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 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 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 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 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 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 FAT 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 FAT 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 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 subMTH 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 Tables Descriptions Page 1.2.2.1. A summary of plantar shear sensors reported in the literature 2.2.2.1. 2.2.4.2. 23 Summary of FE model listing element type and material 37 properties for different model entities The material constants of the hyperfoam strain energy function for the foam pad used as the foot-supporting interface 44 The input forces in the muscles applied through the nodes 2.3.2.2. connected to tendon elements to drive the finite element foot 50 model 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 Calibration results of strain-gauged sensors corresponding to 27 channels used in the by sensor array. For each channel (AP: anterioposterior; ML: mediolateral; V: vertical) of an individual sensor measurements were performed. 3.2.2.1. Measurement errors were quantified as the standard deviation 63 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 axes, respectively Typical targeting errors showing the Xi and Yi offset values for 3.2.3.1. each of the five successive trials at the 2nd MTH (PPP: peak plantar pressure; PSS-AP: peak anterioposteiro shear stress; 87 PSS-ML: peak mediolateral shear stress) Summary of peak plantar stresses measured by sensor array and predicted by the finite element model under individual 4.1.2.1. metatarsal heads (MTHs) (PSS-AP: peak anterioposteiro shear 99 stress; PSS-ML: peak mediolateral shear stress) The average strain in the 2nd metatarsal mid-shaft in 4.1.3.1. comparison with the cadaver study results by Sharkey et al., 99 (1995) 4.2.2.1. Variations of G-S complex muscle force (FAT) studied in the present model sensitivity analysis 104 Model predicted changes in plantar stress peaks under 2nd 4.3.3.1. MTH due to different foot support conditions. (MSP-5: 116 Metatarsal support positioned mm proximal to the 2nd MTH) Correspondence of gastrocnemius-soleus muscle forces (indicated as FAT) and the ankle () and metatarsophalangeal 4.2.2.1. () joints’ angles during heel rise. The amount of the muscle forces in FAT was varied between 1620N (100% effectiveness) 105 and 972N (60% effectiveness). The angles were calculated relative to the joint configurations at foot’s neutral position Percentage changes of local pressures under individual MTHs for different ankle joint angles (). Nodal points just underneath 4.2.2.2. five MTHs were selected for analysis. Note the most significant 107 pressure reduction site was under the 2nd MTH for the particular model analyzed in this study Changes in resultant plantar tissue shear stress distributions in 4.2.2.3. response to incrementally reduced gastrocnemius-soleus (G-S) 108 muscle forces. Percentage changes of local pressures under individual MTHs for different ankle joint angles (). Nodal points just underneath 4.2.2.4. five MTHs were selected for analysis. Note the most significant 110 pressure reduction site was under the 2nd MTH for the particular model analyzed in this study Finite element model of a flat insole with an integrated 4.3.2.1 metatarsal support component interfacing with the forefoot 114 plantar surface Finite 4.3.3.1. 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 115 metatarsal support 5.3.1.1. 5.3.1.2. FE mesh of a musculoskeletal foot model with flexors and extensors for stance phase gait simulation 122 A further gait platform system with a larger sensor array can be installed in a typical gait lab for large-scale experiments 123 13 LIST OF ABBREVIATIONS AND SYMBOLS a Contact radius AP Anterior-posterior CT Computer tomography DOF Degree-of-freedom DAQ Data Acquisition DM Diabetes mellitus E Young’s modulus EVA Ethylene-vinyl acetate FAT Gastrocnemius-soleus complex FTIBP Tibialis posterior FFHL Flexor hallucis longus FFDL Flexor digitorum longus FPB Peroneus brevis FPL Peroneus longus Fx Anterior-posterior friction force Fxy Resultant shear forces Fz Normal force FEM Finite element method FHL Flexor hallucis longus FDL Flexor digitorum longus GRF Ground reaction force G-S Gastrocnemius-soleus