A Dynamic Finite Element Analysis of Human Foot Complex in the Sagittal Plane during Level Walking

The objective of this study is to develop a computational framework for investigating the dynamic behavior and the internal loading conditions of the human foot complex during locomotion. A subject-specific dynamic finite element model in the sagittal plane was constructed based on anatomical structures segmented from medical CT scan images. Three-dimensional gait measurements were conducted to support and validate the model. Ankle joint forces and moment derived from gait measurements were used to drive the model. Explicit finite element simulations were conducted, covering the entire stance phase from heel-strike impact to toe-off. The predicted ground reaction forces, center of pressure, foot bone motions and plantar surface pressure showed reasonably good agreement with the gait measurement data over most of the stance phase. The prediction discrepancies can be explained by the assumptions and limitations of the model. Our analysis showed that a dynamic FE simulation can improve the prediction accuracy in the peak plantar pressures at some parts of the foot complex by 10%–33% compared to a quasi-static FE simulation. However, to simplify the costly explicit FE simulation, the proposed model is confined only to the sagittal plane and has a simplified representation of foot structure. The dynamic finite element foot model proposed in this study would provide a useful tool for future extension to a fully muscle-driven dynamic three-dimensional model with detailed representation of all major anatomical structures, in order to investigate the structural dynamics of the human foot musculoskeletal system during normal or even pathological functioning.     

Subject-specific finite element modelling of the human foot complex during walking: sensitivity analysis of material properties,boundary and loading conditions

The objective of this study was to develop and validate a subject-specific framework for modelling the human foot. This was achieved by integrating medical image-based finite element modelling, individualised multi-body musculoskeletal modelling and 3D gait measurements. A 3D ankle–foot finite element model comprising all major foot structures was constructed based on MRI of one individual. A multi-body musculoskeletal model and 3D gait measurements for the same subject were used to define loading and boundary conditions. Sensitivity analyses were used to investigate the effects of key modelling parameters on model predictions. Prediction errors of average and peak plantar pressures were below 10% in all ten plantar regions at five key gait events with only one exception (lateral heel, in early stance, error of 14.44%). The sensitivity analyses results suggest that predictions of peak plantar pressures are moderately sensitive to material properties, ground reaction forces and muscle forces, and significantly sensitive to foot orientation. The maximum region-specific percentage change ratios (peak stress percentage change over parameter percentage change) were 1.935–2.258 for ground reaction forces, 1.528–2.727 for plantar flexor muscles and 4.84–11.37 for foot orientations. This strongly suggests that loading and boundary conditions need to be very carefully defined based on personalised measurement data.     

Greater toe grip and gentler heel strike are the strategies to adapt to slippery surface

This study investigated the plantar pressure distribution during gait on wooden surface with different slipperiness in the presence of contaminants. Fifteen Chinese males performed 10 walking trials on a 5-m wooden walkway wearing cloth shoe in four contaminated conditions (dry, sand, water, oil). A pressure insole system was employed to record the plantar pressure data at 50Hz. Peak pressure and time-normalized pressure-time integral were evaluated in nine regions. In comparing walking on slippery to non-slippery surfaces, results showed a 30% increase of peak pressure beneath the hallux (from 195.6 to 254.1kPa), with a dramatic 79% increase in the pressure time integral beneath the hallux (from 63.8 to 114.3kPa) and a 34% increase beneath the lateral toes (from 35.1 to 47.2kPa). In addition, the peak pressure beneath the medial and lateral heel showed significant 20-24% reductions, respectively (from 233.6-253.5 to 204.0-219.0kPa). These findings suggested that greater toe grip and gentler heel strike are the strategies to adapt to slippery surface. Such strategies plantarflexed the ankle and the metatarsals to achieve a flat foot contact with the ground, especially at heel strike, in order to shift the ground reaction force to a more vertical direction. As the vertical ground reaction force component increased, the available ground friction increased and the floor became less slippery. Therefore, human could walk without slip on slippery surfaces with greater toe grip and gentler heel strike as adaptation strategies.     

Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis

No technology is presently available to provide real-time information on internal deformations and stresses in plantar soft tissues of individuals during evaluation of the gait pattern. Because internal deformations and stresses in the plantar pad are critical factors in foot injuries such as diabetic foot ulceration, this severely limits evaluation of patients. To allow such real-time subject-specific analysis, we developed a hierarchal modeling system which integrates a two-dimensional gross structural model of the foot (high-order model) with local finite element (FE) models of the plantar tissue padding the calcaneus and medial metatarsal heads (low-order models). The high-order whole-foot model provides real-time analytical evaluations of the time-dependent plantar fascia tensile forces during the stance phase. These force evaluations are transferred, together with foot-shoe local reaction forces, also measured in real time (under the calcaneus, medial metatarsals and hallux), to the low-order FE models of the plantar pad, where they serve as boundary conditions for analyses of local deformations and stresses in the plantar pad. After careful verification of our custom-made FE solver and of our foot model system with respect to previous literature and against experimental results from a synthetic foot phantom, we conducted human studies in which plantar tissue loading was evaluated in real time during treadmill gait in healthy individuals (N = 4). We concluded that internal deformations and stresses in the plantar pad during gait cannot be predicted from merely measuring the foot-shoe force reactions. Internal loading of the plantar pad is constituted by a complex interaction between the anatomical structure and mechanical behavior of the foot skeleton and soft tissues, the body characteristics, the gait pattern and footwear. Real-time FE monitoring of internal deformations and stresses in the plantar pad is therefore required to identify elevated deformation/stress exposures toward utilizing it in gait laboratories to protect feet that are susceptible to injury.     

Determining the centre of pressure during walking and running using an instrumented treadmill

In this paper, a new method of determining spatial and temporal gait parameters by using centre of pressure (CoP) data is presented. A treadmill is used which was developed to overcome limitations of regular methods for the analysis of spatio-temporal gait parameters and ground reaction forces during walking and running. The design of the treadmill is based on the use of force transducers underneath a separate left and right plate, which together form the treadmill walking surface. The results of test procedures and measurements show that accurate recordings of vertical ground reaction force can be obtained. These recordings enable a separate analysis of vertical ground reaction forces during double support phases in walking, and the analysis of changes in the centre of pressure (CoP) position during subsequent foot placements. From the CoP data, temporal gait parameters (e.g. duration of left/right support and swing phases) and spatial gait parameters (i.e. left/right step lengths and widths) can be derived.     

Role of gastrocnemius-soleus muscle in forefoot force transmission at heel rise - A 3D finite element analysis

The functions of the gastrocnemius-soleus (G-S) complex and other plantar flexor muscles are to stabilize and control major bony joints, as well as to provide primary coordination of the foot during the stance phase of gait. Geometric positioning of the foot and transferring of plantar loads can be adversely affected when muscular control is abnormal (e.g., equinus contracture). Although manipulation of the G-S muscle complex by surgical intervention (e.g., tendo-Achilles lengthening) is believed to be effective in restoring normal plantar load transfer in the foot, there is lack of quantitative data supporting that notion. Thus, the objective of this study is to formulate a three-dimensional musculoskeletal finite element model of the foot to quantify the precise role of the G-S complex in terms of biomechanical response of the foot. The model established corresponds to a muscle-demanding posture during heel rise, with simulated activation of major extrinsic plantar flexors. In the baseline (reference) case, required muscle forces were determined from what would be necessary to generate the targeted resultant ground reaction forces. The predicted plantar load transfer through the forefoot plantar surface, as indicated by plantar pressure distribution, was verified by comparison with experimental observations. This baseline model served as a reference for subsequent parametric analysis, where muscle forces applied by the G-S complex were decreased in a step-wise manner. Adaptive changes of the foot mechanism, in terms of internal joint configurations and plantar stress distributions, in response to altered muscular loads were analyzed. Movements of the ankle and metatarsophalangeal joints, as well as forefoot plantar pressure peaks and pressure distribution under the metatarsal heads (MTHs), were all found to be extremely sensitive to reduction in the muscle load in the G-S complex. A 40% reduction in G-S muscle stabilization can result in dorsal-directed rotations of 8.81° at the ankle, and a decreased metatarsophalangeal joint extension of 4.65°. The resulting peak pressure reductions at individual MTHs, however, may be site-specific and possibly dependent on foot structure, such as intrinsic alignment of the metatarsals. The relationships between muscular control, internal joint movements, and plantar load distributions are envisaged to 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.     

