Finite Element Modeling of the Human Foot and · PDF fileFinite Element Modeling of the Human Foot and Footwear ... 2Human Performance Laboratory, ... sustaining tension ~45% of applied

Finite Element Modeling of the Human Foot and Footwear

Jason Jason 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, China

2Human Performance Laboratory, University of Calgary, Calgary, Alberta, Canada

Department of Health Technologyand Informatics

醫療科技及資訊學系

Common Foot Problems

Calluses Corns

http://www.foot.com

Bunions

Hammertoe

Claw Toe

Mallet ToeMetatarsalgia

Achilles Tendonitis

Plantar Fasciitis

Heel Spurs

Calluses Corns

http://www.foot.com

Bunions

Hammertoe

Claw Toe

Mallet ToeMetatarsalgia

Achilles Tendonitis

Plantar Fasciitis

Heel Spurs

Why Finite Element (FE) Approach?• Experimental measurements of the biomechanical

variables 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 tissue structures.

– efficient parametrical analyses of loading conditions, structural and material variables.

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).

Objectives• To develop a comprehensive 3D FE model to

quantify the biomechanical response of the human foot and ankle (joint motion, load distribution of bony and soft tissue structures and foot-support interface).

• To provide a systematic tool for the parametric analyses of different foot structures, surgical and footwear performances.

Development of the Finite Element Model• Coronal MR images of 2mm

intervals obtained from the right foot of a healthy male subject in unloaded, neutral position

3D Reconstruction of Foot Structures

Boundaries for Foot Bones

Boundary for Soft Tissue

Segmentation (Mimics v7.10, Materialise.)

Surface ModelSolid Model(SolidWorks v2001, SolidWorks Corp.)

Finite Element Mesh of Bony and Soft Tissue Structures Automatic mesh creation in ABAQUS v6.4, HKS.

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.

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)

Joint Articulations of the Model• The phalanges were connected together using

2 mm thick structural elements to simulate the connections.

• The interaction between the metatarsals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined by contact surfaces with a prescribed contacting stiffness of articularcartilage to allow relative bone movement.

Material Properties of Ankle-Foot ModelEncapsulated soft tissue (Hyperelastic) Bony & ligamentous structures (Homogeneous, Linearly elastic)

Component Element Type Young’s ModulusE (MPa)

Poisson’s Ratioν

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).

Hyperelastic Material Model for Soft Tissue2i

el

2

1i i

ji2

1jiij (J

D)I(I(C )113)3U 2

__

1

__−+−−= ∑∑

==+

where U is the second-order strain energy per unit of reference volume; Cij and Di are material parameters;

1

__I 2

__Iand are the first and second deviatoric strain invariants:

I2

3

__2

2

__2

1

__

1

__λ+λ+λ=

I)2(

3

__)2(

2

__)2(

1

__

2

__ −−−

λ+λ+λ=

with the deviatoric stretches i

__λ = Jel

-1/3 λi ;Jel and λi are the elastic volume ratio & the principal stretches.

ABAQUS v6.4, Hibbitt, Karlsson & Sorensen, Inc.

Application of Loading and Boundary Conditions

Fixed SurfacesConnector Elements for Muscles Force Application

Moving Support for Foot-Insole Interface and Ground Reaction Force Application

References for Muscular Insertion Points

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

Muscles and Ground Reaction Forces for Standing and Midstance Simulation

Tendon/External Forces Standing MidstanceAchilles 175N

-----

Reaction of Lateral Retinaculum - 50NReaction of Medial Retinaculum - 60N

350N

750Tibialis Posterior 70N

Flexor Hallucis Longus 35NFlexor Digitorum Longus 40N

Peroneus Brevis 40NPeroneus Longus 35N

Vertical Ground Reaction 550N

The active extrinsic muscles forces during midstance were estimated from normalized EMG data using a constant muscle gain and cross-sectional area relationship (Dul, 1983; Kim et al., 2001; Perry, 1992).

Simulation of Midstance Contact

10 Degrees

Plantar PressureF-scan Measurement FE Prediction

MPa MPa

Contact Area68.8 cm2

ContactArea68.3 cm2

Predicted Von Mises Stress of Bony and Ligamentous Structures

MPa

Plantar View Dorsal View

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.

The Plantar Fascia and Plantar Ligaments

Plantar fascia

Long plantar lig.

Short plantar lig.

Spring lig.

