proposal of a passive marker set for paediatric gait …€¦ · the gait lab research group....

PROPOSAL OF A PASSIVE MARKER SET FOR PAEDIATRIC GAIT DATA ANALYSIS

Hemen Paru1 Shukla

A thesis submitted in cooformity with the requirements for the degree of Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering Institute of Biomaterials and Biomedical Engineering

University of Toronto

O Copyright by Hemen Panil Shukla 2000

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Proposa2 of a passive marker set for paediatric gai? data anaiysis Hemen P a d Shukla Master of Applied Science, 2000 Graduate Department of Mechanical and Industriai Engineering Institute of Biornaterials and Biomedical Engineering University of Toronto

The purpose of this study was to propose a static and a dynamic marker set for gait data

analysis. A test of marker placement repeatability was perfonned to determine the

precision with which markers could be placed over specific matornical landmarks. Also,

a cluster of eight markers was placed on both the thigh and shank to determine which

markers contributed the most to the ngidity of each cluster. The results showed that

marker placement on the pelvis, in general, is more variable than marker placement for

other segments. The results of the cluster analysis identified three markers for both the

shank and thigh that could be used for the collection of gait data. The methodology

represents a novel approach in the irnplernentation of a passive marker set. This approach

can be used to identify marker placement locations that are least susceptible to movement

artefact in different dinical populations.

ACKNOWLEDGEMENTS

First and foremost, I would iike to thank my parents and my brother. Their unparalleled

love and support helped me through the really tough times. Also, 1 extend thanks to the

rest of my farnily. 1 appreciate them more now than 1 ever have before.

I would like to thank Drs. Naumann and Cleghom for believing in me. Switching to

engineering was a difficult and challenging option, and 1 thank them both for letting me

accept this challenge.

This thesis would never have been completed if it weren't for the help of the people in

the Gait Lab research group. Thanks AIan for your help with just about everything. 1

appreciate al1 of the time you spent gohg over and over and over things until they hal ly

clicked. Thanks Kim for helping me Iearn about gait data collection and about what it

takes to be a true engineer. Thanks Tom for al1 of your help with the optimization and the

statistical analysis. Finally, th& Jan, my roomrnate and fkiend, as you are probably the

only person who could relate to my stniggles and hs t r~ t ions with certain parts of the

project.

1 would like to thank the members of the Rehabilitation Engineering Department at

BlooMew Macmillan Centre. Specifically, thanks to Kent for his help with the statistics,

and to Dayle for al1 of her help in making the past two years enjoyable.

1 would like to thank a i l of my fiiends, both in and out of Toronto. 1 can't emphasize how

much 1 appreciate ail of your support.

Finally, I would Like to thank the Natural Sciences and Engineering Research Council of

Canada, The Department of Mechanical and Industrial Engineering at University of

Toronto, and to the Bloorview Childrens Hospital Foundation for their generous financial

support.

TABLE OF CONTENTS

ABSTRACT . * .................................................................. ACKNOWL,ED GEMENTS II ... ..................................................................... TABLE OF CONTENTS rii

..................................................................... LIST OF APPENDICES vi . . ........................................................................... LIST OF FIGURES mi ... .......................................................................... LIST OF TABLES ..vm

...................................................... 1.0 THESIS OVERVIEW I 1.1 PROBLEM ........................................................................ 1

.................................................................. 1.2 MOTIVATION 2 1.3 CLINICAL SIGNIFICANCE.. ................................................ 2 1.4 PURPOSE ........................................................................ 3 1.5 OBJECTTVES .................................................................... 3

............................................................. 1.6 CONTRISUTIONS 4 ................................................... 1.7 CHAPTER DESCRIPTION 4

2.0 REVIEW OF LITERATURE ............................................. 6 2.1 GAIT ANALYSIS ............................................................... 6

2.1.1 htroduction ......................................................... 6 2.1.2 Anatomical Terminology .......................................... 6

................................................... 2.1.3 Gait Terminology 7 ..................................................... 2.1.4 Instrumentation 14

............................ 2.1.4.1 Video-bused motion analysis 14 2.1.5 Gait Parameters ..................................................... 16

................................. 2.1.5. I Guit and Cerebral Pafsy 16 2.1.6 Summary ............................................................ 20

2.2 M E C m C A L MODELING ................................................. 21 2.2.1 Introduction ......................................................... 21 2.2.2 Segments ............................................................ 21

......................................... 2.2.2.1 Reference Frames 22 ................................. 2.2.2.1.1 Euler Method 27

2.2.2.2 Ana to mical Reference Frames ........................... 29 2.2.2.3 Motion Between Segments .............................. -31

2.2.3 Static and Dynamic Marker Sets ................................. 38 2.2.4 Marker Placement Repeatability ................................. 40 2.2.5 Summary ............................................................ 41

......................... 2.3 SIUN MOVEMENT ARTEFACT .............. .... 4 1 2.3.1 Introduction ......................................................... 41 2.3.2 Memernent Techniques ......................................... 42 2.3.3 Measuring Movement Artefact ................................... 42 2.3.4 Summary ............................................................ 48

2.4 MARKER CLUSTERS AND NON-RIGID MOVEMENT ............... 49 ......................................................... 2.4.1 Introduction 49

2.4.2 The Inertia Tensor .................................................. 49 ........................... 2.4.2.1 Eigenvalues and Eigenveciors 52

2.4.3 Point Cluster Technique ........................................... 53 2.4.3.1 Optirnizution ................................................ 57

2.4.4 Other Optimization Approaches in Gait Studies ............... 58 2.4.5 Summary ............................................................ 61

2.5 SUMMARY AND CONCLUSIONS ......................................... 61 2.5.1 Sources of Error .................................................... 51 2.5.2 Implications ......................................................... 63

3 . 0 METHODOLOGY ......................................................... 64 3.1 INTRODUCTION ............................................................... 64 3.2 HUMAN MOVEMENT LABORATORY ................................... 64 3.3 PROPOSED MARKER SET ................................................... 66 3.4 MARKER PLACEMENT REPEATABILITY .............................. 69

3.4.1 Data Collection ..................................................... 69 3.4.2 Data Analysis ....................................................... 74

....... 3.5 CLUSTER METHOD TO DETERMINE MASS WEIGHTINGS 75 3 .5 . 1 Data Collection ..................................................... 75 3.5.2 Data Analysis ....................................................... 76 3.5.3 Optimization ........................................................ 81

3.6 SUBJECTS ....................................................................... 84 3.7 SUMMARY ...................................................................... 85

4.0 MARKER PLACEMENT REPEATABILITY ........................ 86 4.1 INTRODUCTION ............................................................... 86 4.2 SUBJECTS ....................................................................... 86 4.3 RESULTS ........................................................................ 86 4.4 DISCUSSION .................................................................... 89 4.5 SUMMARY ...... ,. .............................................................. 94

5 . 0 CLUSTER ANALYSIS ................................................... 95 5.1 INTRODUCTION .............................................................. -95 5.2 RESULTS ........................................................................ 95

5.2.1 Thigh Cluster ....................................................... 95 5.2.2 Shank Cluster ....................................................... 97 5.2.3 Validation Test ...................................................... 99

5.3 DISCUSSION .................................................................... 100 5.3.1 Thigh Cluster ....................................................... 100 5.3.2 Shank Cluster ....................................................... 105

...................................................................... 5.4 SUMMARY 108

6.0 RECOMMENDATIONS AND CONCLUSIONS ..................... 6.1 RECOMMENDATIONS .......................................................

...................................................... 6 . 1.1 Static Markers 6.1.2 Dynamic Markers ...................................................

6.2 FUTURE WORK ................................................................ 6.3 CONCLUSIONS ................................................................

REFERENCES ................................................................................ 115 APPENDICES ................................................................................ i l 9

LIST OF APPENDICES

A Custom Programs Written in MATLAB .......................................... 119 B Ethical Approval and Consent Fom ............................................... 133

LIST OF FIGURES

Anatomical planes of the body ..................................................... 8 Directional information used in anatomy ......................................... 8 The lateral view (a) and medial view (b) of the pelvis .......................... 8 The antenor (A) and postenor (B) view of the femur ........................... 9 The anterior (A) and posterior (B) view of the tibia and fibula ................ 10 The dorsal (A). plantar (B) and lateral (C) views of the bones of the foot ... 1 I The motion of segments in thc anatamical planes ............................... 12

........................................................................ The gait cycle -13 Generated kinematic and kinetic gait curves ..................................... 18

..................................... Generated kinematic and kinetic gait curves 19 Points A, B. C and D. and the GCS for the system .............................. 23 The position vector of each point in the GCS .................................... 23 Creation of a LCS from points B. C and D. and the transformation

.......................................................................... kom the GCS 24 ............................................... The position vector of A in the LCS 24

Rotations about axes ................................................................. 30 An example of simulated annealhg ................................................ 60 Carnera setup in the Human Movement Laboratory ............................. 65 The curent marker set used for gait data collection ............................. 67 The proposed rnarker set for gait data collection ................................. 68 Flow chart of the data collection methodology for the marker placement . . repeatability study .................................................................... 71 Marker placement locations for the marker placement repeatability shidy ... 72 Thigh and shank marker cluster placement locations for the cluster

......................................................................... analysis study 78 Outhe of data analysis for the cluster method .................................. 80 Marker placement repeatability .................................................... 88 Relation between marker placement and BMI .................................... 91 Marker weightings for the thigh cluster ........................................... 96

.......................................... Marker weightings for the shank cluster 98 Validation test results ................................................................ 100 Cluster analysis on seven thigh markers .......................................... 104 Cluster analysis on seven shank markers .......................................... 107

LIST OF TABLES

Gait parameters ....................................................................... 17 Anatornical locations for the marker placement repeatability study .......... 73 Anatomieal locations for the cluster analysis study .............................. 79 . . ................................................................. Subject information -87 Friedman test summary .............................................................. 88 SNK Post-hoc analysis results ...................................................... 89 Order of variabiiity in marker piacement locations, irom greatest to ieast, in the two studies ..................................................................... 90 Friedman test summary for the thigh markers .................................... 96 SNK post-hoc analysis results for the thigh marken ............................ 96 Friedman test summary for the shank markee ................................... 98 SNK post-hoc analysis results for the shank markers ........................... 98 Results of the Friedman test for the seven marker thigh cluster ............... 104 SNK post-hoc analysis results on the seven marker thigh cluster ............. 104 Results of the Friedman test for the seven marker shank cluster ............... 107 SNK post-hoc analysis results on the seven marker shank cluster ............ 107

THESIS O VER VIE W

1.1 PROBLEM

Gait analysis is used to quanti@ how an individuai waiks. A popular method of video-

based data collection involves taping reflective markers over specific anatomical

landmarks to track the three-dimensional position of body segments during gait. Clinical

applications include studying the effects of various therapies and medical procedures on

children who have waiking problems. It is important to know whether a meaningful

change has occurred to a child's walking as a result of such treatments.

As in any rnethod of data collection, soi:-les of error exist. The largest sources of error in

this type of data collection are due to marker placement and the movement of markers

relative to bony landmarks during movement. Marker placement involves correctly

identifjmg specific anatomical landmarks on body segments. These landmarks are used

in creating a mathematical mode1 of the segments. A marker that is not placed over the

correct anatomical landmark will affect how the associated segment is modeled, and will

ultimately affect the kinematic calculations of the interaction between segments.

The movement of markers relative to the underlying skeletal structure is another large

source of error. The markers are mounted on the skin using adhesive tape. During gait,

these markers are affected by soft tissue movement, such as that of muscles, tendons and

Ligaments. The magnitude of this error varies for different locations on each segment, and

also between segments. Much effort has been expended to quanti@ and manage this

source of error.

1.2 MOTNATION

The motivation for this thesis stems fiom the need to improve the accuracy of gait data

collection. The recent addition of two i n h e d video cameras to the laboratory has

created an oppominity to modiQ our data collection methodology and to reduce the

effects of some errors associated with this type of data collection.

This research was conducted in the Human Movement Laboratory at Bloorview

MacMillan Centre in Toronto, Canada. The centre is primady a children's rehabilitation

institution, whose mission is '70 help children and youth with disabilities and special

needs to achieve their personal best". The laboratory is used to conduct gait analyses on

populations, such as children with cerebral palsy or amputàtions, in order to refine

treatment programs or technologies to assist arnbulation. This study will ultimately

improve the data collection accuracy used to guide treatment for these and other

populations.

The purpose of this study is to develop a method to minimize ewon

associated with the variability in marker placement and the non-rigid

nr ovement of markers resulting front sofi tissue movement.

The work described in this thesis had the following goals:

To quanti@ marker placement repeatability in terms of the precision in Iocating and

placing a marker on the correct anatornical landmark.

To identiS sets of markers used to defme limb segment orientation during gait

through calculating the relative mas weightings of the markers under dynamic

conditions needed to minimize the change in marker cluster ngidity.

To combine these results and implement static and dynamic marker sets for paediatric

gait data collection and analysis.

THESIS O VER VIE W

1.6 CONTRIBUTIONS

This project builds upon existing methods of gait data analysis. The only tnie method to

quanti@ng dynamic marker movement is through the use of pins with markers attached

to them inserted into bones. As this is not a practical option for many laboratones, o u

methodology allows for the minimization of movement artefact without the use of

invasive procedures. AImost any human movement laboratory can implement the

methodology proposed in this study in an effort to understanding marker movement and

improving the accuracy of the data collected.

1.7 CHAPTER DESCRIPTION

Chapter 2 is a review of the relevant literature. Section 2.1 is an overview of gait

anal ysis, including anatomical terminology, gai t termino logy and instrumentation.

Section 2.2 examines mechanical modeling by reviewing static and dynamic marker sets,

modeling of segments and marker replacement

reviewed in Section 2.3. Section 2.4 examines

repeatability. Skin movement artefact is

the concept of a cluster of markers and

non-rigid movement. Moments of inertia and the inertia tensor, eigenvalues, similar

studies, and optimization approaches for data analysis are reviewed. Section 2.5 explores

the implications of the fiterature review to this study and discusses different sources of

error.

THESIS O VER VZEW

Chapter 3 describes the methodology and data analysis approaches of this study,

including marker placement repeatability, rneasuring movement artefact by mass

weightings, and the subjects used in the study. Chapter 4 provides the results of data

collection, Chapter 5 is a discussion of these results, and Chapter 6 lists the conclusions.

Chapter 7 outlines potential future work and recommendations.

2.1 GAIT ANALYSIS

2.1.1 Introduction

Human gait analysis requires a multidisciplinary approach. Different fields of study,

including neurophysiology, kinesiology and biomechanics to name a few, have made

respective contributions to study human motion. This section will identiQ relevant

anatomical and gait terminology, and will descnbe the instrumentation used in gait

anal ysis.

2.1.2 Anaiornical Terminology

An introduction to lower body anatomy is an important foundation for understanding the

methodology of this thesis. The human body is studied in three anatornicai planes:

sagittal, frontal (or coronal) and transverse. niese planes are shown in Figure 2-1 (Inman

et al., 198 1). Figure 2-2 (Thompson and Floyd, 1994) describes directional information in

anatomical tenns.

REWE W OF LITERATURE

Figures 2-3, 2-4, 2-5 and 26 show the pelvis, femur, tibia and fibula, and bones of the

foot, respectively, dong with the associated relevant anatomical landmarks (Swan (ed.),

1983; Tortora and Grabowski, 1993). Anatomical landmarks such as the lateral malleolus

of the fibula (Figure 2-5) that can be palpated are important. By identifjmg relevant

anatomical landrnarks, a mode1 of the segment c m be created. This procedure will be

expanded in Section 2.2.3.

The motion of different body segments, such as the pelvis, the thigh (femur), the shank

(tibia and fibula) and the foot are described in terms of these planes. Figure 2-7 ( h a n et

al., 1981) shows the motion of the segments in these planes. Flexion and extension of the

th@ and shank, and plantadiexion and dorsiflexion of the foot, occur in the sagittal

plane. Abduction and adduction of the thigh and shank, and inversion and eversion of the

foot occur in the frontal plane. Intemal and extemal rotation of the th@, shank and foot

occur in the transverse plane.

2.1 3 Gait Terminology

The gait cycle descnbes the events that occur for one stride of one limb during human

motion. Figure 2-8 (Gage et ai., 1995) is a graphical representation of this cycle. A stride

is a cycle representing two successive gait events for one limb. A stride is bmken up into

swing and stance phases. Stance phase is the part of the gait cycle when the foot is in

contact with the ground. It begins with heel-strike and ends at toe-O fC The swing phase

RE ME W OF LITERATURE

:oronal Plane

agittal Plane

Figure 2- 1 : Anatomical planes of the body (Inman et al., 198 1).

Figure 2-2: Directional information used in anatomy (Thornpson and Floyd, 1994).

- -- - - - 1 Figure 2-3: The laterai view (a) and medial view (b) of the pelvis Tortora and

1 Grabowski, 1993).

RE VIE W OF LITERATURE

Figure 2-4: The antenor (A) and posterior (B) view of the femur (Swan (ed.), 1983).


Figure 2-5: The anterior (A) and posterior (B) view of the tibia and fibula (Swan (ed.), 1983).

Talus 6c Head Cllaneus SwUnUailum Uli Tubor ukmnai

Ir&"( Of 7 Phrlingas

Nrvicular 8 Çaurnoidbnes Nlvicular tubamity Cubaid Cunaifom bonus MaauniIr Bue Shrh

Figure 2 6 : The dorsal (A), plantar (B) and laterai (C) views of the bones of the foot (Swan (ed.), 1983).

