A study of plantar stresses underneath metatarsal heads in the human foot 4

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 charac

CHAPTER 4 EVALUATION OF MODEL

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

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

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

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

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

9 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.)

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

of both AP and ML shear stress distribution, in terms of peak shear found under individual MTHs compare well with experimental data

4.1.3 Metatarsal bone 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 conditions with the current FE model In their experiments, each foot was loaded to a maximum of 750N of ground-reaction force by simulated contraction of the triceps surae, and strains were 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 directly from FE analyses Simulation results were extracted from the mid-spans of the 2nd metatarsal shafts; nodal values with an area of 5 ｘ 10 mm were averaged for comparison with strain gauge measurements by Sharkey et al (1995) The predicted strains were highest at the dorsal mid-shaft region (2395.1με), followed by those at the medial area (946.2με), and they were lowest at the lateral mid-shaft vicinity (376.7με); these were comparable to experimental data (Table 4.1.3.1.), suggesting that the finite element model provides a reasonable reflection of the internal foot mechanics, and is thus a suitable tool for further investigation

Table 4.1.3.1 Model predicted average strain in the 2nd metatarsal mid-shaft in comparison with the cadaver study results by Sharkey et al., (1995)

Dorsal Strain (με) Medial Strain (με) Lateral Strain (με)

Sharkey et al.,

4.2 Sensitivity of model to flexor muscle force variations

The present model is a truly musculoskeletal FE model which allows quantitative analysis of altered muscular control on biomechanical behavior of the foot The aim of this sensitivity analysis was to address a clinical-relevant topic: what role does the gastrocnemius-soleus (G-S) complex plays in normal weight-bearing function by the foot The results obtained from this model’s sensitivity analysis may have important clinical implications on tendo-Achilles lengthening procedures, and to provide surgeons with an understanding of the underlying mechanism for relieving forefoot pressure in diabetic patients suffering from ankle equinus contracture

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

The functional roles of the extrinsic plantar flexor muscles are to provide stability

to the foot during the stance phase of gait (Sutherland et al., 1980) Anatomically, these musculotendinous units usually possess unique long-tendon structures, which allow them to influence multiple joints inside the foot This multi-articular characteristic in extrinsic flexors facilitate control and stabilization of major bony joints, including the talo-crural, the subtalar, and indirectly the metatarsophalangeal (MTP) joints, thus providing primary coordination of the stance-phase placement of the foot, which is essential for normal weight-bearing during gait (Perry, 1992)

The gastrocnemius-soleus (G-S) complex associated with the Achilles tendon is the most dominant extrinsic plantar flexor Various studies using cadaveric foot models have established the important biomechanical linkage among the Achilles tendon, plantar fascia and MTP joints, both statically (Carlson

et al., 2000) and dynamically (Erdemir et al., 2004), earlier described by Hicks (1955), as the Windlass mechanism With the foot stabilized by flexor muscles upon heel-rise, substantial dynamic ground reaction forces (GRF) are imposed only on the forefoot, thereby generating highly localized stresses, particularly underneath the metatarsal heads (MTHs) Such potentially ‘detrimental’ stresses may only last for a short-dwelling time in a normal foot, provided that the coordinative muscles involved activate the right amount of force at the exact appropriate time during gait (Perry, 1992, Hayafune et al., 1999)

When equinus contracture is present, normal muscle activation in the G-S complex may be compromised (Damron et al., 1994, Lin et al., 1996) The contractured G-S muscle consistently exerts tension through the Achilles tendon, resulting in an earlier Windlass effect accompanied by premature heel-rise, and the maintenance of this abnormal posture throughout the whole stance phase of walking (D'Ambrogi et al., 2005, Hastings et al., 2000) Many believe that this leads to prolonged and high-magnitude forefoot loading exposure, which may induce pain, injury or other structural deformities in these areas over time, such

as metatarsalgia and plantar forefoot ulceration (Bowers and Castro, 2007)

Manipulation of the muscle force in the G-S complex via surgical intervention, such as tendo-Achilles lengthening, can negate the ‘abnormal’

Windlass mechanism associated with G-S muscle contracture (Salsich et al., 2005), and appears effective in restoring normal forefoot load transfer by relieving the abnormally high stresses under the MTHs (Armstrong et al., 1999, Maluf et al., 2004) This facilitates the healing of ulcers within that vicinity in a diabetic foot (Lin et al., 1996, Mueller et al., 2003) In contrast, Orendurff et al (2006) showed that equinus contracture accounts for only a small amount of the increased forefoot plantar pressure A major point of debate has been the precise role the G-S complex plays in normal weight-bearing by the foot; there is no comprehensive documentation of this topic (McGuire, 2010)

Only few investigators have attempted experimental studies on the role of extrinsic flexor muscles on forefoot skeletal loads and plantar stress distribution Most of these studies focus on the effects of one over another The interrelationship among muscular control, internal joint movements, and plantar loading distributions have not been fully explored due to experimental difficulties Sharkey et al (1995) simulated flexor muscle action in a cadaveric foot model and successfully achieved a maximum ground reaction force of 750 N during heel-lift; strains in the second metatarsal bone were also measured Similar loading conditions were applied by Ferris et al (1995), in their study on the influence of extrinsic plantar flexors on loads borne by the toes; no variation of

Achilles tendon forces was considered In another in vitro investigation, Aronow

et al., (2006) found that upon heel-rise, the plantar pressure shifts from the hindfoot to the forefoot when Achilles tendon forces are increased, but the

values (e.g according to Finni et al (1998), the in-vivo measured peak Achilles

tendon force can range from 750 to 2360 N )

Previous finite element (FE) modeling of the foot has demonstrated the potential of such numerical 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 Precise determination

of such relationships may help explain the etiology of many foot and ankle disorders associated with G-S contracture, and an understanding of the possible benefits, if any, related to these biomechanical quantities following surgical tendo-Achilles lengthening This study also directly addresses, some significant limitations of previous FE models related to foot biomechanics, namely the absence of muscle actuation and stabilization

4.2.2 Parametric study on F AT variations

To study the effects of varying the G-S complex muscle force (denoted as F AT)

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 F AT was reduced in steps of 10% down to 60% of the original, to simulate reduced muscle effectiveness of the G-S complex (Table 4.2.2.1) The stresses and strains of the baseline model were updated in sequential steps to elicit the results of