Effect of varying Young’s modulus of fascia on arch height and arch length

3738394041424344

0 175 350 525 700

Young's Modulus of Fascia, MPa

Arc

h H

eigh

t, m

m

Arch Height

141142143144145146147148149

0 175 350 525 700


Arc

h Le

ngth

, mm

Arch Length

Deformed Arch Height(42.5 mm) FE

(44 mm) Measured

Unloaded Arch Height(52.5 mm)

Effect of varying Young’s 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


Fasc

ia T

ensi

on, N

Total Tension

0

50

100

150

0 175 350 525 700Young's Modulus of Fascia, MPa

Liga

men

t Ten

sion

, N

Long Plantar Lig.Short Plantar Lig.Spring Lig.

With Fasciotomy

Clinical Implications• The plantar fascia is one of the major stabilizers of the

longitudinal 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.

Parametrical Studies• Effect of plantar fascia stiffness.

• Effect of plantar soft tissue stiffening (Up to 5 times).




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 0.5

Strain

Stre

ss (M

Pa)

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).

Effect of Soft Tissue Stiffening on Plantar Pressure Distribution

5 Times3 Times

MPaMPa

2 TimesNormal

MPa MPa

Peak0.230 MPa

Peak0.263 MPa

Peak0.291 MPa

Peak0.306 MPa

Increasing Soft Tissue Stiffness

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

Con

tact

Are

a (c

m2 )

ForeFoot

MidFoot

RearFoot

WholeFoot

0

0.1

0.2

0.3

0.4

1 2 3 4 5

Factor of Soft Tissue Stiffening

Peak

Pre

ssur

e (M

Pa)

ForeFoot

MidFoot

RearFoot

Five times Heel (33%), Forefoot (35%) 47%Soft tissue stiffness Peak Plantar Pressure Contact Area

Clinical Implications• Stiffening of plantar soft tissue may induce excessive

pressure 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 viable method in addition to plantar pressure measurement for routine identification of diabetic feet at risk of ulceration.

Parametrical Studies• Effect of plantar fascia stiffness.

• Effect of plantar soft tissue stiffening.

• Effect of Achilles tendon loading (0 to 700 N).



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.

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

Specimen PreparationAfter thawing at room temperature• Skin, subcutaneous tissues and muscles above the ankle joint

level dissected with all muscular tendons left intact• Distal fibula and tibia potted in acrylic resin

Compression Test of Cadaveric Foot

F-scan pressure sensor(Tekscan, Inc.)

Implanted displacement transducer (Microstrain, Inc.)

Load cell(MTS Systems)

Cadaveric Foot under Vertical Compression up to 700 N

Vertical Deformation and Plantar Fascia Strain under Vertical Compression

0

2

4

6

8

10

0 100 200 300 400 500 600 700

Vertical compression, N

Vert

ical

def

orm

atio

n, m

m

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

Stra

in o

f pla

ntar

fasc

ia, %

Specimen_2 Specimen_3 Specimen_4Specimen_5 Specimen_6 FE_AverageFE_Max

Displacement Fascia Strain Fascia strain (>100N)ICC (Consistency) : 0.892 0.880 0.994

Effects of Vertical Compression and Achilles Tendon Loading on the Plantar Fascia Tension

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600 700Vertical compressive/Achilles tendon forces, N

Tota

l fas

cia

forc

es, N

Vertical compressive forces (0-700N)350N compression preload + Achilles tendon forces (0-700N)

Clinical Implications• Achilles tendon loading produces a greater straining

effect 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 and Achilles tendon may be beneficial in terms of plantar fascia stress relief.

Parametrical Studies• Effect of plantar fascia stiffness, partial and total plantar

fascia release.





Simulated Conditions

Intact PTTD

PTTD + Fasciotomy Fasciotomy

Simulations of Fasciotomy

Intact

Fasciotomy

Experimental Setup

F-scan Pressure Sensor(Plantar foot pressure)

Bone Marker(Joint movement)

Displacement Transducer (Microstrain, Inc.)(Fascia strain)

Tendon Clamp(Muscle forces application)

Stance Phase Simulation3D Laser Scanner

Deadweights

Marker Scanning

(Realscan USB 200, 3D Digital Corp.)