LOPS Loss of protective sensation MTPJ Metatarsophalangeal joint MPEAI Metatarsal Pad Elasticity Acquisition Instrument ML Medial-lateral MRI Magnetic resonance imaging MTHs Metatarsal heads NLS Nonlinear least squares 14 PCSA Physiological cross-sectional areas PB Peroneus brevis PL Peroneus longus PPP Peak plantar pressure PSS-AP Peak anterior-posterior shear stress PSS-ML Peak medial-lateral shear stress R Radius of the rigid indenter TIBP Tibialis posterior TMF Total muscle force U Strain-energy function VMS Von Mises stresses σ Principal Cauchy stresses  Indentation pressure  Indentation strain δmax Maximum probe depth  Loading/unloading rate  Ground state shear modulus µ Friction coefficient  Poisson’s ratio λ1, λ2, λ3 Principal stretches 15 CHAPTER INTRODUCTION ~If you want to accomplish the goals of your life, you have to begin with the spirit~ Oprah Winfrey 16 1.1. Biomechanics of neuropathic diabetic foot ulcers Diabetes mellitus (DM) is a syndrome of disordered metabolism characterized by the common trait of excessive levels of glucose in the blood (e.g., when diabetes is not under control). Sustained elevations of blood glucose are often not noted by the patient; yet long term diabetes-associated lower extremity complications, including distal peripheral neuropathy, to a lesser extent, peripheral vascular disease, has been recognized for many years (Catterall et al., 1956). The diabetic neuropathy leads to ‘loss of protective sensation’ (LOPS), whereby a person is unable to feel minor trauma from repetitive mechanical stress during daily activity that ultimately result in foot ulceration (Cavanagh et al., 1993). The most costly and feared consequence is plantar ulceration that too often results in partial or total amputation of the foot. The lifetime risk for a patient with diabetes developing a foot ulcer could be as high as 25%, and diabetes related limb amputation occurs 10 to 30 times more often in DM patients than in the general population (Singh et al., 2005). In the past, many in vivo and in vitro studies that addressed foot risks have focused on delineating the potential overloading of the foot. Some early investigators have utilized pressure transducers, and shown that sites of maximum pressure coincided with plantar ulcer sites present in the patients with neuropathic lesions (Stokes et al., 1975). The authors concluded that mechanical loading acting on the foot plantar surface plays a “central pathogenic role” in the onset of neuropathic ulcers. Since then, the predictive value of foot plantar pressure (i.e. normal stress resulting from vertical force) has been widely 17 evaluated (Duckworth et al., 1985, Giacomozzi and Martelli, 2006, Stess et al., 1997, Veves et al., 1992). Many investigators attempted to establish the relationship between peak plantar pressures and the foot risks for tissue breakdown. However, only moderate correlation between peak plantar pressure and the occurrence of diabetic foot ulcers has been found so far (Armstrong et al., 1998, Lavery et al., 2003). Recent studies have suggested that peak plantar pressure may only be 65 % specific for the development of ulcers (Cavanagh et al., 2000). Many authorities thus believed that the shear component (i.e. resulting from horizontal force) of the repetitive plantar loading, which has been largely ignored previously, may be of equal importance to peak plantar pressure in putting foot in greater risks for lesions (Delbridge et al., 1985). For plantar shear, what we have observed is mainly based on force plate measurements during gait analysis: the existence of medial-lateral (ML) and anterior-posterior (AP) components of the ground reaction force (GRF), originating from foot-ground interaction during walking. However, due to technical characteristics of force plates, these only recorded the resultant GRF under the whole foot. Currently, there is still a lack of suitable systems or approaches capable of characterizing the three-dimensional stress states acting on localized anatomical sites such as areas under metatarsal heads (MTHs), a common site for plantar ulcerations. This chapter will provide a brief overview of the biomechanics of neuropathic diabetic foot ulcers in general, and more attention will be given to emerging techniques for shear measurement and modeling of foot-support interface. 