A study of plantar stresses underneath metatarsal heads in the human foot 1

A STUDY OF PLANTAR STRESSES UNDERNEATH METATARSAL HEADS IN THE HUMAN FOOT CHEN, WEN-MING NATIONAL UNIVERSITY OF SINGAPORE 2011... A STUDY OF PLANTAR STRESSES UNDERNEATH METATARSAL HEAD

A STUDY OF PLANTAR STRESSES UNDERNEATH METATARSAL HEADS IN THE HUMAN FOOT

CHEN, WEN-MING

NATIONAL UNIVERSITY OF SINGAPORE

2011

A STUDY OF PLANTAR STRESSES UNDERNEATH METATARSAL HEADS IN THE HUMAN FOOT

CHEN, WEN-MING

(B.Sc (Double Degree), M.Eng)

A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DIVISION OF BIOENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2011

ACKNOWLEDGMENTS

This work was supported by a grant entitled, ‘TDSI/09-009/1A: development of next generation combat boots with reduced shear force mechanism’ from the Temasek Defense Systems Institute, and I am also very grateful to NUS Faculty

of Engineering Scholarship which financially supported me during my four-year doctoral studies in Singapore

The work would not have been possible without continuous guidance and support from my thesis committee members I would like to express here my sincere respect and deepest gratitude to Dr Taeyong Lee, Prof James Goh, and Assoc/Prof Toh SL I would particularly like to thank Prof Victor Shim from Department of Mechanical Engineering NUS, for the use of his lab facilities on strain-gauging, DAQ (oscilloscope), as well as the numerous helpful discussions during our monthly meetings Special thanks are due also to my previous mentor Prof Sung-Jae Lee, from INJE University, and Assoc/Prof Peter Lee, from University of Melbourne, for taking intense academic interest in this study as well

as encouraging me throughout these years Sincere thanks are extended to our clinical collaborator, Dr Adriaan Erasmus from Rehabilitation Center, National University Hospital, for many valuable comments which indeed helped improve this thesis

Finally, I would like to express my loving thanks to my wife Miao who accompanied me at NUS through every hardship that I have encountered in the past few years Without her understanding, encouragement and support it would not have been possible for me to finish this work I love you, and thank you

TABLE OF CONTENTS

List of Tables……….…………7

List of Figures……… ….………….9

List of Abbreviations and Symbols……… 14

Chapter 1 Introduction 1.1 Biomechanics of neuropathic diabetic foot ulcers……… 17

1.2 Literature review……… 19

1.2.1 Plantar stresses and mechanical etiology of diabetic foot ulcers…19 1.2.2 Challenges in measuring plantar shear stresses………21

1.2.3 Modeling and simulation of foot mechanism for three-dimensional interfacial stress predictions……….… 24

1.3 Objectives and overview of thesis………27

Chapter 2 Numerical modeling of human foot 2.1 Finite element model of the foot-ankle complex………30

