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Finite Element Modeling of the
Human Foot and Footwear
JasonJason TakTak--Man CheungMan Cheung1,21,2, Ph.D., Ph.D.
Ming ZhangMing Zhang11, Ph.D., Ph.D.
1Department of Health Technology & Informatics,
The Hong Kong Polytechnic University, Hong Kong, China2Human Performance Laboratory,
University of Calgary, Calgary, Alberta, Canada
Department of Health Technology
and Informatics
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Common Foot Problems
Calluses Corns
http://www.foot.com
Bunions
Hammertoe
Claw Toe
Mallet Toe
Metatarsalgia
Achilles
Tendonitis
Plantar Fasciit is
Heel Spurs
Calluses Corns
http://www.foot.com
Bunions
Hammertoe
Claw Toe
Mallet Toe
Metatarsalgia
Achilles
Tendonitis
Plantar Fasciit is
Heel Spurs
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Why Finite Element (FE) Approach?
Experimental measurements of the biomechanicalvariables such as joint motion and load distribution are
costly and difficult for the ankle-foot complex.
Finite element method allows
predictions of joint motion, load distribution between
the foot and supports and in bony and soft tissuestructures.
efficient parametrical analyses of loading conditions,
structural and material variables.
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Summary on FE Analysis on Foot & Footwear
Previous FE foot models
have shown the contributions to the understanding of
biomechanics of the foot and footwear
were developed under certain simplifications(Simplified or partial foot structures, assumptions of linear
material properties, simplified loading and boundary conditions).
Bandak et al (2001), Camacho et al (2002), Chen et al (2003), Chu et al (1995),
Erdemir et al (2005), Gefen et al (2000), Goske et al (2005), Jacob & Patil (1999),
Lemmon et al (1997), Shiang (1997).
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Objectives
To develop a comprehensive 3D FE model toquantify the biomechanical response of the
human foot and ankle (joint motion, load
distribution of bony and soft tissue structuresand foot-support interface).
To provide a systematic tool for the parametric
analyses of different foot structures, surgical and
footwear performances.
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Development of the Finite Element Model Coronal MR images of 2mm
intervals obtained from theright foot of a healthy male
subject in unloaded, neutral
position
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3D Reconstruction of Foot Structures
Boundaries forFoot Bones
Boundary forSoft Tissue
Segmentation (Mimics v7.10, Materialise.)
Surface ModelSolid Model(SolidWorks v2001, SolidWorks Corp.)
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Finite Element Mesh of
Bony and Soft Tissue Structures
Automatic mesh creation inABAQUS v6.4, HKS.
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Anatomical References of the Ligaments
Interactive Foot & Ankle, Ver.1.0.0, Primal Picture Ltd.Interactive Foot & Ankle, Ver.1.0.0, Primal Picture Ltd.
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Structural Components of the FE Model
28 bones embedded in a volume of soft tissue
(Tetrahedral elements)
72 associated ligaments (excluding the
ligaments between the toes) and the plantar
fascia(Tension-only truss elements)
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Joint Articulations of the Model
The phalanges were connected together using2 mm thick structural elements to simulate theconnections.
The interaction between the metatarsals,cuneiforms, cuboid, navicular, talus, calcaneus,
tibia and fibula were defined by contact surfaceswith a prescribed contacting stiffness of articularcartilage to allow relative bone movement.
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Material Properties of Ankle-Foot ModelEncapsulated soft tissue (Hyperelastic)
Bony & ligamentous structures (Homogeneous, Linearly elastic)
Component Element TypeYoungs Modulus
E (MPa)
Poissons Ratio
Cross-sectional Area
(mm2)
Bony Structures 3D-Tetrahedra 7,300 0.3 -
Soft Tissue 3D-Tetrahedra Hyperelastic - -
Cartilage 3D-Tetrahedra 1 0.4 -
Ligaments Tension-only Truss 260 - 18.4
Fascia Tension-only Truss 350 - 58.6
Nakamura et al., 1981 (Bone); Lemmon et al., 1997 (soft tissue); Athanasiou et al., 1998
(Cartilage); Siegler et al., 1988 (ligaments); Wright and Rennels, 1964 (Plantar Fascia).
