cheung presentation.pdf

8/13/2019 Cheung Presentation.pdf

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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


2/78

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


3/78

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.


4/78

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).


5/78

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.


6/78

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


7/78

3D Reconstruction of Foot Structures

Boundaries forFoot Bones

Boundary forSoft Tissue

Segmentation (Mimics v7.10, Materialise.)

Surface ModelSolid Model(SolidWorks v2001, SolidWorks Corp.)


8/78

Finite Element Mesh of

Bony and Soft Tissue Structures

Automatic mesh creation inABAQUS v6.4, HKS.


9/78

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.


10/78

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)


11/78

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.


12/78

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).


13/78

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.


14/78

Application of Loading and Boundary Conditions

Fixed SurfacesConnector Elements

for Muscles ForceApplication

Moving Support for Foot-Insole Interface andGround Reaction Force Application


15/78

References for Muscular Insertion Points

Interactive Foot & Ankle, Ver.1.0.0, Primal Picture Ltd., UK, 1999


16/78

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).


17/78

Simulation of Midstance Contact

10Degrees


18/78

Plantar PressureF-scan Measurement FE Prediction

MPa MPa

Contact

Area

68.8 cm2

Contact

Area

68.3 cm2


19/78

Predicted Von Mises Stress ofBony and Ligamentous Structures

MPa

Plantar View Dorsal View


20/78

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.


21/78

The Plantar Fascia and Plantar Ligaments

Plantar

fascia

Long

plantar l ig.Short

plantar lig.

Spring lig.


22/78

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


ArchLeng

th,mm

Arch Length

Deformed Arch Height

(42.5 mm) FE

(44 mm) Measured

Unloaded Arch Height(52.5 mm)


23/78

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


FasciaTension,N

Total Tension

0

50

100

150

0 175 350 525 700


Ligame

ntTension,

N

Long Plantar Lig.Short Plantar Lig.Spring Lig.

With Fasciotomy


24/78

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.


25/78


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.



26/78

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


28/78

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


29/78


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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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.



31/78

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.


32/78

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


34/78

Compression Test of Cadaveric Foot

F-scan pressure sensor

(Tekscan, Inc.)

Implanted displacement transducer

(Microstrain, Inc.)

Load cell(MTS Systems)


35/78

Cadaveric Foot under

Vertical Compression up to 700 N


36/78

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


37/78

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)


38/78


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.


39/78


Effect of plantar fascia stiffness, partial and total plantarfascia release.






40/78

Simulated Conditions

Intact PTTD

PTTD + Fasciotomy Fasciotomy


41/78

Simulations of Fasciotomy

Intact

Fasciotomy


42/78

Experimental Setup

F-scan Pressure Sensor

(Plantar foot pressure)

Bone Marker(Joint movement)

Displacement

Transducer

(Microstrain, Inc.)(Fascia strain)

Tendon Clamp

(Muscle forces application)


43/78

Stance Phase Simulation

3D Laser Scanner

Deadweights

Marker Scanning

(Realscan USB 200, 3D Digital Corp.)


44/78

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


45/78

Effect of PTTD on Plantar Fascia Strain

0

0.5

1

1.5

2

2.5

Intact PTTD Intact PTTD

FE Prediction Measurement

FasciaStrain,%


46/78

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.


47/78

Prediction of Joint Motion


48/78

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%


49/78


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.


50/78


Effect of plantar fascia stiffness, partial and total plantarfascia release.






51/78

Geometry of Foot OrthosisLaser scanning during

balanced standing

INFOOT Laser Scanner,

I-Ware Laboratory Co. Ltd.


52/78

Geometrical Model of Foot Orthosis

(MATLAB, The MathWorks, Inc)Foot SurfaceModel

Solid Model of Foot Orthosis(SolidWorks 2001, SolidWorks Corporation)

Orthosis Surface Model


53/78

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


54/78

Compression Test of Insole Material

Hounsfield material testing machine (Model H10KM),Hounsfield Test Equipment, UK


55/78

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


56/78

Simulation of Midstance


57/78

Effect of Insole Thickness on Plantar Pressure

Shod Insole3 Insole6 Insole12 Insole24MPa

Increasing Insole Thickness


58/78

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


59/78

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


60/78

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.


61/78

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


62/78

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


63/78


64/78

Fabrication of Foot Orthosis


65/78

Plantar Pressure Measurement

F-scan in-shoe sensors

F-scan System,Tekscan, Inc.

Video capture of

foot-shank position

Sensor calibration bysingle-leg standing


66/78

Plantar Pressure & Foot-Shank PositionMeasurement during Normal Walking

Normal walking with

self-selected pace(~1.15s cycle time)

Synchronization of pressure

and video data


67/78

Predicted and Measured Plantar Pressure

Distributions during Midstance

MPa MPa

Flat Arch supported Flat Arch supported


68/78

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


69/78

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.


70/78

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


71/78

Incorporation of FootIncorporation of Foot--Shoe InterfaceShoe Interface


72/78

Simulations of

Stance Phases of Gait


73/78

Extension to

Knee-Ankle-FootFE Model

Tissue Testing


74/78

Plantar Heel PadPlantar Heel Pad -- Compression TestCompression Test

Fascia and LigamentsFascia and LigamentsTensile TestTensile Test


75/78

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.


76/78

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)


77/78

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


78/78

Department of Health Technology

and Informatics

cheung presentation.pdf

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