S14 extended carniocaudally from the apex of the lateral malleolus
to its inferior edge. The remaining slices of S14 were described using trapezoid plates.
( )18
51212
cblhM
ar += γ
( )2
)( 1131313
cbhhlM
ar +−= γ
1113
3
2l
ll +=
lal =13
4
3lla >
______________________________________________________ Appendix B. 212
The M of the hind foot parabolic plates (M14h) were given by
(10)
and the M of the fore foot parabolic plates (M14f) were given by
(11)
For the remaining slices of S14, inferior to the lateral malleolus, the M of the
these trapezoid plates were given by
(12)
In Equations (10-12), w describes the number of slices of the proximal section of
S14, and was given by
(13)
where, the numerator describes the half height of the lateral malleolus, or that portion of
S14 between the apex of the lateral malleolus and its inferior border. The denominator
( )
∑=
−
=w
i
iii
h
hhclh
M1
12.
14
31002
4γ
( )
∑=
−
=w
i
iii
f
hhblf
M1
12.
14
31002
4γ
( ) ( ) ( )∑
−
+=
+
−+
=w
wi
iiiii cbhh
lhlfM
100
1
12
14
2100
γ
−
= 10012
2hh
rr
w
______________________________________________________ Appendix B. 213
describes the height of S14. The integer value of w was expressed relative to the total
number of slices of S14.
In Equations (10-12), γγγγi describes the density, lhi describes the hind foot length,
ci describes the hind foot width, lfi describes the fore foot length and bi describes the
width of the fore foot; for the i-th segment. The derivation of these parameters shall
now be described in detail.
Density for the i-th segment, γγγγi, was given by
(14)
Hatze, (1979), where γγγγ100 and γγγγ1 were given as constants in Table 2.1.3
The hind foot length for the i-th segment, lh(i) varied linearly and was given by
(15)
and the hind foot width for the i-th segment, c(i) also varied linearly and was given by
(16)
For the intact foot, the anatomical contour of the forefoot length and width was
mathematically depicted by differential equations describing logistic growth with a
maximum limit as defined in its basic form by
where the initial state A(0) was
(17)
)]()[()(' tAMtkAtA −=
MktCe
MtA −+
=1
)(
( )100
iaaphflhfaaphflhi ⋅−+=
( )100
iamlcamlci ⋅−+=
⋅
−−= 2
1
10041 1101 ii
γγγγ
______________________________________________________ Appendix B. 214
Sentilles, (1989). This differential equation describes growth in a limited environment
where M is the upper limit to which A can grow. M-A(t) is a measure of the remaining
capacity for change in A. A(t) is the growth at time (t), K and C are constants. By
substituting the appropriate foot parameters into Equation (17), the minimum foot
height of S14 (h1) at any given foot length (l) was given by
(18)
where, K and C are constants, h1 is the minimum height of the foot at any given length
(l), and h2 is the maximum height of the foot. By solving equation (18) for l, foot length
for each slice of S14 was given as a function of foot height such that
(19)
where h(i) was given by
(20)
C in equation 19, was given by solving equation 18 for C when l = 0
(21)
KlhCe
hh
2
1
21 −+=
1
12
h
hhC
−=
112
)( .100
hihh
h i +
−=
( ) Kh
Ch
h
l
i
i
.001.0
1001.0
log
2
)(
2
)(
+−
−+
=
______________________________________________________ Appendix B. 215
The value of K in Equation 19, was given by the solution of Equation 18 when (l0) gives
the minimum foot height (h1) and, (l100) gives the maximum foot height (h2),
(22)
In Equation 22, 0.001 was added to h2 as there is no solution for the log of zero
and lk was given by
(23)
The length of the forefoot for the i-th segment, (lfi) was given by
(24)
until such time as
After this time, the fore foot length for the remaining i-th segments was given by
(25)
The width of the forefoot for the i-th slice (bi) could be calculated by
substituting the appropriate foot parameters into Equation (17) and the minimum foot
height of S14 (h1), at any given forefoot width (wb), was given by
(26)
( ) klh
Ch
h
K.001.0
1001.0
log
2
2
2
+−
−+
=
( )( )aaphfaaplhfllk −+−= 13
( ) ii laaphfaaplf +−=
lhfllfi −= 13
KwbhCe
hh
2
1
21 −
+=
ii lhlfl +=>13
______________________________________________________ Appendix B. 216
where, K and C are constants, h1 is the minimum height of the foot at any given width
(wb), and h2 is the maximum height of the foot. By solving equation (26) for wb, foot
width for each slice of S14 was given as a function of foot height such that
(27)
where h(i) was given by
(28)
such that when i = 75, the maximum width of the foot (b) will have been reached at the
minimum height of S14 (h1) which is assumed to correspond with the Metatarsal heads.
C in Equation 27, was given by solving Equation 26 for C when wb = 0 and K in
Equation 27, was given by the solution of Equation 27 when (wb0), gives the minimum
foot height (h1) and, (wb100) gives the maximum foot height (h2),
(29)
In Equation 29, 0.001 was added to h2 as there is no solution for the log of zero
and bk was given by
(30)
( ) kbh
Ch
h
K.001.0
1001.0
log
2
2
2
+−
−+
=
( )Kh
Ch
h
wb
i
i
.001.0
1001.0
log
2
)(
2
)(
+−
−+
=
amlbbk −=
112
)( .75
hihh
h i +
−=
______________________________________________________ Appendix B. 217
The width of the forefoot for the i-th segment, (b(i)) was given by
(31)
until such time as the width of the forefoot reached its assumed maximum at the
Metatarsal heads (i=75). After this time, the forefoot width for i-th segment was given
by
(32)
For the amputated foot, the forefoot lengths and widths for the i-th slice of S14
were governed by the proportion of the remnant foot to the intact foot, expressed
relative to the number of slices of S14, such that when
(33)
the forefoot length (lfi) was given by Equation 24, li in Equation 24 was as given by
Equation 19, K in Equation 19 was given by Equation 22 and hi in Equation 19 was
given by
(34)
and the forefoot width (bi) was given by Equation 31, wbi in Equation 31 was given by
Equation 27, K in Equation 27 was given by Equation 29 and hi in Equation 27 was
given by Equation 34.
ii wbamlb +=)(
bb i =)(
<= 100.
l
lai
112
.
100.
hi
l
la
hhhi +
−=
______________________________________________________ Appendix B. 218
Until such time as
then lfi was given by Equation 25 and bi was given by Equation 32.
The M of the foot was given by summation of the M of each component plate
comprising the model such that
(35)
B.3 Determining foot centre of mass
Coordinates for CM of the foot can be determined by calculating the CM of each
component trapezoidal plate comprising the model. The basic equations describing the
CM of a trapezoidal plate were given by Equations 36-38 (Hatze, 1979).
(36)
(37)
(38)
The CM of a parabolic plate were given by Equations 39 and 40 (Hatze, 1979)
(39)
(40)
hffoot MMMMMMM 141414131211 +++++=
( ))(3
2'
cb
cblZ
++=
0' =X
2'
hY =
> 100.
l
lai
aX 4.0' −=
0'' == ZY
______________________________________________________ Appendix B. 219
The coordinate system utilised by Hatze (1979) has been modified to match the
coordinate system of the kinematic and kinetic data. The X', Y', Z' coordinate system
used in Equations 36-40 is that of Hatze (1979) and does not represent the coordinate
system utilised in this model. The coordinate system illustrated in Figures (1) and (2)
demonstrates the local coordinate system utilised for this model and governs all
subsequent equations. Coordinates of the CM were given from the origin, located at lhf,
from the most posterior portion of the foot.
CM of S11 was given by,
(41)
(42)
(43)
CM of S12 was given by
(44)
(45)
(46)
1111
1111
)8(3
)5(2
3
2M
cb
cbllhfl
lCMx
++−
−
+=
11211
2M
hhCMz
ar
+−=
011 =CMy
1212
)5(9
)8(
3M
cb
cbllhf
lCMx
++−+
−=
12212
2M
hhCMz
ar
−= −
012 =CMy
______________________________________________________ Appendix B. 220
CM of S13 was given by
(47)
(48)
(49)
The CM of the hindfoot parabolic plates of S14 were given by
(50)
(51)
(52)
The CM of the forefoot parabolic plates of S14 were given by
(53)
(54)
(55)
( ) 1313
1313
)(3
)2(M
cb
cbllhflCMx
++−−=
131
213
2M
hhhhCMz
arar
−++−=
013 =CMy
( )[ ]∑=
−=w
i
hiih MlhCMx1
1414 4.0
∑=
−−=
w
i
hih Mhh
iCMz1
1412
14
100
014 =hCMy
∑=
−−=
w
i
fif Mhh
iCMz1
1412
14
100
014 =fCMy
( )[ ]∑=
=w
i
fiif MlfCMx1
1414 4.0
______________________________________________________ Appendix B. 221
For the remaining slices of S14, inferior to the lateral malleolus, the CM of the
these trapezoid plates were given by
(56)
(57)
(58)
CM of the foot was given by
(59)
(60)
(61)
+++++=
foot
fhfoot
M
CMzCMzCMzCMzCMzCMzCMz
141414131211
+++++=
foot
fhfoot
M
CMxCMxCMxCMxCMxCMxCMx
141414131211
0=footCMy
( )( )( )∑
+=
+++−=
100
1
1414
3
2
wi
i
ii
iiiii M
cb
cblhlflfCMx
014 =CMy
∑+=
−−=
100
1
1412
14
100.
wi
iMhh
iCMz
______________________________________________________ Appendix B. 222
B.4 Determine mass moment of inertia of the foot
Calculating and summing the value of I, about the CM, of each trapezoid and
parabolic plate comprising the foot model, can determine values of I of the foot, about
the CM. The basic equations describing the value of I of a trapezoid plate were given by
Equations 62-64 (Hatze, 1979).
(62)
(63)
(64)
The value of Iyy given by the sum of Ixx and Izz (Equation 65) seems to be an
approximation to the true value of Iyy derived from first principles (IyyP) (Equation 66).
(65)
(66)
( )
+
++= 2
222
18
..4..
cb
ccbblMIxx
+=24
22cb
MIzz
IzzIxxIyy +=
( )
+
++++++=).(24
)..(12..4)..(2..222223
cb
MlclbhcbcbcbbIyy
P
Mcb
lcbcbIzzIxxIyy .
)(
).3.(4.
24
12
22
+
+++=+=
______________________________________________________ Appendix B. 223
The approximation of Iyy (Equation 65) seems a useful alternative to the true
value of Iyy (Equation 65) given its numerical simplicity. This approximation can be
used when the trapezoidal plate is 'thin', or when the height, h, is much smaller than b, c
or l. The error associated with this approximation is;
Hatze (1979) did not acknowledge the approximation of Iyy or the error
associated with adopting this approximation. Given the current application, the error
associated with approximating Iyy seems negligible given the thinness of the slices of
S14. As such the approximation of Iyy shall be used for its numerical simplicity.
The basic equations describing the value of I of a parabolic plate, were given by
Equations 67-69 (Hatze, 1979).
(67)
(68)
(69)
12
.2
Mh
+=
125
22hb
MIxx
+=
12175
1222
haMIyy
+=
5175
1222
baMIzz
______________________________________________________ Appendix B. 224
The value of I for S11 about the CM was given by,
(70)
(71)
(72)
( )
( )
11
2
1111
2
2
2
22
211
11
)8(3
)5.(.2
3
2
...2
...
3
2.18
3
2
3
2.4
.
M
CMxcb
cbllhfl
l
CMzh
h
cbb
cbcbbb
l
Iyy
foot
footar
−
++−
−
++
+
−+
++
++
++
=
( )
−
++−
−
+
+
++
+
++
+
++
=
11
2
1111
2
111122
2211
11
)8(3
)5).(.2(
3
2
3
218
..3
24
3
2
24
MCMxfcb
cbllhfl
l
cbb
Mlccb
bb
cbb
M
Izz
oot
11
2
2
22
11
2243
2
MCMzfh
h
cbb
Ixx ootar
+
−+
++
=
______________________________________________________ Appendix B. 225
The value of I for S12 about the CM was given by;
(73)
(74)
+
++−+
−+
+
−+
+
+
++
+
=
2
2
2
2
22
2
12
)5(9
)8(
3
...2
...
3
5.18
3
2.4
3
2
.3
foot
footar
CMxcb
cbllhf
l
CMzh
h
cb
ccb
ccb
l
Iyy
+
++−+
−+
+
+
+
++
+
+
+
+
=
12
2
2
12
22
2
22
12
12
)5(9
)8(
3
...
3
218
.3
.3
24
3
2
...3
2
24
MCMxcb
cbllhf
l
ccb
Ml
cccbcb
ccbM
Izz
foot
______________________________________________________ Appendix B. 226
(75)
The value of I for S13 about the CM was given by
(76)
(77)
12
2
2
2
12
224
3
2
MCMzh
h
ccb
Ixx footar
+
−+
+
+
=
( ) ( )
( ) ( )
13
2
1313
2
12
2
22
213
13
)(3
2.
2
.18
..4.
M
CMxcb
cbllhfl
CMzhh
hh
cb
ccbbl
Iyy
foot
footar
ar
−
++−−
+
+
−−−
+
+
++
=
( ) ( )( )( )
( )
−
+
+
−−+
+
+++
+
=
13
2
13
13
2
132
1322
2213
13
)(33
2.