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Hyperelastic Material Model for Soft Tissue
2i
el
2
1i i
ji2
1jiij (JD)I(I(C )1
1
3)3U 2
__
1
__
+= ==+where U is the second-order strain energy per unit of reference volume;
Cij
andDi
are material parameters;
1
__
I 2__
Iand are the first and second deviatoric strain invariants:
I2
3
__2
2
__2
1
__
1
__
++=
I)2(
3
__)2(
2
__)2(
1
__
2
__ ++=
with the deviatoric stretches i__
=Jel-1/3 i ;
Jel and i are the elastic volume ratio & the principal stretches.ABAQUS v6.4, Hibbitt, Karlsson & Sorensen, Inc.
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Application of Loading and Boundary Conditions
Fixed SurfacesConnector Elements
for Muscles ForceApplication
Moving Support for Foot-Insole Interface andGround Reaction Force Application
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References for Muscular Insertion Points
Interactive Foot & Ankle, Ver.1.0.0, Primal Picture Ltd., UK, 1999
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Muscles and Ground Reaction Forces for
Standing and Midstance Simulation
Tendon/External Forces Standing Midstance
Achilles 175N
-
-
-
-
-
Reaction of Lateral Retinaculum - 50NReaction of Medial Retinaculum - 60N
350N
750
Tibialis Posterior 70N
Flexor Hallucis Longus 35N
Flexor Digitorum Longus 40N
Peroneus Brevis 40N
Peroneus Longus 35N
Vertical Ground Reaction 550N
The active extrinsic muscles forces during midstance were estimated fromnormalized EMG data using a constant muscle gain and cross-sectionalarea relationship (Dul, 1983; Kim et al., 2001; Perry, 1992).
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Simulation of Midstance Contact
10Degrees
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Plantar PressureF-scan Measurement FE Prediction
MPa MPa
Contact
Area
68.8 cm2
Contact
Area
68.3 cm2
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Predicted Von Mises Stress ofBony and Ligamentous Structures
MPa
Plantar View Dorsal View
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Parametrical Studies
Effect of plantar fascia stiffness (E = 0 to 700 MPa).
Effect of plantar soft tissue stiffness.
Effect of Achilles tendon loading.
Effect of posterior tibial tendon dysfunction.
Effect of different parametrical design of foot orthoses.
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The Plantar Fascia and Plantar Ligaments
Plantar
fascia
Long
plantar l ig.Short
plantar lig.
Spring lig.
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Effect of varying Youngs modulus of fascia
on arch height and arch length
37
38
39
4041
42
43
44
0 175 350 525 700
Young's Modulus of Fascia, MPa
ArchHeight,mm
Arch Height
141
142
143
144
145
146
147
148
149
0 175 350 525 700
Young's Modulus of Fascia, MPa
ArchLeng
th,mm
Arch Length
Deformed Arch Height
(42.5 mm) FE
(44 mm) Measured
Unloaded Arch Height(52.5 mm)
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Effect of varying Youngs modulus of fascia
on the tensions of the ligamentous structures
Plantar fascia Major arch-supporting ligamentous structuresustaining tension ~45% of applied body weight
short plantar lig. > long plantar lig. > spring lig.Tension of plantar ligaments
0
50
100
150
200
0 175 350 525 700
Young's Modulus of Fascia, MPa
FasciaTension,N
Total Tension
0
50
100
150
0 175 350 525 700
Young's Modulus of Fascia, MPa
Ligame
ntTension,
N
Long Plantar Lig.Short Plantar Lig.Spring Lig.
With Fasciotomy
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Clinical Implications
The plantar fascia is one of the major stabilizers of thelongitudinal arch of the foot.
Laceration or surgical dissection of plantar fascia may
induce excessive loading in the ligamentous and bony
structures.
Surgical release of the plantar fascia should be well-planned to minimize the effect on its structural integrity to
reduce the risk of possible post-operative complications.
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Parametrical Studies
Effect of plantar fascia stiffness.
Effect of plantar soft tissue stiffening (Up to 5 times).
Effect of Achilles tendon loading. Effect of posterior tibial tendon dysfunction.
Effect of different parametrical design of foot orthoses.
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Simulation of Stiffened Soft Tissue
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5Strain
Stress(MPa)
F5
F3
F2
Normal
Nonlinear compressive stress-strain response of plantar soft tissue was adopted
from the in-vivo measurements (Lemmon et al., 2002). F2, F3 and F5 correspond
to simulations of two, three and five times the stiffness of normal tissue.Pathologically stiffened tissue with increasing stages of diabetic neuropathy
(Klaesner et al., 2002; Gefen et al., 2001).