18 1.2. Literature review 1.2.1. Plantar stresses and mechanical etiology of diabetic foot ulcers A proper understanding of the etiology of foot ulcers may date back to the paper by Catterall and Oakley et al., (1956) who drew attention to the peripheral neuropathy as the most important contributory cause in the pathway to foot ulcers. The diabetic neuropathy is an anatomically diffuse process that primarily affects all three components of nerves (sensory, motor and autonomic), though sensory symptoms are often most apparent. This leads to LOPS, whereby a person is unable to feel minor trauma from repetitive mechanical stress during daily activity that ultimately result in ulceration, which is now known as neuropathic ulcers. Thus, in the causal pathway to neuropathic diabetic foot ulcers, the major contributing factors are believed to be the presence of LOPS due to peripheral neuropathy and repetitive excessive mechanical stresses acting on the sole of the insensate foot during gait, such as walking. Despite the fact that the plantar foot experiences three-dimensional force vectors during gait, only the plantar pressure (arising from vertical component) has been studied thoroughly. An early investigation conducted (Stokes et al., 1975) using customized pressure transducers, was the first to show that sites of maximum pressure coincided with plantar ulcer sites present in the patients with neuropathic lesions. Since then, the predictive value of foot plantar pressure has been widely evaluated (Duckworth et al., 1985, Giacomozzi and Martelli, 2006, Stess et al., 1997, Veves et al., 1992). Many investigators attempted to establish the relationship between peak plantar pressures and the foot risks for tissue 19 breakdown. However, only moderate correlation between peak plantar pressure and the occurrence of diabetic foot ulcers has been found so far (Armstrong et al., 1998, Lavery et al., 2003). Recent studies have suggested that peak plantar pressure may only be 65 % specific for the development of ulcers (Cavanagh et al., 2000). Many authorities thus believed that shear component (resulting from horizontal force) of the repetitive loading, which has been largely ignored for long, may be an equally important pathogenic factor to pressure in putting foot in greater risks for lesions under local MTH sites (Fig. 1.2.1.1.). MTH Subcutaneous tissue Pure Pressure Muscle Fat Skin Plantar Shear Shear + Pressure Fig. 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 1.2.2. Challenges in measuring plantar shear stresses Because of the technical challenges for measuring the horizontal components, anterior-posterior (AP) and medial-lateral (ML) shear, there is little known about the actual distribution of the magnitude and direction of plantar shear during daily activities, nor about the role that shear plays in causing plantar ulceration. So far, only few devices have been designed to measure plantar shear stress during the last decade. In 1980, Tappin et al. reported the first plantar shear sensor in the literature. The device is based on magneto-resistive principle. Relative displacements of two stainless steel discs induce measurable changes in resistance from magneto-resistor which is proportional to the unidirectional shear force. The apparent drawbacks of the work are 1) positioning and holding the sensor in place could have had a perturbing effect on the local plantar stresses (e.g., causing elevated forces) that were generated at contact interface; 2) it measures shear in the longitudinal or AP direction only. Lord and colleagues (1992) later enhanced this magneto-resistive device by allowing measurement to be made in two orthogonal directions. By mounting the sensor into the ‘extradepth’ orthopaedic shoes, the authors measured shear stress of 20 to 60 kPa, which are approximately 10% of the vertical stress values that are commonly encountered. However, the device was only calibrated at quasi-static condition and showed a large hysteresis of 18.5% of full-scale output with the range of 30N. To avoid this problem, Akhlaghi and Pepper (1996) proposed a copolymer piezoelectric film based sensor. This design is superior in linear response and small hysteresis. Its disadvantages are that it is extremely sensitive to 21 temperature changes and thus not practical for clinical application where hostile testing environments are expected. Davis and associates (1998, 2002) have designed and tested a strain-gauged device that is composed of 16 sensors, each 2.54ｘ2.54 cm2, capable of measuring three components of the applied load. The device sensor showed excellent linearity (5%) and minimal hysteresis (7.5%). Based on this design of