...18
..4
24
MCMxcb
cbl
lhfl
cb
Mlcbcbcb
M
Izz
foot
______________________________________________________ Appendix B. 227
(78)
The value of I for the hindfoot and forefoot parabolic plates, of the proximal
section, of S14 were given by
(79)
(80)
(81)
13
2
12
22
13
224MCMz
hhhh
cbIxx foot
arar
+
−−−+
+=
( )
∑=
−−+
+
−
+
−
+
=w
i
hi
ifootfoot
i
h M
lhCMxCMzhh
i
hhlh
Iyy1
14
2
2
12
212
2
14
4.0100
...12
100175
12
( )
∑=
−+
+
−
+
−
+
=w
i
fi
ifootfoot
i
f M
lfCMxCMzhh
i
hhlf
Iyy1
14
2
2
12
212
2
14
4.0100
...12
100175
12
( )∑=
−−+
+
=
w
i
hiifootii
h MlhCMxclh
Izz1
142
22
14 4.05175
12
______________________________________________________ Appendix B. 228
(82)
(83)
(84)
The value of I for the remaining trapezoid plates of S14 were given by
(85)
( )( )
∑+=
−
+
++−+
+
−
+
++++
=100
1
2
2
12
14
2
14222
14
)(3
)2.(
...100
.
...)(18
....4
wi
foot
ii
iiii
i
foot
i
ii
iiiiiii
CMxcb
cblhlflf
CMzhh
i
M
cb
Mlhlfccbb
Iyy
∑=
+
−+
−
+
=
w
i
hifooti
h MCMzhh
i
hhc
Ixx1
14
2
12
212
2
14
10012100
5
∑=
+
−+
−
+
=
w
i
fifooti
f MCMzhh
i
hhb
Ixx1
14
2
12
212
2
14
10012100
5
( )∑=
−+
+
=
w
i
fiifootii
f MlfCMxblf
Izz1
142
22
14 4.05175
12
______________________________________________________ Appendix B. 229
(86)
(87)
The value of I for the foot was given by
(88)
(89)
(90)
( )
( )( )( )
( )( )
∑+=
−
+++−
+
+
+++
+
+
=100
1
14
2
2
14222
2214
14
)(3
2.
18
..4
24
wi
ifoot
ii
iiiii
ii
iiiiiii
iii
MCMxcb
cblhlflf
cb
Mlhlfccbb
cbM
Izz
∑+=
+
−+
+=100
1
14
2
1222
14
10024wi
ifootii
MCMzhh
icb
Ixx
[ ]141414131211 IyyIyyIyyIyyIyyIyyIyy fhfoot +++++=
[ ]141414131211 IxxIxxIxxIxxIxxIxxIxx fhfoot +++++=
[ ]141414131211 IzzIzzIzzIzzIzzIzzIzz fhfoot +++++=
______________________________________________________ Appendix B. 230
B.5 Determining foot volume
Calculating and summing the V of each component plate of the foot model
determined the V of the foot. Hatze (1979) described the basic equation for determining
foot V from pre-determined foot M (Equation 91).
(91)
The V of S11..13 was given by,
(92)
V of S14 is given by,
(93)
(94)
B.6 An example of the effect of errors in anthropometric input data
A comprehensive error analysis would in its self be a substantial piece of work
given the mathematical complexity of the model and the number of cross correlations.
For example, while it may be possible to take a single input parameter such as intact
foot length (l) and add/subtract a given error margin, it is not easy to identify how this
single change will affect the many calculations that include this input parameter.
However, in an attempt to determine how robust the model is likely to be to errors in
anthropometric input data a very basic error analysis was undertaken.
Input anthropometric measurements were taken on each of three intact feet on
two consecutive days. The author was blind to the measurements taken on the first day.
The maximum error for each input parameter across the two days was determined as the
∑=i
i
iMV
γ.1000
13..11
13..1113..11 .1000
γM
V =
∑=i
i
iMV
14
1414 .1000
γ
1413..11 VVVfoot +=
______________________________________________________ Appendix B. 231
largest error in any one of the three intact feet studied (Table B.4). The parameters of
heel width (c), medio-lateral width of the ankle (aml) and width of the lateral malleolus
(rr) had the smallest error across the two days with a maximum difference of 1mm
(Table B.4). The length of hind foot (lhf) and the ankle anterioposterior dimension of
the hind foot only (aaphf) had the largest maximum error, which was 4mm (Table B.4).
Table B.4 Maximum errors in anthropometric input data
N/A - parameters of la and ha were not measured because only intact feet were studied. The value of la
was equal to the value of l for all conditions and the value of ha was equal to zero.
Subject 1 Subject 2 Subject 3Parameter
Day 1 Day 2 Day 1 Day2 Day1 Day2
Maximum
error (∝)
b (m) 0.106 0.103 0.100 0.102 0.095 0.093 ±0.003
c (m) 0.064 0.063 0.057 0.057 0.054 0.054 ±0.001
l (m) 0.264 0.262 0.246 0.246 0.242 0.243 ±0.002
la (m) 0.264 0.262 0.246 0.246 0.242 0.343 N/A
h2 (m) 0.074 0.077 0.070 0.071 0.066 0.065 ±0.003
h1 (m) 0.035 0.032 0.034 0.033 0.024 0.025 ±0.003
ha (m) 0 0 0 0 0 0 N/A
aml (m) 0.074 0.075 0.070 0.070 0.068 0.068 ±0.001
aap (m) 0.089 0.089 0.083 0.080 0.078 0.077 ±0.003
lhf (m) 0.060 0.058 0.058 0.059 0.048 0.052 ±0.004
aaphf (m) 0.050 0.048 0.047 0.050 0.040 0.044 ±0.004
rr (m) 0.032 0.031 0.029 0.028 0.029 0.030 ±0.001
As an example of the effect of errors in anthropometric input data, each
anthropometric input parameter for subject 1 (Day 1) was independently manipulated by
subtracting/adding the maximum error associated with each input parameter and
recording the BSP calculated. These results were compared to baseline BSP data
calculated using input parameters obtained on day 1 for subject 1. Results have been
presented for each parameter in Tables B.5-B.14.
______________________________________________________ Appendix B. 232
These data highlight that errors in h2 and h1 resulted in the largest differences in
the prediction of BSP data and as such should be measured with greatest care. A ±3mm
error associated with the measurement of either h2 or h1 resulted in a 30ml change in
foot V (3.4%), 40g change in foot M (3.8%) and 2mm change in CMz (4.3%) for subject
1 (Tables B.8 and B.9). Errors in the measurement of lhf of ±4mm resulted in ±3mm
changes (6.3%) in the location of the mass centroid along the z-axis (Table B.12). No
other significant differences were observed.
Table B.5 Errors in BSP data caused by errors in parameter b
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
b-∝ Absolute % b+∝ Absolute %
V (l) 0.970 0.956 -0.014 1.5 0.984 0.014 -1.5
M (kg) 1.032 1.017 -0.015 1.4 1.047 0.015 -1.4
CMx (m) 0.050 0.049 -0.001 1.2 0.050 0.000 0.0
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
kxx (m) 0.032 0.031 -0.001 1.0 0.032 0.000 0.0
kyy (m) 0.069 0.069 0.000 0.0 0.070 0.001 -0.1
kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0
______________________________________________________ Appendix B. 233
Table B.6 Errors in BSP data caused by errors in parameter c
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
c-∝ Absolute % c+∝ Absolute %
V (l) 0.970 0.965 -0.005 0.5 0.975 0.005 -0.5
M (kg) 1.032 1.027 -0.005 0.5 1.037 0.005 -0.5
CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0
kyy (m) 0.069 0.070 0.001 -0.1 0.069 0.000 0.0
kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0
______________________________________________________ Appendix B. 234
Table B.7 Errors in BSP data caused by errors in parameter l,la
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4. Differences in both l and la were assesses simultaneously
because when an intact foot is studies, the amputated foot length, la, is equal to intact foot length, l.
Condition Differences Condition DifferencesBaseline
l,la-∝ Absolute % l,la+∝ Absolute %
V (l) 0.970 0.964 -0.006 0.6 0.976 0.006 -0.6
M (kg) 1.032 1.026 -0.006 0.6 1.039 0.006 -0.6
CMx (m) 0.050 0.049 -0.001 1.6 0.051 0.001 -1.4
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0
kyy (m) 0.069 0.069 0.000 0.0 0.070 0.001 -0.9
kzz (m) 0.072 0.071 -0.001 0.7 0.073 0.001 -0.8
______________________________________________________ Appendix B. 235
Table B.8 Errors in BSP data caused by errors in parameter h2
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
h2-∝ Absolute % h2+∝ Absolute %
V (l) 0.970 0.937 -0.033 3.4 1.003 0.033 -3.4
M (kg) 1.032 0.993 -0.039 3.8 1.072 0.040 -3.8
CMx (m) 0.050 0.051 0.001 -2.2 0.049 -0.001 2.4
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.039 0.002 4.4 -0.043 -0.002 -4.2
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 1.9 0.006 0.001 -3.8
kxx (m) 0.032 0.031 0.000 1.3 0.032 0.000 0.0
kyy (m) 0.069 0.070 0.001 -0.3 0.069 0.000 0.0
kzz (m) 0.072 0.072 0.000 -0.6 0.072 0.000 0.0
______________________________________________________ Appendix B. 236
Table B.9 Errors in BSP data caused by errors in parameter h1
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
h1-∝ Absolute % h1+∝ Absolute %
V (l) 0.970 0.937 -0.033 3.4 1.003 0.033 -3.4
M (kg) 1.032 0.993 -0.039 3.8 1.072 0.040 -3.8
CMx (m) 0.050 0.051 0.001 -2.2 0.049 -0.001 2.4
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.039 0.002 4.4 -0.043 -0.002 -4.2
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.006 0.001 -9.8 0.006 0.000 0.0
kxx (m) 0.032 0.031 -0.001 1.3 0.032 0.000 0.0
kyy (m) 0.069 0.070 0.001 -0.3 0.069 0.000 0.0
kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0
______________________________________________________ Appendix B. 237
Table B.10 Errors in BSP data caused by errors in parameter aml
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
aml-∝ Absolute % aml+∝ Absolute %
V (l) 0.970 0.968 -0.002 0.2 0.972 0.002 -0.2
M (kg) 1.032 1.030 -0.002 0.2 1.035 0.002 -0.2
CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
kxx (m) 0.032 0.031 -0.001 0.3 0.032 0.000 0.0
kyy (m) 0.069 0.069 0.000 0.0 0.069 0.000 0.0
kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0
______________________________________________________ Appendix B. 238
Table B.11 Errors in BSP data caused by errors in parameter aap
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
aap-∝ Absolute % aap+∝ Absolute %
V (l) 0.970 0.965 -0.005 0.6 0.975 0.005 -0.6
M (kg) 1.032 1.026 -0.007 0.6 1.039 0.007 -0.6
CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0
kyy (m) 0.069 0.070 0.001 -0.3 0.069 0.000 0.0
kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0
______________________________________________________ Appendix B. 239
Table B.12 Errors in BSP data caused by errors in parameter lhf
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
lhf-∝ Absolute % lhf+∝ Absolute %
V (l) 0.970 0.968 -0.002 0.2 0.972 0.002 -0.2
M (kg) 1.032 1.030 -0.003 0.3 1.035 0.003 -0.3
CMx (m) 0.050 0.053 0.003 -6.2 0.047 -0.003 6.4
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.006 0.001 -3.8 0.005 0.000 0.0
kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0
kyy (m) 0.069 0.070 0.001 -1.4 0.069 -0.001 1.2
kzz (m) 0.072 0.073 0.001 -1.3 0.071 -0.001 1.1
______________________________________________________ Appendix B. 240
Table B.13 Errors in BSP data caused by errors in parameter aaphf
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
aaphf-∝ Absolute % aaphf+∝ Absolute %
V (l) 0.970 0.973 0.003 -0.3 0.967 -0.003 0.3
M (kg) 1.032 1.035 0.003 -0.3 1.029 -0.003 0.3
CMx (m) 0.050 0.051 0.001 -1.4 0.049 -0.001 1.6
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0
kyy (m) 0.069 0.069 0.000 0.0 0.070 0.001 -0.7
kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0
______________________________________________________ Appendix B. 241
Table B.14 Errors in BSP data caused by errors in parameter rr
V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and
z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes
the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes
maximum errors described in Table B.4.
Condition Differences Condition DifferencesBaseline
rr-∝ Absolute % rr+∝ Absolute %
V (l) 0.970 0.971 0.001 -0.1 0.969 -0.001 0.1
M (kg) 1.032 1.034 0.002 -0.1 1.031 -0.002 0.1
CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0
CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0
CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0
Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0
Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0
kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0
kyy (m) 0.069 0.069 0.000 0.0 0.069 0.000 0.0
kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0
______________________________________________________ Appendix C. 242
Validation of the incremental immersion technique for
determining volume and centre of volume.
C.1 Introduction
The incremental immersion technique has been widely used in many forms
(Clauser et al., 1969; Contini, 1972; Drillis and Contini, 1966) however the accuracy of
the technique does not seem to have been reported. Given the many forms of the
technique, the experimental error for the technique used in the present investigation was
assessed by determining the volume (V) or centre of volume (CV) of objects of known
dimensions where these same anthropometric descriptions could be determined
theoretically.
During the pilot investigation, the volume of liquid held in the immersion tank
before the test was deemed an important predictor of the volume displaced during
immersion of the foot replica. Once the tank appeared full, it was possible to add more
liquid creating a meniscus on the surface of the tank. For this reason, it was decided to
assess the effect of surface tension on experimentally derived V and CV estimates
under two experimental conditions; a water only condition and water with soap
condition.
Appendix C
______________________________________________________ Appendix C. 243
The aim of this investigation was to:
1. determine the error of the incremental immersion technique by comparing
experimentally derived V and CV data against theoretically derived values for
an object of known dimensions;
2. determine whether surface tension of the immersion liquid, affected
experimentally derived V and CV estimates.
C.2 Method
Subject
A steel calibration block was milled and the dimensions of the block recorded,
in metres, as 0.1849 x 0.0900 x 0.3970 m3.
Apparatus
All equipment used for these experiments has been described in Chapter 2.