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Effect of Soft Tissue Stiffening onPlantar Pressure Distribution
5 Times3 Times
MPaMPa
2 TimesNormal
MPa MPa
Peak
0.230 MPa
Peak
0.263 MPa
Peak
0.291 MPa
Peak
0.306 MPa
Increasing Soft Tissue Stiffness
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Effect of Soft Tissue Stiffening on Peak
Plantar Pressure and Contact Area
0
20
40
60
80
1 2 3 4 5
Factor of Soft Tissue Stiffening
ContactArea(cm
2)
ForeFoot
MidFootRearFoot
WholeFoot
0
0.1
0.2
0.3
0.4
1 2 3 4 5
Factor of Soft Tissue Stiffening
PeakPressu
re(MPa)
ForeFoot
MidFoot
RearFoot
Five times Heel (33%), Forefoot (35%) 47%
Soft tissue stiffness Peak Plantar Pressure Contact Area
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Clinical Implications
Stiffening of plantar soft tissue may induce excessivepressure in the plantar foot possible link to tissue
breakdown and foot ulceration.
The percentage increase in peak plantar pressure is less
pronounced than the increase in soft tissue stiffness.
Screening of plantar soft tissue stiffness can be a viablemethod in addition to plantar pressure measurement for
routine identification of diabetic feet at risk of ulceration.
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Parametrical Studies
Effect of plantar fascia stiffness.
Effect of plantar soft tissue stiffening.
Effect of Achilles tendon loading (0 to 700 N). Effect of posterior tibial tendon dysfunction.
Effect of different parametrical design of foot orthoses.
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Simulated Conditions
(1) Pure Compression
Vertical compression up to 700 N.
(2) Compression with Achilles tendon loading
Vertical compression preload of 350 N with an
increasing Achilles tendon tension up to 700 N.
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Six nonpaired fresh cadaveric ankle-foot specimens
Middle-aged male donors
Unknown body masses
Average foot length: 24.2 cm
Average foot width: 9.4 cm
Kept under -20 0C before experiment
Cadaveric Experiment
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Specimen PreparationAfter thawing at room temperature
Skin, subcutaneous tissues and muscles above the ankle jointlevel dissected with all muscular tendons left intact
Distal fibula and tibia potted in acrylic resin
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Compression Test of Cadaveric Foot
F-scan pressure sensor
(Tekscan, Inc.)
Implanted displacement transducer
(Microstrain, Inc.)
Load cell(MTS Systems)
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Cadaveric Foot under
Vertical Compression up to 700 N
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Vertical Deformation and Plantar Fascia
Strain under Vertical Compression
0
2
4
6
8
10
0 100 200 300 400 500 600 700
Vert ical compression, N
Ve
rticaldeformation
,mm
Specimen_1 Specimen_2 Specimen_3Specimen_4 Specimen_5 Specimen_6FE
0
1
2
3
4
0 100 200 300 400 500 600 700
Vertical compression, N
Strainofplantarfascia,%
Specimen_2 Specimen_3 Specimen_4
Specimen_5 Specimen_6 FE_Average
FE_Max
Displacement Fascia Strain Fascia strain (>100N)ICC (Consistency) : 0.892 0.880 0.994
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Effects of Vertical Compression and Achilles
Tendon Loading on the Plantar Fascia Tension
0
50100
150
200
250
300
350
0 100 200 300 400 500 600 700
Vertical compressive/Achilles tendon forces, N
Totalfasciaforces,N
Vertical compressive forces (0-700N)
350N compression preload + Achilles tendon forces (0-700N)
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Clinical Implications
Achilles tendon loading produces a greater strainingeffect on plantar fascia than the weight on the foot.
Overstretching of the Achilles tendon is plausible
mechanical factors for overloading the plantar fascia.
Lengthening or tension relief of the Achilles tendon
especially in subjects with tight calf muscles andAchilles tendon may be beneficial in terms of plantar
fascia stress relief.
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Parametrical Studies
Effect of plantar fascia stiffness, partial and total plantarfascia release.
Effect of plantar soft tissue stiffness.
Effect of Achilles tendon loading.