Sagittaf Plane CoronaJ Plane

Transverse Plane A

shankqlnterr ta l Rotation = + Foot

Dorsiflexion

1 Figure 2-7: The motion of segments in the aaatomical planes (Inman et ai., 1981). I

occurs from toe-off to heel-strike. The foot is not in contact with the ground during this

part of the gait cycle.

Figure 2-8: The gait cycle (adapted from Gage et a[., 1995).

2.1.4 Instrumentation

Gait can be measured using different measurement systems. Some of the more common

methods of motion analysis include electrogoniornetry and video-based motion analysis,

kinetic anaiysis with the use of a force plate, and surface electromyography. This project

entailed the use of video-based motion analysis.

2.1.4.1 Video-bosed motion analysis

Video-based systems track the motion of small markers placed on the body. These

marken may either be active or passive. Active markers emit an infiared pulse that is

captured using special cameras. One potential negative aspect to this method of motion

analysis is the requirement that a portable power supply be wom, which may impede

movernent .

This study was conducted using a passive marker system. Passive markers are coated

with a reflective material, and these markers are mounted onto the body using small

pieces of double-sided tape. Mared light is emitted from Light emitting diodes placed

about a charge-coupled device (CCD) carnera, and the reflected light, which is caphired

by the camera, conveys the position of the marker in the lab space. In order to obtain the

three-dimensional coordinate information for a marker, a minimum of two cameras must

be able to track it simuitaneously. Most human rnovement laboratories have between

three and six carneras (Whittle, 1 99 1).

Dabnichki et al. (1997) looked at the accuracy and reliability of the ELITE motion

analysis system (ELITE, Bioengineering Technology & Systems, My) . This system is

similar to the VICON system (VICON370, Oxford Meûics Inc., Oxford, UK), which is

used in the Human Movement Laboratory at BlooMew MacMillan Centre. They created

a device that uses a motor to move a rigid bar with markers mounted upon it around the

capture space. They varied the camera to object distance, the size of the calibration field,

the position of the marker in the calibration field and the rotational speed of the device.

They found that the positional error is sensitive to small changes in the distance of the

object kom the camera, and in the position of the object within the calibrated area.

Richards (1999) conducted a study to compare comrnercially available measurement

systems. He placed a mechanical testing device, similar to that of Dabnichki et al. (1997),

in the capture space of the camera system. He devised a series of tests to measure the

distance between two markers under dynamic conditions, and the variability of a marker

location under static conditions. He found that the majority of systerns had a positional

error of less than 2 mm for the marker under dynamic conditions, and an error of less

than 1 mm when deteminhg the position of a marker under static conditions.

Interestingiy, the VICON system showed lower than average positional error values.

2.1.5 Gait Parameters

Gait is most commonly measured in ternis of temporal, kinematic and kinetic data. Some

temporal measures include swing time, stance time, sûide length, and gait velocity.

Kinematic measures look at angular motion occuning between segments, such as

displacement, velocity and acceleration. Kinetic meanires include parameters that study

the effect of different forces acting on the body. The gait parameters that c m be

generated include moments occurring about different joints, such as the hip or knee, or

ground reacfion forces acting on the feet. A summary of these parameten, taken from

Benedetti es al. (1998), is shown in Table 2-1. The data curves corresponding to these

parameters can be found in Figures 2-9 and 2-10 (Benedetti et al., 1998). These data

represent walking for an able-bodied individual.

2.1 S. 1 Gait and cerebral palsy

Ultimately, the results f?om this study will benefit children fkom clinical populations who

are clients at BLooMew MacMillan Centre. One population that makes use of the

laboratory is that of children with cerebrai palsy. Cerebral palsy is a neuromuscular

disorder that affects motor development. Children with cerebral palsy undergo various

therapies and surgical procedures to help them achieve a more eEcient gait (DeLuca,

1991). Gait analysis, when performed throughout the course of a therapy, or pre- and

RE VTEW OF LITERATURE

-dinina data Srance airPtion Swing durition Sm'de bngth Sm'& kngtti Cvcle duration Cadence Vekxily Velocity

Ground nrdon forus 4% of body waight) FI Max. vert. F. h d i n g nrponse T i Min. vert C. mid-~Uin~1 F3 Max. vart, F. m i n a i s t s m F4 Max. fora-ift F. loidina mponre FS Min. km-ait. F. micbtsnce F6 Max. fora-ah, F. term. stance F i Min. med-tPt F. lording rssponre FB Man mrd- l i t F. mid-ltuica F9 Max. msd-kt. F. tminat stance (K stridel T l firnsatF1 1 2 Time i t F2 l3 Tirne nt F3 14 Tune et Fd T5 Time et F5 16 Time et F6 n l ima st F7 TB Time at F8 T9 Time at F9

Hlp rw les pu im. t rn (DwI H 1 Flexion r hael nrikr HZ Mu. f b r . i t looding rssponse Ki Max. a r t in SUnca phi- H4 Fkrion at too OH H5 Mm. fkx. in swing phase H6 Total sagittal phna excunbn H7 Total coronal plana rxcunion H8 Mm. dd. in stance phase H9 Max rw. in swing phare H l0 Total transverse phne excursion H l t Mix. int mt. m suncu piusa H l 2 Max. ea*t rot in swing phase I% sald.1 TH2 Emoi tH2 TH3 Tirne i t H3 TH5 T i m i t H5 TH8 TimciatH8 TH9 TirneatH9 TM11 TiinertH11 TH12 Timaat Hi2

Knn rqkr prur i .un (0.0) Kt Ruion It w strib KZ Max. k m et losdfng rerponse K3 Max. ext. h stmcs phasa K4 Flexion r t toe off K5 Muc Ilaw, in swing ph- K6 T o d rrgirÉsl p h excursion K7 Toul caronal piana ucunion i(B Max. add. in stance phase K9 MIL add in swing phase Kt0 fatal transverse plane excursion K11 Max. ht. rot. in stance phwe K I 3 Max. axt :=t in miq p ? m (K stdde) TK2 TimeitK2 TK3 Tirne i t K3 TK5 Ems at K5 TK8 iÏmeatiC8 TK9 TimsitK9 TK l l T i rner tKl l lK12 Tima 81 KI2

Ankh rnglrs prrunrtmn Pre l A l Fkrion r t hed Nika A2 W. pbnt I las loading response A3 Max. donifiex. in stance phase A4 Flexion r t toe off A5 Max- dorrillox. in swing phase A6 Total wgitîal pkne excursion A7 Total coronal pfane axcunion A8 Max. avenion in stance phase A9 Max. invanion in swing phwe (.k -4 TA2 f i e at A2 TA3 Tima r t A3 TA5 Tune i t AS TA8 Time a t m TA9 Tune at A9

Hip joint momrnts 1% of body wrlqht tirnrs helghtl HM1 Max. flrx. moment HM2 Max. ta. moment HM3 ln maa. id& moment HM4 2nd Mut. idd. moment HM5 M a ext. r o t marnant HM6 Max, int. rot. moment 4% nrw 'THMI TirnartHMI TtiMZ runei tHM2 THM3 T i i r t H M 3 THMO Tmer t HM4 THMS Tm8 at HM6 THM6 Tima r t HM6

1 Table 2-1 : Gait parameters (Benedetti et al., 1998).

Knw joint moments (SC of bodr wmight dmas haight) KM1 1st m. est. moment KM2 Max flex mamunt KM3 2nd m a eat. moment KM4 Ma*. a b d moment KM5 1st max. rdd. moment KM6 2nd m. add. moment KM7 Max. eat. ro t moment KM0 Mm. int. rat. marnent (Y. stridr) T W l Tirne at KM1 TKM2 TirneatKM2 f ex! YITC 3: K%?? TKM4 TimeatKM4 TiCMS Tirne at KM5 R M 6 TirneatKM6 TKM7 firneat KM7 TKMB Tirne at KM8

Ankh jalnt momanu 1% ai M y wdght tfmes hrlght) AM1 Max. planurlîex. marnent AM2 Max. doniflex. moment AM3 Max. aversion moment AM4 Max. inversion moment (% suide) TAMI tirne at AMI TAMZ Tirne ar AM2 TAM3 lime ar AM3 TAM4 Time at AM4

Pmhib rotations (O.al HR1 Min. rot. sagittal plane HR2 Max. rot. coronal pisne H R 3 Max. rot. coranal phne HR4 Max. rot transverse plane (9; I t r idr l T H R 1 fime at HRt 1 HA2 Time at HR2 THW l ime ot Hfl3 THR4 Time at HA4

FOOT-GROUND REACTION FORCES

KINEMATICS - KINETICS

1 Figure 2-9: Generated bernatic and kinetic sait curves (Benedetti el al., 1998). 1


Knat AblPddudior\ Moments

Figure 2-1 0: Generated kinematic and kinetic gait c w e s (Benedetti et al., 1998).

RE VIE W OF LITERA TURE 4

post-surgery, can identify whether or not a meaningful change has occurred in the child's

walking (Lee et al, 1992; Thomas et ai., 1997; Abe1 et al., 1998). Steinwender et al.

(2000) fond that the repeatability of gait data for some parameters was lower in children

with spastic diplegia, a sub-classification of cerebral palsy, than in able-bodied children.

lmproving the efficiency of gait is important for this population and certain therapies aim

to achieve this result. Therefore, the accuracy by which gait efficiency is measured is

important, as it helps medical professionais determine whether or not meaningful changes

have been made to the gait of the child.

Gait analysis crosses many disciplines and it has the potential to help any clinical

population that requires treatment affecthg ambulation. Gait can be measured ushg

different parameters, and new technoiogies continue to emerge that keep improving the

accuracy with which gait data are collected.

2.2 MECHANICAL MODELING

2.2.1 Introduction

Mechanical modeling is used as a tool to denve the motion of segments during gait,

based upon markers placed on the limb segments. The literature is abundant with

different approaches to creating such rnodels. Static and dynamic marker sets can be used

to mode1 the segments in an attempt to reduce erron associated with gait data collection.

As well, the repeatability with which markers are placed on the body in generating a

mode1 of the segment is of importance.

2.2.2 Segments

The study of gait is concemed with the relative motion of segments, such as the pelvis,

thigh, shank and foot. The motions between these segments are expressed through

measures such as the anguiar velocity occurring at a joint. It is important, then, to

undentand how the orientation of segments is modeled, how the segments are dehed

using anatomical reference frames, and how the motion between segments is measured.

REVIEW OF LITERATURE

2.2.2.1 Reference Mmes

The positions of markers are measured in terrns of a global coordinate system (GCS).

This system is a Cartesian frarne of reference with three perpendicular axes that coincide

at an origin. To measure the interaction between segments, a local coordinate system

(LCS) must be created. How one LCS relates to another LCS is shown through the

calculation of kinematic parameters (Craig, 1986).

Figure 2-1 la shows four points in space: A, B, C and D, and the GCS for the system.

Figure 2-1 1b shows the location of each point in the GCS, identified by position vectors

- - - A, B, C, and D . The position vector for point A is represented by:

The other position vectors are caiculated in the same manner. The next step in gait

anaiysis is to create a LCS from the anatomicai reference markers. Figure 2-1 1c shows

how points B, C and D are used to create a LCS. The orientation of the LCS, is calculated

in ternis of the GCS. The axes of the LCS must be orthogonal and are deterniined using

the foilowing calculations:

Calculate the vectors DC and BC :

Figure 2-11 a: Points A, B, C and D, and the GCS for the systcm

Figure 2-llb: The position vector of each point in the GCS

figure 2-11c: Crcation of anLCS Eom points B, C and D, and the transformation fMm the GCS

Figure 2-lld: The position vector of A in the LCS


Determine the magnitude of both of these vectors:

The new X-axis, X', is arbitrarily chosen to be in the direction of :

The new Z-axis is the cross product of X' and divided by its magnitude:

Finally, the new Y-axis, Y', is the cross product of 2' and X':

The rotation from the GCS to the LCS (i.e. the LCS oriented in the GCS) is described as:

R : ~ = [ x ' Y' Z']

where X', Y' and 2' are column vectors.

Also:

This calculation shows that the point C is the origin of the LCS. Therefore, the translation

from the GCS to the LCS (i.e. the location of the LCS in the GCS) is given as:

Finally, it is desired to determine the position of A in the LCS. This is important because

the markers are rnounted on the segments, which are modeled as rigid bodies. The motion

of a marker in the GCS only descnbes how a marker is moving in space. It is more

meaningful to know how a marker moves with respect to a LCS as it is these coordinate

systems that interact. Figure 2-1 Id depicts the calculation of the position of A in the LCS.

The transformation matrùt Crom the GCS to the LCS (Le. the LCS measured in the GCS),

is composed of the rotation matrix nom the GCS to the LCS, and the translation fiom the

GCS to the LCS. This is s h o w by:

Finally, the location of point A in the LCS can be calculated as:

where:

Historically, the most widely used method of describing the orientation of one LCS to

another in gait studies has been the Euler method. This method will be briefly outlined

below.

2.2.2.1.1 Euler method

In studies of kinematic and kinetic gait parameters, the orientation of one LCS with

respect to another LCS has been primarily descnbed in te- of Euler angles. A fiame of

reference has three orthogonal axes. It is important to know how to rotate one LCS to

make the axes coincide with another LCS. In other words, we would like to know the

magnitude of rotation about each axis, in ternis of an angular displacement, and the order

of these rotations, to make the original hune of reference coincident with the second one

(Zatsiorsky, 1998).

One important feature to remember when using the Euler method is that the order of

rotation about each axis is important. Figure 2-12 shows the rotation about each axis. The

first rotation is about the X-mis. This rotation cm be described as the rotation fiom £%me

A to A':

The rotation about the Y-axis is given by:

The final rotation is one about the 2-axis. This is represented as:

[UV '1' H] R:' = RZ(y) = siny cosy

For exarnple, Zatsiorsky (1998) describes a sequence of rotations about the 2, then Y , and

then X-axes, given by:

REVIE W OF LITERATURE

cospcos0 cosysinOsin/-sinycosI cosysin6cos/+sinylsh~

sinycosB sinpsinBsin(+cosylcos( sinysinBcos/-cosysin(

-sin B cos Bsin / cos @cos (

The sequence of rotations is important. If the above example were rotated in the X-Y-Z

sequence, Equation 2-18 would be different, as would the resulting angular values.

2.2.2.2 Anatomieai reference frames

A video-based motion analysis system such as the VICON system tracks the position of

markers in the GCS, which in our case is the human movement laboratory, or lab fiame.

Markers are placed over anatomical landrnarks, and a model of these landmarks is created

in the data analysis software. By recording the coordinate values for each marker over the

entire gait trial, the movement of each segment, based on the model, can be calculated.

Segment models are matornical reference W e s created by placing markers over

selected anatomical landrnarks. What is important for researchers is how these segments

interact with one another. This interaction depends on how the segments are modeled and

what is the chosen method of calculation.

Rotation about Y

Y Y z

1 Figure 2-12: Rotations about axes 1


2.2.2.3 Motion between segments

Ultirnately, it is necessary to calculate the relation of one segment to another, such as the

thigh and the shank. This is the relation between one LCS to another, and the interaction

is usually modeled to occur at a joint centre. There are six degrees of fi-eedom between

two segments: three orientation degrees of freedom and three translation degrees of

£teedom.

Studies have been performed looking at three versus six degrees of freedom, the Euler

versus the helical screw method of determining orientation, and the corresponding effects

on kinematic and kinetic gait data. The results fiom these studies differ based on the

different methodologies.

Grood and Suntay (1983) proposed a non-orthogonal joint coordinate system that

described, in clinical terms, the rotations occurring at the knee joint. They defined axes of

rotation in terms of knee flexionfextension, adductionlabduction, and intenidexterna1

rotation. They claimed that the order by which they calculated the angles about these axes

were sequence independent. However, there is still debate in the biomechanics

community as to whether the proposed method of rotations is t d y sequence independent.

They modeled the knee joint based on a four-link kinematic chah, wiîh the femur and

tibia being the fïrst and last links, with two imaginary links in between them. The axes of

rotation were defined to make the measurements clinically understandable, such as knee

flexion and extension. They did not test this mode1 with gait data to support their theory.


However, their model has been used in many subsequent studies because of the ease with

which joint rotations could be understood in the clinical sense.

Du1 and Johnson (1985) modeled the ankle joint cornplex. They proposed a three-

segment interaction between the shank, the talus and the foot. The motion in the sagittal

plane (plantar flexioddorsi flexion) was measured with an axis approximated by a line

between the latcral and medial malleoii. This axis descnbed the location of interaction

between the talus and the shank. The motion in the frontal plane (inversion/eversion) was

measured with an axis approximated by a line between the posterior-lateral calcaneus and

navicular. This a i s descnbed the location of interaction between the talus and the foot.

They palpated and identified bony landmarks using a pen to mark the locations, and then

measured the distances between these landmarks using a ruler and tape measure. They

measured rotation between local Cartesian coordinate systems representing each segment

using Euler angles. They found that there was up to 4% of error in calculating angles, and

they detennined that one large source of e m r was the measurement technique (Le. taking

the measurements by hand).

Apkarian et al. (1989) descnied a three-dimensional kinematic and dynamic model of

the lower limb. They proposed a method in which each joint of the lower limb is modeled

as a sequence of three single axis rotary joints, totalling three degrees of fkeedom for each

joint. The pelvis with respect to the lab frames was also measured, and the model

contained twelve degrees of freedom for the lower lirnb. Three markers created a LCS

and identified each segment. The pelvis and thigh shared the greater trochanter marker.