Procedure
Prior to immersion of the calibration block, immersion increments were marked
every 4cm along the 0.1849m face (x-axis) and every 2cm along the 0.0900m face (z-
axis). The last segment for each axis accommodated the remnant portion.
Two experiments were conducted to investigate the effect of water surface
tension on the prediction of V and CV. The first experiment was set up and executed as
previously described in Chapter 2 for both the z and x-axes using the water only
condition. The second experiment used the water/soap mixture to decrease surface
tension. V and CV of the steel calibration block were calculated using standard
geometric equations and comparisons were made between this benchmark data and the
experimentally derived V and CV values under both experimental conditions.
The weight of water in the immersion containers was measured pre- and post-
experiment to assess how much liquid was lost as a result of the experiment as the
accuracy of the later immersion increments in the experiment would not be accurate if
substantial water loss was observed. The immersion increments were randomised to
avoid potential effects water loss.
______________________________________________________ Appendix C. 244
C.3 Results
Mathematically derived and experimental V and CV data describing the steel
calibration block has been presented in Tables C.1 and C.2 for the water only and water
with 0.25% soap conditions.
The weight of liquid in the immersion containers pre- and post experiment has
been presented for the water only and water with 0.25% soap conditions in Tables C.3
and C4.
Table C.1 Comparison of theoretical and experimentally derived V and CV of the steel
calibration block for the water only condition.
Standard errors are reported in brackets.
Theoretical Experimental Difference
Water only % Abs
Volume (litres)
X axis 0.6606 0.6179
(0.00358)
6.46 0.0427
Z axis 0.6606 0.6262
(0.00480)
5.21 0.0344
CV (m)
X axis 0.0925 0.0895
(0.00016)
3.24 0.0030
Z axis 0.045 0.0400
(0.000006)
11.11 0.005
______________________________________________________ Appendix C. 245
Table C.2 Comparison of theoretical and experimentally derived V and CV of the steel
calibration block for the water plus soap condition.
Standard errors are reported in brackets.
Theoretical Experimental Difference
Water/soap % Abs
Volume (litres)
X axis 0.6606 0.6386
(0.00176)
3.33 0.022
Z axis 0.6606 0.6599
(0.00074)
0.00 0.0007
CV (m)
X axis 0.0925 0.0943
(0.00008)
-1.95 -0.0018
Z axis 0.045 0.0431
(0.00015)
4.22 0.0019
Table C.3 Weight of liquid in the immersion container pre and post experiment for the
water only condition.
Experiment Difference
Pre Post % Abs
Weight of water in immersion container (kg)
X axis 2.7138 2.7014 0.46 0.0124
Z axis 5.7830 5.7627 0.35 0.0203
______________________________________________________ Appendix C. 246
Table C.4 Weight of liquid in the immersion container pre and post experiment for the
water plus soap condition.
Experiment Difference
Pre Post % Abs
Weight of water in immersion container (kg)
X axis 2.7232 2.7065 0.61 0.0167
Z axis 5.7986 5.7749 0.41 0.02369
C.4 Discussion
V and CV were mathematically calculated for the steel calibration block and
compared to experimentally derived values using two experimental conditions; water
only and water plus 0.25% soap.
Results from these experiments demonstrated that the V and CV of the
calibration object could best be experimentally determined when the water/soap mixture
was used. The water only condition resulted in larger absolute and percentage
differences when compared with the water/soap condition.
This observation my be due to the reduced surface tension, caused by the
addition of soap to the water, resulting in a smaller meniscus on the surface of the
immersion container. The overflow volume measured, more accurately represented the
actual volume of the immersion object resulting in more accurate V and CV
measurements.
To account for the effect of water loss, the amount of water in the immersion
containers were recorded pre- and post- experiment. Less than 1% of the water weight
was lost as a result of the experimental process across the water only and water/soap
conditions. More water was lost in the water/soap condition than the water only
condition again perhaps due to the reduced surface tension.
______________________________________________________ Appendix C. 247
C.5 Conclusion
The error associated with the prediction of V and CV, when 0.25% soap was
used in the immersion water was greatly reduced possibly due to a decrease in water
surface tension. 0.25% soap should be added to water in the immersion container to
improve the accuracy of V and CV predicted using this the incremental immersion
method. Randomisation of immersion increments was believed to overcome any
systematic errors due to water loss.
______________________________________________________ Appendix D. 248
Subject consent form
This appendix contains a copy of the subject consent form as required by the
University Human Research Ethics Committee for subjects.
Appendix D
______________________________________________________ Appendix D. 249
CONSENT TO PARTICIPATE IN RESEARCH PROJECT
BIOMECHANICAL MODELLING OF PARTIAL FOOT AMPUTEEGAIT
Chief Investigators: Michael Dillon (Postgraduate student)
Dr. Timothy Barker (School of Mechanical, Manufacturingand Medical Engineering) Dr. Michael McDonald (School of Human Movement Studies)
Current information of the biomechanics of partial foot amputee gait is scarce. Thepurpose of this study is to document data on the way partial foot amputees walk, so thatprosthetists have a better understanding of how prosthetic devices function and the waythat it affects the performance of subjects whilst walking. This data will also be used toexamine current treatment principles.
Subjects will be required to attend a single testing session of approximately 5 hoursduration, or two sessions of approximately 2.5 hours, and will be required to wearbathers during this session. All measurements will be taken while you wear yourprosthesis or orthosis.
During the session, a patient history will be documented and measurements of weight,height and foot length, leg circumferences and joint range of motion and musclestrength will be taken. A plaster cast of both your feet will be made. Reflective markerswill then be placed upon the joints of the leg and foot and video cameras will record thetrajectory of these markers during walking. Electromyography information will becollected simultaneously, and will require small pads to be places on muscle groups ofyour leg to record electrical activity of your muscles while you walk. Participants willbe required to walk along a 10 metre walkway and contact the force platform with eithertheir right or left foot. Several practice trials may be required so that the subject cancontact the platform while walking at a constant speed and in a normal fashion.
This project is being conducted by a research Postgraduate student as part of a Doctor ofPhilosophy program.
I acknowledge that the nature, purpose and contemplated effects of the examination sofar as it affects me have been fully explained to my satisfaction by the investigator andmy consent is given voluntarily.
______________________________________________________ Appendix D. 250
The details of the procedure proposed has been explained to me, including theanticipated length of time it will take, and an indication of any effects which may beexperienced during the examination.
Although I understand that the purpose of this research is to improve the quality ofmedical care, it has been explained to me that my involvement may not be of directbenefit to me.
I am informed that no information regarding my medical history will be divulged andthe results of any tests involving me will not be published so as to reveal my identify.
I understand that my involvement in the project will not affect my relationship with mymedical advisers in the management of my health.
I also understand that I am free to withdraw from the project at any time.
Feedback to the participants involved in this study will be provided, where this isrequested by the participants and is practicable.
If you have any complaints about this project or any questions which the investigatorsare unable to answer, you may also contact the Chairperson of the University ResearchEthics Committee.
SecretaryUniversity Research Ethics CommitteeQueensland University of TechnologyTelephone (07) 3864 2902
I, ________________________________ the undersigned have read and understood theinformation above, and any questions I have had, have been answered to mysatisfaction. I agree to my involvement in the research project on Biomechanicalmodelling of Partial Foot Amputee Gait.
Signatures: _____________________________________ Date _________Chief Investigator
_____________________________________ Date _________ Participant
______________________________________________________ Appendix E. 251
Software to process and report kinematic and kinetic data
E.1 Introduction
Information in this appendix describes, in detail, how kinematic, force and
kinetic data were processed through various pieces of software. The titles of individual
programs have been underlined through out this text. The actual Matlab 5.3
programming scripts are lengthy and as such have been included on CD. A detailed
description of the workings of some minor scripts and functions have not been included
in this appendix. However, programs have been commented.
E.2 Processing force plate data
Raw force plate data, recorded in volts, were imported into force4.m. The raw
voltage data were filtered using a zero lag, 4th order Butterworth digital filter with
125Hz cut-off frequency to remove unwanted electrical noise affecting the signal. A
Fast Fourier Transform (FFT) and power spectral density analysis revealed an array of
high frequency components affecting the signal. There were no specific frequencies
affecting the quality of the signal. With this in mind, the choice of cut-off frequency
was assessed in two ways.
Appendix E
______________________________________________________ Appendix E. 252
Firstly, the raw and filtered data were overlayed to observe any unwanted effects
of the filtering process with specific attention to attenuation of the signal at heel contact,
toe-off and the heel strike transient. The cut-off frequency and filter order were
systematically altered, on a small sample of data, until the voltage data were unduly
attenuated. The heel strike transient was affected before the heel contact and toe-off
times and as such, the cut-off frequency was selected to avoid unwanted filtering of this
component of the signal.
Secondly, heel contact and toe-off times were susceptible to small changes in the
filter order as evidenced in the time domain. To ensure the accuracy of both the filter
cut-off frequency and filter order, heel contact and toe-off times were compared
between the raw and filtered voltage data on a small sample of data. Differences in the
timing of these events were negligible with the filter characteristics specified.
Force and moment voltage data were converted to Newtons using the force
plate's calibration matrix, the amplifier's bridge excitation voltage and gain. Processing
the signal in this manner accounted for cross talk caused by the mechanical orientation
of the strain gauges within the force plate.
Small offsets in force and moment data, from absolute zero, were observed and
seemed to be due to the inherent inaccuracies of balancing the bridge excitation voltages
on the force platform amplifier. Each amplifier channel has its own pair of Light
Emitting Diodes (LED), D1 and D2. When D1 was lit the amplifier output was less than
-0.05V and when D2 was lit the output was greater than 0.05V (AMTI, 1991). By
adjusting the balance potentiometer until both LEDs went out, the voltage could be set
to approximately zero. To overcome this inaccuracy, force and moment data were offset
by the mean of a one-second sample of data, obtained prior to initial contact, for each
channel of force or moment data (Dillon and Frossard, 1999).
Force platform data were then sub-sampled from 1000Hz to match the kinematic
sampling rate of 50Hz. The difference between the sampling rates was not optimal but
unavoidable because the electromyographic data had to be sampled at 1000Hz, and all
analog data had to be sampled at the same rate. It was not necessary to filter data
following sub-sampling as evidenced in the time domain.
______________________________________________________ Appendix E. 253
Stance phase and the events of heel contact and toe-off were determined using a
threshold-based criterion. Stance phase was defined as the period when the magnitude
of the vertical force (Fz) exceeded 10N (Hreljac and Marshall, 2000). Previous
investigations have utilised a 5N vertical force threshold (Hennig and Milani, 1995;
Hennig et al., 1993). Irrespective of the threshold criterion chosen, initial contact times
were comparable to those obtained from footswitch data given the rapid rise in the
vertical force with time. Small differences in toe-off times were evident between the
two threshold based techniques. These differences in toe-off times were not of concern
given that the resolution of determining contact times at 50Hz is 20ms, which was
substantially larger than the error caused by differences in toe-off times determined
using either a 5N or 10N threshold.
The choice of threshold criterion was also a primary influence on the accuracy
of the centre of pressure (CoP), during initial and terminal stance. During these times,
when the magnitude of the vertical force is very small (<2% body mass), errors in the
vertical force represent large percentage errors in the CoP (Winter, 1990) because the
vertical force is the denominator of the CoP equation. The 10N-threshold criterion
resulted in practically no errors in the excursion of the CoP compared with the lower
threshold criterion.
CoP excursion were calculated as described by Winter (1990) and accounted for
the offset between the true and geometric origin of the force plate in the vertical
direction (AMTI, 1999). Offsets between the true and geometric origin of the force
platform in the horizontal directions were less than 1mm (AMTI, 1999) and were
therefore not of concern. The total excursion of the CoP was determined as the
difference between the two end-points selected manually using a set of mouse driven
crosshairs. Manual intervention was preferable to the automated systems trialed, which
were unable to accurately identify errors in the CoP during initial or terminal stance.
These problems have received little attention in the literature probably because errors in
the excursion of the CoP are coincident with very small ground reaction forces and
therefore, do not greatly influence the accuracy of joint moments or powers.
______________________________________________________ Appendix E. 254
Shear force data were inverted to account for differences in the direction of
approach during analysis of the right of left limbs.
Force and CoP data were then cut to the stance phase using the predetermined
heel contact and toe off times. Data were displayed on screen for visual inspection and
stored to file for further analysis.
Footswitch data were utilised to determine the duration of single and double
support phases and the second initial contact of the stride (the first having been
determined from the force platform). Initial contact times determined using the
footswitches were comparable to those determined from the force platform. Typically,
the registered onset of stance is delayed by about 2% with the use of footswitches
compared to force platform derived recordings (Perry, 1992). In the present
investigation, no systematic errors were observed, however initial contact times
obtained from the footswitches differed, on average, by approximately 0.5% compared
to the force platform derived values. These errors did not seem to be due to the
sensitivity of the footswitches necessary to prevent inadvertent activation as described
by Perry (1992) given that no systematic differences were observed. However, these
errors seem to be the result of differences in determining initial contact times using
footswitch data sampled at 1000Hz compared to force platform data sampled at 50Hz.
These differences were accounted for by determining the difference between
initial contact times obtained using the force platform and footswitches and adjusting
footswitch data such that the initial contact times matched the force platform derived
initial contact times. Subsequent initial contact times were adjusted bilaterally to
preserve the temporal relationship.
Footswitch data consistently resulted in delayed toe-off compared to
simultaneous force platform recordings by up to 70ms. These errors are likely to be an
artefact of the compression closing footswitches, which seem to respond poorly when
the force time profile is not steep, as it is during initial contact. The toe-off times
obtained from the footswitches were replaced with those determined from the force
platform. For the contralateral limb, where no force platform was available, the data
______________________________________________________ Appendix E. 255
were unable to be utilised. However, the periods of single and double support could still
be calculated.