Effect of posterior tibial tendon dysfunction.
Effect of different parametrical design of foot orthoses.
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Simulated Conditions
Intact PTTD
PTTD + Fasciotomy Fasciotomy
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Simulations of Fasciotomy
Intact
Fasciotomy
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Experimental Setup
F-scan Pressure Sensor
(Plantar foot pressure)
Bone Marker(Joint movement)
Displacement
Transducer
(Microstrain, Inc.)(Fascia strain)
Tendon Clamp
(Muscle forces application)
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Stance Phase Simulation
3D Laser Scanner
Deadweights
Marker Scanning
(Realscan USB 200, 3D Digital Corp.)
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Predicted Changes in Arch Height
3.7
3.8
3.9
4
4.1
4.2
4.3
Intact PTTD PFR PTTD+PFR
Simulated Condit ions
ArchHeig
ht,cm
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Effect of PTTD on Plantar Fascia Strain
0
0.5
1
1.5
2
2.5
Intact PTTD Intact PTTD
FE Prediction Measurement
FasciaStrain,%
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Predicted Changes inFascia & Ligaments Tension
0
50
100
150
200
250300
350
400
450
Intact PTTD PFR PTTD+PFRSimulated Conditions
Tension,N
Plantar Fascia Long Plantar Lig. Short Plantar Lig. Spring Lig.
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Prediction of Joint Motion
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Effect of PTTD & PFR on Joint Motion
Relative
Bones Intact with PTTD Intact with PFR PFR with PTTD
Talus
to Tibia
Plantar
FlexionEversion
External
Rotation
Plantar
FlexionEversion
Internal
Rotation
EversionExternal
Rotation
ExternalRotation
External
Rotation
Internal
Rotation
Eversion
Inversion
Plantar
FlexionEversion
Internal
Rotation
Calcaneus
to Talus
Dorsi
FlexionEversion
External
Rotation
Inversion
Plantar
Flexion
DorsiFlexion
Dorsi
Flexion
Dorsi
Flexion
Dorsi
FlexionInversion
External
Rotation
Navicularto Talus
DorsiFlexion
Eversion InternalRotation
DorsiFlexion
Eversion ExternalRotation
1st Metatarsal
to Navicular
Plantar
FlexionInversion
Internal
Rotation
Dorsi
FlexionEversion
Internal
Rotation
1st Metatarsal
to Talus
Dorsi
FlexionEversion
External
Rotation
Dorsi
FlexionEversion
External
Rotation
FE Prediction
67%
78%
44%
22%
56%
Green: Agreement with cadaveric studies
Red: Disagreement agreement with cadaveric studies
Percentage of Agreement (%)
Sagittal plane Coronal Plane Transverse Plane73% 60% 27%
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Clinical Implications
Both PFR and PTTD decreased the arch height and
resulted in foot pronation.
PFR in general have a greater arch flattening effect than
PTTD.
The lack of foot arch support with PFR and PTTD may lead
to attenuation of surrounding soft tissue structures and
progressive elongation and flattening of foot arch.
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Parametrical Studies
Effect of plantar fascia stiffness, partial and total plantarfascia release.
Effect of plantar soft tissue stiffness.
Effect of Achilles tendon loading.
Effect of posterior tibial tendon dysfunction.
Effect of different parametrical design of foot orthoses.
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Geometry of Foot OrthosisLaser scanning during
balanced standing
INFOOT Laser Scanner,
I-Ware Laboratory Co. Ltd.
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Geometrical Model of Foot Orthosis
(MATLAB, The MathWorks, Inc)Foot SurfaceModel
Solid Model of Foot Orthosis(SolidWorks 2001, SolidWorks Corporation)
Orthosis Surface Model
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Finite Element Model of the Foot Support
Insole (Polyurethane forms, Poron)
Midsole (Ethylene Vinyle Acetate, Nora SL)
Outsole (Ethylene Vinyle Acetate, Nora AL)
Component Element Type Thickness
Insole (Poron) 3D-Brick 3mm, 6mm. 12mm, 24mm
3mm (base), 30mm (arch)12mm
Midsole (Nora SL) 3D-BrickOutsole (Nora AL) 3D-Brick
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Compression Test of Insole Material
Hounsfield material testing machine (Model H10KM),Hounsfield Test Equipment, UK
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Hyperfoam Material Model for Orthotic Material
=
+++
=2
1
2 3
2
i
el
ii
i iiiii (J
-
)11U 321
where U is the second order strain energy per unit of reference volume;
i are principal stretches;
elJ= 321
ABAQUS v6.4, HKS, Inc.