The thigh and shank shared the h e e marker, which was placed on a point in between the

lateral epicondyle of the femur and the head of the fibula. Finally, the shank and the foot

shared the lateral rnalleolus of the fibula marker. The thigh and the shank had wands

made of plastic with a plastic base attached to them using pieces of elastic wrapping.

Each wand had a marker attached to the tip. These wands were oriented by the clhician

to be parallel to the fiontal plane of the thigh. Kinematic gait parameters were generated,

as were kinetic parameters based on kinematic information, force plate data, and

anthropometric measurements from each segment. They found that although parameten

measured in the sagittal plane showed similar trends, the parameters in the frontal and

transverse planes differed between subjects. In children with cerebral palsy, some

therapies attempt to correct problerns in intemal and extemal rotations of segments, and

they concluded that it was important to accurately quanti@ changes to the gait parameters

in these planes of motion. They also presented the motion of the pelvis in two frames of

reference. They calculated the rotation of the pelvis with respect to the fixed laboratory

frame, and also with respect to the thigh. They found that the kinematic parameters

generated by these two calculations were quite different. They proposed that both

measures are important when analyzing the gait of pathological populations, such as in

children with cerebrd paisy, where the motion at the hip can be obscured by movement

of the pelvis and torso.

A sensitivity analysis on the effect of uncertainties in d e m g the segment LCS on joint

angles was conducted by Kadaba et al. (1990). The first axis calculated in the sequence

of Euler rotations was the flexiodextension axis. They stated that if this axis was not

correctly identified anatomically, a corresponding error would affect the calculation of

the adductiodabduction axis, and the intemaYextemal rotation axis. Varyhg the

definition of the knee flexiodextension axis in the transverse plane fkom -15' to + 1 5 O at

5" intervals showed the effect of this error. The flexiodextension angle was largely

unaffected while the other two angles showed errors during different phases of the gait

cycle. They found that the magnitude of these errors was a function of knee flexion angle,

and they computed a maximum error of 15" in intemaVexternal rotation, and 13' in

adductiodabduction. The ranges of motion about these axes were approximately of equal

value to the calculated error values, and they cautioned the use of these measures in light

of the large potential errors. They concluded that ir is important to properly identify

anatornical landmarks for gait analysis to properly d e h e the LCS for each segment.

Scott and Winter (1991) descnbed the kinematics and kinetics of the talocrural and

talocalcaneal joints during the stance phase of waiking. They stated that the motion at the

ankle could be represented by these two hinge joints (Le. one degree of keedom each).

Motion about a hinge joint should ideally occur in a circular arc, and they compared the

deviation of motion fiom this arc. They found errors in percent deviation from this arc of

up to 7% for the talocalcaneal point about the talocrural joint, and up to 9% for the

talocrural point about the talocalcaneal joint. These values related to an absolute measure

e m r of up to 4mm. They stated that this mal1 amount of error allows them to make the

assumption that these axes act as hinge joints.

Ramaknshnan and Kadaba (1991) performed a sensitivity analysis on joint kinematic

data. They followed a similar protocol to Kadaba et al. (1990). However, this study

differed in that they analyzed motion at the hip joint as well as the Imee, and they

compared the effects of perturbing the knee rotation axis in the transverse plane on the

calculation of both the Euler and helical screw angles. They found similar error values for

both of these methods, but concluded that Euler angles may prove more meaningful to

clinicians because the axes are established to correspond with anatomical reference

points. They conclude that helical angles are of "limited use" because, in their

calculations, a theoretical neutral orientation exists where the axes of the proximal and

distal segments coincide. Further calculations are then based on this neutral position, and

the authors feel that the manifestations of certain clinical populations, such as a

contracture in children with cerebral palsy, could cause a difficulty in attaining this

neutral position and in interpreting the results.

Lafortune et al. (1992) studied the threeaimensional kinematics of the tibiofemord joint

during wallcing. In their study, pins were inserted into the nght tibia and femur of the

subjects. A cluster of four markers was attached to each of these pins. This allowed the

researchers to create a LCS that coincided with the rnovement of the bones. They found

that angular motion of adductiodabduction had a maximal value of SO, and

intemal/extemal rotation had a maximal value of IO0, and that these values were

relatively small compared to maximal flexion/extension values of 70°. They also found

that the magnitude of the three-dirnensional translation between the segments was 6 mm.


Woltring (1994) proposed the standardization of joint coordhate systems by employing

the use of an attitude vector, 8. This method involved using one LCS that was coincident

with another LCS (Le. they share the sarne origin), and then rotating one Erame about a

vector n by a given angle 8, such that M n . He did not discuss translation between the

two LCSs in this study. Therefore, instead of rotating the k t LCS in an Euler sequence,

oniy a single rotation was required about n. The orthogonal components of bis vector

were then identified in either of the two LCSs. He aiso discussed the error inherent in the

Euler method of calculating kinematic parameters. For a given value of flexion/extension,

intemaYexterna1 rotation, and adductiodabduction, he discussed how srnail differences in

the calculated angle occur when the knee is almost in full extension. But for rotations

where the knee is in flexion, he showed that the angles vary greatly depending on the

sequence of rotations, and that this may not be the best method of calculating kinematic

parameters. He compared gait parameters generated using his protocol with that of other

studies using Euler angles, and found that the results were similar. However, he

concluded by stating that his method may be an improvement because of the sequence

dependence of Euler angle caiculations and the conesponding effects on kinematic

parameters.

Kidder et al. (1996) identified a method to study the kinematics of the foot and ankle.

They identified four segments for analysis: the tibiaKibula, the hind foot (calcaneus, talus

and navicular), the forefoo t (cunei forms, cuboid and metatarsals), and the proximal

phalanx of the hallux. Euler angles were calculated to describe the rotation between

segments. The authors failed to report the definitions of the axes about which the motion

between segments o c c d . However, they found that their results were sMi1a.r to other

published kinematic data, and they concluded that their method of using four segments to

analyze motion at the ankle and foot was a clinically feasible option.

Liu et al. (1997) described a technique to measure the three-dimensional, six degrees of

freedom kinematics that occur at the hindfoot during the stance phase of the gait cycle.

They claimed that although one and two degree of fieedom models may be adequate in

descnbing motion at the hindfoot in able-bodied subjects, this method is probably not

useful for the sîudy of clinical populations. They stated that the kinematics about the

hindfoot are affected by the soft tissue surrounding it, and any changes to this tissue

which can occur in some clinical populations, will affect the kinematic data. They felt it

was important to measure the motion with as many degrees of fieedom as possible. They

defined the plantar/dorsi flexion axis to be coincident with a line connecting the lateral

and medial malleoli. InternaVextemal rotation occurred about an axis from the midpoint

between the lateral and medial malleoli, and the midpoint between the lateral and mediai

tibia1 condyles. Finally, inversiodeversion occurred about an axis that was calculated as

perpendicular to the previous two axes. They used the method proposed by Grood and

Suntay (1983) to calculate the transformation between segments. They determined that

the effect of system error on their calculations was less than 1 O for angular displacements

and less than 1.4 mm for linear displacements This related to an approxirnate error of

10% in angular motion and 30% in linear motion. They used the coefficient of multiple

correlation nom Kadaba et al. (1989) to quanti@ the repeatabiiity of the generated gait

parameters. Plantaddorsi flexion, followed by adduction/abduction, then intemaVextemal

rotation had the most to l e s t repeatability. respectively. These results matched those of

other studies.

2.2.3 Static and Dynamic Marker Sets

Another method of collecting gait data involves the use of static and dynamic rnarker

sets. Certain anatomical locations have more associated skin rnovement than others

(movement artefact), and this rnovement affects the position of the marker with respect to

the underlying skeletal structure. This issue is addressed in Section 2.3. By knowing the

movement artefact values at different locations, the effects of this error cm be reduced by

creating two marker sets. One set of markers, known as the static set, is the set that

primarily identifies anatornical landrnarks. As previously discussed in Section 2.2.2.1,

these markers provide positional information that allows the calculation of an anatomical

LCS for each segment. It is the relation of one anatomical LCS to another anatomical

LCS that will ultimately be used to calculate gait parameters. However, because sorne

anatomical locations have larger movement artefact emrs than other locations, it is not

necessarily beneficial to use al1 of these marken during data collection.

This problem may be overcome by the introduction of a second set of markers, which is a

subset of the static marker set, known as the dynamic set. Thess markers are placed on

segment Iocations that have a Iow associated amount of skin rnovement artefact. These

locations do not necessarily correspond to an anatomical position. During gait, a dynamic

LCS is calculated for each segment, which is not necessady the same as the segment

anatomical LCS. The purpose of the dynamic LCS is to relate the position of each

segment during gait.

Before gait data are collected, the static marker set is placed on the segments, and a trial

of data is collected with the subject motionless. From this positional infornation, the

anatomical LCS and dynarnic LCS can be determined for each segment. Transformation

matrices that descnie the relation between these two LCSs are then generated. Once a

static frame of data is collected, the markers that have higher levels of movement artefact

are removed and the dynarnic marker set remains. Gait data are then collected with the

dynarnic marker set. During data analysis, the dynarnic LCS is generated for each

segment for each time step of data. The anatomical LCS for each segment can then be

calculated. This is accomplished by using the transformation matrix between the

anatomical LCS and the dynarnic LCS that was caiculated in the static h e . This

method of gait data collection is more time consuming than simply placing markers on

the segments and collecting gait data However, the benefits of not placing markers on

areas with higher levels of skin movement artefact potentially outweigh the additional

time required during data collection.

2.2.4 Marker Placement Repeatabiiity

Oniy one study has addressed the variability involved in marker placement. Della Croce

et al. (1999) measured the precision of marker replacement in ternis of inter- and k a -

tester repeatability. They also assessed the potential effects of this variability on the

calculation of joint angles. They tested 21 different anatomical landmarks on the pelvis,

thigh, shank and foot. They detemiined that intra-examiner precision was on average

greater than inter-examiner precision. They calculated precision, which expresses the

degree of dispersion of the marker coordinates, as the root mean square of the deviation

of the data from their mean value. The markers on the pelvis (anterior superior iliac spine

and postenor supenor iliac spine) both showed greater than 10 mm of replacement error.

Measurements for the femur, the greater trochanter, the lateral epicondyle, and the

antero-medial ridge of the patellar surface groove showed greater than 10 mm of enor.

The most lateral ridge of the lateral tibia1 plateau and the upper ridge of the calcaneus

posterior surface showed greater than 10 mm of replacement error on the shank and foot,

respectively. They calculated the mean transformation matrix fiom a reference LCS to

the bone LCS. From these values, they determincd the change in joint angles between

segments when the subjects were in a neutral, &tic posture. They also analytically

created rotations of the segments to determine the effects on generated joint angles. They

found that the variability in marker placement affects the intemdexternal rotation angles

the most, followed by adduction/abduction, then flexiodextension. The intemaVextema1

rotation angle varied by 5.3' at the hip, 5.8" at the knee, and 3.9' at the ankle. They aiso

stated that the e m r in these angles varied with the amount of flexiodextension at the

joint. As knee flexion h a s e d , for example, the error in h e e intemal/extemal rotation

decreased, but the e m r in adductiodabduction increased. They concluded by stating that

the error in calculating some joint angles is almost as great as the corresponding joint

range of motion, and therefore this may reduce the reliability of such gait parameters.

2.2.5 Summary

Mechanical modeling is a vital tool in the study of gait data. In a clinical setting, it is

important for the parameters generated from these data to be meaningfbl and

understandable by the end user of the data.

2.3 SIUN MOVEMENT ARTEFACT

2.3.1 Introduction

Skin movement artefact is the movement of a skin mounted marker with relation to the

associated underlying skeletal structure. This type of error has been quantified in recent

literatwe through the use of invasive and other measurement techniques. Movement

artefact values Vary for different regions of one segment and between segments. The

effects of movement artefact on kinernatic parameters have also been studied. Based on

REVTEW OF LITERATLIRE

these results, marker placement positions have been suggested to reduce the effects of

this error.

2.3.2 Measurement Techniques

Skin movement artefact has been measured primarily by invasive surgical techniques.

The specific protocol for this and similar techniques will be addressed in the next section.

ln general, a surgeon will perform a procedure to insert a pin into a bone. Markers are

attached to a frame, and this eame is then attached to the exposed end of the pin. Markets

are also attached to anatornical landmarks on the segment in the way they would

normally be attached for gait analysis. Gait data are collected, and the rnovement of the

skin mounted markers is calculated by measuring their position with relation to the bone

embedded b e markers. This bone embedded firame is assumed to have no movement

with relation to the bone. Thus, measures of movement artefact can be determined by

placing markers over different regions of the segment.

2.3.3 Measuring Movement Artefact

Cappoao (1991) proposed one of the earliest methodologies to measuring movement

artefact. He constructed a rigid h e out of plaster of Paris and proceeded to mount

several markers on it. He made the assumption that there was negligible motion between

this M e and the underlying bone. He found that the greater trochanter marker had a

maximal movement artefact value of 10 mm while the lateral fernord condyle marker

had a maximal artefact value of 7 mm. These values were measured as radial variations in

the thigh plane fiom their mean positions.

An important study in rneasuring movement artefact was perfonned by Cappozzo et al.

(1996). They conducted experiments on individuals who were wearing extemal fracture

fixator devices, which are used to help heal fractures of the femu. or tibia. Markers were

placed on these hunes, which they assumed did not move relative to the bone. They

tested rnarker positions at the greater trochanter (GT), lateral epicondyle of the femur

(LE), head of the fibula (HF), and Iateral malleolus of the fibula (LM). Movement

artefact of the GT was primarily in the anterior/postenor direction. Its value increased

with an increase in hip flexion, to a maximal value of 30 mm. Artefact in the

mediaVlateral and proximai/dinal directions both had a maximal value of 15 mm. The LE

marker showed a maximal artefact value of 40 mm in the anteriodpostenor direction, and

up to 10 mm in the other two directions. The HF marker showed similar artefact values in

al1 three directions, with an average value of approximateiy 15 mm and a maximal value

of 25 mm. The LM marker showed the least movement artefact, with a maximal value of

15 mm in each direction.

They also tested various other locations on the thigh and shank. They found that markers

at the proximal end of the thigh had more associated movement artefact than those

markers at the distal end. They found that the proximal thigh markers have a large

REVlE W OF LITERATURE

associated artefact with increased values of hip extemal rotation. A marker placed on the

lateral aspect of the gastrocnemius showed greater artefact tha. a marker located on the

tibialis anterior. They state that markers located on the proximal aspects of the thigh and

shank may lead tu errors in calculating motion about the hip, knee and ankle.

Several important conclusions were proposed. Their results showed that movement

artefact error is much greater than the error associated with the data collection equipment.

The artefact values of markers placed over the GT, LE, HF and LM markers typically

ranged between 10 and 30 mm, which they considered unacceptable. Markers that were

placed on the distal ends of joints were preferable to the proximal markers as they

showed less movement artefact. Finally, movement artefact can have a potentially large

impact on the calculation of kinernatic data. They estimated that knee tlexiodextension

can have up to 10% of its range of motion amibuted to movernent artefact. Simila. values

for adduction/abduction and internaYextemd rotation are 50% and 100%, respectively.

This clearly demonstrates the need to select marker locations based on low associated

movement artefact.

Holden et aï. (1997) studied the surface movement ema in shank kinematics during gait.

They measured the movement of surface mounted targets (SMT), which were markers

mounted to a type of ngid shell that was attached around the shank with an elastic

bandage. The markers were not placed directly on the skin. A percutaneous skeletal

tracker (PST) was used to track the motion of the bones. This device was attached to the

tibia and fibula at the malleoli with pins, and consists of a frame with markers attached to


it. They found that movernents of the SMT reached a peak value of 10.5 mm in the

proximaVdista1 direction, and less than 6 mm in the mediaMateral and antenor/posterior

directions. They also determined that the maximal rotational error was 8' for

internaVextena1 rotation, and less than 3" each for flexionlextension and

adduction/abduction. They concluded that the SMT technique is a useful method for

measuring shank kinematics, but the limitation is that specific anatomical landmarks are

not chosen as reference points, which makes modeling difficult.

Kinematic errors occurring in the knee and ankle joints during gait due to skui movement

artefact were anaiyzed by Reinschmidt et al. (1997). They surgically inserted bone pins

into the lateral femoral condyle, the lateral tibial condyle, and into the posterolateral

aspect of the calcaneus. Marken were then attached to each of these pins. They used the

method proposed by Grood and Suntay (1983) to calculate motion between segments. At

the knee, they proposed that the only reliable measure was flexion/extension. They

showed that the error in intemallexternal rotation and adduction/abduction was almost as

great as the motion about each mis. At the anWe joint complex, they detennined that the

smallest effects of movement artefact were on inversiodeversion, in the order of Y,

which they felt was an acceptable amount of variation. The values for plantaddoni

flexion and intemailextemal rotation showed that s k i n movement artefact did not change

the general trends of the kinematic curves, but they did affect the magnitude the rotations

somewhat. However, because they used markers placed on a shoe and not on anatornical

landmarks at the foot, they could not arrive at any conclusions for these two rotations.

They summed up their study by stating that rotations other than knee fIexion/extension,

and ankle plantaddorsi flexion should be interpreted with caution, as rnovement artefact

has the potential to greatly affect the resulting parameters.

