CHAPTER EVALUATION OF MODEL PERFORMANCE ~ Success is not measured by what you accomplish, but by the opposition you have encountered, and the courage with which you have maintained the struggle against overwhelming odds~ Orison Swett Marden 92 4.1 Comparison of FEM results with experimental data Finite element analyses and experimental studies (in vivo study and in vitro cadaveric testing) are complimentary techniques to characterize the complex biomechanical behavior of the foot and its components, involving muscular control, joint movements, bone stresses, as well as the foot-ground interactions. In general, experimental investigations have provided clinically relevant data (e.g. plantar pressure distribution, foot deformities etc.) with regards to normal and pathological foot conditions. However, in terms of plantar shear stresses, internal tissue stresses, and roles of muscles, ligaments, plantar fascia, and other soft tissue structures in the weight-bearing function of the foot, these experimental studies are often limited. The FE models of the foot thus supplement those experimental studies. Once such models are verified by experimental data, they offer additional extrapolated information. In this study, a comprehensive finite element musculoskeletal model of the foot was constructed. Compared to the majority of existing foot models which focus on standing (Gefen, 2002, Cheung et al., 2005, Chen et al., 2010a), the current model accommodates realistic musculoskeletal loads and simulates a muscle-demanding posture corresponding to heel-rise, which facilitates a detailed investigation into the foot mechanism that involves complex interplay of muscular control, articulating joint movements, and forefoot plantar loading distributions. Meanwhile, great efforts were made experimentally in order to 1) provide a model with accurate material property inputs for the sub-MTH soft tissue; 2) validate the model’s predictions for foot-ground interactions at local 93 MTH sites. In this section, an experimental validation will be conducted by comparing of FEM results with experimental data obtained from the developed gait platform and those reported in the literature. It will be demonstrated that with accurately quantified tissue property, muscular loading characteristics, and foot’s geometric positioning, a realistic stress response of the model during foot-ground interactions can be reproduced. 4.1.1 Simulated muscular loads Since the number of flexor muscles present in the model is larger than necessary to achieve mechanical equilibrium for all foot geometrical positioning, the system is indeterminate. In other words, infinitely many different muscle force combinations can balance the same foot geometrical positioning during stance. Thus, for simplification, one of the most important assumptions made in the modeling study is for the calculation of muscle forces, i.e. the extrinsic flexor tendons were loaded to their relative strengths according to the physiological cross-sectional areas (PCSA) of their respective muscle bundle. However, this assumption may be justified by the fact that the force-generating capacity of a muscle is known to be directly proportional to its PCSA (Wickiewicz et al., 1983, Fukunaga et al., 1996). With this assumption, it possible to inversely deduce the combinations of extrinsic flexor forces required to generate the targeted GRF that match the given boundary conditions. When comparing the FE model calculated muscular loads with literature data, the calculated G-S muscle force of 1620N is very close to the in vivo peak 94 Achilles tendon loading (1430 ±500 N) measured by Finni et al. (1998) for walking. Forces in the other extrinsic muscles were also within their physiological ranges and generally comparable to those utilized in actuating a cadaveric foot (Sharkey and Hamel, 1998) to emulate walking. A detailed quantitative comparison of the calculated six flexors muscle forces used in the current finite element model with those estimated by Salathe and Arangio (2002) in an analytical foot structure model is presented in Fig. 4.1.1.1. Fig. 4.1.1.1. Comparison of the muscular loads obtained from the finite element model with those calculated by Salathe and Arangio (2002) and Gefen (2000) In the analytical model proposed by Salathe and Arangio (2002), the anatomical structures of the foot bones, ligaments, and muscles were considered with foot bones being articulated through various joints, such as hinge and universal joints. Due to the indeterminacy encountered for calculating the muscle forces, the authors made a similar assumption that each muscle of a given group 95 contributes to the total support provided by that group an amount proportional to its PCSA. Good agreement between the numerical and analytical values of flexor muscle forces was found. The muscular loads applied in the current model were also quantitatively similar to those calculated by Gefen et al. (2000) in a 3-D FE foot model simulating stance-phase of walking. Thus, the muscles modeled and magnitudes of forces simulated are considered representative of a specific instant in the gait cycle, corresponding approximately to the occurrence of the second GRF peak during walking. 4.1.2 Plantar stress distribution With all muscular loads applied, the foot model was successfully solved in a typical geometry following heel rise, with the ankle and MTP joints maintained at plantar-flexed and extended configurations, respectively. Corresponding to this foot posture, the predicted contours of plantar pressure and shear stress distributions were plotted in Fig. 4.1.2.1. The plantar pressure was mainly concentrated at areas under the 2nd and 3rd MTHs, with peak plantar pressure of 570.6 KPa found under the 2nd MTH. This is generally in agreement with literature data on foot roll-over characteristics, i.e. after heel off, the forefoot has a more central push-off over the second metatarsal at the terminal stance of walking (De Cock et al., 2005). While for the predicted plantar shear, it shows a different stress patterns from the plantar pressure. The peak anterior-posterior (AP) shear stress of 123.6 kPa was found under the 1st MTH