For example, if the right stride included stance on the force platform, then the
initial contact and toe-off times could be derived from the force platform. The
subsequent right initial contact, concluding the right stride, could be determined from
the footswitch data. Single support for the left side, was simply the difference between
the second initial contact of the right stride, obtained from the footswitch and the toe-off
time obtained from the force platform for the right stride (Figure E.1).
Figure E.1 Schematic of support phase calculation using a combination of force
platform and footswitch derived event times.
Superscript FP denotes force platform derived variables while superscript FS denotes footswitch derived
parameters. Subscript R denotes right and L denotes left limb. HC denotes heel contact and TO denotes
toe-off. The blue section of the left stance phase indicates a period of double support.
______________________________________________________ Appendix E. 256
Only one double support phase could be determined at any time without
accurate bilateral toe-off times. Using the previous example, the double support phase
following initial contact for the left limb could be determined as the duration between
the right toe-off and left initial contact (Figure E.1). Similarly, when the stride from the
left limb contacted the force platform, the double support period subsequent to the right
initial contact could be determined.
The timing of the contralateral heel contact was also determined from the
adjusted footswitch data. Utilising the current example, the left or contralateral initial
contact could be expressed as a percentage of the right or ipsilateral gait cycle given the
difference between the first initial contact for the left and right strides divided by the
right gait cycle time.
E.3 Processing kinematic data
Reconstructed and interpolated 3D marker coordinate data were imported into
angles4.m to calculate joint angles of rotation for the hip, knee and ankle.
Raw XYZ marker displacement data were then filtered using a zero-lag, 4th
order low pass Butterworth digital filter with 6Hz cut-off frequency. The filter
characteristics were selected by analysing the frequency components of the heel and toe
markers on a small sample of subjects. These marker displacement data have been
demonstrated to have the highest harmonics (Winter et al., 1974) and as such the
frequency components of these markers were assessed using a FFT and power spectral
density analysis.
Heel marker displacement data had higher frequency components than those
observed for the toe displacement data. For the bulk of the toe displacement data it was
possible to filter the data with a cut-off frequency as low as 3Hz without unduly
attenuating the signal as evidenced in the time domain. However, for the displacement
data of the heel marker a 5Hz cut-off frequency was necessary to avoid unwanted
attenuation of the signal.
______________________________________________________ Appendix E. 257
It appears that the bulk of the power of the signal was below the 6th harmonic
(5Hz) with much of the signal after this point being characteristic of the noise observed
at higher frequencies. Given the uncertainty in the small sample of displacement data
analysed, a slightly higher cut-off frequency of 6Hz was selected as advocated by
Winter et al., (1974) who performed such an analysis on a larger number of subjects.
This cut-off frequency did not appear to increase the noise level in the time domain.
Marker displacement data were transformed to account for the direction of
approach during analysis of the right of left limbs.
Segment angles describing the orientation of the pelvis, thigh, leg and foot
relative to the horizontal axis of the global coordinate system (GCS) were determined
using an arc tangent function (Winter, 1990).
Neutral segment angle data were established in quiet standing and processed as
for the dynamic segment angle data. Neutral segment angle data were averaged and
used to account for errors in marker placement affecting the description of the neutral
joint position.
Joint angles were then determined as the difference between adjacent segment
angles (Winter, 1990).
Joint angle data were displayed to screen for visual inspection to determine if the
gait cycle to be analysed was representative of the subject’s normal pattern. In this way
it was possible to see if subjects altered their gait pattern or coordination to target the
force platform.
Dynamic joint angle data were cut to the gait cycle using the heel contact times
(derived during force4.m), normalised to 100 data points and displayed for visual
inspection. Unrepresentative joint angle data were excluded from further analysis at this
stage. The following data were then exported for further analysis: normalised joint angle
data, uncut joint angle data, dynamic and neutral marker displacement data as well as
the coordinates for the marker located on the walkway.
______________________________________________________ Appendix E. 258
E.4 Processing kinetic data
Kinetic parameters such as joint moments and powers were calculated using
moments4.m. A large number of input data were required to calculate joint moments
and powers such as body segment parameter (BSP) data, joint and limb segment
rotations, linear and angular velocities/accelerations of the centre of mass (CM) and
ground reaction forces.
A program called bspinput.m was used to either enter body segment parameters
measured from a subject or load an existing set of measurements describing the physical
characteristics of the foot, leg and thigh segments as well as general characteristics of
age, height, weight and sex. Mathematical models of the foot (bspfoot.m), leg
(bspleg.m) and thigh (bspthigh.m) were used to compute the volume, mass (M), centre
of mass (CM ) and mass moment of inertia (I) of each limb segment. Experimental
measurements were used to obtain these anthropometric descriptions of the
prosthesis/orthosis and shoes.
If partial foot model- B was selected the M, CM and I of the lumped leg, foot
and prosthesis/shoe segment were computed (Appendix F) and described the
characteristics of a 'lumped' leg, foot and prosthesis/shoe segment relative to the knee
joint. If partial foot model-A was selected the combined M, CM and I of the foot and
prosthesis/orthosis (if any) and shoe were computed (Appendix F) and described the
characteristics of the 'lumped' segment relative to the ankle joint. These input BSP data
and computed anthropometric descriptions were displayed for visual inspection and
stored to disk.
Filtered XYZ marker coordinates describing the position of the marker on the
walkway relative to the kinematic/global coordinate system (GCS) were imported. A
transformation between the origin of the force platform and the GCS was then
computed.
Filtered XYZ marker coordinates describing the displacement of each limb
segment were imported and angles of the pelvis, thigh, leg and foot segments were
calculated relative to the GCS in radians (Winter, 1990). Limb segment velocities and
______________________________________________________ Appendix E. 259
accelerations were then computed (Winter, 1990). Limb segment velocity data were low
pass filtered, using a 4th order Butterworth digital filter with 6Hz cut-off frequency,
prior to calculating limb segment accelerations.
Filtered XYZ marker coordinates describing the neutral limb position were
imported. Coefficients describing the position of the CM relative to these kinematic data
were computed (Appendix F). Displacements of the CM of the thigh, leg and foot
segments were calculated (Appendix F) as were linear and angular velocities of the CM
(Winter, 1990). Again, linear velocity data were low pass filtered, prior to calculating
linear accelerations of the CM.
Joint angle and force platform data, which had previously calculated in
angles4.m and force4.m respectively, were imported. The force platform data had
previously been cut such that only the stance phase was considered. The remaining data
were padded with zeros such that all matrices feeding into the joint moment equations
were of equal length. Force platform data collected prior to and following the stance
phase of interest were equal to zero.
CP data were expressed relative to the GCS using the previously determined
transformation between the origin of the force platform and kinematic/GCS. All
kinematic and force platform data were now expressed relative to the origin of the
kinematic/GCS.
Net joint moments were then calculated by resolving joint reaction forces prior
to calculating moments about the joint (Appendix F) and adjusted for the sign
convention such that all extension moments were positive (Ounpuu, 1994). Joint powers
were calculated as the scalar product of the moment and angular velocity and accounted
for power transfer across joints (Winter, 1990). Power generation across the joint was
considered to be positive on the y-axis (Ounpuu, 1994). The resultant joint moments
and powers were then normalised by body mass, cut to the gait cycle using the events of
heel contact derived from force4.m, and normalised to 100 data points (Ounpuu, 1994).
______________________________________________________ Appendix E. 260
Joint angle, moment and power data were displayed to screen for visual
inspection and stored to file. Padded force platform data were also cut to the gait cycle
and normalised to 100 data points prior to being stored to file.
E.5 Processing Temperospatial data
Temporal and spatial parameters were calculated using tempero.m. Parameters
describing the duration and proportions of the gait cycle were determined using the
initial contact and toe-off times obtained from force4.m according to the definitions of
Ounpuu (1994). Measurements of stride length and walking velocity utilised
displacement data of the ankle marker. During processing of the force platform data
(force4.m), the total excursion of the CP was obtained, as was the timing of the
contralateral initial contact. The total excursion of the CP was normalised by the
individuals shoe length and expressed as a percentage. The timing of contralateral initial
contact was expressed as a percentage of the ipsilateral gait cycle.
E.6 Reporting kinematic and kinetic data
Gait data were synthesised into a report for the right and left limbs of each
subject (Appendix I). Multiple trials of joint angle, moment and power data were
imported together with temperospatial, support phase and ground reaction force data to
form a matrix for each gait parameter. The CP data were offset such that initial contact
for each trial comprising the matrix was represented by a zero, indicating no excursion
of the CP. The CP data were subsequently normalised by shoe length to reduce
variability. The mean, standard deviation, range as well as the maximum and minimum
values were reported for the temperospatial and support phase data. For the joint angle,
moment, power and ground reaction force data, the multiple trials were averaged and a
time-based standard deviation was calculated for each parameter. The coefficient of
variation (CV) was calculated for each parameter as described by Winter (1983). The
variability of these data were also reported using the adjusted coefficient of multiple
determination (CMC) as described by Kadaba et al., (1989).
A number of figures portraying a variety of aspects of gait including variability
and average kinematic and kinetic data were generated. Of these figures, a number were
______________________________________________________ Appendix E. 261
used to elicit information about the timing and magnitude of specific mean joint angles,
moments, powers and ground reaction forces using a set of mouse driven crosshairs.
The exact x and y-axis values of the data point currently in the centre of the crosshair
were displayed on the top of the figure so that the true maximum/minimum could be
easily determined (Figure E.2). The crosshair location and the actual data values were
matched by scaling the figure so that there were the same number of pixels along each
axis. The actual data point had the smallest Euclidean distance, from the pixel currently
in the centre of the crosshair.
All data and figures generated from reportkin.m were stored to disk for future
reference and including in gait reports such as that presented in Appendix I.
______________________________________________________ Appendix E. 262
Figure E.2 Mean joint powers for the control sample plotted against ±2 standard
deviations of the control sample.
The circles show previously selected data points. The crosshair is placed on the ankle power generation
peak (AP2) and the corresponding x and y-axes values appearing in the boxes on the top of the figure.
The solid vertical line identifies toe-off at 60%GC.
10 20 30 40 50 60 70 80 90 100-1
0
1
2
Hip Power
(W/k
g) G
en
.
10 20 30 40 50 60 70 80 90 100
-2
-1
0
1
2Knee Power
(W/k
g) G
en
.
10 20 30 40 50 60 70 80 90 100-2
0
2
4
6Ankle Power
(W/k
g) G
en
.
Gait Cycle
HP2
HP3
HP4
KP1
KP2
KP3KP4
AP1
AP2
_______________________________________________________ Appendix F. 263
Linked-segment inverse dynamic models for the analysis
of partial foot amputee gait: implementation
F.1 Introduction
Implementation of these two partial foot inverse dynamic models (Chapter 3)
was mathematically relatively simple, although somewhat involved. The process used to
implement these models and calculate kinetic parameters involved:
• obtaining anthropometric descriptions of the partial foot residuum, leg and
thigh segment of the amputee as well as anthropometric descriptions of any
prosthetic/orthotic intervention and footwear
• combining the individual anthropometric characteristics of each of these
segments (ie: foot, leg, thigh, prosthesis, shoe) such that only one set of body
segment parameter (BSP) data reflects the contributions of all of the
individual segments
• creating a time series describing the location of the CM of each segment
relative to the global coordinate system
• deriving the remainder of the moment equation input data in the usual
fashion ie: calculate joint angles, linear and angular velocities and
accelerations, transpose force plate derived data into the global coordinate
system etc…
• calculating joint moments and powers
Appendix F
_______________________________________________________ Appendix F. 264
F.2 Obtaining the necessary anthropometric descriptions
Anthropometric characteristics of the normal and partial foot were determined
using the anthropometric model, and measurement techniques described in Chapter 2.
Anthropometric characters of the leg and thigh segments were obtained as described in
Chapter 3 as were these descriptions of the prosthesis/orthosis and footwear.
The anthropometric measurements obtained directly from the subject were
entered into software developed to geometrically model the residual foot, leg and thigh
segment and calculate body segment parameter (BSP) data including the mass (M),
centre of mass (CM) and mass moment of inertia (I) of these limb segments (Appendix
3.3). The M of the prosthesis/orthosis/shoe and the location of the mass centroid were
obtained directly and the value of I was calculated from the period of oscillation values
obtained (Chapter 3). With these input measurements the software returned a cell matrix
with BSP data such as that presented of a single individual with Chopart amputation and
clamshell prosthetic socket (3004-1102A) (Table F.1). The location of the mass centroid
for all limb segments including the prosthesis/orthosis/shoe were given in x, y, z
coordinates from the proximal end of the segment (joint centre) commensurate with the
laboratory coordinate system. The location of the CM of the prosthesis/shoe was given
relative to the knee joint as described in the assumptions of partial foot model-B (Table
F.1). The value of I was taken through the CM of the 'lumped' or modelled limb
segment.
Table F.1 Anthropometric data of the remnant foot, leg, thigh and prosthesis/shoe
stored in cell matrix format
Anthropometric characteristics of the isolated foot segment (anth.foot), leg segment (anth.leg), thigh
segment (anth.thigh) and combined prosthesis/shoe (anth.pros) were described. N/O denotes parameters
not obtained.
anth. Volume
(l)
Mass
(kg)
CMx
(m)
CMy
(m)
CMz
(m)
Ixx
(kg.m2)
Iyy
(kg.m2)
Izz
(kg.m2)
foot 0.4045 0.4434 -0.0127 0 -0.0364 0.0003 0.0006 0.0006
leg 2.4370 2.6728 0.0000 0 -0.1584 0.0394 0.0398 0.0031
thigh 9.9998 10.6541 0.0000 0 -0.1803 0.1518 0.1583 0.0403
pros N/O 1.5890 0.0280 0 -0.3750 N/O 0.0339 N/O
_______________________________________________________ Appendix F. 265
F.3 Combining the individual anthropometric descriptions
Given the individual anthropometric descriptions of the remnant foot, leg, thigh
and prosthesis/shoe it was necessary to combine these so that only one set of BSP data
reflects the contributions of all of the individual segments.