Fuller et al. (1997) compared lower extremity kinernatics between skin and pin mounted

rnarkers. Surgical screws were inserted into the greater trochanter, the lateral femorai

condyle, and the mid-tibia. Gait data were collected with marker amys attached to each

pin. The pins were removed, markers were placed on the skin, and walking data were

again collected. They used the helical axis method to de fine the transformation between

segments. They found that a marker near the lateral femoral condyle had movement

artefact values of up to 20 mm in both the proximal/distal and mediaMateral directions.

Their kinematic study Iooked at a cycling task, and they did not report results for gait

trials.

Cappello et al. (1997) proposed a multiple anatomical landmark calibration procedure to

detemine the optimal position of the underlying bone. Markers were placed on an

extemal fracture fixator device similar to that used in Cappozzo et al. (1996), as well as

on the segments with skin mounted markers. They coiiected positional data of rnarkers

while the thigh was in a fully extended position, then in a Mly flexed position. They

calculated the change in position of each marker in the LCS, as defined using the ka tor

(rigid) marken, fiom the initial to the h a l position. They expressed the relationçhip of

this change between positions as "quasi-linear" and used linear interpolation to create a

mode1 of this movement. They used the attitude angle described by Wolhing (1994) to

express attitudes and rotations between segments. A cycling task was used to test their

REYlEW OF LITERATURE

procedure. They caiculated a root mean square (RMS) positional error as the total error in

the anterior/posterior, medialLaterd and proximal/distal directions of the LCS. They

found that the RMS error in the position of the greater trochanter marker was 17.2 mm

when the th@ was in flexion, 15.5 mm when in extension, and 9.8 mm when the linear

interpolation was used for flexion and extension. They did not report results for gait trials

or for any other markers.

The estimation of knee-joint kinematics based on skin movement artefact was studied by

Lucchetti et al. (1998). They proposed a rnethod to compensate for skin movement

artefact by using the linear transformation model established by Cappello et al. (1997),

and they used the same protocol and data. The present study differed in that they

identified different motor tasks for analysis. As well, they used the Grood and Suntay

(1983) conventions to define the axes of rotation. They compared flexionlextension,

adductiodabduction and internailextemal rotation values for two subjects, using data that

were processed with their linear transformation model, and data that were not processed

in this manner. They found that for flexiodextension, the inter-subject results for both

processed and non-processed data were similar. For the other two rotations, however, the

non-processed data showed different inter-subject trends. Once the data had been

processed, the inter-subject trends became simila.. They felt that these results

demonstrated the usefuiness of their linear transformation model.

Karlsson and Tranberg (1999) identified two dynamic eEects that affect skin markers.

They looked at the stiffhess of different matornicd locations, and they rneasured the

resonant fiequency of wand markers. Both tests were conducted under static conditions.

Skin markers were mounted on a piece of tape that was attache4 Lo the skin. A tangential

load of 2.5 N was applied to the tape and the deflection of the marker was rneasured. The

stifiess was measured as the ratio of the load to the deflection. In the second experiment,

markers were mounted on a 100 mm long steel wand that was attached to an aluminurn

base that was k e d to an elastic strap around the thigh or shank. The wand marker was

displaced by an initial amount and the free oscillation was recorded. A fast Fourier

transfomi was performed to d e t e d e the resonant frequency. Al1 data were collected for

different thigh and shank positions, and with the muscles either relaxed or tensed. The

largest deflection values were found for markers tested at the proximal region of the

thigh, and at the lateral malleolus of the fibula. In general, the shank deflection values

were smaller than those of the thigh, except at the lateral malleolus. The deflection values

when the muscles were tensed were lower than when the muscles were relaxed. They also

found that wand markers on tensed muscles had a higher resonant fiequency than those

wands on relaxed muscles. They concluded by stating that M e r testing is required

under dynamic conditions to help determine skin attachent sites for markers.

2.3.4 Summary

Skin movement artefact af5ects gait data. This artefact has such an adverse effect that

some authoa have questioned the reliability of certain gait parameters. It is imperative,

then, to find ways to reduce the effects of this error on gait data


2.4 MARKER CLUSTERS AND NON-RIGID MOVEMENT

2.4.1 Introduction

A sliis~er af skn muünied surface markers should ideally mave as a rigid b d y during

gait. However, due to movement artefact. non-rigid motion of this cluster will mcur. By

studying the mechanical properties of a cluster of markers, a data anaiysis technique cm

be identified and implemented to reduce the effects of skin movement artefact.

2.4.2 The Inertia Tensor

In rigid body mechanics, the angular momentum of a body cm be represented by

where H is the anguiar momentum of a body;

- r is the distance of the body from a particular axis;

o is the angular mornentum of the body.

Substituting for the inertia (I):

we c m write the general solution:


(2-20)

However, Ï has many components. These components c m be represented using the

inertia tensor notation. This is shown as:

The elernents I,, I, and I, are known as the moments of inertia of the body about each

respective axis, and I , I, and 1, are the products of inertia about the axes. By definition:

The moments of inertia and products of inertia are calculated by:

The moments of inertia and the products of inertia describe how the mass of a body is

distnbuted about the axes. It is importmt to note that these mesures arc taken about axes

that are attached to the rigid body. As the orientation of these axes change, so do the

values of the inertia tensor. For any given three-dimensional rigid body there is a unique

orientation of the coordinate axes that will result in zero values for the products of inertia.

In this orientation the axes are called the principal axes. The inertia tensor for this

onentation is represented by a diagonalized matrix, and is shown by:

where the values of the diagonal eiements of this matrix are the principal moments of

inertia, and they represent a maximum, minimum, and an intermediate value for the

moments about the principal axes (Kieppner and Kolenkow, 1973; Meriam and Kraige,

1987).

A useful calculation c m be performed on the tensor ma& using hear algebra. The

calculation of eigenvalues and eigenvectors will now be briefly discussed.

2.4.2.1 Eigenvalues and Eigenvectors

For an n x n square matnx A (such as the inertia tensor matrix), a scalar value R is the

eigenvalue of A iE

where X is an n x I vector cailed the eigenvector, and X+O. Equation 2-26 c m be

rewritten as:

where I is the n x n identity matrix. Also, a matrix B is invertible only if BX = O, impiying

that X= O. So, A is an eigenvalue of A if AI- A is not invertible, implying that:

The characteristic polynomiai of A is written as:

c, (y ) = det(y1- A)

Substituthg A fory in Equation 2-29, we can state:

Therefore, the eigenvalues of A are the real roots of the characteristic polynomial of A.

Relating back to the inertia tensor, the eigenvalues of this matrix will be:

Therefore, the eigenvalues of the inertia tensor are equal to the p ~ c i p l e moments of

inertia (Nicholson, 1995). This concept will be further explored in Section 2.4.4.

2.4.3 Point CIuster Technique

Andriacchi et al. (1998) describe the use of a point cluster method to estimate the motion

of bones fiom skin-mounted markers. The method was not used to measure movement

artefact but, instead, to minimize its effects. A cluster of markers was placed on a

segment, with each marker given an arbiûary mass weighting. The inertia tensor of the

cluster of markers was calculated based on the caicuiated centre of mass. The eigenvalues

of the inertia tensor of the cluster represent the principal moments of inertia, and the

eigenvectors represent the principal axes of the segment. They stated that the cluster

moves as a rigid body as long as the eigenvalues of the inertia tensor do not change. They

REKEW OF LITERATURE

used an optirnization algorithm to rninimize the effects of movement artefact. They tested

their algorithm using a cornputer simulation. They also collected data on subjects during

gait trials and tested their algorithm on these data. They compared their results to studies

that used markers mounted on pins inserted into bones. They found that their algorithm

generated similar kinematic and kinetic data trends to those curves for the study that used

bone-embedded marices (Aiexander, I998).

Their approach to reducing the effects of movement artefact will be explored in more

detail as it is pertinent to the methodology proposed in this thesis. They placed a cluster

of markers uniformly on a segment, and the centre of mass of the segment was calculated

based on the marken with initial equal masses. The inertia tensor rnaû-ix was calculated

by determinhg the products and moments of inertia for each marker about the calculated

centre of mass. Before gait data were collected, they captured a fkarne of data with the

subject standing motionless. This allowed them to determine the principal moments of

inertia for the most ngid position of the cluster. They calculated the eigenvalue nom for

the initial (static) position, /b, as:

where AI, /22 and /ZJ are same values as calculated in Equation 2-34. Next, they captured

gait data, without changing the position of any of the markers in the cluster. During data

analysis, they calculated the eigenvalue nom for each time step (t) as:

They used an optimization routine to minimize the value of this error function:

They rationalized that non-rigid movement of the cluster is represented by a change in

eigenvalue nom. The function in Equation 2-34 was minimized by changing the weights

of the markers during the calculation of the inertia tensor. Their minimization routine

used a downhill simplex method (Nelder and Mead, 1965) to find the minîmized value of

this error function for each time step of data. This optimization was non-linear. They then

used the minimized eigenvalue nom to calculate the correspondhg eigenvectors for each

time step. To reiterate, the eigenvectors represent the principal axes of the cluster, which

is the cluster LCS. They used transformation matrices to relate this LCS to a bone-

embedded LCS. The bone embedded LCS was calculated in the static position as well.

They used an approach that minimized the change in cluster rigidity by adjusting the

weightings of the markers. This allowed them to calculate a cluster LCS that they

theorized had minimai associated skin movement artefact erroa (Alexander, 1998).

To test their algorithm, they used a cornputer simulation. They created a cluster of eight

points, and then added systematic emon of between O and 5 mm to the position of each

point in random directions. This systernatic error was assigned to a subset of the markers

to represent s h movement artefact for a particular region of the segment. Half of the

REVIEW OF LJTERA TCIRE

markers were then given a positionai e m r value îhat increased hearly fiom O to 60 mm

over 20 time steps. They found that the change in eigenvalue nom increased to a

maximal value of 20%. This experiment was perfoxmed without the use of the

optimization algonthm. They also determined that the centre of mass moved by a

maximal value of 30 mm. They stated that using a cluster of markers without invoking an

optimization algorithm is suficient for anticipated marker movement of less than 20 mm

(Alexander, 1998).

Next, they tested their algorithm on data collected during gait trials. They used the same

approach as Lafortune et al. (1992), who used the Grood and Suntay (1983) convention

to determine the joint coordinate system. They also used the results of Lafortune et al.

(1992) as a basis for cornparison because their data were collected using marken

mounted on pins inserted into bone. They compared their generated kinematic parameters

and found that knee flexiodextension curves were very similar. The results for both

intemaIlextemal rotation and adductiodabduction were also similar, with slight

differences occurring during the swing phase. As well, the translation between the

segments showed comparable results between studies. The eigenvalue nom changed on

average between 4.7%-7.4% for the thigh and 2.8%-6.9% for the shank, after the

optimization (Alexander, 1998).

They stated that their algorithm was not designed for efficiency. They took this approach

because they wanted to test whether or not the algorithm was feasible. They proposed

that fiiture work should attempt to reduce the amount of computational effort necessary to

RE VIEW OF L I T E R A T L / .

achieve their optimized results in the hopes of making the process more practicd for

clinical gait data analysis. A smarter approach to optimization should be attempted

(Alexander, 1998).

They listed two limitations to their study. They felt that placing eight markers on a

segment rnight make it difficuit to track each one, depending on the setup and resolution

of the camera system. As well, the cluster should not have a rotational axis of symrnetry

as this may affect the calculation of the principal moments of inertia. However, with

these limitations in mind, they felt that the point cluster technique had ment in reducing

the effects of skin movement artefact on calculated gait parameten (Alexander, 1998).

2.4.3.1 Optirnizution

The optimization approach taken by Andnacchi et al. (1998) involved the use of the

simplex method and simulated annealing.

The simplex method of multidimensionai minimization, as described by Fletcher (1987)

and Press et al. (1992), is concemed with finding the minimum of a function with more

than one independent variable. The method is only concemed with the objective function

values and not the derivatives of this function. Using derivatives is an approach used in

similar optimization functions. The simplex method creates a set of possible function

values. The function values are analytically perturbed until they converge to a minimum

value. Some type of termination cntenon is identifie4 based on tolerance limits, and the

algorithm stops when the change in bc t ion value falls within these limits.

In their pmtocol, Andriacchi et al. (1998) created many different initial guess values for

the simplex. They used the simplex method to identify various minimum function values,

and then used a simulated annealing approach to determine the global minimum. A

pphical representation of this procedure is shown in Figure 2-13. Figure 2-13(a) shows

the values of each local minimum function value, derived from the simplex method,

among al1 possible function values. In Figure 2-13@), each local minimum function value

is numerically perturbed, and the minimum among the candidate local function values is

found. This is performed on al1 of the local minima The set of candidate function values

for each minimum is slowly and systematically increased (Figure 2-13(c)), such that

eventually two local minima will share the same set of candidate function values (Figure

2-13 (d)). Through continuing iteration, only one of these values will remain as the local

minimum (Figure 2-13 (e)). This method is then continued (Figure 2-13(f)) and the

solution set is increased until one global minimum value is achieved (Press et al., 1 992).

2.4.4 Other Optimization Approaches in Gait Studies

Other studies have also used optimization methods to reduce errors in calculated gait

parameters. One approach defined by Soderkvist and W e h (1993), who modified the

methods of Spoor and Veldpaus (1980), looked at defining skeletai movements by using

well-codigured markers. This approach was used and expandeci by other stuclies (Cheze

et ai., 1995; Challis, 1995; Cappello et ai., 1996; Cheze et ai., 1998; Lu and O'Connor,

1999). These studies incorporated an error analysis using singular value decomposition

(SVD) of a matrix representing the position of the markers on a segment. They created a

matrix based on the distances between marken and then generated a "condition number"

based on the singular values fkom the SVD. This condition number described the

positional error of markers and their effects on the rotational matrix. Initially, they

rnodeled the segment as a ngid body and looked at the transformation of the segment

fkom one data hune to the next. Because of movement artefact and other errors, the

rnapping of the markers fiom one hime of data to the next deviated from their model.

They used a least-squares method to detennine the optimal marker positions for one

segment interacting with another by minimizing the positional errors determined by the

SVD. Lu and O'Connor (1999) took the approach one step forward by identifjmg a

model based on the interaction of more than one segment. They wanted to detennine the

marker positions in each segment such that the positional error between segments was

minimized. Thus, they weighted the markers on each segment based on interactions with

two other segments, and not sirnply one, as in the previous studies. Their results showed

improvements over the previous approaches. However, Cheze et al. (1995) identified one

important limitation to this approach: the calculation and analysis of gait parameters

increased in complexity with greater than three markers placed on a segment. Lu and

O'Connor (1999) stated that more research is necessary to explore the distribution of

movement artefact over the segments in creating a more accurate segment model.

Figure 2-1 3: An example of simuiated amealing.

Marker clusters and non-ngid movement can be studied using methods £?om mechanics

and linear algebra. Studies in the literature have shown how properties of a cluster of

marken can be analyzed and optimized to produce the best results in Light of the various

erron affecting gait analysis.

2.5 SUMMARY AND CONCLUSIONS

2.5.1 Sources of Error

The sources of error in the collection of gait data are the error inherent in the

measurement system, the variability in identifjmg anatomical landmarks, and the

movement of skin mounted markers with relation to the underlying skeletal structure.

These errors have been individually discussed in the above sections.

Errors inherent in the measurement system are unavoidable. It is important, however, to

undentand how these erron can affect the tnie spatial position of a marker. Kidder et al.

(1996) stated that this positional error was approxirnately 0.1% of the largest dimension

of the capture volume. For example, a camera system with a capture volume of 1000 mm

x 1000 mm x 3000 mm could have a marker positional error of up to 3 mm. Most studies,

however, have reported the error inherent in the measurement system to be between 1

mm and 2 mm.

The second source of error is the repeatability in placement of markers over the correct

anatomical landmarks. The results from Della Croce et al. (1999), described in Section

2.2.4, reflect this error, with marker replacement error values of up to 21.0 mm. It would

be interesting to compare the results of this study to the methodology and results of

Kadaba et al. (1990), descnbed in Section 2.2.2.3. The latter study perturbed the knee

flexiodextension angle in the transverse plane systematically. Changes in this knee angle

could occur simply due to the variability in marker placement. The repeatability of

rnarker placement over the correct anatomical landmarks has not been widely studied. It

would be beneficial to conduct a study that combined the protocol of Della Croce et al.

(1999) and o f Kadaba et al. (1990). This, or another similar study, wouid potentidly help

to bring more attention to this oflen overlooked source of error.

The largest source of error on the collection of gait data is skin movement artefact. The

pertinent information is located in Section 2.3.3. Movement artefact enor has been

documented in the literature to be as large as 40 mm (Cappozzo et al., 1996). This

information can be used to create a marker set that attempts to reduce the number of

marken placed over body segment locations associated with high levels of movement

artefact-

2.5.2 Implications

Sections 2.1 and 2.2 have covered important concepts that are fundamental to gait and the

analysis of gait data. These sections have dso shed new light on how to compare the

results of different studies. Section 2.3 dealt with understanding and quantifjmg skin

movement artefact. Section 2.4 has helped to define an approach and create a specific

methodology for this study. This will be described in more detail in Chapter 3:

Experimental Methodology and Data Anaiysis Methods.

3.0 METHODOLOGY

3.1 INTRODUCTION

The methodology and data analysis used in this study are outlined in the following

sections. The experiment was perfiormed in two parts. The first part was the study of

marker placement repeatability, and the second part was anaiyzing the movement of a

cluster of markers. As well, there is an overview of the optimization approach used to

analyze the data fiom part two.