the force sensor, the authors have made some rudimentary measurements of planar shear stress in diabetic patients during walking (Yavuz, M. 2007, 2008). Apart from the foregoing review on shear sensors, Wang WC and Ledoux WR (2005) presented a novel means of transducing plantar pressure and shear stress with a fiber-optic sensor. They constructed a map of normal and shear stresses based on observed macrobending through the intensity attenuation from the physical deformation of two adjacent perpendicular fibers. To overcome the hurdle in calibrating sensors at the individual level, Mackey and Davis (2006) developed a prototype system based on optical methods, where each sensing element is made from the same polycarbonate material. Therefore, the authors claim that sensing linkages may be calibrated only once under zero-load conditions over the entire array of sensors. Although each sensor has clear indication of both shear and pressure and a good spatial resolution of mm, it is still subject to technology limitations such as some hysteresis in the system and slightly larger distance between stress sensor linkages. A summary of these reported plantar shear sensors with their technical specifications are given in Table 1.2.2.1. 22 Table 1.2.2.1. A summary of plantar shear sensors reported in the literature Author Tappin (1980) Year Sensor Type et al., 1980 magneto-resistive Lord et al., (1992) 1992 magneto-resistive Akhlaghi&Pepper, (1996) 1996 Davis et al., (1998) Wang et al., (2005) Resolution 16 mm in diameter 15.96 mm in diameter inshoe use copolymer 10 x 10 mm piezoelectric film Strain gage 1998 2.5 x 2.5 cm2 technology 2005 fiber-optic sensor × cm2 Polycarbonate Mackey and Davis, mm 2006 stress linkage (2006) diameter (optical based) Capacity Longitudinal (AP) shear Longitudinal (AP) shear Bi-axial shear (AP plus ML) Pressure and shear sensor Pressure and shear sensor in Pressure and shear sensor 23 1.2.3. Modeling and simulation of foot mechanism for three-dimensional interfacial stress predictions Computational modeling using finite element method (FEM), as a promising alternative to experimental approaches, has gained popularity in the biomechanical study of foot and its interactions with supporting interface. The FEM, as a powerful computer-aided mathematical tool, originated in the mid1950s and is suited to the analysis of a variety of complex problems in the design of engineering structures. In recent years, the biomechanics research community has adopted FE analysis to study foot biomechanics, particularly with regard to the modeling of foot and footwear interactions. The advantages of this numerical method is apparent, since it allows not only the complex contact interactions to be modeled between the foot and its supporting interface and analyzed, but also the stress responses of the whole foot that arise from many other contributing biomechanical factors, e.g., muscular control, internal bony joint movements, and stabilization effects of ligaments, to be obtained in a single comprehensive event investigation. Thus, FE models of human foot have previously been widely explored to understanding the mechanical etiology of diabetic foot ulcers, effects of plantar cushioning as well as other factors involved in the design of therapeutic footwear particularly for diabetic patients. The efficacies of various types of insoles used in therapeutic footwear and surgical interventions for unloading the diabetic foot have also been studied and recorded in the literature. A finite element model of the 2nd ray, inclusive of a sagittal section through the second metatarsal bone with dorsal and plantar soft tissue, was 24 proposed by Lemmon et al. (1997), to explore the effects of insoles with different thickness in therapeutic footwear on peak plantar pressure. The accuracy of this model was found to be encouraging and peak pressure predicted by the models were, on average, within 5.9% of experimentally measured values. Thompson et al. (1999) also used finite element modeling to study influence of tissue property changes in skin and other soft tissues due to long-term diabetes. For diabetic patients with stiffer skin and more compliant fat tissue, the models predicted approximately 25% stress increase at the skin–fat tissue interface, suggesting a high risk of internal tissue breakdown in diabetic feet. Gefen (2002) performed finite element analysis in a standing foot following surgical plantar fascia release. A series of 2-D models, each representing one