2.1.1 Finite element method………30

2.1.2 3-D reconstruction of foot geometry………31

2.1.3 Model discretization (element selection) ………33

2.2 Material properties for finite element modeling………34

2.2.1 Cortical and cancellous bones, ligaments, and cartilages………….34

2.2.2 Achilles and other flexor tendons……… 35

2.2.3 Constitutive model for plantar soft tissue……… …38

2.2.3.1 Hyperelastic material models……… ………38

2.2.3.2 Ogden model……….40

2.2.4 Material model for foot-support surface………41

2.2.4.1 Insoles as supporting interface for foot……… 41

2.2.4.2 ABAQUS® hyperfoam material model………43

2.3 Loading and boundary conditions at push-off………44

2.3.1 Articular joint movement ………45

2.3.2 Plantar flexor muscle forces ……….47

2.3.2.1 Roles of the extrinsic plantar flexor muscles……….47

2.3.2.2 Calculation of musculoskeletal loads……… 48

2.3.3 Foot-ground interaction with frictional contact……… 51

2.3.3.1 Coulomb friction……… 51

2.3.3.2 Contact problems at foot support interface………… ……53

2.4 Finite element foot model outputs………54

Chapter 3 Experimental technique 3.1 Instrumented soft tissue tester………57

3.1.1 Measurement of soft tissue properties under metatarsal heads…57 3.1.2 Development of tissue tester………59

3.1.2.1 Multiple DOF foot positioning apparatus……….59

3.1.2.2 Portable motorized indentor……… …60

3.1.3 Assessing in-vivo tissue properties under metatarsal heads…… 62

3.1.3.1 Repeatability of MPEAI tests……… 62

3.1.3.2 Force-displacement response of soft tissue under metatarsal heads ……… … 66

3.1.4 Derivation of material constants for plantar soft tissue……….67

3.1.4.1 Classical Hertz contact theory……… ….67

3.1.4.2 Direct extraction of hyperelastic material constants… …67

3.1.4.3 Use of material constants in plane-strain FEM……….….72

3.2 Gait platform for measuring 3-D plantar stresses……… 75

3.2.1 3-D plantar stress measurement……….……75

3.2.2 Design, fabrication and calibration of pressure/shear sensor… 77

3.2.2.1 Mechanical design of force sensor……….77

3.2.2.2 High-resolution sensor array………78

3.2.2.3 Design of force sensor electronics……… 80

3.2.2.4 Sensor calibration……… 81

3.2.2.5 Construction of new gait platform………84

3.2.3 Assessing sub-MTH loads……… 85

3.2.4 Calculation of shear traction ratio ……….89

Chapter 4 Evaluation of model performance

4.1 Comparison of FEM results with experimental data………93

4.1.1 Simulated muscular loads……….94

4.1.2 Plantar stress distribution……… 96

4.1.3 Metatarsal bone strain………99

4.2 Sensitivity to flexor muscle force variations……….…100

4.2.1 Role of gastrocnemius-soleus (G-S) muscle complex……… …100

4.2.2 Parametric study on F AT variations………104

4.2.2.1 Effects of Achilles tendon forces variations on movements at the ankle and metatarsophlageal joints……… 105

4.2.2.2 How Achilles tendon forces variations affects the forefoot plantar pressure/shear stresses distribution……… 107

4.2.2.3 Effects of F AT variations on sub-MTH pressure peaks…110 4.3 Possible application of model in design of therapeutic footwear………….112

4.3.1 Insoles for stress relief under MTHs……….112

4.3.2 Modification of insoles for foot-support interface applications… 114

4.3.3 Efficacy of modified insole in relieving loads under MTHs….… 115

Chapter 5 Conclusions 5.1 Summary……… ……….118

5.2 Original Contributions……… … 120

5.3 Future Directions……….121

Appendix A: Finite element analysis (FEA) ………124

References ………133

Publications arising from the thesis ……… 141

ABSTRACT

A musculoskeletal finite element model (FEM) of the human foot was developed

to investigate plantar stresses underneath metatarsal heads (MTHs) in the

forefoot Vertical and shear forces at individual MTH sites were also measured in vivo through use of a specially-designed novel gait platform system, which allows

three-dimensional interfacial stresses and local shear traction ratios to be calculated Average peak vertical pressures obtained are within the range of published data based on commercial capacitance sensors The measurements from experiments were employed as inputs to the FEM model to define sliding contact with Coulomb friction at the foot-support interface, as well as to validate the foot model The mechanical properties of the soft tissue under MTHs were quantified by means of an instrumented indentation device It was found that sub-MTH pad tissue behavior is unique and dependent on metatarsophalangeal joint dorsiflexion angle The data obtained was also employed to determine the material constants in the hyperelastic constitutive model adopted to describe such tissue This facilitated accurate estimation of the sub-MTH stresses induced during foot-ground interactions

Simulations were undertaken to predict changes in foot mechanism, in terms of internal joint configurations and plantar loads distributions, which would occur to accommodate any reduction in muscle effectiveness of the gastrocnemius-soleus complex The results correspond well with clinical observations in diabetic patients who underwent tendo-Achilles lengthening procedures Stress reductions at individual MTHs were found to be site-specific

and possibly dependent on foot structures, such as intrinsic alignment of the metatarsals These highlight the clinical relevance of the model established in terms of analyzing the foot mechanism To illustrate possible application of the model developed to therapeutic footwear intervention, the effects of modified foot-support interfaces were also examined This showed that inclusion of a metatarsal support into a flat foam pad has the potential to relieve sub-MTH plantar stresses Forefoot plantar stress distribution is sensitive to positioning of the metatarsal support, as well as the material used

The level of complexity of the foot model established is unprecedented and enables examination of the biomechanical interplay among muscular control, bony joint movement, and foot/support interface interactions This is also the first attempt at such a comprehensive investigation of the foot mechanism The instrumented tissue tester and gait platform system developed are unique experimental tools which facilitate determination of material model parameters,

as well as model validation This is also a pioneer study of the efficacy of design variables for therapeutic footwear in relieving contact stress, including plantar shear, at sub-MTH region

LIST OF TABLES

1.2.2.1 A summary of plantar shear sensors reported in the literature 23 2.2.2.1 Summary of FE model listing element type and material

properties for different model entities 37

2.2.4.2 The material constants of the hyperfoam strain energy function

for the foam pad used as the foot-supporting interface 44

2.3.2.2

The input forces in the muscles applied through the nodes connected to tendon elements to drive the finite element foot model