i,
iand
iare material parameters with
irelated to the initial shear modulus,
0, by
=
=2
1i
i0
and the initial bulk modulus, K0 defined by )1
(2 ii
i0 K +== 3
2
1
The coefficient i
determines the degree of compressibility, which is
related to the Poisson's ratio, i,byi
ii
2-1
=
Jel is the elastic volume ratio with
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Simulation of Midstance
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Effect of Insole Thickness on Plantar Pressure
Shod Insole3 Insole6 Insole12 Insole24MPa
Increasing Insole Thickness
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Effect of Insole Thickness on Plantar Pressure
0
0.05
0.1
0.15
0.2
0 3 6 9 12 15
Insole Thickness
Pea
kPlantarP
ressure,
MPa
Forefoot Rearfoot
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0
24
6
8
10
12
14
16
18
20
Shod Insole3 Insole6 Insole12 Insole24
Foot Support
Bone
Stress(Vo
nMises),M
Pa
ForeFoot MidFoot RearFoot
Effect of Insole Support on Bone Stress
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Design Factors & Levels of Taguchi Method
Level
Design factor Level 1 Level 2 Level 3 Level 4
Arch Type F FWB HWB NWB
Insole Thickness (mm) 3 6 9 12
Midsole Thickness (mm) 3 6 9 12
Insole Material
(Hardness)10 20 30 40
Midsole Material(Hardness) 20 30 40 50
F: Flat, FWB: Full-weight-bearing, HWB: Half-weight-bearing, NWB: Non-
weight-bearing. Hardness values of 10, 20, 30, 40 and 50 correspond to
Poron_L24, Poron_L32, Nora_SLW, Nora_SL, Nora_AL, respectively.
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Taguchi Experimental Design
Experiment
No. Arch HeightInsole
Thickness
Midsole
Thickness
Insole
Stiffness
Midsole
Stiffness
1 1 1 1 1
2
3
4
34
1
2
4
3
21
2
1
4
3
2 1 2 2
1
2
3
4
43
2
1
2
1
43
3
4
1
3 1 3 3
4 1 4 4
5 2 1 26 2 2 1
7 2 3 4
8 2 4 3
9 3 1 3
10 3 2 4
11 3 3 112 3 4 2
13 4 1 4
2
14 4 2 3
15 4 3 2
16 4 4 1
Example of an LExample of an L1616 Orthogonal ArrayOrthogonal Array
Robust Simulation = 16 < Full Factorial Simulation = 45 = 1024
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0.06
0.07
0.08
0.09
1 2 3 4
Level
MidfootPlantarPressu
re,
MPa
Arch Type
Insole Thickness
Midsole Thickness
Insole Stiffness
Midsole Stiffness
Mean Effects of Design Factors at Each Level onthe Predicted Peak Plantar Pressure
0.1
0.15
0.2
0.25
1 2 3 4
Level
ForefootPlantarPressure,MPa
Arch Type
Insole Thickness
Midsole Thickness
Insole Stiffness
Midsole Stiffness
0.1
0.125
0.15
0.175
1 2 3 4
Level
RearfootPlantarPressur
e,
MPa
Arch Type
Insole Thickness
Midsole Thickness
Insole Stiffness
Midsole Stiffness
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Fabrication of Foot Orthosis
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Plantar Pressure Measurement
F-scan in-shoe sensors
F-scan System,Tekscan, Inc.