3.2 HUMAN MOVEMENT LABORATORY

Data were collected using the VICON system (VICON370, Oxford Metrics Inc., Oxford,

UK). This system used infrared (IR) LED cameras that sent out pulses of IR light. The

light was reflected off passive markers attached to the body and back to the cameras.

Each marker had a diameter of approximately one inch (2.54 cm). This reflected light

contained positionai information about each marker. The system compnsed of six

infked CCD cameras. The carnera setup is shown in Figure 3-1. It depicts the

configuration of the cameras in relation to the walkway, and the position of the force

plate. It also shows the direction of the X-, Y- and 2-axes. Gait data were

1 Figure 3-1 : Camera setup in the Human Movement Laboratory. ]

captured at 60 Hz. These data were transferred to a PC for processing and analysis using

custom sottware written in MATLAB (MATLAB version 1 1.1, 1999).

Before the start of a data collection session, the VICON system was calibrated. The

purpose of calibration was to create a known position and orientation of each camera with

respect to the lab frame of reference, which was also the GCS. This was performed by

means of a static and dynamic calibration. The static calibration entailed placing markers

mounted on a rigid fiame over the force plate in the middle of the capture volume. This

static &une created the origin (0,0,0) of the Iab GCS at one corner of the force plate. The

dynamic calibration was used to determine the positional error that occurred when

reconstructing the position of a marker Ui the GCS during data collection. A wand with

two markers of lcnown distance separation was waved through the capture volume. The

VICON system software calculated the e m r of marker position reconstruction for each

canera. Residual error values that were less than 0.1% of the largest dimension of the

capture volume were considered acceptable (VICON370 Version 2.5 User's Manual,

1998). For our laboratory, residual values were accepted that were less than 1.5 mm.

3.3 PROPOSED MARKER SET

The current marker set used for gait data collection is showi in Figure 3-2 (Andrysek,

1999). This marker set was used when only four IR cameras were available for data

collection. With the addition of wo IR cameras, an opportunity to improve the marker set

arose,

Andrysek (1999) proposed a new marker set for bilateral gait data collection (Figure 3-3).

In his study, a static and dynamic marker set was created through a review of the

Iiterature. He worked with other members of B i o o ~ e w MacMillan's Human Movernent

Laboratory to determine how to mode1 each segment for gait data analysis. After the

marker set was created, only one type of test was perforrned using this marker set. The

inter-marker Euclidean distance was measured between the dynarnic markers during gait.

However, this measure was limited in that both of the markers were mounted on the skin

and afYected by movement artefact. An absolute measure of movement artefact was not

available to test the marker locations. He suggested that the dynamic markers be tested in

- t u c CREST - ANTERfOR SUPERIOR IUAC SPiNE - GREA'IER TROCHANTER - THIGH WAND - KNEE AICE - SFUNK WAND - [Am MAUEOLUS - LATERAL H E U - BASE OF sR' MFfATARSAL

1 Figure 3-2: The curent marker set used for gait data collection (Andrysek, 1999). (

- ANTERIOR SUPERIOR I U C SPINE -UJAcCREST - SACRUM - GREATER TR- - DSTULA'fEIULWGH - DISTAL ANTERIOR TWGH - LATERAL Drs-rAL TI6 tA -MEDtALDrSTALnatA -HEADOFFxBuLA -AHfERlORLATERUSHANK * LATERAL MAUEOWS - MEDML MALLEOLUS - POSIPüOR CALCANEUS - HEAD OF if'' METATMAL - HEAD OF 5" METATARSU - NAVICUUR m m

Figure 3-3: The proposed marker set for gait data collection (Andrysek, 1999).

some other manner in order to deterxnine which ones would minimize movement artefact

and hence be more ngid with respect to the underlying skeletal structure.

3.4 MARKER PLACEMENT REPEATABILITY

The fint part of the study involved a test of the repeatability of maker placement over

anatornical landmarks that could be palpated. The objective of this experiment was to

quanti@ marker placement repeatability in tems of the precision in locating and placing

a marker on the correct anatomical landmark. The data showed quantitatively which

static markers were placed with more precision. Precision, in accordance with Della

Croce et al. (1999), was defined as the variance of the magnitude of each marker kom the

origin of the respective LCS, nom trial to trial.

3.4.1 Data Collection

A flow chart of the data collection methodology is given in Figure 3-4. Figure 3-5 shows

the placement locations of the various markers for the replacement repeatability study.

The anatomical locations are listed in Table 3-1. In Figure 3-5, the square shaped markers

are the reference markers and the circular markers are the ones that were replaced. A grey

marker is one that is on the other side of the segment.

When the subjects arrived for the data collection session, they were asked to Wear a pair

of tight fitting shorts. This was done to reduce the amount of movernent between markers

that were placed on the shorts to identiq the greater trochanter landmark and the &in.

Shorts made f?om a spandex type of material were prefened. The subjects were also

asked to remove their shoes and socks. They were then asked to sit down.

The reference markers (markers 14 to 25) were placed on the appropriate segment

locations. These markers did not necessarily correspond to any anatomical landmark, and

so the exact placement of these markers was not explicitly defined. The markers were

attached to the skin with a srnall piece of double-sided tape. Two small marks around

each marker were made with washable ink. This was perfomed so that if one of the

reference markers was accidentally removed or knocked off, it could be accurately

rep laced.

The subjects were asked to stand up and the static markers (markers 1 to 13) were placed

on the body. Each anatomical landmark was carefûlly palpated, and a marker was placed

on the position that the tester felt was the best representation of that landmark. These

markers were attached to the body using a less adhesive tape. This was done to prevent

any discornfort to the subject that came with the constant placement and removal of

markers. Also, when markers are fkequently placed and removed with the normal tape, a

srnall outline of the marker location can be seen on the skin. This could potentidy act as

a guide for the tester in finding an anatomical landmark. The less adhesive tape was used

to ameliorate this potential problem, as it did not leave any marks on the skin with

METHODOLOGY

Place the reference markers on the limb segment P

1 Palpate the relevant anatomical / landmarks and place a marker over

each one c T

Capture a trial of data with the subj ect standing motionless

Remove the static markers

Have the subject walk around the laboratory bnefly

* Repeat this loop 7 tirnes

Figure 3-4: Flow chart of the data collection methodology for the marker placement repeatability study.

I

Reference Marker Replaced Marker AntenodLateraI PosteriorMedial

Figure 3-5: Marker placement locations for the marker placement repeatability study.

1 Marker Number 1 Anatomical Location 1 1 Sacrum 2 Iliac crest

5 Lateral Femoral Condyle 6 Medial Femoral Condvle - -

I C) f j 1 1 Head of the Fi'ouia I

Table 3-1 : Anatomical locations for the marker placement repeatability study.

b

8 9 10 I l

replacement. A consequence of using this tape was that it had to be changed more often

than the original tape.

Laterai Malleolus of the Fibula Medial Mdleolus of the Tibia Calcaneus Navicular Point

The subject was asked to stand in the centre of

captured with the subject standing as motionless

approximately five seconds at 60 Hz, resulting in

12 13 Base of the 1'' Metatarsal

mean value of these

were then removed,

300

and

alleviate any discornfort

the laboratory, and a trial

as possible. The trial was

approximately 300 fiames

of data was

captured for

of data. The

hunes was

the subject

cdculated and used for andysis. The static markers

was asked to briefly walk around the laboratory to

fkom standing still. The static markers were again placed on the

body, and the procedure was repeated. A total of seven data trials were necessary for

statistical analysis. This number of trials was determined in a pilot study where a ninning

value of the variance was found to be statistically insignificant beyond seven trials. M e r

the data were collected, d l of the markers were removed.

3.4.2 Data Analysis

The data were processed using custom programs written in MATLAB. These programs

are listed in Appendix A. The variance in magnitude of each marker from its mean

marker position in the LCS was calculated.

The data were analyzed using the Friedman test of ranked surns. This type of analysis is

perfomed on data that do not necessarily follow a normal distribution, unlike an analysis

of variance (ANOVA) which does make this assumption. The Friedman test mimics a

repeated measures ANOVA in that it ranks the differences in marker placement variance

for each subject. The null hypothesis, Ho, is that there is no difference in marker

placement variance between markers. If this hypothesis is accepted, then the rank sums

for each marker will be simiiar. However, if the null hypothesis is rejected at a

reasonably high confidence level (a<0.05), then there would be a statistically significant

difference in rnarker placement variance between at least two marken. This calculation is

based on the chi-squared (2) distribution (Glantz, 1997).

A Student-Newman-Keuls (SNK) post-hoc andysis was performed on the results of the

Friedman test. This analysis is comparable to a r-test. However, it is a more robust test

than the t-test in that it does not require a Bonferroni correction. The S N K analysis

compares the results of raaked sums of groups to determine whether or not there is a

statistically significant difference between them. It also calculates these differences based

on the X2 distribution (Glantz, 1997).

3.5 CLUSTER METHOD TO DETERMINE MASS WEIGHTINGS

The second part of the procedure involved placing a ciuster of markers on both the thig

and shank to analyze the change in rigidity of this cluster during gait. The objective of

this experiment was to identify the relative mass weightings of the markers that resulted

in the most rigid cluster under dynamic conditions. The methodology was adapted fkom

Andriacchi et al. (1998).

3.5.1 Data Collection

A cluster of eight markers was placed on both the thigh and shank (Figure 3-6). Their

anatomicd locations are Iisted in Table 3-2. These markers were chosen f h m the

proposed marker set and through pilot testing of the marker positions. These markers

were mounted on the skin using double-sided tape. The subject was then asked to stand in

the centre of the Iab. A tnal of data was captured with the subject standing as motionless

as possible.

METHODOLOGY

Next, the subject was asked to wak at a comfortable pace along the walkway in the

laboratory. Positional data for each marker were captured during each gait trial. Again,

seven trials of data were necessary for statistical comparison. This number was also

determined f?om pilot data. However, as a trial of data can be collected relatively quickly,

approximately 1 0 to 1 5 trials were collected for each subject.

When the data collection was completed, the markers were removed. A measurement was

taken of the height and weight of each subject. The data collection session was then

completed.

3.5.2 Data Analysis

After the data were collected, they were processed using software fiom the VICON

system. The trajectory of each marker was identified and labeled. Occasionally, a marker

would "drop out" from the screen. This would happen if it was not seen by at least two

cameras or if it came too close to the trajectory of another marker, and hence both of

them were seen as one. When this occurred, a cubic spline interpolation was used to

create positional data for the marker in this gap (VICON370 Version 2.5 User's Manual,

1998). The maximum number of time steps in which a gap was filled was ten, which was

also the default setting of the software.

Once the data were processed, the static trials were individually read into a program that

calculated the eigenvalue nom (A,) values for both the thigh and the shank clusters

under static conditions. The static position was considered to be the rnost rigid

configuration of the markers for each cluster. The output of this program was the

eigenvalue n o m for both the thigh and shank.

The eigenvalue noms and the positional data for each marker over an entire gait trial

were input into "clustbatch.m" (Figure 3-7). The marker positionai data were acquired,

and then filtered using a 2nd-order, zero-phase lag Butterworth filter. The data were

filtered at 6 Hz, which was determined to be the highest fiequency value for hurnan

waiking and the optimal value for filtering (Winter, 1990). The coordinate data for the

thigh and shank markers were split into two individual matrices. Each of these matrices

was processed in the same manner, but separately. The following calculations outline the

methodology used for one cluster of marken, either that of the thigh or the shank.

The objective of the second experiment was to determine the mass weightings for the

cluster markers for both the thigh and shank that would yield the most rigid cluster over a

gait triai. The mass weighrings were determined through a senes of calculations. An

outline of the analysis is shown in Figure 3-7. In this figure, each box represents a

MA- function. For, clarity the data analysis calculations are descnbed in reverse

order in the following paragraphs.

r

Figure 3-6: Thigh and shank marker cluster placement locations for the cluster analysis study.

1 Marker Number 1 Anatomieal Location 1 - --

1 2 3

l 4 5 6

Greater Trochanter Lated Thigh Anterior Medial Proximal Thigh Antenor Laterai Proximal Thigh Medial Thigh

. Anterior Laterai Distal Thich I

c.

1 / Anterior Mediai Disrai Thigh

, T

Table 3-2: Anatomical locations for the cluster analysis study.

8 9 10 1 Lateral Head of the Gastrocnemius

The program '?ensor.mW was used to calculate the ermr hc t ion (A, for one time

step of data for a given value of mass weightings. uiitially, the inputted mass weighting

values were m, = m, = ... = m, = 1. For each time step, the algorithm determined the value

Lateral Femoral Condyle Head of the Fibula

11 12 13 14 15 16

of the error function based on the mass values.

Lateral Proximal Shank Anterior Medial Proximal Shank Anterior Laterd Shank Lateral Distd Shank Antenor Medial Distal Shank Lateral Malleolus of the Fibula

The error hinction value for each t h e step was passed back to the function "generate.m9'.

This program calculated the mean value of the error function for a given set of mass

weightings. The output of this program was minimized by the optimization routine

"hincon.m". This program changed the mass weightings that were input into

Fminc0n.m

aread in the positional data, initia1 mass values, and eigenvalue norm values

amanipulates the m a s weightings

minirnizes the output of generate.m

Clustbatch.m

eget the eigenvalue norm values for the thigh and shank fiom pct6static.m

mget the positional data for the thigh and shank

*filter the data

*cal1 the optimization routine fininconm

-

I i

.OUTPUT: mass weightings for markers on one segment

Gencrate.m

ereads in the positional data, mass weighting values and eigenvalue n o m values

walculates the COM of the cluster and the distance of each marker fkom it for each time step

@caUs tens0r.m

eread in the position of each marker Fom the COM, mass weighting values and eigenvalue norm values

*OUTPUT: the value of the error function for one time step of data for a given set of mass weightings

.OUTPUT: the mean value of the output of tens0r.m for the entire gait trial for a given set of mass weightings

.change the rnass weightings to minimize the ouput of generate.m

*OUTPUT: optimized mass weighhngs for markers on one segment

Figure 3-7: Outline of data analysis for the cluster method.

"generate.m9' to rninimize the mean value of the error function. The algorithm for this

optimization is discussed in Section 3.5.3. The mass weightings were passed back to

"clustbatch.m", and identical calculations were performed for the other cluster of

markers, either for the thigh or shank.

The values for the mass weightings were analyzed using the Friedman test descnbed in

Section 3.4.2. The nuil hypothesis was that there were no differences in relative mass

weighting between the markers. A SM< post-hoc analysis was performed on the results

of the Friedman test.

3.5.3 Optimization

The minimum value for the mean of the error function was found using a constrained

non-linear optimization, or non-linear programming, approac h. The MATLAB program

"finincon.m" was used for the optimization (MATLAB version 1 1.1, 1999). This

prograrn used a sequential quadratic programming (SQP) algorithm for mhimization.

Many algorithms exist in quadratic progranunhg (QP) that can efficiently find the

minimum of an unconstrained function (Fletcher, 1987). The SQP method employs a QP

sub-program at each iteration and adds constraints to the function. This is perfonned by

defining the Lagrangian hinction:

where f (x) is the objective function to be minirnized,

c,.(x) are the implicitly dehed constraints on the input values,

A, are the Lagrange multipliers corresponding to each constraint.

The second term in the Lagrangian function, &ci (x) , can be thought to represent a 1

type of penalty function. If a constraint, c i ( x ) , on the input value is satisfied, then the

term Aici(x) = O . If the constraint is not satisfied, the Lagrangian function in (3-1) will be

increased by &ci(x). The A values are scalar factors modified by the optimization

routine. Although a minimum value may be found for f (x) , the overall minimum for

G(x,R) may not be achieved due to a constraint violation. The SQP method attempts to

fmd the minimum value for the Lagrangian function (Fletcher, 1987; Coleman et al.,

1999).

The SQP algorithm works in three steps. The first step involves hding an estimate of the

Hessian, or second denvative, of the Lagrangian function. The exact value for the

Hessian sometimes can not be calculated anaiytically. This is mostly due to the inability

in analytically denning the gradient function, or first derivative, of the Lagrangian

function. In such a case, an estimate of the Hessian is made using the value of the

gradient at t and at t + l , and of the Hessian at t, where t is the number of iterations

(Fletcher, 1987; Coleman et al., 1999).

The esthate of the Hessian function is passed to the next step in the procedure. Step two

uses a QP subprogram to determine the search direction of the algonthm in step three.

The estimate of the Hessian represents the change in the gradient of the Lagrangian

function. This allows the algorithm to determine whether the function is increasing or

decreasing based on a set of input values. This is quickly accomplished by determining

the areas of the function where the gradient is positive, negative or zero. The algorithm

cm then determine, based on this information, which direction to search for the minimum

value (Fletcher, 1987; Coleman et al., 1999).

Finally, in step three, a line search procedure is used to search for the minimum fùnction

value in the search direction calculated in step two. The search direction is a

representation of where the algorithm will "look" for the minimum function value. The

line search algorithm systematically tests input values that lie dong the search direction

to determine the associated function values. This process is iteratively repeated until the

global minimum is reached (Fletcher, 1987; Coleman et al., 1999).

As the number of iterations kicreases for the SQP algorithm, the search direction will test

values that corne increasingly closer to finding the minimum function value. A

termination criterion, or tolerance, is explicitly defmed into the aigorithm. Once the

change in function value is less than the tolerance value, the optïrnization ends and the

fûnction value is determined to be the minimum value (Fletcher, 1987; Coleman et al.,

1999).