of the five foot rays in the sagittal plane, were constructed. Partial and total plantar fascia release was simulated by gradually decreasing the fascia’s thickness. The authors further used this model to simulate the effects of stiffening the plantar pad in a diabetic foot and found consequent elevated stresses in soft tissue under the medial metatarsal heads (MTHs) (Gefen et al., 2003). This approach has some potential for understanding etiology of ulcer formation at the MTH region in neuropathic diabetic feet. Cheung et al. (2005) developed a three-dimensional finite element foot model, corresponding to a standing posture, and the effects of stiffening of the soft tissues on plantar pressure distribution were analyzed. Similar models have been used in investigations of varying the Achilles tendon force from to 700 N (Cheung et al., 2006) and the effects on plantar fascia tension under standing 25 load. Recently, Cheng et al. (2008) studied the windlass effects for various toe dorsiflexion angles in a 3-D model that incorporated detailed bony and plantar fascia structures; the significance of muscle loads on model’s performance was not evaluated. As discussed above, the FE modeling is potentially a powerful tool to study foot and footwear biomechanics. However, any model is only as good as its validation, because in the modeling process, the assumptions define the limitations of the model and the structural simplifications that have been made. For instance, regarding the material properties of the different biological structures, plantar soft tissue was previously modeled as isotropic linear elastic material, although it is known that it is anisotropic and viscoelastic. Therefore, complex biomechanical foot models often need verification from experiments to assure that the concepts modeled are correct before they can be used in clinical applications, such as investigations of effects of surgical interventions or different footwear design on model responses. Validation of FE models generally requires a comparison of the predicted output of the model with the measured output of the system. For example, in terms of interfacial stress predictions, previously, great efforts have been placed into plantar pressure (arising from vertical forces) verification. Existing models with different levels of complexity have been found to have reasonable accuracy when various aspects (e.g. geometry detail, material property and loading boundary conditions) required for structural model were accounted for. However, due to experimental limitations to obtain reliable 26 plantar shear measurements, FE modeling of plantar shear interactions between the foot and footwear has not been fully explored. 1.3. Objectives and overview of thesis High plantar shear stress is thought to play a role in neuropathic ulcer development. So far, there is little information about the actual magnitude and direction of plantar shear stresses during daily activities. One critical reason why these data have not been obtained previously is the lack of approaches to obtain the localized three-dimensional plantar stresses. Thus, this research arose from the need for a complete solution for obtaining the plantar stresses underneath the metatarsal heads (MTHs) in the human foot. A systematic approach was proposed using computational modeling and novel pressure/shear sensors in order to investigate plantar stresses, in particular to the sub-MTH region, during interactions between the foot and its supporting interface. The specific goals of the research were:  to develop a sophisticated musculoskeletal finite element (FE) model of human foot to investigate plantar stresses underneath MTH  experimentally, to construct an instrumented tissue tester and a novel pressure/shear gait platform for FE model input and validation  to conduct experimental validation and sensitivity analysis of the foot FE model  to preliminarily apply the FE model in designing therapeutic footwear for enhanced sub-MTH stress relief 27 This thesis focuses on finite element modeling of a human foot assigned with patient-specific material property inputs and validated by sub-MTH pressure and shear stress measurements. Both the numerical and experimental methods are restricted to single-subject design to allow patient-specific analysis to be conducted. Any anomalies in the subject’s muscular control (e.g. reduced muscle effectiveness in gastrocnemius-soleus complex) were accounted for by sensitivity analysis. The applications of the developed model to design therapeutic footwear were preliminary and are limited to sub-MTH stress relief using metatarsal support; study of other design factors are beyond the scope of this study. 