50

3.1.4.3 The material properties used in the current finite element foot

model in comparison with those existing models for heel pad 71

3.2.2.1

Calibration results of 9 strain-gauged sensors corresponding to

27 channels used in the 3 by 3 sensor array For each channel

(AP: anterioposterior; ML: mediolateral; V: vertical) of an individual sensor 6 measurements were performed Measurement errors were quantified as the standard deviation

of the maximum local force amplitude in the AP, ML, and vertical

directions, respectively Average measurement errors are 2.8%,

3.1%, and 2.7% for directional forces in the vertical, AP and ML

stress; PSS-ML: peak mediolateral shear stress)

99

4.1.3.1

The average strain in the 2nd metatarsal mid-shaft in comparison with the cadaver study results by Sharkey et al., (1995)

99

4.2.2.1 Variations of G-S complex muscle force (F AT) studied in the

present model sensitivity analysis 104

4.3.3.1

Model predicted changes in plantar stress peaks under 2nd MTH due to different foot support conditions (MSP-5: Metatarsal support positioned 5 mm proximal to the 2nd MTH)

116

LIST OF FIGURES

1.2.1.1

Diagram illustration of the effect of shear stress and pressure

on plantar tissue deformation modes underneath the metatarsal

head (MTH) The distortion associated with pure pressure is

compression Shear stress results in tissue distortions in

parallel planes (i.e., angular deformation), which give rise to

elevated stress and tend to cause a “tear” within the tissue

close to bone prominences (Cavanagh and Ulbrecht, 2006)

20

2.1.2.1

Segmentation of a human foot from individual coronal CT

slices The bones were modeled as articulated parts enveloped

into a bulk soft tissue

31

2.1.2.2

3-D solid model of foot geometry, including a bulk soft tissue

(A) and bones (B) Note that the foot skeletal was stabilized by

various ligaments

32

2.1.3.1 Finite element mesh the foot (A) soft tissue, (B) internal bony

structures, and (C) various ligaments 33

2.2.4.1 Stress-strain curve obtained from uni-axial compression test of

deformable four different types of foam padding materials 42

2.3.1.1

Master/Slave approach to model contact interactions The

contact behavior strictly follows the kinematic implications that

slave nodes cannot penetrate master surface segments

(Hibbert and Karssonn, 2006)

46

2.3.2.2

Cut through the element mesh of the finite element model of

muscular foot and ankle complex, incorporating internal soft

tissue, skeletal structures, ligaments, plantar fascia, and

musculotendinous units for push-off simulation Application of

muscle forces were simulated by force vectors align with the

tendons attached FAT = Gastrocnemius-soleus complex, FTIBP

= Tibialis posterior, FFHL= Flexor hallucis longus, FFDL = Flexor

49

digitorum longus, FPB = Peroneus brevis, and FPL = Peroneus

longus

2.3.3.1

Relative sliding of points with contact constraint Note the

possible evolution of contact between node 101 and its master

surface, BSURF, with sliding contact conditions with friction

52

2.3.4.1

The finite element predicted stress response of a whole human

foot subjected to comprehensive musculoskeletal loading corresponding to a heel-rise posture Outcome measures of

primary interest in foot biomechanics, including stress distributions of bulk soft tissue, metatarsal bones, ligaments

and plantar fascia, can be obtained

55

3.1.2.1

Schematic diagram of the sub-Metatarsal Pad Elasticity Acquisition Instrument (MPEAI), showing details of probe tip,

accommodation of sub-MTH pad and inside components of

actuator to drive probe tip

60

3.1.2.2

(A) Photograph and (B) schematic diagram of test set-up,

showing ‘trapped’ 2nd sub-MTH pad and initial contact with

probe tip

61

3.1.2.3 (A) Displacement-time profile of indentation cycle for probe tip 61

3.1.3.1

Typical tissue reaction force patterns obtained for 2nd sub-MTH

pad for similar indentation, but with MTP joint (MTPJ) at

different dorsiflexion angles There was qualitative similarity in

all sets of curves for given testing conditions, and this indicated

that the experiments were well-controlled All the curves possess similar characteristic profiles, such as nonlinear loading/unloading phases and a substantial force relaxation

component Note that the sub-MTH pad tissue response is

dependent on MTP joint angle, i.e lower stiffness at lower joint

dorsiflexion and increasing stiffness at higher joint angles

64

3.1.3.2 Calculated initial stiffness (= peak tissue reaction force/ δ, δ1

3.1.3.3 Calculated end-point stiffness (= peak tissue reaction force/

3.1.3.4 Force relaxation as percentages at δmax for 2nd Sub-MTH pad

of two normal subjects, for increasing MTP joint angles 65

3.1.4.1

Values of material constants (;α) obtained through nonlinear

least squares (NLS) minimization using the deduced contact

equations for of the 1st-order Ogden hyperelastic model in

MATLAB The calculated root-mean-square-error (RMSE) was

as small as 0.512 N with a R2 value of 0.9821

70

3.1.4.2

Comparison of the stress–strain behavior for the current

sub-MTH pad tissue model and those previously models: heel pad

by Erdemir et al (2006), heel fat pad and skin model by Spears

et al (2007)