In continuing with the example using the Chopart amputee, the M of the leg,
residual foot and prosthesis/shoe (LFP) (Table F.1) were added together to yield the M
of the combined segment (Mlfp) which would be 4.7052kg.
The location of the mass centroid of the LFP, from the knee joint centre, was
given by the parallel axis theorem. The M of each segment comprising the LFP has
been represented by M123 and the distance from the segment origin to the segment CM,
has been represented by X123 in a pictorial representation (Figure F.1). This pictorial
representation depicts the various body segments, which need to be considered to
describe the anthropometry of a Chopart amputee wearing a clamshell PTB prosthesis
(Figure F.1).
The location of the CM of the LFP was given, from the knee joint centre, along
the z-axis by
(1)
where the length of the leg segment (l) was 0.41m.
Using the same method, the location of the CMlfp along the x-axis, from the knee
joint centre, was determined to be 0.0083m. The location of the mass centroid of the
LFP in x, y, z coordinates from the knee joint centre as [0.004 0 -0.259], assuming the
CM was located in the x-z plane (y=0).
( ) ( )( ) ( )( )
+++−+=321
332211 ...
MMM
XMlXMXMCM
z
lfp
( ) ( )( ) ( )
++−+−−+−=
589.1443.0673.2
375.0.589.1410.0036.0.443.0159.0.673.2z
lfpCM
mCMz
lfp 259.0−=
_______________________________________________________ Appendix F. 266
Figure F.1 Schematic illustrating how anthropometric characteristics of each limb
segment were combined to yield one set of characteristics describing the 'lumped' leg,
foot and prosthesis (LFP) of a chopart amputee.
From left to right, the leg and remnant foot, exploded view of the leg and remnant foot, Clamshell PTB
prosthesis and combined leg, remnant foot and prosthesis. The orthogonal axes sets describe the knee and
ankle joint local coordinate systems. X1,2,3,lfp is the distance from the proximal joint centre to the segment
CM. M1,2,3,lfp is the mass of the leg, foot and prosthesis and lumped limb segment, respectively.
Using the parallel axis theorem, the value of I of the foot, leg and prosthesis,
through the CM of that segment, was expressed relative to the mass centroid of the LFP
(CMlfp). As an example, the value of I of the leg segment taken through the CM of the
leg about the yy-axis (Iyyleg) was expressed relative to the CM of the LFP (Iyyleg_CMlfp)
by
(2)
( ) ( )( )( )222
2587.01584.00083.00.6728.20398.0_ +−+−+=lfpleg CMIyy
2.0669.0_ mkgCMIyy lfpleg =
( ) ( )( ) 222
._
++= −−ZZXX
lfpleglfpleglegleglfpleg CMCMCMCMMIyyCMIyy
_______________________________________________________ Appendix F. 267
where Mleg denotes the M of the leg, CMleg and CMlfp denote the location of the
mass centroid of the leg and LFP respectively. Superscript x and z denotes the x and z-
axes. Numeric values were for these variables were obtained from Table F.1.
Using the same method, the value of Iyy of the foot and prosthesis/shoe
segments through the CM of the LFP was determined to be 0.0376 kg.m2 and 0.0560
kg.m2, respectively.
The value of I of the LFP through the mass centroid was given by the sum of the
values of I of the foot, leg and prosthesis through the CM of the LFP. The value of I of
the 'lumped' leg, foot and prosthesis through the mass centroid of the LFP was 0.1605
kg.m2.
A complete set of anthropometric characteristics of the combined leg, residual
foot and prosthesis/shoe for this Chopart amputee using partial foot model-B are given
in Table F.2.
Table F.2. A complete set of anthropometric characteristics of the 'lumped' leg, foot,
prosthesis and shoe for the affected limb of a single Chopart amputee
The CM of the LFP was expressed relative to the knee joint local coordinate system and the value of I
about the yy axis through the mass centroid of the LFP. N/O denotes parameters not obtained.
anth. Volume
(l)
Mass
(kg)
CMx
(m)
CMy
(m)
CMz
(m)
Ixx
(kg.m2)
Iyy
(kg.m2)
Izz
(kg.m2)
lfp N/O 4.7052 0.0083 0 -0.2587 N/O 0.1605 N/O
F.4 Transformation of the mass centroid location between the local/joint
and global coordinate systems
To this point, the location of the mass centroid of each isolated limb segment
and of the 'lumped' segments has been described in x, y, z coordinates relative to the
joint or local coordinate systems (LCS). Prior to calculating joint moments,
transformations between the LCS and the global or laboratory coordinate system (GCS)
_______________________________________________________ Appendix F. 268
were undertaken using two different methods depending on whether the segment's CM
was located in the sagittal mid-line between the segment's end points, or in some other
location not on the sagittal mid-line.
For example, the thigh segment's CM is located in x, y, z coordinates from the
hip joint's LCS (0, 0, -0.1803) indicating that CM is located in the sagittal mid-line of
the segment (x = 0 and y = 0) but displaced inferiorly along the segment's z-axis (z = -
0.1803). The location of the thigh segment's CM in the GCS can be calculated by firstly,
expressing the location of the CM as a proportion of the segment length. So if the thigh
segment was 0.41m in length, the location of the mass centroid could be expressed as a
coefficient of the segment length given by the location of the CM in along the z-axis
divided by the segment length, which would equal 0.4398. Thus indicating that the
location of the thigh segment's CM was 43.98% of the length of the segment from the
proximal joint centre. The location of the thigh segment's centre of mass in the GCS can
then given by
(3)
where CMthighX,Z described the position of the CM of the thigh segment in the CGS
along the X and Z-axes. Hx,z and Kx,z describe the position of the hip and knee joint
along the X and Z-axes in the GCS. i is the increment of time
When the segment's CM is not located along the segment's mid-line, as would be
the case for the LFP or the foot segment, then the location of the segment's CM in the
GCS was calculated using a simple transformation matrix. Whereby the location of the
mass centroid was referenced to the LCS and in turn, was referenced back to the GCS.
The only additional information required was the angle of the segment with respect to
the horizontal (GCS).
As an example, the CM of the LFP previously calculated of the Chopart
amputee was located in x, y, z coordinates from the knee joint's LCS at (0.0083, 0, -
0.2587) and is depicted in Figure F.2.
( ) ( ) ( ) ( )( )( )iKiHiHiCM xxxX
thigh −−= .4389.0
( ) ( ) ( ) ( )( )( )iKiHiHiCM zzzZ
thigh −−= .4389.0
_______________________________________________________ Appendix F. 269
If the angle of the LFP segment was 106.46 degrees from the horizontal (Figure
F.2.) then the CM of the LFP in terms of the GCS could be calculated as follows
(4)
where CMlfpX,Z describes the location of the segment's mass centroid with
respect to the GCS and CMlfpx,z describes the location of the segment's mass centroid of
the LFP with respect to the LCS. The value of θθθθ describes the rotation of the LCS with
respect to the GCS and was given by the segment angle, with respect to the horizontal,
less 90 degrees. The segment angle was 106.46 θθθθ = 16.46. KX,Z describes the 2D
coordinates of the knee joint in the GCS (Figure F.2).
F.5 Deriving the remaining input data necessary to calculate joint moments
and powers
With the location of the mass centroid expressed relative to the GCS, linear
velocities and accelerations of the mass centroid could now be calculated in the normal
fashion (Winter, 1990). It has been assumed that the remaining input data necessary to
calculate joint moments and powers have been derived and do not require detailed
explanation.
+
−=
Z
X
zlfp
xlfp
Zlfp
Xlfp
K
K
CM
CM
CM
CM.
cossin
sincos
θθ
θθ
( ) ( )( ) ( )
−+
−
−=
5256.0
0196.0
2587.0
0083.0.
46.16cos46.16sin
46.16sin46.16cos
Zlfp
Xlfp
CM
CM
=
2799.0
0616.0
Zlfp
Xlfp
CM
CM
_______________________________________________________ Appendix F. 270
Figure F.2. Depiction of a frame of the gait cycle shortly after heel contact for a
Chopart amputee.
The figure illustrates the LFP segment with the segment's CM described with reference to the knee LCS.
The angle of the LFP segment from the horizontal was 106.46 degrees. GCS denotes the global
coordinate system, LCS the local coordinate system of the knee joint. X,Z are the X and Z-axes in the
GCS. x,z are these axes in the LCS and x',z' when the LCS was rotated back to match the GCS (see knee
joint denoted by K). The location of the knee was given in X and Z coordinates from the GCS.
F.6 Calculating joint moments and powers
A complete inverse dynamic link-segment analysis yields the net muscle
moment at every joint during the time course of movement by analysing each free body
segment typically from the most distal to the most proximal segment. Each free body
segment acts independently under the influence of reaction forces and muscle moments,
which act at either end, plus the forces due to gravity. Of these influences, several are
_______________________________________________________ Appendix F. 271
known including kinematics, anthropometrics and reaction forces at the distal end of the
segment. The unknown influences include the reaction forces at the proximal joint and
the net muscle moment acting on the segment at the proximal joint and are represented
mathematically using the following notation
Known
m mass of the segment
CMx, CMz location of the mass centroid
Io mass moment of inertia taken through the CM
Jxd , Jzd kinematic coordinates describing the location of the distal end of the free
body segment. For the foot segment, these describe the location of the
centre of pressure
Jxp , Jzp kinematic coordinates describing location of the proximal end of the free
body segment
αααα angular acceleration of the segment in the plane of movement
ax, az acceleration of the segment centre of mass
Rxd, Rzd reaction forces acting at the distal end of the segment, usually determined
from a prior analysis of the proximal forces acting on distal segment or for
the foot segment, usually the ground reaction forces
Md net muscle moment acting at distal joint, usually determined from an
analysis of the proximal muscle acting on distal segment
Unknown
Rxp, Rzp reaction forces acting at proximal joint
Mp net muscle moment acting on segment at proximal joint
Several equations are necessary to calculate net joint moments. Proximal
joint reaction forces were given by
(5)xxdxp
xx
amRR
amF
.
.
=−
=∑
_______________________________________________________ Appendix F. 272
(6)
and the proximal joint moment can be derived using
(7)
where equation 7 was taken about the segment mass centroid.
It is valuable to illustrate how the reaction force data from the force plate are
combined with the segment anthropometric and kinematic data to calculate muscle
moments and joint reaction forces. The best way of illustrating this would be through an
example calculation for each of the partial foot models used.
For the 'lumped' foot segment of a Transmetatarsal amputee during mid-stance
(Figure F.3) the following data were obtained using partial foot model-A: αααα = 1.6686
rad/s2 and the value of I through the CM was 0.0096 kg.m2. The remaining input data
has been described in Figure F.3.
zzdzp
zz
amgmRR
amF
..
.
=−−
=∑
∑ = α.IoM
_______________________________________________________ Appendix F. 273
Figure F.3 Free body diagram of a Transmetatarsal amputee at mid-stance modelled
using partial foot model-A .
The centre of pressure (CP) is acting at the floor level. The joint reaction forces (Fx,Fz), linear
accelerations (ax,az), joint moment (Mp), inertia (I), angular acceleration (α), segment mass (m) and
gravity (g) represented, describe the sign convention, where these values are positive, not the actual data
values for this example. The value 'K' denotes the knee joint and values in brackets describes the
kinematic coordinates along the x and z -axes.
_______________________________________________________ Appendix F. 274
The muscle moment at the proximal end of the segment can be calculated by
solving equations 5-7 and substituting the algebraic terms for data described in Figure
F.3. Resolving equations 5-6 yields the proximal joint reaction forces Rxp and Rzp which
were given by
(8)
Using equation 7, the net muscle moment at the proximal (Mp) or ankle moment
(MA) end of the segment was given by
(9)
( )( ) ( )( ) ( )( )( )( ) α
α
..
......
.
opxpxzp
zzpxpxxdzdzdzxd
IMJCMR
CMJRCMJRJCMR
IoM
=+−−
−−−+−
=∑
( )( ) ( )( )( )( ) ( )( )xpxzpzzpxp
xxdzdzdzxdop
JCMRCMJR
CMJRJCMRIM
−+−+
−−−−=
..
......α
( ) ( )( )( )( ) ( )( )
( )( )NmM
M
A
A
9852.38
2274.01975.0.9817.589
...0745.01146.0.5890.141975.02274.0.7447.607
...0745.0.7147.156686.1.0096.0
=
−−+
−+−−
−−=
( ) ( )
( ) ( ) ( )NR
R
NR
R
zp
zp
xp
xp
9817.589
4777.60781.9.8019.11001.0.8019.1
5890.14
7147.156247.0.8019.1
−=
−+−=
=
−−−=
zdzzp
xdxxp
RgmamR
RamR
−+=
−=
..
.
_______________________________________________________ Appendix F. 275
The proximal joint reaction forces (Rxp and Rzp) and the proximal joint muscle
moment (Mp) calculated could then be used as the distal reaction forces (Rxd and Rzd)
and distal joint moment (Md) for the more proximal segment. The distal joint reaction
forces and moment act in the opposite direction on the more proximal segment. As such
a sign change would be required.
For the 'lumped' foot, leg and prosthesis/shoe segment of a Chopart amputee
(Figure F.4) the following data were obtained using partial foot model-B: αααα = -40.2086
rad/s2 and the value of I through the CM of the LFP was 0.1605 kg.m2. The remaining
input data has been described in Figure F.4. The knee joint reaction forces for the
chopart amputee were computed using equations 8 as described by
For the Chopart amputee, the knee joint moment was given by
( ) ( )NR
R
xp
xp
0635.74
3481.253524.10.7052.4
−=
−−=
xdxxp RamR −= .
zdzzp RgmamR −+= ..