Predicted Changes in Arch Height

3.7

3.8

3.9

44.1

4.2

4.3

Intact PTTD PFR PTTD+PFRSimulated Conditions

Arc

h H

eigh

t, cm

Effect of PTTD on Plantar Fascia Strain

0

0.5

1

1.5

2

2.5

Intact PTTD Intact PTTDFE Prediction Measurement

Fasc

ia S

trai

n, %

Predicted Changes in Fascia & Ligaments Tension

0

50

100

150

200

250

300

350

400

450

Intact PTTD PFR PTTD+PFRSimulated Conditions

Tens

ion,

N

Plantar Fascia Long Plantar Lig. Short Plantar Lig. Spring Lig.

Prediction of Joint Motion

Effect of PTTD & PFR on Joint MotionRelative Bones Intact with PTTD Intact with PFR PFR with PTTD

Talus to Tibia

PlantarFlexion Eversion External

RotationPlantarFlexion Eversion Internal

Rotation

Eversion External Rotation

External Rotation

External Rotation

Internal Rotation

Eversion

Inversion

PlantarFlexion Eversion Internal

Rotation

Calcaneusto Talus

DorsiFlexion Eversion External

Rotation

Inversion

PlantarFlexion

DorsiFlexion

DorsiFlexion

DorsiFlexion

DorsiFlexion Inversion External

Rotation

Navicularto Talus

DorsiFlexion Eversion Internal

RotationDorsi

Flexion Eversion External Rotation

1st Metatarsal to Navicular

PlantarFlexion Inversion Internal

RotationDorsi

Flexion Eversion Internal Rotation

1st Metatarsal to Talus

DorsiFlexion Eversion External

RotationDorsi

Flexion Eversion External Rotation

FE Prediction

67%

78%

44%

22%

56%

Green: Agreement with cadaveric studiesRed: Disagreement agreement with cadaveric studies

Percentage of Agreement (%)Sagittal plane Coronal Plane Transverse Plane

73% 60% 27%

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.

Parametrical Studies• Effect of plantar fascia stiffness, partial and total plantar

fascia release.





Geometry of Foot OrthosisLaser scanning during balanced standing

INFOOT Laser Scanner,I-Ware Laboratory Co. Ltd.

Geometrical Model of Foot Orthosis

(MATLAB, The MathWorks, Inc)Foot Surface Model

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

Orthosis Surface Model

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, 24mm3mm (base), 30mm (arch)

12mmMidsole (Nora SL) 3D-BrickOutsole (Nora AL) 3D-Brick

Compression Test of Insole Material

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

Hyperfoam Material Model for Orthotic Material

∑=

−⎥⎦

⎤⎢⎣

⎡−+λ+λ+λ

α=

2

1

αααα

23

2

i

βel

ii

i iiiii (Jβ

-μ )11ˆˆˆU 321

where U is the second order strain energy per unit of reference volume;

iλ̂ are principal stretches;elJ=λλλ 321

ˆˆˆ

ABAQUS v6.4, HKS, Inc.

µi, αi and βi are material parameters with µi related to the initial shear modulus, µ0, by ∑

=

=2

1ii0 μμ

and the initial bulk modulus, K0 defined by )1(2 ii

i0 βμK += ∑= 3

2

1

The coefficient βi determines the degree of compressibility, which is related to the Poisson's ratio, νi , by

i

ii ν

νβ

2-1=

Jel is the elastic volume ratio with

Simulation of Midstance

Effect of Insole Thickness on Plantar Pressure

Shod Insole3 Insole6 Insole12 Insole24MPa

Increasing Insole Thickness

Effect of Insole Thickness on Plantar Pressure

0

0.05

0.1

0.15

0.2

0 3 6 9 12 15

Insole Thickness

Peak

Pla

ntar

Pre

ssur

e, M

Pa

Forefoot Rearfoot

02468

101214161820

Shod Insole3 Insole6 Insole12 Insole24Foot Support

Bon

e St

ress

(Von

Mis

es),

MPa

ForeFoot MidFoot RearFoot

Effect of Insole Support on Bone Stress

Design Factors & Levels of Taguchi MethodLevel

Design factorLevel 1 Level 2 Level 3 Level 4

Arch Type F FWB HWB NWBInsole Thickness (mm) 3 6 9 12

Midsole Thickness (mm) 3 6 9 12Insole 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.