71

3.1.4.3

Application of the calculated material constants in a plane-strain

finite element model The MTH geometry was simplified as a

sphere with a diameter of r The r values was determined

through optimal surface fitting of the 3-D contour lines which

defines the actually shape of the 2nd MTH The sub-MTH soft

tissue thickness t was defined as the shortest line distance

between the MTH and the plantar surface

72

3.2.2.1

(A) Schematic diagram of sensor showing the positions of the

strain gauges and (B) photograph showing the attachment of

strain gauges to the front surfaces of the sensor body Gauges

are also bonded to the rear surfaces The positions of the

vertical and shear channels are also shown

77

3.2.2.2

(A) Nine strain-gauged sensors were assembled into (B) a 3 by

3 sensor array; for a single strain-gauge channel, (C) the

electronic interface of a full-bridge circuit configuration was

shown

79

3.2.2.3

A screen shot of the dynamic data acquisition (DAQ) system for

real-time strain measurements of the force sensor array using

LabVIEW (National Instrument) The block diagram of the program is not shown

79

3.2.2.4 Calibration graphs showing linearity of the vertical channel 82 3.2.2.5 Calibration graphs showing linearity of the AP shear channel 82 3.2.2.6 Calibration graphs showing linearity of the ML shear channel 15

3.2.2.7

(A) Schematic diagram of the gait platform with mounted sensor

array (B) Photo of the foot making contact with the gait plate

that was embedded in a 7-meter walk way, sensor location in

relation to the placement of the foot plantar surface can be

monitored from the reflected mirror image by a high speed

camera (Fascam) positioned to capture the side view

84

3.2.3.1

Method to create the “MTH template”: Images of the plantar

surface of the forefoot (A) without and (B) with sensor during

barefoot walking Bony mark was used to identify the target

metatarsal site (C) R1~R3 represents three non-collinear markers for image registration between A and B Xi and Yi are

errors due to metatarsal site and sensor location discrepancy

86

3.2.3.2

Force traces in vertical, AP and ML directions measured under

the 1st (A), 2nd (B), 3rd (C) and 4th (D) MTHs during barefoot

walking trails

88

3.2.3.1

Local traction ratios obtained at sub-MTH area for the example

reading of horizontal (F x and F y ) and vertical forces (F z) from

our customized pressure/shear sensor array

Model predicted (A) plantar pressure, (B) AP and (C) ML shear

distributions, and (D) VMS stress distributions in metatarsal

bones

97

4.2.2.1

Correspondence of gastrocnemius-soleus muscle forces (indicated as FAT) and the ankle () and metatarsophalangeal

() joints’ angles during heel rise The amount of the muscle

forces in FAT was varied between 1620N (100% effectiveness)

and 972N (60% effectiveness) The angles were calculated

relative to the joint configurations at foot’s neutral position

105

4.2.2.2

Percentage changes of local pressures under individual MTHs

for different ankle joint angles () Nodal points just underneath

five MTHs were selected for analysis Note the most significant

pressure reduction site was under the 2nd MTH for the particular model analyzed in this study

107

4.2.2.3

Changes in resultant plantar tissue shear stress distributions in

response to incrementally reduced gastrocnemius-soleus (G-S)

muscle forces

108

4.2.2.4

Percentage changes of local pressures under individual MTHs

for different ankle joint angles () Nodal points just underneath

five MTHs were selected for analysis Note the most significant

pressure reduction site was under the 2nd MTH for the particular model analyzed in this study

110

4.3.2.1

Finite element model of a flat insole with an integrated metatarsal support component interfacing with the forefoot plantar surface

114

4.3.3.1

Finite element predicted plantar anterio-posterior shear stresses with different foot-supporting interfaces (A) rigid ground, (B) soft foam pad, (C) a soft insole integrated with

metatarsal support

115

5.3.1.1 FE mesh of a musculoskeletal foot model with flexors and

extensors for stance phase gait simulation 122 5.3.1.2 A further gait platform system with a larger sensor array can be

installed in a typical gait lab for large-scale experiments 123