It is not possible to analytically determine if the local minimum achieved is truly the

global minimum. Therefore, the optimization for one gait trial was repeated several times

to detemine whether the relative mass weightings retumed in the output were similar in

value to the mass weightings from the previous trial. The returned mass values for the

repeated optirnizations were within the to lerance limits established for the mass values.

An ethical review for this study was conducted in accordance with the guidelines

established by Bloorview MacMillan Centre's Ethics Review Cornmittee. Ethical

approvd for the study was granted in April2000. A copy of the Consent Foxm is found in

Appendix B.

In order to detemiine the marker set least susceptible to movement artefact, subjects were

drawn from the able-bodied population. To eliminate the variability in gait due to

maturation, subjects older than 16 years of age were recruited.

Subjects were recruited fiom emplo yees and volunteen at BlooMew MacMillan Centre

and fkom graduate students at the University of Toronto. These subjects formed a

convenient sample and were assumed to have low within-subject gait variability. Gait

maninty is usually achieved by the age of 7 years, but the refinement of gait

characteristics does not usually occur until the age of about 12 years (Sutherland et al.,

1980; Katoh et al., 1993).

The formulation of the methods for the marker placement repeatability study and the

cluster analysis study were outlined in Chapter 3. The marker placement repeatability

study followed the rationaie of Della Croce er al. (1999), and the cluster analysis study

modified the methods of Andnacchi et al. (1998) and Alexander (1998). The results and

discussion of the marker placement repeatability study are presented in Chapter 4, and the

cluster analysis study in Chapter 5 .

MARKER PLA CEMENT REPU TMILITY

4.0 MARKER PLACEMENT REPEATABILITY

4.1 INTRODUCTION

The variability in marker placement repeatability was tested and measured in accordance

with the methodology proposed in Section 3.4. Chapter 4 presents the results and

discussion of this experiment.

4.2 SUBECTS

Table 4-1 depicts different measures of the subjects. Eight fernales and three males

participated in the study 1). The mean age of the subjects was 25.7 years. The mean

body mass index (BMI) was 22.6 kg/m2, and d l of the subjects were within the range of

20-25 kg/m2.

4.3 RESULTS

Figure 4-1 shows the precision in marker placement for each rnarker position tested. The

position at the greater trochanter showed the largest variance, followed by that of the

antenor superior iliac spine, and then the iliac crest. The resuits show that rnarker

MARKER P U CEMENT REPEA TABIWTY

Sub'ect Sex H

1 Table 4-1: Subject information. 1

Height (m) 1.57

placement repeatability, in general, was the most variable for locations on the pelvis

(markers 2-4).

Table 4-2 contains the results of the statistical analysis. The Friedman test showed a

statistically significant difference in the variance of marker placement between at least

two of the groups, at a confidence level of a~O.0005.

Mass (kg) 58.6

The results of the Student-Newman-Keuls (SNK) post-hoc analysis are shown in Table 4-

3. This table shows that marker positions for the greater trochanter (4), iliac crest (2),

base of the first metatarsal (13) and the anterior supenor iliac spine (3) showed

statistically significant differences in variance of marker placement fiom the medial

malleolus of the tibia (9), lateral femoral condyle (S), medial fernord condyle (6), lateral

malleolus of the fibula (8) and head of the fibula (7) marker positions. The rnarker

position at the base of the fi& metatarsal(12) showed statistically significant differences

BMI (kg/rnL) 23.8

Age 19

in variance of marker placement fkom the medial malleolus of the tibia (9), lateral

fernord condyle (5) and medial femoral condyle (6) marker positions. The calcaneus (10)

and navicular point (1 1 ) marker positions showed statistically significant differences in

variance of marker placement fiom the media1 malleolus of the tibia (9) marker position.

Finally, the sacral (1) marker position showed statistically significant differences in

variance of marker placement fiom the base of the first metatanal (1 3), iliac crest (2) and

greater trochanter (4) marker positions.

Marker Placement Repeatabilitv

2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3

Marker Position

Figure 4- 1 : Marker placement repeatability.

Table 4-2: Friedman test summary. 1

Mi RKER PLACEMENT REPU TABIWTY

Marker Rank Sum 37.83 53.17 54.34 59.15 59.15 63.83 101.7 107.5 1 12.3 1 18.2 128.8 137.2 150.2

X X X X X X X X X X X X X X X X X X X X X X X .. Y . Y . X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

1 Table 4-3: S N K Post-hoc analysis results. 1

4.4 DISCUSSION

The results of the marker placement repeatability study were compared to those of Della

Croce et al. (1999). Ten anatornical positions tested for repeatability of marker placement

were common to both studies. These were the greater trochanter (GT), antenor supenor

iliac spine (MIS), calcaneus (CA), base of the fust metatarsal (IMT), media1 malleolus

of the tibia (MM), base of the fifth metatarsal @MT), lateral malleolus of the fibula

(LM), lateral fernorai condyle (LFC), medial femoral condyle W C ) and the head of the

fibula @F).

Table 4-4 lists which markers were found to be the most variable in each study. Table 4-4

shows that, in general, the results of the current study support those of Delia Croce et al.

(1 999). For example, the GT location showed the most variability in marker placement

MARKER PLACEMENT REPEATABlZITY

by Della Croce et al. (1999). Therefore, it was placed at the top of the order. The same

marker position was also found to be the most variable in the current study. Table 4-4

shows that most of the marker locations, except for those at MM and MFC were within 2

ordered positions of each other. However, this analysis does not allow for a meankgfil

statistical cornparison of the results.

I ASIS I ASIS 7 -- -

Deiia Croce et uL (1999) GT

Current Study GT 1

Table 4-4: Order of variability in marker placement locations, from greatest to least, in the two studies.

CA 1MT MM 5MT LM LFC MFC HF

In the current study, the marker placed at the greater trochanter showed the greatest

variability in marker placement. Also, the markers placed on the pelvis, foiiowed by

those placed on the foot, showed the most variability in marker placement.

1MT SMT CA

MFC W C LM HF MM

There is more adipose tissue surrounding the pelvis than there is surrounding the foot. A

logical assumption is that marker placement variability is directly proportional to the

amount of adipose tissue surrounding a specific landmark.

MARKER PLACEMENT REPEA TABILITY

TO undentand the relation of adiposity and marker replacement repeatability, the

correlation between the variance in marker placement and BMI was calculated for d l

marker positions across al1 subjects. The results are shown in Figure 4-2. The correlation

between BMI and marker placement variability was positive for markers on the pelvis

and thigh, except for the sacral marker, and negative for al1 markers on the shank and

foot.

1 Correlation: Marker Placement Repeatability and BMI

-1 J 1 Marker Position

Figure 4-2: Relation between marker placement and BMI.

AhilL-R PLACEMENT REPEA TMIILITY

The shank and the foot both have less adipose tissue between the skin and the underlying

skeletal structure than do the pelvis and the thigh. On subjects with lower BMI measures,

there was less adipose tissue. This resulted in more prominent bony landmarks that were

used to identim the marker placement locations. The landmarks were, therefore, easier to

palpate. However, this presented the experimenter with a larger area upon which to place

a marker. The prominence at the base of the fint metatarsal was palpated on both the

medial and dorsal surfaces of the foot. Sirnilarly, the prominence at the base of the fifth

metatarsal was palpated on the lateral and dorsal surfaces of the foot. It was not specified

a priori as to which aspect of the bone should be used to identify the placement of the

marker. This resulted in the experimenter placing the marker on locations over the entire

bony prominence of both of these marker locations.

Therefore, the large variance in marker placement may be attnbuted to inconsistency in

marker placement by the experimenter. Della Croce et al. (1999) reported higher inter-

examiner variances in rnarker placement than in intra-examiner variance. The present

study used a methodology with only one experimenter. However, perhaps an

inconsistency arose in marker placement selection due to the large bony prominences that

were palpated on the foot. Although it wodd seem logical that the experimenter should

place the marker approximately in the rniddle of a palpated landmark, perhaps this did

not occur.

This large variability in marker placement on an anatomical landmark that was easily

palpated emphasized the need to identiQ marker placement locations with specific

UARKER PLACEMENT REPEA TABIWTY

anatomical locations. For example, the marker placement location on the base of the fifth

metatarsal should be specific as to whether it is placed on the dorsal surface, or on the

lateral side.

Della Croce et al. (1999), in their paper, do not discuss the sources of marker placement

variance in the intra-examiner study. They mention that some landmarks, such as the

calcaneus or the greater trochanter, present broad palpatcd edges rather than a distinct

point upon which to place a marker.

The markers placed on the pelvis and greater trochanter showed a large variability in

marker placement for a different reason. For these locations, it was difficult to palpate the

various anatomical landmarks (iliac crest, anterior superior iliac spine and greater

trochanter) due to the larger amount of soft tissue between the skin and underlying

skeletal structure. These results suppoaed those of Della Croce et al. (1999) in that they

also found the two Iargest locations of marker placement variability were at the greater

trochanter and the antenor supenor iliac spine.

Della Croce et al. (1 999) calculated the effect of variability in marker placement on joint

angle caiculation. They found that the variability in marker placement affects the

intemal/extemal rotation angles the most, followed by adductiodabduction, then

flexion/extemion. They concluded that the error in calculating some joint angles is

almost as great as the correspondhg joint range of motion, and therefore this may reduce

the reliability of such gait parameters. This type of analysis was not performed in the

curent shidy. However, it would be interesting to know the results of such an analysis.

The results of the marker placement repeatability study showed that the marken on the

pelvis, in general, exhibited larger marker placement variance values than those marken

placed on other segments. The landmarks on the foot and shank displayed more variance

in marker placement with lower levels of adiposity, as rneasured by the BMI. The

landmarks on the pelvis and thigh, in general, showed more variance in marker placement

with higher levels of BMI. Finally, the precise location for rnarker placement, such as on

the antenor or medial aspect of a bone, was not specified and therefore resulted in an

increased variability in marker placement by the experimenter. The complete static

marker set is proposed in Chapter 6: Recornmendations and Conclusions.

5.0 CLUSTER ANALYSIS

5.1 INTRODUCTION

The relative mass weightings for the thigh and shank clusters were detennined in

accordance with the methodology proposed in Section 3.5. Chapter 5 presents the results

and discussion of this experiment.

5.2 RESULTS

5.2.1 Thigh Cluster

Figure 5-1 shows the mean weighting values of the thigh cluster markers. The results

show that the markers on the laterd thigh (2) and the lateral femoral condyle (8) had the

highest relative mass weighting. The rernaining markers al1 had rnean values of less than

the initial mass weighting of 1 unit.


statistically significant difference in relative mass weighting between at least two of the

groups, at a conndence level of acO.OOO5.

CLUSTER ANALYSIS

4.5 , Cluster Analysis: Thigh I

Marker Number

Figure 5-1 : Marker weightings for the thigh cluster.

Table 5- 1 : Friedman test summary for the thigh markers.

marker

Table 5-2: SNK post-hoc analysis results for the thigh markers.

CLUSTER ANAL YSIS

Table 5-2 shows a summary of the SM post-hoc analysis. These results show that the

lateral thigh marker position (2) had a statistically significant difference in relative mass

weighting from the anterior lateral distal thigh (6), anterior media1 distd thigh (7), and

the anterior lateral proximal thigh (4) marker positions. Also, the anterior lateral distal

thigh marker position (6) showed a statistically significant difference in relative mass

weighting 6om the media1 thigh (S ) , the greater trochanter (1), the lateral femoral

condyle (8), and the lateral thigh (2) marker positions.

5.2.2 Shank Cluster

Figure 5-2 shows the mean relative m a s weighting values of the shank cluster markers.

The results show that the rnarker on the antenor medial proximal shank (12) had the

highest relative mass weighting.


statistically significant difference in relative mass weighûng between at least two of the

groups, at a confidence level of a<O.OOO5.

Table 5-4 shows a summary of the SM( post-hoc analysis. These results show that the

anterior medial proximal shank marker position (12) had a statistically significant

diflerence in relative mass weighting h n d l of the other marker weightings. No other

marker locations showed statisticaily significant differences.

CL WSTER ANAL YSIS

4.5 -, Cluster Analysis: Shan k 1

Marker Number

Figure 5-2: Marker weightings for the shank cluster.

[ Number of subjects 1 1 1 1

- --

Table 5-3 : Friedman test summary for the shank markers. i

Chi-square , Degrees of fieedom Simificame level

I I

Table 5-4: SM( post-hoc analysis results for the shank marken.

29.033 7 <0.0005

CL LISTER ANAL YSIS

5.2.3 Vaiidation Test

A test was performed to validate the methodology of the cluster analysis. The objective

of the test was to determine whether the results of the cluster analysis reported which

markers contributed to the most rigid marker cluster. Eight markers were placed on a

rigid body. Four were attached with double-sided adhesive tape that eliminated

movement between the marker and the body, and these were the rigid markers. The non-

rigid marken were mounted on the rigid body using loosely attached adhesive tape.

These four marken did not move rigidly with the rigid body. The rigid body was rnoved

through the capture volume in a manner that caused the loosely-attached markers to move

with respect to it, and positional data were collected. This simulated movement artefact.

The results of this test are shown in Figure 5-3. These results show that the rigidly

attached markers had higher relative mass weightings than the non-rigidly attached

markers. These results helped support the conclusion that the cluster analysis

methodology provided the optimal relative mass weightings for markers that minimized

non-rigid movement.

CLUSTER ANAL YSlS

Validation Test Results

R NR R NR R NR NR R

Marker Type (R=Rigid, NR=Noni-igid) --

Figure 5-3: Validation test resultç. 1

5.3 DISCUSSION

5.3.1 Thigh Cluster

The results fkom Section 5.2.1 showed that the marker located at the lateral thigh (2)

contributed the most to marker cluster rigidity, while the marker placed at the anterior

laterai distal thigh (6) contributed the least. The lateral thigh marker (2) had a statistically

significant difference in relative mass weighting fiom the anterior lateral distal thigh (6),

antenor media1 distal thigh (7), and the anterior lateral proximal thigh (4) marker

CLUSTER ANALYSIS

positions. This result supports the conclusion that the lateral thigh marker contributes the

most to cluter rigidity.

A negative correlation was found between relative mass weighting and BMI for the

lateral thigh marker location (r' = -0.50). This implies that as BMI increases, which is a

measure of adiposity, relative mass weighting decreases. This supports the notion that

sofl tissue movement, such as that of adipose tissue, contributes negatively to marker

cluster rigidity.

The results Eom Section 5.2.1 also showed that the marker on the lateral femoral condyle

(8) had the largest mass weighting. However, no statistically significant differences were

found in relative mass weighting between this and the other marken. This was due to the

large inter-subject variability in relative mass weighting at this location.

This inter-subject variability may be attributed to the adiposity of the subjects. The lateral

femoral condyle is a bony prominence with little soft tissue between it and the skin. The

only soft tissue present between the skin and the bone is the fibula collateral Ligament,

which passes from the lateral femoral condyle to the head of the fibula, and the origin of

the popliteus muscle, which has a small tendon attachment on the posterior surface of the

lateral femoral condyle (Thompson and Floyd, 1994). The source of movement artefact at

this site, therefore, was not likely due to movement of the soft tissue, such as a muscle,

between the skin and the bone.

CL USTER ANAL YSIS

The movement artefact was most likely attributed to the movement of the skin over the

bone. As motion occurs about the knee joint, the skin becomes stretched and unstretched

over the laterai femoral condyle. With increased adiposity, less of the bone is actually

palpated on the surface. This results in less movement artefact due to less stretch of the

skin over the bone. This notion is supported by the positive coefficient of correlation

between the relative mass weighting of the lateral femoral condyle marker and BMI (2 =

0.36). This indicated that relative m a s weighting at this marker location was proportional

to BMI. However, the inter-subject variability in BMI resulted in the lateral femord

condyle marker position to have either a high or low relative mass weighting. There were

no statistically significant differences between this marker position and othen.

The marker at the anterior lateral distal thigh (6) showed a statistically significant

difference in relative mass weighting h m the media1 thigh marker (5) , the greater

trochanter marker (1), the lateral femoral condyle marker (8), and the lateral thigh marker

(2). The anterior lateral distal thigh marker location had lower relative mass weightings

compared to the other markers. Based on these results, this marker location was not

chosen as suitable for gait data collection.

The laterai thigh marker position showed statistically significant differences in relative

mass weighting fkom the other marker locations in the thigh cluster. However, at l es t

three markers must be placed on a segment during gait data collection. The lateral thigh

was the only marker in the study that could be chosen as a dynarnic marker. Therefore, a

second test was performed to determine the relative mass weightings of markers in a

CL USTER ANAL YSIS

thigh cluster that did not include the marker at the lateral thigh (2). This test involved

placing all of the markers fiom the thigh cluster on the thigh, except for marker 2, and

collecting gait data. The results of this test are shown in Figure 5-4. These results show

that the greater trochanter ( 4 media1 thigh (5) and lateral fernoral condyle (8) marker

locations had the largest relative mass weightings in the cluster. Table 5-5 gives the

results of the Friedman test. Table 5-5 shows that there is a statistically significant

difference in relative mass weighting between at l e s t two of the groups, at a confidence

level of a~0.0005. Table 5-6 displays the results of the post-hoc SNK analysis. These

values show that the rnedial thigh (5) and lateral femoral condyle (8) marker locations

have statistically significant differences in relative mass weightings ftorn the anterior

medial proximal thigh (3), antenor lateral proximal thigh (4), anterior lateral distal thigh

(6) and antenor medial distal thigh (7) marker locations. The greater trochanter (1)

marker location had a statistically significant difference in relative marker weighting

from the antenor medial proximal thigh (3) and anterior lateral distal thigh (6) marker

locations. The medial thigh (5), lateral femoral condyle (8) and greater trochanter (1)

rnarker locations did not show statistically significant differences in relative mass

weighting between each other.