( ) ( ) ( )NR
R
zp
zp
1202.119
3053.16281.9.7052.46319.0.7052.4
−=
−+−=
( )( ) ( )( )( )( ) ( )( )xpxzpzzpxp
xxdzdzdzxdop
JCMRCMJR
CMJRJCMRIM
−+−+
−−−−=
..
......α
( ) ( )( )( )( ) ( )( )
( )( )( )NmM
M
K
K
2650.49
0481.00434.0.1202.119
...2859.05280.0.0635.740434.00849.0.3053.162
...02859.0.3481.252086.40.1605.0
−=
−−−+
−−+−−
−−−=
_______________________________________________________ Appendix F. 276
Again these joint reaction force and muscle moment data would be carried over
to the proximal limb segment in the same manner as described in the example using
partial foot model-A.
Figure F.4. Free body diagram of the 'lumped' foot, leg, prosthesis and shoe of a
Chopart amputee just after heel contact modelled using in partial foot model-B.
The centre of pressure (CP) is acting at the floor level. The joint reaction forces (Fx,Fz), linear
accelerations (ax,az), joint moment (Mp), inertia (I), angular acceleration (α), segment mass (m) and
gravity (g) represented, describe the sign convention, where these values are positive, not the actual data
values for this example. The value 'K' denotes the knee joint and values in brackets describes the
kinematic coordinates along the x and z -axes.
______________________________________________________ Appendix G. 277
Physical assessment forms
This appendix contains a copy of the anthropometric measurement forms, joint
range of motion assessment forms and muscle strength test assessment forms used in
this investigation.
Appendix G
______________________________________________________ Appendix G. 278
Data storage and filenames
Path: __________________________
Right: *.anth - ________________ Left: *.anth - _______________
Right: *.bsp - ________________ Left: *.bsp - _______________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
General
Stature (m): _____ Weight (kg): _____ Age: _____
Affected side: ❏ Right ❏ Left
Anthropometric Measurement Form Subject ID:
______________________________________________________ Appendix G. 279
Prosthesis/Orthosis Characteristics
Mass (kg): _____
Position of the CoM (m) - X: _____ Y: _____ Z: _____
Time for 10 cycles (s) - X: _____ Y: _____ Z: _____
Calculated Inertia (kg.m2) - X: _____ Y: _____ Z: _____
Shoe Characteristics
Shoe length (m): _____
Shoe mass (kg): _____
Position of the CoM (m) - X: _____ Y: _____ Z: _____
Time for 10 cycles (s) - X: _____ Y: _____ Z: _____
Calculated Inertia (kg.m2) - X: _____ Y: _____ Z: _____
Combined prosthesis/orthosis and shoe characteristics
Mass (kg): _____
Position of the CoM (m) - X: _____ Y: _____ Z: _____
Time for 10 cycles (s) - X: _____ Y: _____ Z: _____
Calculated Inertia (kg.m2) - X: _____ Y: _____ Z: _____
Anthropometric Measurement Form Subject ID:
______________________________________________________ Appendix G. 280
Right Foot Characteristics
Met. head width (m): _____ Heel width (m): _____________(Include WB and NWB measurements)
Intact foot length (m): _____ Amp. foot length (m): _____(for normal use intact foot length )
Lat. Malleolus height (m): _____ Metatarsal height (m): _____
Amp. residuum height (m): _____ Radius of lat. malleolus (m): ____(for normal use 0 )
Ankle A-P (m): _____ Ankle M-L (m): _____
Length of hind foot (m): ______ Length of hind foot AP (m): ____
Left Foot Characteristics
Met. head width (m): _____ Heel width (m): _____(Include WB and NWB measurements)
Intact foot length (m): _____ Amp. foot length (m): _____(for normal use intact foot length )
Lat. Malleolus height (m): _____ 1st Metatarsal height (m): _____
Amp. residuum height (m): _____ Radius of lat. malleolus (m): ____(for normal use 0 )
Ankle A-P (m): _____ Ankle M-L (m): _____
Length of hind foot (m): ______ Length of hind foot AP (m): ____
Anthropometric Measurement Form Subject ID:
______________________________________________________ Appendix G. 281
Right Leg Characteristics
Leg circumferences (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Leg M-L measurements (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Leg length (m): _____ Malleolus width (m): _____
Left Leg Characteristics
Leg circumferences (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Leg M-L measurements (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Leg length (m): _____ Malleolus width (m): _____
Anthropometric Measurement Form Subject ID:
______________________________________________________ Appendix G. 282
Right Thigh Characteristics
Thigh circumferences (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Thigh M-L measurements (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Thigh length to GT (m): _____ Thigh length to pubis (m): _____
Width across GT (m) - Soft tissue: _____ No soft tissue: _____
Sex of subject ( Males -1 Females - 0 ) : _____
Left Thigh Characteristics
Thigh circumferences (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Thigh M-L measurements (m):
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Thigh length to GT (m): _____ Thigh length to pubis (m): _____
Anthropometric Measurement Form Subject ID:
________
Left
Subject ID:
ROM assessment form______________________________________________ Appendix G. 283
Right
Hip
Flexion (0-120°)
Extension (0-30°)
Abduction (0-45°)
Adduction (0-30°)
Internal rotation (0-45°)
External rotation (0-45°)
Comments:
Knee
Flexion (0-135°)
Comments:
Ankle
Dorsiflexion (0-20°)
Plantarflexion (0-50°)
Inversion (0-35°)
Eversion (0-15°)
Comments:
___
Le
Muscle strength assessment form
_______________________________________
ft
Hip
Flexion
Extension
Adduction
Abduction
Internal rotation
External rotation
Knee
Flexion
Extension
Ankle
Dorsiflexion
Plantarflexion
Internal rotation
External rotation
Subject ID:
____________ Appendix G. 284
Right
_______________________________________________________Appendix H. 285
Additional results and discussion
Chapter 2: Additional results
H2.1 Bland and Altman plots for assessing agreement between two methods of
measurement
In Chapter 2, paired two tailed t-tests and linear regression analyses comparing
the slope of the regression line to the theoretical line of identity were used to assess the
similarity of body segment parameter (BSP) predicted using the geometric model and
experimental techniques. While these tests provide information about differences
between paired observations and describe the linearity of changes in BSP predicted
using these two techniques, the magnitude of the differences observed is not obvious.
To augment the interpretation of the two basic statistical techniques presented in
Chapter 2, the mean differences between BSP data predicted using the model and
experimental techniques have been presented in Figures H2.1-H2.7 according the
method described by Bland and Altman (1986).
Appendix H
_______________________________________________________Appendix H. 286
Figure H2.1 Differences between modelled and experimentally derived foot mass for
both the normal and amputee samples
Figure H2.2 Differences between modelled and experimentally derived foot volume for
both the normal and amputee samples
-0.25
-0.15
-0.05
0.05
0.15
0 0.5 1 1.5 2
Average foot mass by model and experimental techniques (kg)
Diff
ere
nce
be
twe
en
m
odelle
d a
nd e
xperim
enta
lly
de
rive
d f
oo
t m
ass
(kg
)
Intact sample
Amputee sample
-0.25
-0.15
-0.05
0.05
0.15
0 0.5 1 1.5
Average foot volume by model and experimental techniques (l)
Diff
ere
nce
be
twe
en
m
od
elle
d a
nd
exp
eri
me
nta
lly
de
rive
d f
oo
t vo
lum
e (
l)
Intact sample
Amputee sample
_______________________________________________________Appendix H. 287
Figure H2.3 Differences between modelled and experimentally derived foot CM in the
x direction for both the normal and amputee samples
Figure H2.4 Differences between modelled and experimentally derived foot CM in the
z direction for both the normal and amputee samples
-0.004
-0.002
0
0.002
0.004
0.006
-0.02 0 0.02 0.04 0.06 0.08
Average foot CMx by model and experimental techniques (m)
Diff
ere
nce
be
twe
en
mo
de
lled
and e
xperim
enta
lly d
eriv
ed
CM
x (m
)
Intact sample
Amputee sample
-0.015
-0.01
-0.005
0
0.005
0.01
-0.06 -0.04 -0.02 0
Average foot CMz by model and experimental techniques (m)
Diff
ere
nce
be
twe
en
mo
de
lled
a
nd
exp
eri
me
nta
lly d
eri
ved
C
Mz
(m)
Intact sample
Amputee sample
_______________________________________________________Appendix H. 288
Figure H2.5 Differences between modelled and experimentally derived k about the x-
axis through the CM for both the normal and amputee samples
Figure H2.6 Differences between modelled and experimentally derived k about the y-
axis through the CM for both the normal and amputee samples
-0.06
-0.04
-0.02
0
0.02
0 0.02 0.04 0.06 0.08
Average foot kxx by model and experimental techniques (m)
Diff
ere
nce
be
twe
en
mo
de
lled
and e
xperim
enta
lly d
eriv
ed
k xx (
m)
Intact sample
Amputee sample
-0.06
-0.04
-0.02
0
0.02
0 0.02 0.04 0.06 0.08 0.1
Average foot kyy by model and experimental techniques (m)
Diff
ere
nce
be
twe
en
mo
de
lled
and e
xperim
enta
lly d
eriv
ed
k yy (
m)
Intact sample
Amputee sample
_______________________________________________________Appendix H. 289
Figure H2.7 Differences between modelled and experimentally derived k about the z-
axis through the CM for both the normal and amputee samples
Chapter 3: Additional results and discussion
H3.1 Peak moments and powers observed during stance phase
Peak joint moment and powers generated using a standard and the partial foot
linked-segment models were presented for only swing phase in Chapter 3. These same
data were not presented for stance phase or for the ankle joint given that there were no
significant differences observed between the different linked-segment models. To
augment the results presented in Chapter 3, Tables H3.1-H3.6 describe the magnitude of
peak joint moments and powers observed during both stance and swing phase for the
hip, knee and ankle.
H3.2 Influence of anthropometry on joint moments and powers
Clinical interpretations of the joint moment profiles provide useful information
about the causes of movement. However, their usefulness for observing how
-0.04
-0.02
0
0.02
0 0.02 0.04 0.06 0.08 0.1
Average foot kzz by model and experimental techniques (m)
Diff
ere
nce
be
twe
en
mo
de
lled
and e
xperim
enta
lly d
erive
d k
zz
(m)
Intact sample
Amputee sample
_______________________________________________________Appendix H. 290
anthropometric changes affect the net joint moments are limited because only changes
caused by differences in anthropometric data as a whole can be observed. This appendix
detail how the moment equations were manipulated to determine the individual
influences of mass, centre of mass and mass moment of inertia.
Table H3.1 Mean hip joint moment peaks for both the standard and partial foot linked-
segment models
HM denotes hip moment. Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
HM1 (Nm/kg) 1.107
(0.376)
1.144
(0.366)
0.037 -3.3
HM2 (Nm/kg) -0.430
(0.118)
-0.443
(0.114)
-0.013 -3.0
HM3 (Nm/kg) 0.208
(0.041)
0.301
(0.032)
0.093 -44.7
Sample B - without ankle motion
HM1 (Nm/kg) 0.953 0.981 0.028 -2.9
HM2 (Nm/kg) -0.271 -0.249 0.022 8.1
HM3 (Nm/kg) 0.188 0.242 0.054 -28.7
_______________________________________________________Appendix H. 291
Table H3.2 Mean knee joint moment peaks for both the standard and partial foot
linked-segment models
KM denoted knee moment. Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
KM1 (Nm/kg) -0.585
(0.230)
-0.618
(0.240)
-0.033 -5.6
KM2 (Nm/kg) 0.630
(0.248)
0.628
(0.246)
-0.002 0.3
KM3 (Nm/kg) -0.120
(0.019)
-0.129
(0.192)
-0.009 -7.5
KM4 (Nm/kg) 0.116
(0.034)
0.120
(0.034)
0.004 -3.5
KM5 (Nm/kg) -0.195
(0.024)
-0.256
(0.026)
-0.061 -31.3
Sample B - without ankle motion
KM1 (Nm/kg) -0.453 -0.473 -0.020 -4.4
KM2 (Nm/kg) 0.297 0.296 -0.001 0.3
KM3 (Nm/kg) -0.790 -0.798 -0.008 -1.0
KM4 (Nm/kg) 0.040 0.066 0.026 -65.0
KM5 (Nm/kg) -0.181 -0.222 -0.041 -22.7
_______________________________________________________Appendix H. 292
Table H.3 Mean ankle joint moment peaks for both standard and partial foot linked-
segment models
AM denotes ankle moment. For the Chopart amputee (Sample-B), ankle moment was not calculated due
to the assumptions of the linked-segment model Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
AM1 (Nm/kg) -0.218
(0.166)
-0.215
(0.166)
0.003 1.4
AM2 (Nm//kg) 0.846
(0.238)
0.848
(0.238)
0.002 -0.2
Table H3.4 Mean hip joint power peaks for both the standard and partial foot linked-
segment models
HP denotes hip power. Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
HP1 (W/kg) 0.894
(0.550)
0.887
(0.546)
-0.007 0.8
HP2 (W/kg) -0.188
(0.126)
-0.175
(0.122)
0.013 6.9
HP3 (W/kg) 0.843
(0.278)
0.919
(0.294)
0.076 -9.0
HP4 (W/kg) 0.079
(0.080)
0.132
(0.160)
0.053 -67.1
Sample B - without ankle motion
HP1 (W/kg) 0.948 0.943 -0.005 3.8
HP2 (W/kg) -0.177 -0.161 0.016 9.0
HP3 (W/kg) 0.431 0.460 0.029 -7.0
HP4 (W/kg) -0.013 -0.016 -0.003 -23.1
_______________________________________________________Appendix H. 293
Table H3.5 Mean knee joint power peaks for both the standard and partial foot linked-
segment models
KP denoted knee power. Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
KP1 (W/kg) -0.817
(0.480)
-0.814
(0.474)
0.003 0.4
KP2 (W/kg) 0.462
(0.210)
0.459
(0.208)
-0.003 0.6
KP3 (W/kg) -0.675
(0.232)
-0.697
(0.234)
-0.022 -3.3
KP4 (W/kg) -0.831
(0.176)
-1.070
(0.278)
-0.239 -28.8
Sample B - without ankle motion
KP1 (W/kg) -0.179 -0.179 0.000 0.0
KP2 (W/kg) 0.147 0.148 0.001 -0.7
KP3 (W/kg) 1.391 1.426 0.035 -2.5
KP4 (W/kg) -0.665 -0.797 -0.132 -19.8
_______________________________________________________Appendix H. 294
Table H3.6 Mean ankle joint power peaks for both standard and partial foot linked-
segment models
AP denotes ankle power. For the Chopart amputee (Sample-B), ankle power was not calculated due to the
assumptions of the linked-segment model Standard deviation reported in brackets.