Taguchi Experimental DesignExperiment

No. Arch Height Insole Thickness

Midsole Thickness

Insole Stiffness

Midsole Stiffness

1 1 1 1 1234341243212143

2 1 2 2123443212143341

3 1 3 34 1 4 45 2 1 26 2 2 17 2 3 48 2 4 39 3 1 310 3 2 411 3 3 112 3 4 213 4 1 4

2

14 4 2 315 4 3 216 4 4 1

Example of an LExample of an L1616 Orthogonal ArrayOrthogonal Array

Robust Simulation = 16 < Full Factorial Simulation = 45 = 1024

0.06

0.07

0.08

0.09

1 2 3 4

Level

Mid

foot

Pla

ntar

Pre

ssur

e, M

Pa

Arch Type

Insole Thickness

Midsole Thickness

Insole Stiffness

Midsole Stiffness

Mean Effects of Design Factors at Each Level on the Predicted Peak Plantar Pressure

0.1

0.15

0.2

0.25

1 2 3 4

Level

Fore

foot

Pla

ntar

Pre

ssur

e, M

Pa

Arch Type

Insole Thickness

Midsole Thickness

Insole Stiffness

Midsole Stiffness

0.1

0.125

0.15

0.175

1 2 3 4

Level

Rea

rfoo

t Pla

ntar

Pre

ssur

e, M

Pa

Arch Type

Insole Thickness

Midsole Thickness

Insole Stiffness

Midsole Stiffness

Fabrication of Foot OrthosisComputerized Numerical Control (CNC) Machining

LeadWell CNC Machines MFG. CORP.

Insole Milling

Fabrication of Foot Orthosis

Plantar Pressure Measurement

F-scan in-shoe sensors

F-scan System, Tekscan, Inc.

Video capture of foot-shank position

Sensor calibration by single-leg standing

Plantar Pressure & Foot-Shank Position Measurement during Normal Walking

Normal walking with self-selected pace (~1.15s cycle time)

Synchronization of pressure and video data

Predicted and Measured Plantar Pressure Distributions during Midstance

MPa MPa

Flat Arch supported Flat Arch supported

F-scan measured mean peak plantar pressure with different configurations of foot orthosis

Configurations of foot orthosis F-scan measurement, MPa

Trial Number

ArchType

Insole (Poron_L32)

Thickness, mm

Midsole (Nora_SL)

Thickness, mmForefoot Midfoot Rearfoot

1 F 0 3 0.133 0.077 0.1002 F 3 3 0.120 0.070 0.0873 F 6 3 0.113 0.073 0.090

4 FWB 0 3 0.117 0.073 0.0705 FWB 3 3 0.097 0.053 0.0606 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 0.0579 HWB 6 3 0.100 0.060 0.060

10 NWB 0 3 0.083 0.063 0.04711 NWB 3 3 0.073 0.047 0.04712 NWB 6 3 0.087 0.050 0.043

F: Flat, FWB: Full-weight-bearing, HWB: Half-weight-bearing, NWB: Non-weight-bearing

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.

Other Parametrical AnalysisShape Design Material Design

Custom-molded Shape

Heel ElevationForefoot Region

Number of Layers & Thickness

Insole Body

Metatarsal Padding

Heel Region

Shank & Arch Profile

Incorporation of FootIncorporation of Foot--Shoe InterfaceShoe Interface

Simulations of Stance Phases of Gait

Extension to Knee-Ankle-Foot

FE Model

Tissue TestingPlantar Heel Pad Plantar Heel Pad -- Compression TestCompression Test

Fascia and Ligaments Fascia and Ligaments –– Tensile TestTensile Test

ConclusionsThe 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 pressure redistribution, foot arch support or bone and ligament stress relief.

AcknowledgementsDr. Ameersing Luximon, Dr. Terry Koo, Research Students & ColleaguesDepartment of Health Technology & Informatics, The Hong Kong Polytechnic University, Hong Kong.

Prof. Kai-Nan An and ColleaguesBiomechanics Laboratory, Department of Orthopedic Surgery, Mayo Clinic, Rochester, Minnesota, USA.

Dr. Jun Auyeung and ColleaguesInstitute 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)

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 ankle for 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 foot orthoses using statistical-based finite element method, Journal of Biomechanics, submitted.

Peer-reviewed Journal Publications

Department of Health Technologyand Informatics

醫療科技及資訊學系

Documents

Finite Element Modeling of the Human Foot and · PDF fileFinite Element Modeling of the Human Foot and Footwear ... 2Human Performance Laboratory, ... sustaining tension ~45% of applied