Based on the resuits of this test, the medial thigh, lateral femoral condyle and greater

trochanter are options as dynamic marker locations for the thigh. The rnedial thigh

marker was chosen because it had the highest marker weighting for the test, and because

of the statistically signi ficant di fferences f?om the other marker locations. And although

the lateral fernord condyle marker showed similar results as the medial tligh marker, it

CL LISTER ANALYSIS

Cluster Analysis on Seven Thigh Markers 3.5 r

Thigh Marker Location

Figure 5-4: Cluster analysis on seven thigh markers.

1 Number of data trials 1 17 1

1 Deg~ees of fieedom 1 6 1 - 1 Significance level 1 cO.OOO5 1 1 Table 5-5: Results of the Friedman test 1 1 for the seven marker thigh cluster. 1

Marker

3 6 7 4 1 8 5

Rank Surn 28.56 28.56 58.99 62.05 86.02 99.96 1 12.03

Table 5-6: SM( post-hoc analysis results on the seven marker thigh cluster.

CL USTER ANAL ISIS

was not chosen as one of the thigh marken. This was due to the large inter-subject

variability in marker weighting at this marker position. This supported the choice of the

greater trochanter marker as one of the dynamic thigh markers.

The markers that were selected as the thigh dynarnic markers, therefore, were the lateral

thigh, the media1 thigh, and the greater trochanter marker locations.

5.3.2 Shaak Cluster

The results of the marker weightings for the shank cluster showed that the marker at the

anterior media1 proximal shank (12) contributed the most ro marker cluster rigidity. This

marker location showed statistically significant differences in relative mass weighting

fkom al1 of the other shank marker locations. There was little soft tissue between the skin

and the bone, making the anterior medial proximal shank an ided location for marker

placement in gait data collection.

The anterior medial proximal shank showed statistically significant differences in relative

mass weighting fiom the other marker locations in the shank cluster. As in Section 5.3.1,

a second test was performed to determine the relative mass weightings of markers for a

shank cluster that did not include the marker at the anterior medial proximal shank (12).

This test involved placing al1 of the markers kom the shank cluster on the shank, except

for marker 12, and collecting gait data The results of this study are shown in Figure 5-5.

CL USTER ANAL YSIS

These results showed that the head of the fibula (9), antenor lateral shank (13). and

anterior medial distal shank marker locations (15) had the largest relative mass

weightings in the cluster. Table 5-7 gives the results of the Friedman test. Table 5-7

shows that there is a statistically significant difference in relative mass weighting

between at les t two of the groups at a confidence level of a<0.0005. Table 5-8 displays

the results of the SNK post-hoc analysis. These results show that the head of the fibula

(9), anterior lateral shank (13)' and anterior medial distal shank marker locations (15)

showed statistically significant differences in relative mass weighting from the lateral

head of the gastrocnemius (IO), lateral proximal shank (1 l), lateral distd shank (14) and

lateral malleolus of the fibula (16) marker locations. The head of the fibula, anterior

lateral shank, and antenor media1 distal shank marker locations, however, did not show

statistically significant differences in relative mass weighting bebveen each other.

Based on the results of this test, the head of the fibula, antenor Iateral shank, and anterior

medial distal shank marker locations are options as marker locations for the shank.

Although al1 three markers showed similar results in Table 5-8, the proximity of the

antenor medial distal shank marker to the media1 rnalleolus marker excluded tbis

marker's selection as a dynamic shank marker.

The marker locations that were selected as the shank dynamic markers, therefore, were

the anterior medial proximal sh& the head of the fibula, and the anterior lateral shank

marker locations.

Cluster Analvsis on Seven Shank Markers

10 11 13 14 15

Shank Marker Location

Figure 5-5: Cluster analysis on seven shank markers.

1 Number of data trials 1 20 1

Table 5-7: Resuits of the Friedman test for the seven marker shank cluster*

- - - - - - - -

Degrees of fkeedorn Simificance Ievel

Rank Sum

6 <0.0005

1 Table 5-8: SM( post-hoc andysis results on the seven marker shank cluster. 1

CL USTER ANAL YSlS

The results of the cluster andysis on the thigh showed that the lateral thigh, the media1

thigh, and the greater trochanter marker locations contributed to the most rigid cluster.

Therefore, they were chosen as the thigh dynamic markers. Similady, the antenor medial

proximal shank, the head of the fibula, and the anterior lateral shank marker locations

were chosen as the shank dynamic marker locations.

RECOMMENDA TIONS AND CONCLUSIONS

6.0 RECOMMENDATIONS AND CONCLUSIONS

6.1 RECOMMENDATIONS

6.1.1 Static Markers

It is recornmended that al1 of the markers used in the marker placement repeatability

study be used in defining the pelvis, thigh, shank and foot segments. Some markers

showed statistically significant differences in the variance in marker placement, such as

those on the pelvis and foot. However, the tested anatomical landmarks provide the

easiest references to paipate on each segment. These tested landmarks were the most

widely used in gait studies, such as those outlined in Section 2.2.2.3. The iliac crest,

antenor superior iliac spine and greater trochanter marker locations showed high values

of marker placement variability. However, they also provide the experimenter with the

most easily palpated anatomical landmarks on the pelvis and thigh segments. Therefore,

due to the lack of easily palpated landmarks on the pelvis and thigh, it is recommended

that marker locations tested on these segments, as well as locations tested on other

segments, be used as the static marker set.

It is recomrnended that the markers placed on the foot be given specific anatomicd

locations for marker placement. The marker at the base of the h t metatarsai should be

placed on the most media1 aspect of the palpated surface. This landmark can be palpated

RECOUMENDA TIONS ,&Y. CONCLUSIONS

on both the dorsal and medial surfaces, and the media1 aspect was chosen as it would

increase the distance between it and the marker on the navicular point. It is important to

increase the inter-marker distance when using markers for paediatric gait analysis. The

size of children's feet is smaller than that of adults. The distance between two markers

should be maximized as this would reduce the likelihood of the VICON system seeing

the two markers as one.

The marker at the base of the fifth metatarsal should be placed on the most lateral aspect

of the palpated surface for the same reason as that of the marker on the base of the f k t

metatarsal. This marker is currently used to detemine the toe off gait event during gait

analysis. Therefore, with this marker closer to the ground, the timing of toe off should be

more reliable. Aiso, this marker location may be used in the future to identify a joint

occurring between the forefoot and the midfoot in the mediaMateral direction. This axis

could be defined as that passing through the base of the first and fifth metatarsal markers.

If these two markers were placed on the dorsal surface of the foot, the a i s would not

pass through the foot, but would pass on top of it.

Finally, the marker on the calcaneus should be placed on the most posterior aspect of the

palpated surface. This would allow for more consistency in marker placement as the

palpated surface is large.

RECOMMENDATIONS AND CONCLUSIONS

The dynamic marker locations proposed for the pelvis are the sacrai marker, which is

located at the level of the iliac crest on the most posterior aspect of the pelvis; the iliac

crest markers on both the lefi and right side; and the anterior superior iliac spine marken

on both the left and right side.

The dynamic marker locations proposed for the thigh are the lateral thigh, placed on the

most lateral aspect of the thigh occurring midway between the greater trochanter and the

lateral femoral condyle; the medial th@, placed on the media1 side of the midline of the

antenor surface of the thigh; and the greater trochanter marker location, placed on the

most lateral aspect of the palpated surface.

The dynamic marker locations proposed for the shank are the antenor media1 proximal

shank, placed on the media1 side of the crest that divides the anterior surface of the tibia;

the most lateral aspect of the head of the fibula; and the anterior lateral shank rnarker, on

the lateral side of the of the crest that divides the anterior surface of the tibia, midway

between the head of the fibula and the lateral malleoIus of the fibula.

The dynamic marker locations proposed for the foot are the navicular point; the most

posterior aspect of the calcaneus; and the most lateral aspect of the base of the nfth

metatarsal,

RECOhtMENDATIONS AND CONCLUSIONS

6.1.3 Future Work

Five recommendations for future work are presented. First, the marker placement

repeatability study should be repeated. However, there should be more than one

expenmenter performing the tests, which would allow for inter-tester and intra-tester

cornparisons of the data. Also, the anatornical landmarks should be tested according to

the specific locations proposed in Section 6.1 2.

Second a better test of adiposity is needed. It is proposed that skinfolds be taken at

different locations on the segments to give a better understanding of how adiposity

affects both skin movement artefact and marker placement repeatability.

Third, the local coordinate systems chosen for each segment in the marker placement

repeatability study were given arbitrary orientations. The experiment should be

performed again with the directions of the local coordinate systems coinciding with the

anterior/posterior, mediaMateral and proximaYdistal directions for each segment. This

would result in more meaningful data regarding the direction in which the marker

placement varied.

Fourth, a study to detennine the effects of marker placement repeatability on gait

kinematic parameters would allow for a cornparison of the results of the curent study

with those of Della Croce et al. (1999). This analysis could be perfonned once the

RECOMMEN'ATIONS AND CONCLUSIONS

proposed marker set has been fully integrated for data analysis by the Human Movement

Laboratory .

Finally, a study should be performed to analyze the differences between the proposed and

current marker sets. This would involve comparing kinematic and kinetic gait parameters

using statistical procedures. However, a more meaningful study would involve comparing

the kinematic and kinetic gait parameters of the two marker sets to those of gait data

collected on a subject with markers attached to a pin inserted into the underlying bone.

This would allow for an absolute cornparison of the two marker sets.

6.2 CONCLUSIONS

The results of the marker placement repeatability study showed that marker locations on

the pelvis and foot had the highest levels of variance in marker repeatabiIity.

hnprovements cm be made to the methodology that may provide more insight h t o this

overlooked aspect of gait data collection. The cluster analysis study identified marker

placement locations on the thigh and shank that contributed the most to marker cluster

rigidity. This methodology can be used by any human movement laboratory to create a

set of dynamic markers for gait data collection and analysis for different groups, such as

for a study involving overly obese people, or people with bone defonnities. Finaily, a

static and dynamic marker set was proposed that incorporated the results of these two

RECOMUENDA TIONS AND CONCL USIONS

experiments. This marker set was implemented for use in the Human Movement

Laboratory at Bloorview Macmillan Centre.

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APPENDIX A: CUSTOM PROGRAMS WRITTEN IN MATLAB

f unc tion [Meandata] =replace(f name)

% Replace: Want to determine the repeatability of marker placement by calculating the distances of the proposed markers from the reference markers

% % Author: Hemen Shukla % Date: April 2000 % Institution: Bloorview MacMillan Centre (Gait Laboratoryj % 350 Rumsey Road % Toronto, Ontario % Canada M4G-IR0 % Tel (416) 425-6220 x3524 / Fax (416) 4 2 5 - 1 6 3 4 % % + * * * * * * * t * * t + * * * * * * * * * * * + P , * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

%get the data [coord,analog,nframe~,sframe,eframe,frame~rate~nmarkers,adcperframe,nch annel] =getc3d3 (fnarne) ;

% Indicate size of co-ordinate matrix [FRAMES, MARKERS, MIS] = s i z e (coord) ;

f o r i=l:FRAMES

for j=I:MARKERS pos(j,i) = coord(i, j , l ) ; pos(j,2) = coord(i, j A ; pos(j,3) = c o o r d L j , 3 ) ;

end

% PELVIS % Define orientation of pelvis with respect to lab €rame and it8s inverse % using markers REFl (14 ) , REF2 (15 and REF3 (16) (the reference markers for the pelvis) to d e f i n e the pelvis

for k=1:3 pREF12 (k) =pOS ( 14, k) -pas (15 , k) ; pREF32 (k) =pas (16, k) -pas (15, k) ;

end

pelvis3=pREF12/magREF12 ; % z - a i s pelvis2=cross ( (pREF32/magREF32) ,pelvis31 ; % y-ais pelvisl=cross(pelvis2,pelvis3); % x-axis

% The PELVIS i n the lab fratrie ( i . e . PELVIS-wrt-LAB or LAB-ta-PELVIS) for j=1:3

Tlabpelvis (j , 1) =pelvis1 ( j ) ; Tlabpelvis ( j , 2 ) =pelvis2 (j ) ; Tlabpelvis ( j , 3 1 =pelvis3 (j ) ;

end

Tlabpelvis (4,l) =O ; Tlabpelvis (4,S) =O ; Tlabpelvis (4,3 ) =O ; Tlabpelvis (4,4) =l;

Tlabpelvis (l,4 ) =pos ( l 5 , l ) ; Tlabpelvis (2,4) =pos (l5,2) ; Tlabpelvis ( 3 , 4 ) =pos (15,3) ; %identifying marker nurnber 15 (REFS) as the "origin"

% LAB-wrt-PELVTS Tpelvislab=inv (Tlabpelvis) ;

% THIGH % Define o r i e n t a t i o n of thigh w i t h respect t o lab frame and i t l s inverse 3 using markers REF4 (171, REFS (18) and REF6 (19) (the reference rnarkers fox the t h i g h ) t o define the t h i g h

for k=1:3 pREF64 (k) =Po$ ( 19, k) -POS ( 17 , k) ; pREF54 (k) OS (l8,k) -pas (17, k) ;

end;

thigh3 =pR~F64/rnagREF64 ; % z - a i s thighl=cross ( (pREF54/rnagREF54 1 ,thigh3) ; % x-axis thigh2=cross (thigh3 ,thighl) ; 3 y-axis

3 The THIGH in tne LAB frame (i.e. THIGH-wrt-LAB o r LAB-to-THIGH) for j=l:3

Tlabthigh (j , 1) =thighl( j 1 ; Tlabthigh (j , 2 ) =thigh2 (j ) ; Tlabthigh (j , 3 1 =thigh3 (j 1 ;

end

Tlabthigh (4,l) =O; Tlabthigh(4,S) =O; Tlabthigh ( 4 , 3 =O ; Tlabthigh (4,4) =l; Tlabthigh (1,4 =pos (l7,l) ; % identif ying marker REF4 (#l7 1 as the origin Tlabthigh(2,4) =pos(l7,2l ; Tlabtbigh(3,4) =pos(l7,3) ;

% SHANK % Define orientation of shank with respect t o lab frame and it's inverse % using markers REF7 (201 , REF8 (21) and REF9 (22) (the reference markers f o r the shank) to define t h e shank

for k=1: 3 pFü3F97 (k) =pos (22, k) -pos (20, k) ; pREF87 (k) =pas (21, k) -pos (20 ,k) ;

end ;

shank3=pREF97/rnagREF97; % z-axis shankl=cross((pREF87/magREF87) ,shank3) ; % x-axis shank2=cross(shank3,shankl); % y-ais

% The SHANK in t h e LA5 frame (i.e SHANK-wrt-LA5 o r LAB-CO-SHANK) f o r j=l:3

Tlabshank ( j , 1) =shankl (j ) ; Tlabshank (j ,2 =shank2 ( j ) ; Tlabshank( j, 3) =shank3 (j) ;

end

Tlabshank(4,l) =O; Tlabshank ( 4 , 2 =O ; Tlabshank(4,3) =O; Tlabshank(4,4)=1; Tlabshank (1,4) =pos (20 , 1) ; %def i n e the o r i g i n of t h e shank as marker 20 (REF7f Tlabshank(2,41=pos(20,2) ; Tlabshank(3,4)=pos(20,3) ;

% LAB-wrt-SHANK Tshanklab=inv (Tlabshank) ;

% FOOT % Define o r i e n t a t i o n of foot w i t h respect t o lab frame and it's inverse 3 using markers REFlO (23), REFl1. (24) and REFIS ( 2 5 ) ( t h e reference markers f o r t h e f o o t ) t o define the foot

f o r j=I:3 pRF1210 (j) =pos ( 2 5 , j) -pos(23, j) ; pRFlllO (j 1 =pos ( 2 4 , j ) -pos (23, j) ;

end

foot2=pRF11lO/magRF1~10; % y-axis foot3=cross ( (pRF121O/magRFI2IO) , foot2) ; % z-axis

% The FOOT in the LAB frame (i.e. FOOT-wrt-LAB or LAB-to-FOOT) for j=1:3

Tlabfoot(j, 1) =footl(j) ; Tlabfoot (j ,2) =foot2 (j ; Tlabfoot(j,3)=foot3(j) ;

end

Tlabfoot ( 4 , 1 1 =O; Tlabfoot ( 4 , 2 ) = O ; ~labfoot (4,3 ) =O ; Tlabfoot ( 4 , 4 ) =l; Tlabfoot (l,4) =pas (23 j) ; %identify marker 23 (RF10 as the origin Tlabfoot (2,4) =pos (23,2) ; Tlabfoot ( 3 , 4 ) =pos (23,3) ;

% LAB-wrt-FOOT Tfootlab=inv (Tlabfoot) ;

%**** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * %Determine the position of a marker with respect to the segmenta1

ref erence frame

%Sacral marker (pos 1) templ=pos(l,l:3) l ; % tu rn row vector of marker coordinates into column vector templ(4,l) =l; % add a. 1 to the last element in the macrix templb=Tpelvislab*templ; % multiply the transformation matrix with the column vector for k=1:3