Inverse Dynamic Model Differences
Standard Partial foot absolute %
Sample A - with ankle motion
AP1 (W/kg) -0.991
(0.480)
-0.993
(0.482)
-0.002 -0.2
AP2 (W/kg) 0.800
(0.296)
0.804
(0.290)
0.004 -0.5
By dissecting the joint moment equations into their component parts it was
possible to gather more information about how the moment equations were affected by
individual changes in segment mass (M), centre of mass (CM) and mass moment of
inertia (I). Joint moments were taken about the proximal end of the free body segments,
to better illustrate the mass-acceleration products of the moment equation. As an
illustrative example, a knee joint moment equation (Eq. 1) has been dissected into its
component parts (Eq 2).
(1)
where Ip is the mass moment of inertia about the sagittal plane axis through the
proximal joint, αααα is the angular acceleration, Ma is the carried over moment about the
ankle, Fzd and Fxd are the carry over forces from the distal segment in the z and x
directions, m is the mass of the leg, g is the acceleration due to gravity, ax and az are
the linear accelerations in the x and z directions, CMx and CMz describe the location of
( )( ) ( )( )( )( ) ( )( )( )( )KxCMxazm
CMzKzaxmKxCMxgm
AzKzFxKxAxFzMIM ddapk
−−
−−−+
−−−−−=
..
.......
......α
_______________________________________________________Appendix H. 295
the mass centroid in the x and z directions, x and z describe the kinematic coordinates of
the ankle and knee markers along the x and z axes in the GCS, and A and K denote the
ankle and knee joints respectively.
(2)
Each of the 7 components or 'terms' of the moment equation (Eq 2), allow the
contributions of I and angular acceleration (term 1), the forces acting at the distal end of
the free body (terms 2 and 4), the carry over moment from the distal segment (term 3),
the acceleration of the segment's mass due to gravity (term 5) and the mass-linear
accelerations (terms 6 and 7) to be independently described.
Joint moments were calculated about the proximal end of the segments using a
standard linked-segment model and the partial foot models, to illustrate how individual
changes in M, CM and I contributed to the differences observed in the swing phase knee
and hip joint moments described in Tables H3.1-H3.6. Data for one illustrative
individual in each sample has been presented and discussed.
Sample-A / Partial foot model-A
The knee extension moment peak observed during initial swing (KM4) was
larger with the use of partial foot model-A, than with the standard model due to small
increases in terms 2 and 4 (Figure H3.1). These terms describe the contributions of the
α.1_ ptermk IM =
( )( )KxAxFzM dtermk −−= .2_
atermk MM −=3_
( )( )AzKzFxM dtermk −−= .4_
( )( )KxCMxgmM termk −+= ..5_
( )( )CMzKzaxmM termk −−= ..6_
( )( )KxCMxazmM termk −−= ..7_
_______________________________________________________Appendix H. 296
joint reaction forces, which were carried over from the ankle joint. These reaction forces
merely reflect the mass-acceleration products of the foot segment, which have changed
due to the increased M of the modelled foot segment (Table 3.6). The linear acceleration
terms were not particularly susceptible to changes in the position of the CM such as that
observed between a standard linked-segment model and partial foot model-A.
Partial foot model-A increased the knee flexion moment peak (KM5)
significantly compared with the standard model (Table H3.2) due to an increased
contribution provided by the ankle joint reaction force in the x direction (term 4). The
ankle joint reaction forces were carried over from the foot to the leg segment and
thereby influenced the knee joint moment. The ankle joint reaction forces were
dominated during swing phase by the linear acceleration profiles due largely to there
being no ground reaction force (Figure H3.1). The increased M of the modelled foot
segment amplified these linear acceleration profiles.
During terminal swing, partial foot model-A increased the hip joint extension
moment peak (HM3) compared to a standard linked-segment model (Table H3.1). The
increased hip extension moment was due to an increase in the knee flexion moment
peak (KM5) (term 3) and the knee joint reaction force (term 4) (Figure H3.2). Changes
in knee flexion moment peak have previously been described. The knee joint reaction
force (in the x direction) is, in part, the product of the M and linear acceleration of the
segment (in the x direction). These parameters were not significantly affected by
changes in modelling approaches. Therefore, changes in the knee joint reaction forces
were due to the increase in the ankle joint reaction forces which was carried over to the
distal end of the leg segment free body. As previously described changes in the ankle
joint reaction force, which inturn affected the knee joint reaction force, were due largely
to an increase in the M of the modelled foot segment.
_______________________________________________________Appendix H. 297
Figure H3.1 Contributions to the knee joint moment equation using a standard linked-
segment model (red lines) and partial foot model - A (blue lines)
Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms
in the legend describe contributions listed in Equation 2.
5 10 15 20 25-20
-15
-10
-5
0
5
10
Components of the knee joint moment for subject 2103-2116A
Swing phase (frames @ 50Hz)
Kne
e M
om
ent
(N
m)
Ext
. >C
om
po
nent
s: R
ela
tive
uni
ts
Knee momentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7
Standard model (red dashed), partial foot model-A (blue solid
_______________________________________________________Appendix H. 298
Figure H3.2 Contributions to the hip joint moment equation using a standard linked-
segment model (red lines) and partial foot model-A (blue lines)
Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms
in the legend describe contributions listed in Equation 2.
5 10 15 20 25-25
-20
-15
-10
-5
0
5
10
15
20
25Components of the hip joint moment for subject 2103-2116A
Swing phase (frames @ 50Hz)
Hip
Mo
me
nt (
Nm
) E
xt. >
Co
mp
one
nts:
Re
lativ
e u
nits
Hip MomentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7
Standard model (red dashed), Partial foot model-A (blue solid)
_______________________________________________________ Appendix H. 300
Sample-B / Partial foot model-B
The knee joint moment peaks (KM4 and KM5) were significantly different
between a standard linked-segment model and partial foot model-B (Table 3.8). The
increased knee extension moment peak observed during initial swing (KM4) was due to
the increased value of I of the lumped leg, foot and prosthesis/shoe with partial foot
model-B compared to the leg only segment in the standard linked-segment model
(Figure H3.3). The increase increased value of I was offset by a reduction in the
contributions provided by terms 4-7 (Figure H3.3).
The reduced contributions of terms 5, 6 and 7 toward the knee extension
moment peak (KM4) were largely the result of increased M of the lumped leg, foot and
prosthesis/shoe segment compared to the leg only segment in the standard model.
However, for terms 6 and 7, there were increases in the linear accelerations of the
modelled leg, foot and prosthesis/shoe segment compared to the standard segment as
well as small increases in the moment lever-arms (< 1 cm).
The changes observed in term 4 were the result of differences in the way the
segments were modelled with partial foot model-B compared to a stanrard model. In a
standard linked-segment model, the ankle joint reaction forces provide the input at the
distal end of the leg segment free body, however, for partial foot model-B the leg, foot
and prosthesis were modelled as a single segment and the ground reaction forces act at
the distal end of this free body. For partial foot model-B, the impact of term 4 was
negligible during swing phase when there is no ground reaction force. In the standard
model, when the ground reaction force is zero, term 4 is dominated by the mass-
acceleration terms.
The knee flexion moment peak observed during terminal swing (KM5) was
largely the result of an increase in the value of I of modelled leg segment. However
decreases in the contributions provided by terms 4, 5 and 6 were also evident
(FigureH3.3). The mechanisms by which these terms affect the knee flexion moment
have previously been described with reference to the swing phase knee extension
moment peak (KM4).
_______________________________________________________ Appendix H. 301
Figure H3.3 Contributions to the knee joint moment equation using a standard linked-
segment model (red lines) and partial foot model - B (blue lines)
Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms
in the legend describe contributions listed in Equation 2.
5 10 15 20 25-30
-20
-10
0
10
20
30Components of the knee joint moment for subject 3004-1102A
Swing phase (frames @ 50Hz)
Mo
me
nt: (
Nm
) E
xt. >
Co
mp
one
nts
: Re
lativ
e u
nits
Knee momentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7
Standard model (red dashed), Partial foot model -B (blue solid)
_______________________________________________________ Appendix H. 302
Figure H3.4 Contributions to the hip joint moment equation using a standard linked-
segment model and partial foot model - B
Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms
in the legend describe contributions listed in Equation 2.
5 10 15 20 25-20
-15
-10
-5
0
5
10
15
20
25Components of the hip joint moment for subject 3004-1102A
Swing phase (frames @ 50Hz)
Hip
Mo
me
nt (
Nm
) E
xt. >
Co
mp
one
nts
: Re
lativ
e u
nits
Hip momentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7
Standard model (red dashed), partial foot model-B (blue solid)
_______________________________________________________ Appendix H. 303
The hip joint extension moment peak (HM3) observed during terminal swing
phase reflects the increased flexion moment observed at the knee during this time
(Figures H3.3 and H3.4). The influence of the knee joint moment are exerted distally on
the free body of the thigh segment by way of the carry over of the knee joint moment
(term 3).
The joint moment profiles calculated using partial foot model-A, were
dominated by the additional M of the modelled foot segment and in terms of the
moment equation, the additional M was reflected in the mass-acceleration products. In
turn, these joint reaction forces affected the knee and hip joint moment calculations. The
small differences in the location of the mass centroid and value of I between modelling
approaches seemed to be of little consequence. Hence, only the M of the modelled
segment would be of major concern with this modelling approach (partial foot model-
A).
The knee joint moment patterns, observed with partial foot model-B compared
to the standard linked-segment model, reflected not only changes in the M of the
modelled segments but the influence of I proved dominant during both initial and
terminal swing. Differences in the location of the segment's mass centroid were also
evident. Differences in the hip extension moments observed during terminal swing were
exclusively due to the carry over knee joint moments. With this modelling approach it
seems imperative that not only the M, but also the location of the mass centroid and the
value of I be adequately depicted.
The differences in joint powers were due to changes in the joint moment
profiles. There were no differences evident in the angular velocities of the 'lumped'
segments used in the partial foot models compared to the standard model.
_______________________________________________________ Appendix I. 304
Gait reports
This appendix contains a gait report for the left limb of subject 1004-1307A as
an illustration of the reports generated bilaterally for each subject. The remaining gait
reports have been included on CD.
Appendix I
____
Da
Ca
Am
Af
Gait Analysis Reporting Form
______________________________________
te of amputation: 4 December 1987
use of amputation: ❏❏❏❏ PVD ❏❏❏❏ Trauma ❏❏❏❏
Other: Gangrene secondary to Frostbite
putation Level: MTP ❏❏❏❏ TMT ❏❏❏❏Lisfr
Other:
fected side : Right Left
Subject ID: 1004-1307A
DM Gangrene other
anc ❏❏❏❏ Chopart ❏❏❏❏ other
Skin Condition: Intact ❏❏❏❏ Lesions :
Sensation : Intact ❏❏❏❏ Impaired :
Footware: ❏❏❏❏ Boots ❏❏❏❏ Dress shoes Runners ❏❏❏❏ other
Other:
Gait aids: None ❏❏❏❏ 1 x single point stick ❏❏❏❏ 2 x single point stick ❏❏❏❏ other
Other:
Device category : ❏❏❏❏ Prosthesis Orthosis
Device type: ❏❏❏❏ Clamshell PTB ❏❏❏❏ Below ankle socket
❏❏❏❏ AFO ❏❏❏❏ Toe filler other
Other: Bilateral shoe inserts
Describe device: Full length shoe insert with polypropylene sole, EVA upper andtoe block, silicone pad under the Metatarsal ends. Orthosis covered in leather.
_____________ Appendix I. 305
____
Amp
Left
Degs
136
20
39
22
37
33
147
20
45
20
8
Gait Analysis Reporting Form
______________________________________
utated limb: Right Left
Joint range of motio
.Hip
Flexion (0-120°)
Extension (0-30°)
Abduction (0-45°)
Adduction (0-30°)
Internal rotation (0-45°)
External rotation (0-45°)
Comments:
Knee
Flexion (0-135°)
Comments:
Ankle
Dorsiflexion (0-20°)
Plantarflexion (0-50°)
Inversion (0-35°)
Eversion (0-15°)
Comments:
Subject ID: 1004-1307A
_____________ Appendix I. 306
n Right
Degs.