and the peak medial-lateral (ML) shear stress of 55.7 kPa was found under the 2nd MTH. The 96 peak shear stresses found were generally much lower than the peak plantar pressure values. Fig. 4.1.2.1. Model predicted (A) plantar pressure, (B) plantar shear (vector summation of AP and ML components), and (C) tissue VMS stress distributions To facilitate direct comparison of the plantar stresses calculated by the model and measured by the sensor array, the continuous predicted plantar pressure data were averaged over the sensing area of an individual sensor (9 ｘ mm2). When compared to the averaged plantar stress data, the model agreed extremely well in peak plantar pressure values (570.6 kPa Versus 568.2 kPa). For peak AP and ML shear stresses, the peak shear location compared relative well with experimental data. The peak shear predicted by the model was higher than what was observed experimentally (123.6 kPa Versus 74.2 kPa) (Table 4.1.2.1.). 97 Table 4.1.2.1. Summary of peak plantar stresses measured by sensor array and predicted by the finite element model under individual metatarsal heads (MTHs) (PPP: peak plantar pressure; PSS-AP: peak anterior-posterior shear stress; PSS-ML: peak medial-lateral shear stress. Unit: kPa) Sensor measured plantar stresses Model predicted contact stresses PPP PSS-AP PSS-ML PPP PSS-AP PSS-ML 1st 290.1 74.2 21.9 143.8 123.6 20.0 2nd 568.2 41.1 32.8 570.6 17.9 55.7 3rd 412.2 30.3 24.1 513.7 15.1 45.1 4th 313.9 50.1 8.1 267.2 36.1 9.9 5th 129.1 10.4 7.5 17.1 ([...]... movements at the ankle and metatarsophalangeal joints in the main loading plane arising from adjustments in the muscle forces were analyzed Changes in the foot- ground interactions were characterized by the pressure patterns displayed by contacting elements at the plantar surface The data obtained was compared with those of the baseline model 1 04 4.2.2.1 Effects of Achilles tendon forces variations on... understand the underlying mechanism for relieving forefoot pressure in diabetic patients who suffer from ankle equinus contracture 111 4. 3 Possible application of model in design of therapeutic footwear Therapeutic footwear plays an important role in the prevention of neuropathic plantar ulceration in DM patients, as it is a first line of defense against abnormal plantar loading transfer (Caputo et al.,... patients who are at high risk of plantar ulceration The present study shows that 108 the overall peak plantar pressure decreases by 22.7% in response to prescribed reductions in the FAT Although these changes appear associated with increased ankle dorsiflexion, the actual cause could be the smaller inclination angle of the metatarsals to the horizontal, leading to more even load distribution among the. .. hexahedron elements An additional metatarsal support component (Fig 4. 3.2.1) was merged into the flat insole model by projecting its boundary nodes onto a curved surface that represents the geometrical shape of an actual metatarsal support (Foot in Motion, USA) Fig 4. 3.2.1 Finite element model of a flat insole with an integrated metatarsal support component interfacing with the forefoot plantar surface... plantar surface The analysis starts from the baseline case with the foot model landing on a flat, rigid ground, and then increases complexity of interactions by adding a soft insole integrated with an additional metatarsal support component Parametrical analysis was performed in order to determine the optimal material selection (soft plasterzote versus stiffer EVA) and positioning (just underneath versus... absence of muscle actuation and stabilization 103 4. 2.2 Parametric study on FAT variations To study the effects of varying the G-S complex muscle force (denoted as FAT) on foot mechanism, a multi-step analysis procedure was adopted The initially loaded baseline model served as the reference for the subsequent analysis, in which the maximum GRF was maintained whereby the maximum FAT was reduced in steps of. .. during the terminal stance-phase of human gait, may be risk factors for developing a number of musculoskeletal disorders in foot, such as pain in the 112 MTHs (e.g metatarsalgia in rheumatoid arthritis) (Roy, 1988), joint structural deformities (e.g hallux valgus) (Sanders et al., 1992), and skin lesions in the plantar soft tissue (e.g diabetic foot ulcers) (Cavanagh et al., 1993) Many investigators... tendon by plantar flexion of the metatarsals, may alleviate the risk of cavoid foot formation, which frequently occurs in diabetic patients This again, highlights the importance of Achilles tendon loading in forefoot weight-bearing, which is closely related to stancephase placement of the foot 109 4. 2.2.3 Effects of FAT variations on sub-MTH pressure peaks Fig 4. 2.2 .4 Percentage changes of local pressures... metatarsal support placed at 5 mm proximal to the 2nd MTH helped to reduce local peak pressure by 12.1% as compared to using soft foam pad alone However, placing a stiffer metatarsal support just underneath the 2nd MTH could cause local peak pressure increase to 5 04. 4 kPa Inclusion of a metatarsal support into the foam pad for enhanced sub-MTH stresses relief requires more technical efforts Table 4. 3.3.1... modeling to investigate the effects of specific changes to the foot structure on joint movements and stress responses, via parametric analyses The aims of the present model sensitivity study are to quantitatively analyze adaptive changes of the foot mechanism, i.e movements at the ankle and metatarsophalageal joints and forefoot load transfer in response to force variations generated by the G-S muscle complex . in the F AT . Although these changes appear associated with increased ankle dorsiflexion, the actual cause could be the smaller inclination angle of the metatarsals to the horizontal, leading. recorded in the mid-part of the shaft of the second metatarsal. For the current FE model, local coordinate systems were defined for the metatarsal elements to obtain axial surface strain components. strain The model was further substantiated by comparing predicted metatarsal strains to results obtained from the cadaveric work of Sharkey et al., (1995). This cadaver study had similar loading