Markerpos (if 1, k) =templb(k, 1) ; Bread in the positional data into the Markerpos matrix end

%Iliac crest marker (pos 2) temp2=pos(2,1:3) ; temp2 (4,l) =1; temp2b=Tpelvislab*temp2; fox k=1: 3

Markerpos (i, 2, k) =temp2b (k, 1) ; %read in the positional data into the Markerpos rnatrix end

%ASfS marker ( p o s 3 ) temp3=pos(3,1:3) l ;

temp3 (4,l) =l; temp3b=Tpelvislab*temp3; for k=1:3

Markerpos(i,3,k)=temp3b(k,l); %read in the positional data into t h e Markerpos matrix end

%Greater trochanter (pos 4 ) temp4=po~(4,1:3)~; % turn row vector of marker coordinates into column vector temp4 (4,l) =l; % add a 1 to the last element i n the matrix temp4b=Tthighlab*temp4; S multiply the transformation m a t r i x w i t h t h e column vector for k=I : 3

~arkerpos(i,4,k)=temp4b(k,l); %read in the positional data into t h e Markerpos rnatrix end

%Lateral tibial condyle (pos 5 ) tempS=pos(5,1:3) ' ; % turn row vector of marker coordinates into column vector temps (4,l) =l; % add a I to the last element i n t h e matrix temp5b=Tthighlab*tempS; % rnultiply the transformation rnatrix with the column vector for k=1:3

~arkerpos(i,S,k)=temp5b(k,l); %read in the positional data into the Markerpos rnatrix end

SMedial tibial condyle (pas 6 ) temp6=po~(6,1:3)~; % turn row vector of marker coordinates into column vector temp6(4,1) 11; % add a 1 to the last element in the m a t r i x temp6b=Tthighlab*tenlp6; % multiply the transformation matrix with the column vector for k=1:3

~arkerpos(i,6,k)=temp6b(k,l); %read in the positional data into the Markerpos matrix end

%Head of the fibula temp7=pos (7,1: 3 1 ' ; % t u r n row vector of marker coordinates into column vector temp7 (4,U =l; % add a 1 to the last element in the m a t r i x temp7b=Tshanklab*temp7; % multiply the transformation mat r i x with t he column vector for k=1:3

Markerpos(i17,k)=temp7b(k,l) ; %read in the positional data i n t o the Markerpos matrix end

%Lateral malleolus of fibula temp8=pos (8,1:3) ; 5. turn row vector of marker coordinates into column vector temp8 (4,1) =l; 3 add a 1 to the last element in the matrix

tempBb=Tshanklab*tempS; % multiply the transformation matrix with the column vector for k=1:3

Markerpos (i, 8, k) =temp8b (k, 1) ; %read in the positional data into the Markerpos matrix end

%Medial malleolus of tibia tempg=pos(9,1:3) ' ; 3 turn row vector of marker coordinates into column vector temp9 (4,l) =l; 3 add a 1 to the last elemenc in the matrix ternp9b=Tçhanklab*ternp9; 3 multiply the transformation matrix with the column vector for k=1:3

Markerpos (i, 9, k) =ternp9b (k, 1) ; %read in the positional data into the Markerpos matrix end

%Posterior calcaneaus templO=pos (10,l: 3) ; S turn row vectox of marker coordinates into column vector templ0 (4,l) =l; % add a 1 to the last element in the matrix templOb=Tfootlab*templO; % multiply the transformation matrix with the column vector for k=1:3

Markerpos (i, 10, k) =templOb (k, 1) ; %read in the positional data into the Markerpos matrix end

%Navicular process templl=pos(ll,l:3) l ; % turn row vector of marker coordinates into column vector ternpll(4,l) =l; 3 add a 1 to the last element in the matrix t e ~ l l b = ~ f o o t l a b * t e r n ~ l l ; b multiply the transformation matrix with the colum vector for k=1:3

Markerpos (if il, k) =temprlb(k, 1) ; %read in the positional data into the Markerpos matrix end

%Base of 5th rnetatarsal templS=pos (l2,l: 3) l ; % t u r n row vector of marker coordinates into column vector templ2 (4,l) =1; % add a I to the iast element in the matrix templ2b=Tfootlab*ternpl2; % multiply the transformation matrix with the column vector for k=1:3

Markerpos (i, 12, k) =templ2b(k, 1 ) ; %read in the positional data into the Markerpos matrix end

%Base of 1st metatarsal

temp13=pos (13,l: 3) ; % turn row vector of marker coordinates into column vector tep13 (4,l) =l; % add a 1 to the last element in the matrix templ3b=Tfootlab*temp13; % multiply the transformation matrix with the column vector for k=1:3

Markerpos (i, 13, k) =templ3b (k, 1) ; %read in the posit ional data into the Markerpos matrix end

end

%determine the mean positional value for each rnarker and read i r into a matrix called Meandata Meandata=mean (Markerpos) ;

%clustbatch: this program generates the marker weightings for both the thigh and shank in one pragram, using p~t6dynamic.m~ generate-m and tensor. rn

3 %Input: fname (in *,c3d format) % %Output: massthigh: weightings of the thigh rnarkers % fvalthigh: the function value of the optimization for the 0 *L.:-b.

C C & J JI*

% exitflagthigh: tells whether or not the optimization was % successful % outputthigh: gives information about the optimization % massshank: weightings of the shank maxkers % fvalshank: the function value of the optimization for the 91 thigh % exitflagshank: tells whether or not the optimization was % successful 6 outputshank: gives information about the optimization 3 % Author: Hernen Shukla % Date: April 2000 % Institution: Bloorview MacMillan Centre (Gait Laboratory) % 350 Rumsey Road % Toronto, Ontario % Canada M4G - IR8 % Tel (416) 425-6220 x3524 / Fax 1416) 425-1634 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % $ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

% Read in the Enormstatthigh and Enormstatshank values from the saved workspace load sub j llSTAT . mat ; %get the data [coord,analog,nframes,sframe,eframe,frame~ratefnmarkersladcper~rame,nch annell =getc3d2 ( fname);

%filter data fcutoff=6; [fcoordl =bfilterB (coordf 601 fcutoff) ;

% Indicate s i z e of CO-ordinate matrix [FRAMES,MARKERS,AXISI =six (fcoord) ;

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %FOR THE THIGH

%implement the optimization program fmincon.m %first identify the input variables

~ = [ - l 0 0 0 0 0 0 0 ; 0 - 1 O O O O O 0 ; 0 O - 1 O O O O 0 ; 0 O O - 1 0 0 0 O;o O O O -1 O O 0;o O O O O -1 O 0;o O O O O O -1 O;o O O O O O O -1;l 0 0 0 0 0 0 0 ; 0 1 0 0 0 0 0 0 ; 0 0 1 0 0 0 0 0 ; 0 0 0 1 0 0 0 0 ; 0 0 0 0 1 0 0 0 ; 0 0 0 0 0 I 0 0 ; 0 0 0 0 0 0 I 0 ; 0 0 0 0 0 0 0 1 ] ; ~ = [ O ; O ; O ; O ; O ; O ; O ; O ; M A R ~ R ~ ~ M A R K E R S ~ ~ R S ~ M A R K E R S ~ M A R K E R S ; M A R K E R ~ ~ M A R K ERS ; MARKERS] ;

options= [ ] ; options .TolE'un= [l. 0011 ; options .TolX= [O ,011 ;

%cal1 the optimization function fmincom-rn [mass,fval,exitflag,output]=fmincon(~generate~,massO,Atb,Aeq,beqt~b,~, nonlcon,options,fcooxd(:,l:8,:) ,Enormstatthigh);

clear mass; clear fval; clear exitflag; clear output ; clear identifier;

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %FOR THE SHANK

3implement the optirnization program fminc0n.m %first identify the input variables

b=[O;O;O;O;O;O;O;O;MARKERS;MARKERS;MARKERS;~KERS;MARKERS;MARKERS;MARK ERS ; MARKERS] ;

options= (1 ; options .TolFun= [l. 00a ; options .TolX= [O. 011 ;

3 cal1 the optimization function frninc0n.m [mass,fval,exitflag,out~~tl=fmincon(~~nerate~~massO~A,b,~e~,beq,lb,ub, nonlcon, options, fcoord ( : ,9 :16 , : ) , Enormstatshank) ;

clear mass; clear fval; clear exitflag; clear output ; clear identifier;

function [meanvalue] =generate (mass , f coord, Enorms tatvalue) ; % %generate.m: this program generates the squared values of the % difference in the eigenvalue nom and finds the mean value % - this value is passed to pctsdynamic to be rninimized by % fmincon % %input: mass - the weightings of each marker % fcoord - the filtered coordinate data 3 rneanEnormstat - the mean Eigenvalue n o m for the stdtic % condition % S Authox: Hemen Shukla % Date: April 2000 % Institution: Bloorview MacMillan Centre ( G a i t Laboratory) % 350 Rumsey Road % Toronto, Ontario % Canada M4G-1R8 % Tel (416) 425-6220 x3524 / Fax ( 4 1 6 ) 425-1634 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

% Indicate size of CO-ordinate matrix [FRAMES, MARKERS, M I S ] = s i z e ( f coord) ;

for i=l:FRAMES

%Calculate the center of mass (COMI and convert it into a column vector for j = 1 : MARKERS

COMternp(j ,l) = fcoord(i, j, 1) ; COMtemp(j,Z) = fcoord(i, j,2); COMtemp(j,3) = fcoord(i,j,3);

end

%calculate t h e distance of each marker from the COM of the cluster for j=l:MARKERS

pos2 (j,l) = COMtemp(j, 1) -COM(l) ; pos2(j,2) = COMtemp(j,2)-COM(2); posZ(j,3) = COMtemp(j,3) -COM(3);

end

tempmeanvalue (i) =squareEnormchange ;

end

meanvalue=mean (tempmeanvalue) ;

function [squareEnormchange] =tensor (mass, pos2, M A R s t a t v a l u e ) ; % %tensor: calculates the inertia tensor matrix and produces a value for 3 the square of the change in eigenvalue n o m % %input: pos2- position of each maker wrt the COM of the c l u s t e r 3 mass- mass matrix % meanEnormstat- Eigenvalue n o m value of the s t a t i c frame % markers- the number of markers used % % o u t . p i t : scp~a'~En.o-ichangp- the c q ~ s r o cf t k e ck=zge i~ l oiye_n_-zlze z z z . 3 3 Author: Hemen Shukla 3 D a t e : April 2000 % Institution: Bloorview MacMillan Centre (Gait Laboratory) % 350 R u m s e y Road % Toronto, Ontario S Canada M4G-IR8 S Tel (416) 425-6220 x3524 / Fax (416) 425-1634 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

tensortemp (Ill) = sum( templl) ; tensortemp (l,2 1 = surn (templ2 ; tensortemp (l,3) = sum(templ3) ; tensortemp (2,l) = sum(temp21) ; tensortemp (2,2) = sum(temp22) ; tensortemp (2,3 ) = sum (temp23) ; tensortemp (3,l) = surn(temp31) ; tensortemp (3,2 ) = sum (temp3 2 ) ; tensortemp (3,3 1 = sum (tep33 ) ;

%calculate t h e eigenvalues of the tensor matrix Evalues = eig (tensortemp) ;

%find the eigenvalue norm f o r each t i m e s tep Enon = sqrt( (hralues(1) )^2+(Evalues(2) )A2+(Evalues(3) 1 A2);

%Calculate the change in eigenvalue norm nomchange = Enorm - Enormstatvalue;

âcalculate the square of t h e change in eigenvalue nom squareEnormchange = (nomchange) ̂ 2 ;

APPENDM B: ETHICAL APPROVAL LETTER AND CONSENT FORM

ETHICAL CLEARANCE

This is to certify that a Review Cornmittee consisting oE

Doug Biggar, M.D., FRCP(C) - Chair Linda LaRocque, M.Ed. Darryn GU, Ph.D. Kent Campbell, Methodologist & Statistician Peter Rosenbaum, M.D., FRCP(C) Cathy Steele, Ph.D. Alan Wolfish, B.A., LL.B., Q.C.

(*) Meeting may not have been attended by al1 members.

has examined the proposal "The evaluation of two passive marker sets and their effects on Gait Data". PL'S: H.P. Shukla, S. Naumann & W. Cleghorn, including materials relating to information and consent forms, and fuids it to be ethically acceptable.

Doug Biggar, MD, FRCP(C)

PHONE: (416) 425-6220 BLOORVIEW SITE MACMILLAN SITE A TOLL-FREE: 1 (800) 363-2440 25 BUCHAN COURT 350 RUMSEY ROAD

WEB SITE: www.bloorvicwmacmil1an.on.ca WILLOWDALE. ONTARIO MZI SB TORONTO. ONTARIO M ~ C IR^

E-MAIL: familyandcommunityrclations F.W (416) 4 3 4 . ~ 8 ~ ~ ~ ! 3 f t 1 6 1 4s-6191

@bloorviwmacmillan~on.ca Chrrtt~blc ~ ~ ~ ~ m n t ~ o n ~ ~ I I I ~ I L J ~ RROWI

BLOORVIEW MACMILLAN CENTRE PARTICIPANT INFORMATION AND CONSENT FORM

TTTLE OF STUDY: Implementing a passive marker set for paediatric gait data v analysis.

INVESTIGATORS: Hemen P. Shukla (Principal Investigator) M.A.Sc. Candidate, University of Toronto Department of Mechanicd and Industrial Engineering Imtitute of Biornaterials and Biomedical Engineering (41 6) 425-6220, ~3524 Evenings and weekends: (41 6) 898-35 12

Stephen Naumann, PbD., P.Eng Rehabilitation Engineering Department Bloorview MacMillan Centre (4 1 6) 424-3 86 1

William Cleghorn, Ph.D., P.Eng Department of Mechanical and Industrial Engineering University of Toronto (41 6) 978-3043

Purpose of the study

We want to find the set of markers that are placed on different points of the body to rneasure walking and see how the measurements c m be made more accurate. A new marker set has been created in our lab and there is a need to test and see if it is better than the marker set we now use. We hope to measure wallcing more accurately by the end of the study.

Description of the study

This study will be done using two tests. First, a set of srnall, plastic markers will be placed over certain locations on your waist, upper and lower legs and feet. These markers will be taped to your body and your "picture" will be taken with our cameras. The markers will then be taken off and put back on, and another picture will be taken. This will be repeated up to seven rimes. The second test involves waIking. The markers will again be placed over certain body locations. You will then be asked to waik in our lab and we will take pictures of you and the markea. Finally, we will measure your height and weight.

The entire session will take up to two hours. You only have to come to the lab once. If v you can come in more than once, it would also be helpfûl. This will allow us to study how your day to day change in walking can affect our measurements.

BLOORVIEW SITE & 2s BUCHAN COURT

WEB SITE: ~nw.bioo~iewmacmit~an.on.ca WILLOWDALE. ONTAR~O MZI 45'1

E-MAIL: familyandcommunityrelations FAX: (416) -194-9785

/p. , MACMILLAN SITE -

TORONTO. ONTAfB. M4C IR8

FAX: (416) 425-6591

Risks and BeneFits

There are no known nsks to you by taking part in this study. Sometimes when the markers are taken off of the body, it rnay cause a iittle bit of discornfort because the tape may pull on your hair.

There may not be any benefits to you fiorn this study. However, the information gained fiom this study will benefit the analysis of paediatric gait data. More specifically, children with Cerebral Palsy and other clinicai populations receive treatment at the Centre. It i s important to be able to quanti@ changes in wdking patterns resulthg from such treatment. With advances in technology, gait analysis continues to gain recognition as a means to collect rneaningful, clinically relevant gait data.

Con fiden tiality

Ail of the information that we collect about you will be kept confidentid. Your name will be placed on a master list at the start of the study and you will be assigned a number. At the end of the study, the master Iist will be destroyed. Your name will not be p ~ t e d in any fom.

Participation

Participation in this study is voluntary. If you decide during the session in our lab that you want to stop, you can do so. If you have had an injury in the past 6 months that affects how you wdk, or if you have a history of walking problems, please talk to the investigator.

For questions and further information

Please do not hesitate to contact Hemen Shukla at (4 16) 425-6220, x3524 during normal business hours and at (41 6) 898-35 12 on evenings and weekends, with any questions you rnay have about the midy. If you reach my voice mail, please leave your name and phone nurnber and 1 will r e m your call as soon as possible.

Once the study has been completed, we will send you a summary of the results.

CONSENT FORM

TITLE OF STUDY: Implementing a passive marker set for paediatric gait data analysis.

Hemen P. Shukla (Principal Investigator) M.A.Sc. Candidate, University of Toronto (4 16) 425-6220, ~3 524 Evenings and weekends: (41 6) 898-35 12

Stephen Naumann, Ph.D., P.Eng Rehabilitation Engineering Department Bloorview MacMillan Centre (416) 424-3861

William Cleghorn, Ph.D., P.Eng. Department of Mechanicd and Industrial Engineering University of Toronto (4 16) 978-3043

Please complete the consent portion of this form below.

Have you had an injury in the past 6 months that affects how you walk?

Yes

Do you have a history of walking problems?

1 have received an explanation of this study, as described in this fom, by the investigator named below.

1 hereby consent to participate in this study.

Signature

Investigator's Signature Date

proposal of a passive marker set for paediatric gait …€¦ · the gait lab research group....

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