135
20
42
21
39
30
146
22
50
22
5
____
Amp
Left
5
5
5
5
5
5
5
5
5
5
5
5
Gait Analysis Reporting Form
______________________________________
utated limb: Right Left
Oxford Manual Muscle
Hip
Flexion
Extension
Adduction
Abduction
Internal rotation
External rotation
Knee
Flexion
Extension
Ankle
Dorsiflexion
Plantarflexion
Internal rotation
External rotation
Subject ID: 1004-1307A
_____________ Appendix I. 307
strength test Right
5
5
5
5
5
5
5
5
5
5
5
5
____
00
50
100
00
50
100
EM
G a
mpl
itude
(%
MM
T)
00
50
100
Gait Analysis Reporting Form
______________________________________
20 40 60 80 100
Biceps Femoris (-)
Active
20 40 60 80 100
Tibialis Anterior (-)
20 40 60 80 100
Gastrocnemius medial head (-)
Gait Cycle [%]
Threshold = 2.5%MMT
Threshold = 2.5%MMT
Subject ID: 1004-1307A
_____________ Appendix I. 308
Event Active period(% GC)
Mean(MMT%)
BF1 1-5 5.7791BF2 78-100 7.0493
TA1 1-6 12.9584TA2 56-79 4.7813TA3 88-100 10.7459
GM1 20-45 15.2594
____
5
10
5
10
EM
G a
mpl
itude
(%
MM
T)
5
10
Gait Analysis Reporting Form
______________________________________
0 20 40 60 80 1000
0
0Vastus Lateralis (-)
Active
0 20 40 60 80 1000
0
0Gastrocnemius Lateral Head (-)
0 20 40 60 80 1000
0
0Soleus (-)
Gait Cycle [%]
Subject ID: 1004-1307A
_____________ Appendix I. 309
Event Active period(% GC)
Mean(MMT%)
VL1 1-14 10.2401VL2 90-100 9.5480
GL1 24-46 11.4716GL2 90-100 4.8562
SOL1 1-46 9.3923SOL2 95-100 7.7363
____
n =
SoleuGastGastTibiaBiceVast
00
20
40
60
00
10
20
30
40
EM
G -
Nor
mal
ised
to
100%
MM
T
00
5
10
15
20
25
Gait Analysis Reporting Form
______________________________________
❏❏❏❏4 ❏❏❏❏5 6 ❏❏❏❏7 ❏❏❏❏ Other(n = _ )
CV(%) s 59.7517
rocnemius Lateral Head 82.9666rocnemius Medial Head 75.0217lis Anterior 64.6902
ps Femoris Long Head 77.2593us Lateralis 73.8389
0
10
20
30
40
50
0
10
20
30
40
50
EM
G -
Nor
mal
ised
to
100%
MM
T
20 40 60 80 100
Gastrocnemius Medial head (-)
Gait Cycle [%]
20 40 60 80 100
Tibialis Anterior (-)
20 40 60 80 100
Biceps Femoris (-)
0
10
20
30
40
Subject ID: 1004-1307A
_____________ Appendix I. 310
Variability CMC
0.65880.59270.76450.71740.71890.7009
0 20 40 60 80 100
Soleus (-)
Gait Cycle [%]
0 20 40 60 80 100
Gastrocnemius lateral head (-)
0 20 40 60 80 100
Vastus Lateralis (-)
EMG
____
n =
Side
Notefromdeterprese
00
20
40
60
80
100
00
20
40
60
80
100
EM
G a
mpl
itude
(%
MM
T)
00
20
40
60
80
100
Gait Analysis Reporting Form
______________________________________
❏❏❏❏4 ❏❏❏❏5 6 ❏❏❏❏7 ❏❏❏❏ Other(n = _ )
analysed : ❏❏❏❏Right Left
: The threshold for Biceps Femoris Long Head 5% MMT to 2.5% MMT so that reasonamined in line with those expected from visuanted.
0
20
40
60
80
100
0
20
40
60
80
100
EM
G a
mpl
itude
(%
MM
T)
20 40 60 80 100
Gastrocnemius medial head (-)
Gait Cycle [%]
20 40 60 80 100
Tibialis Anterior (-)
20 40 60 80 100
Biceps Femoris (-)
0
20
40
60
80
100Threshold = 2.5%MMT
Threshold = 2.5%MMT
Subject ID: 1004-1307A
_____________ Appendix I. 311
and Tibialis Anterior were reducedble muscle on/off times could bel inspection of multiple MMT data
0 20 40 60 80 100
Soleus (-)
Gait Cycle [%]
0 20 40 60 80 100
Gastrocnemius lateral head (-)
0 20 40 60 80 100
Vastus Lateralis (-)
Active
____
-2
2
4
(Deg
.) F
lex.
>
-2
2
4
6
8
(Deg
.) F
lex.
>
-4
-2
2
(Deg
.) F
lex.
>
Gait Analysis Reporting Form
______________________________________
0 20 40 60 80 100
0
0
0
0
Hip Angle (-)
0 20 40 60 80 1000
0
0
0
0
0Knee Angle (-)
0 20 40 60 80 1000
0
0
0
Ankle Angle (-)
Gait Cycle [%]
Subject ID: 1004-1307A
_____________ Appendix I. 312
Event Time(% GC)
Angle(Deg.)
HA1 1 29.1522HA2 52 -16.9413HA3 60 -9.0434HA4 88 29.8551HA5 100 29.2131
KA1 1 7.6548KA2 14 25.0611KA3 60 38.7125KA4 72 66.2778KA5 100 6.8935
AA1 1 4.6722AA2 8 -5.5039AA3 48 14.5531AA4 60 -3.7889AA5 65 -10.9731AA6 100 3.5277
____
Gait Analysis Reporting Form
______________________________________
0 20 40 60 80 100-1
0
1
2
Hip Moment (-)
(Nm
/kg)
Ext
. >
0 20 40 60 80 100
-1
0
1
Knee Moment (-)
(Nm
/kg)
Ext
. >
0 20 40 60 80 100
0
1
2
Ankle Moment ()
Gait Cycle [%]
(Nm
/kg)
Ext
. >
Subject ID: 1004-1307A
_____________ Appendix I. 313
Event Time(% GC)
Moment(Nm/kg)
HM1 3 1.1345HM2 50 -0.5050HM3 93 0.2786
KM1 2 -0.5330KM2 13 0.8806KM3 45 -0.5023KM4 59 0.0535KM5 93 -0.2547
AM1 6 -0.1699AM2 49 1.5198
____
-
(W/k
g) G
en.
>
-
-
(W/k
g) G
en.
>
-
(W/k
g) G
en.
>
Gait Analysis Reporting Form______________________________________
0 20 40 60 80 1001
0
1
2
Hip Power (-)
0 20 40 60 80 100
2
1
0
1
2Knee Power (-)
0 20 40 60 80 1002
0
2
4
6Ankle Power ()
Gait Cycle [%]
Subject ID: 1004-1307A
_____________ Appendix I. 314
Event Time(% GC)
Power(W/kg)
HP1 15 0.2380HP2 47 -0.4099HP3 62 0.7440HP4 93 0.0645
KP1 10 -1.3152KP2 18 0.7839KP3 59 -0.3139KP4 90 -1.2004
AP1 43 -1.0329AP2 54 2.5126
____
0
-2
0
2
(N/k
g)
0
0
5
10
(N/k
g)
0
0
50
100
(%IF
L)
Gait Analysis Reporting Form______________________________________
E
20 40 60 80 100
Fx (-)
20 40 60 80 100
Fz (-)
20 40 60 80 100
Ax (-)
Gait Cycle [%]
Subject ID: 1004-1307A
_____________ Appendix I. 315
vent Time(%GC)
Force(N/kg)
CoP(%SL)
FX1 12 -2.4817FX2 52 2.1960
FZ1 14 11.8505FZ2 27 6.9045FZ3 47 11.2067
AX1 1 0AX2 59 95.01
____
S
In
PFL
Gait Analysis Reporting Form
______________________________________
Anthropometric d
tature (m) : 1.744 Weight (kg): 64.85
verse dynamic model: ❏ Chopart
Centre of MassVolume
(ltrs.)
Mass
(kg.) X
(m)
Y
(m)
Z
(m)
Foot 0.7036 0.7653 0.0411 0 -0.03
Leg 2.7722 3.0208 0 0 -0.16
Thigh 7.1794 7.6754 0 0 -0.19
PS - 0.5640 0.0720 0 -0.06
FPS - 1.3293 0.0542 0 -0.04
LFPS - - - - -
S : Prosthesis or orthosis and shoePS : combined foot, prosthesis/orthosis and shoe aFPS : combined leg, foot, prosthesis/orthosis and sh
Subject ID: 1004-1307A
_____________ Appendix I. 316
ata
Age (years): 40
Normal / Orthotic
Mass moment of Interia
X
(kg.m2)
Y
(kg.m2)
Z
(kg.m2)
63 0.0007 0.0025 0.0057
83 0.0377 0.0383 0.0038
17 0.1115 0.1144 0.0201
00 - 0.0050 -
63 - 0.0080 -
- - -
s a lumped segmentoe as a lumped segment
____
0
-2
0
2
(N/k
g)
0
0
50
100
(%IF
L)
Gait Analysis Reporting Form______________________________________
Variability
CV(%) CMCFx 1481.2 0.9866Fy 60.1833 0.9283Fz 9.1150 0.9903
CV(%) CMCAx 18.5937 0.968
50 100
Fx (.)
Gait Cycle [%]0 50
-1
0
1
Fy(.)
Gait Cycle [%]
(N/k
g)
50 100
Ax (-)
Gait Cycle [%]0 50
-0.2
0
0.2
0.4
0.6
Ax (.)
Gait Cycle [%]
(M)
Subject ID: 1004-1307A
_____________ Appendix I. 317
7
100 0 50 100
0
5
10
Fz (.)
Gait Cycle [%]
(N/k
g)
100
____
Gait Analysis Reporting Form
______________________________________
Vari
Angle
CV(%) CMC CV(
Ankle 34.6081 0.9546 18.00
Knee 6.7996 0.9925 816.6
Hip 10.8250 0.9948 327.2
Subject ID: 1004-1307A
ability
Moment Power
%) CMC CV(%) CMC
40 0.9861 476.8895 0.9406
160 0.9686 213.3956 0.9336
473 0.9496 114.4886 0.9166
_____________ Appendix I. 318
____
Gait
Stanc
Swin
Stanc
Swin
Cont
Strid
Strid
Walk
Walk
Cade
CoP
CoP
Sing
Sing
Doub
Doub
Gait Analysis Reporting Form
______________________________________
Mean SD
cycle (s) 1.1517 0.0075
e time (s) 0.6933 0.0103
g time (s) 0.4583 0.0075
e time (%GC) 60.2014 0.6908
g time (%GC) 39.7986 0.6908
ralateral HC (%GC) 49.9014 0.4137
e length (m) 1.5591 0.0106
e length / stature 0.8939 0.0060
ing velocity (m/s) 1.3538 0.0089
ing velocity/stature 0.7762 0.0051
nce (steps/minute) 104.2005 0.6821
excursion (m) 0.3021 0.0024
excursion (%SL) 102.0608 0.8153
le support (s) 0.4762 0.0118
le support (%GC) 40.9823 0.8212
le support (s) 0.1099 0.0095
le support (%GC) 9.4651 0.8510
Subject ID: 1004-1307A
_____________ Appendix I. 319
Range Min Max
0.0200 1.1400 1.1600
0.0200 0.6800 0.7000
0.0200 0.4500 0.4700
1.7392 59.1304 60.8696
1.7392 39.1304 40.8696
1.2122 49.3976 50.6098
0.0252 1.5446 1.5698
0.0144 0.8857 0.9001
0.0243 1.3431 1.3674
0.0139 0.7701 0.7840
1.8149 103.4483 105.2632
0.0065 0.2993 0.3058
2.1959 101.1149 103.3108
0.0296 0.4601 0.4897
1.9555 39.6619 41.6174
0.0247 0.1021 0.1268
2.2548 8.6785 10.9333
_____
-20
0
20
40
(Deg
.) F
lex.
>
-20
0
20
40
60
80
(Deg
.) F
lex.
>
-40
-20
0
20
(Deg
.) F
lex.
>
Gait Analysis Reporting Form_____________________________________
20 40 60 80 100
Hip Angle (-)
20 40 60 80 100
Knee Angle (-)
20 40 60 80 100
Ankle Angle (-)
Gait Cycle [%]
20 40 60-1
0
1
2
Hip Moment (-)
(Nm
/kg)
Ext
. >
20 40 60
-1
0
1
Knee Moment (-)
(Nm
/kg)
Ext
. >
20 40 60
0
1
2
Ankle Moment (-)
(Nm
/kg)
Ext
. >
Gait Cycle [%]
Subject ID: 1004-1307A
Gait cycle (sec) : 1.1517 Side analysed : ❏❏❏❏Right Left
Stance time (sec) : 0.6933 Stance time (%GC) : 60.2014Swing Time (sec) : 0.4583 Swing time (%GC) : 39.7986
Single support (sec) : 0.4762 Single support (%GC) : 40.9823Double support - HC (sec) : 0.1099 Double support - HC (%GC) : 9.4651
Cadence (Steps/min) : 104.2005 Contralateral HC (%GC) : 49.9014
Stride length (m) : 1.5591 Stride length / Stature : 0.8939Walking velocity (m/s) : 1.3538 Walking velocity/ Stature: 0.7762CoP excursion (m): 0.3021 CoP (%SL): 102.0608
Ensembled average n = ❏❏❏❏4 ❏❏❏❏5 6 ❏❏❏❏7 ❏❏❏❏ Other (n = _ )
_____________ Appendix I. 320
80 100
80 100
80 100
20 40 60 80 100-1
0
1
2
Hip Power (-)
(W/k
g) G
en.
>
20 40 60 80 100
-2
-1
0
1
2Knee Power (-)
(W/k
g) G
en.
>
20 40 60 80 100-2
0
2
4
6Ankle Power (-)
Gait cycle [%]
(W/k
g) G
en.
>
________________________________________________________ References. 321
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