28 [...]... 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 (A) Schematic diagram of the gait platform with mounted sensor array (B) Photo of the foot making contact with the gait plate 3.2.2.7 that was embedded in a 7-meter walk way, sensor location in relation to the placement of the foot plantar surface... approaches to obtain the localized three-dimensional plantar stresses Thus, this research arose from the need for a complete solution for obtaining the plantar stresses underneath the metatarsal heads (MTHs) in the human foot A systematic approach was proposed using computational modeling and novel pressure/shear sensors in order to investigate plantar stresses, in particular to the sub-MTH region, during... distance between the MTH and the plantar surface (A) Schematic diagram of sensor showing the positions of the strain gauges and (B) photograph showing the attachment of 3.2.2 .1 strain gauges to the front surfaces of the sensor body Gauges 77 are also bonded to the rear surfaces The positions of the vertical and shear channels are also shown (A) Nine strain-gauged sensors were assembled into (B) a 3 by 3.2.2.2... different foot- supporting interfaces (A) rigid ground, (B) soft foam pad, (C) a soft insole integrated with 11 5 metatarsal support 5.3 .1. 1 5.3 .1. 2 FE mesh of a musculoskeletal foot model with flexors and extensors for stance phase gait simulation 12 2 A further gait platform system with a larger sensor array can be installed in a typical gait lab for large-scale experiments 12 3 13 LIST OF ABBREVIATIONS AND... Ulbrecht, 2006) 20 1. 2.2 Challenges in measuring plantar shear stresses Because of the technical challenges for measuring the horizontal components, anterior-posterior (AP) and medial-lateral (ML) shear, there is little known about the actual distribution of the magnitude and direction of plantar shear during daily activities, nor about the role that shear plays in causing plantar ulceration So far, only few... computer-aided mathematical tool, originated in the mid1950s and is suited to the analysis of a variety of complex problems in the design of engineering structures In recent years, the biomechanics research community has adopted FE analysis to study foot biomechanics, particularly with regard to the modeling of foot and footwear interactions The advantages of this numerical method is apparent, since it allows... internal tissue breakdown in diabetic feet Gefen (2002) performed finite element analysis in a standing foot following surgical plantar fascia release A series of 2-D models, each representing one of the five foot rays in the sagittal plane, were constructed Partial and total plantar fascia release was simulated by gradually decreasing the fascia’s thickness The authors further used this model to simulate... musculoskeletal loading 2.3.4 .1 corresponding to a heel-rise posture Outcome measures of primary interest in foot biomechanics, including stress 55 distributions of bulk soft tissue, metatarsal bones, ligaments and plantar fascia, can be obtained Schematic diagram of the sub -Metatarsal Pad Elasticity 3 .1. 2 .1 Acquisition Instrument (MPEAI), showing details of probe tip, accommodation of sub-MTH pad and inside... sensor array; for a single strain-gauge channel, (C) the electronic interface of a full-bridge circuit configuration was 79 shown 11 A screen shot of the dynamic data acquisition (DAQ) system for 3.2.2.3 real-time strain measurements of the force sensor array using LabVIEW (National Instrument) The block diagram of the 79 program is not shown 3.2.2.4 Calibration graphs showing linearity of the vertical... et al., 19 75) The authors concluded that mechanical loading acting on the foot plantar surface plays a “central pathogenic role” in the onset of neuropathic ulcers Since then, the predictive value of foot plantar pressure (i.e normal stress resulting from vertical force) has been widely 17 evaluated (Duckworth et al., 19 85, Giacomozzi and Martelli, 2006, Stess et al., 19 97, Veves et al., 19 92) Many investigators . A STUDY OF PLANTAR STRESSES UNDERNEATH METATARSAL HEADS IN THE HUMAN FOOT CHEN, WEN-MING NATIONAL UNIVERSITY OF SINGAPORE 2 011 A STUDY OF PLANTAR STRESSES UNDERNEATH. 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. 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