Video capture of
foot-shank position
Sensor calibration bysingle-leg standing
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Plantar Pressure & Foot-Shank PositionMeasurement during Normal Walking
Normal walking with
self-selected pace(~1.15s cycle time)
Synchronization of pressure
and video data
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Predicted and Measured Plantar Pressure
Distributions during Midstance
MPa MPa
Flat Arch supported Flat Arch supported
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F-scan measured mean peak plantar pressure withdifferent configurations of foot orthosis
Configurations of foot orthosis F-scan measurement, MPa
TrialNumber
ArchType
Insole(Poron_L32)
Thickness, mm
Midsole(Nora_SL)
Thickness, mm
Forefoot Midfoot Rearfoot
1 F 0 3 0.133 0.077 0.100
2 F 3 3 0.120 0.070 0.087
3 F 6 3 0.113 0.073 0.0904 FWB 0 3 0.117 0.073 0.070
5 FWB 3 3 0.097 0.053 0.060
6 FWB 6 3 0.110 0.047 0.060
7 HWB 0 3 0.103 0.06 0.0708 HWB 3 3 0.090 0.057 0.057
9 HWB 6 3 0.100 0.060 0.060
10 NWB 0 3 0.083 0.063 0.047
11 NWB 3 3 0.073 0.047 0.047
12 NWB 6 3 0.087 0.050 0.043
F: Flat, FWB: Full-weight-bearing, HWB: Half-weight-bearing, NWB: Non-weight-bearing
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Design Guidelines on Pressure-relieving Foot Orthoses
Among five design factors(arch type, insole material, insole thickness, midsole material
and midsole thickness)
Use of an arch-conforming foot orthosis;
Soft insole material;
Increase thickness of Insole; Soft midsole material;
Increase thickness of midsole.
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Other Parametrical Analysis
Shape Design Material Design
Custom-molded
Shape
Heel Elevation Forefoot Region
Number of
Layers &
Thickness
Insole Body
Metatarsal
PaddingHeel Region
Shank & Arch
Profile
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Incorporation of FootIncorporation of Foot--Shoe InterfaceShoe Interface
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Simulations of
Stance Phases of Gait
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Extension to
Knee-Ankle-FootFE Model
Tissue Testing
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Plantar Heel PadPlantar Heel Pad -- Compression TestCompression Test
Fascia and LigamentsFascia and LigamentsTensile TestTensile Test
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Conclusions
The developed finite element ankle-foot model
Allow efficient parametric evaluations of different design
parameters of orthoses without the prerequisite of
fabricated orthoses and replicating patient trials.
Contribute to the knowledge base for the design of
optimal foot orthoses or footwear in terms of pressureredistribution, foot arch support or bone and ligament
stress relief.
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AcknowledgementsDr. Ameersing Luximon, Dr. Terry Koo, Research Students & Colleagues
Department of Health Technology & Informatics,
The Hong Kong Polytechnic University, Hong Kong.
Prof. Kai-Nan An and Colleagues
Biomechanics Laboratory, Department of Orthopedic Surgery,
Mayo Clinic, Rochester, Minnesota, USA.
Dr. Jun Auyeung and Colleagues
Institute of Clinical Anatomy, The Southern Medical University, Guangzhou,
China for facilitating the cadaveric experiment.
Financial support from the Hong Kong Jockey Club endowment, research
grant from The Hong Kong Polytechnic University and the Research Grant
Council of Hong Kong.(Project No. PolyU 5249/04E, PolyU 5317/05E)
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Cheung JT, Zhang M, 2006. Consequences of partial and total plantar fascia release a finite
element study. Foot and Ankle International. 27, 125-132.
Dai XQ, Li Y, Zhang M, Cheung JT, 2006. Effect of sock on biomechanical responses of foot
during walking. Clinical Biomechanics. 21, 314-321.
Cheung JT, Zhang M, An KN, 2006. Effect of Achilles tendon loading on plantar fascia tension
in the standing foot. Clinical Biomechanics. 21, 194-203.
Cheung JT, Zhang M, 2006. A serrated jaw clamp for tendon gripping. Medical Engineering
and Physics. 28, 379-382.
Cheung JT, Zhang M, Leung AK, Fan YB, 2005. Three-dimensional finite element analysis of
the foot during standing A material sensitivity study. Journal of Biomechanics. 38, 1045-
1054.
Cheung JT, Zhang M, 2005. A 3-dimensional finite element model of the human foot and anklefor insole design. Archives of Physical Medicine and Rehabilitation. 86, 353-358.
Cheung JT, Zhang M, An KN, 2004. Effects of plantar fascia stiffness on the biomechanical
responses of the ankle-foot complex, Clinical Biomechanics. 19, 839-846.
Cheung JT, Luximon A, Zhang M, 2006. Parametrical design of pressure-relieving footorthoses using statistical-based finite element method, Journal of Biomechanics, submitted.
Peer-reviewed Journal Publications
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Department of Health Technology
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