Scaling of plantar pressures in mammals

The interaction of the limbs with the substrate can teach a lot about an animal's gait mechanics. Unlike ground-reaction forces, plantar pressure distributions are rarely studied in animals, but they may provide more detailed information about the loading patterns and locomotor function of specific anatomical structures. With this study, we aim to describe pressures for a large and diverse sample of mammalian species, focusing on scaling effects. We collected dynamic plantar pressure distributions during voluntary walking in 28 mammal species. A dynamic classification of foot use was made, which distinguished between plantiportal, digitiportal and unguliportal animals. Analysis focused on scaling effects of peak pressures, peak forces and foot contact areas. Peak pressure for the complete mammal sample was found to scale to (mass)^1/2, higher than predicted assuming geometric similarity, and we found no difference between the different types of foot use. Only the scaling of peak force is dependent on the dynamic foot use. We conclude that plantar peak pressure rises faster with mass than expected, regardless of the type of foot use, and scales higher than in limb bones. These results might explain some anatomical and behavioural adaptations in graviportal animals.     

Estimating the complete ground reaction forces with pressure insoles in walking

This study presented a method to estimate the complete ground reaction forces from pressure insoles in walking. Five male subjects performed 10 walking trials in a laboratory. The complete ground reaction forces were collected during a right foot stride by a force plate at 1000Hz. Simultaneous plantar pressure data were collected at 100Hz by a pressure insole system with 99 sensors covering the whole plantar area. Stepwise linear regressions were performed to individually reconstruct the complete ground reaction forces in three directions from the 99 individual pressure data until redundancy among the predictors occurred. An additional linear regression was performed to reconstruct the vertical ground reaction force by the sum of the value of the 99 pressure sensors. Five other subjects performed the same walking test for validation. Estimated ground reaction forces in three directions were calculated with the developed regression models, and were compared with the real data recorded from force plate. Accuracy was represented by the correlation coefficient and the root mean square error. Results showed very good correlation in anterior-posterior (0.928) and vertical (0.989) directions, and reasonable correlation in medial-lateral direction (0.719). The root mean square error was about 12%, 5% and 28% of the peak recorded value. Future studies should aim to generalize the methods or to establish specific methods to other subjects, patients, motions, footwear and floor conditions. The method gives an extra option to study an estimation of the complete ground reaction forces in any environment without the constraints from the number and location of force plates.     

Contributions of muscles to mediolateral ground reaction force over a range of walking speeds

Impaired control of mediolateral body motion during walking is an important health concern. Developing treatments to improve mediolateral control is challenging, partly because the mechanisms by which muscles modulate mediolateral ground reaction force (and thereby modulate mediolateral acceleration of the body mass center) during unimpaired walking are poorly understood. To investigate this, we examined mediolateral ground reaction forces in eight unimpaired subjects walking at four speeds and determined the contributions of muscles, gravity, and velocity-related forces to the mediolateral ground reaction force by analyzing muscle-driven simulations of these subjects. During early stance (0-6% gait cycle), peak ground reaction force on the leading foot was directed laterally and increased significantly (p<0.05) with walking speed. During early single support (14-30% gait cycle), peak ground reaction force on the stance foot was directed medially and increased significantly (p<0.01) with speed. Muscles accounted for more than 92% of the mediolateral ground reaction force over all walking speeds, whereas gravity and velocity-related forces made relatively small contributions. Muscles coordinate mediolateral acceleration via an interplay between the medial ground reaction force contributed by the abductors and the lateral ground reaction forces contributed by the knee extensors, plantarflexors, and adductors. Our findings show how muscles that contribute to forward progression and body-weight support also modulate mediolateral acceleration of the body mass center while weight is transferred from one leg to another during double support.     

Joint kinetic response during unexpectedly reduced plantar flexor torque provided by a robotic ankle exoskeleton during walking

During human walking, plantar flexor activation in late stance helps to generate a stable and economical gait pattern. Because plantar flexor activation is highly mediated by proprioceptive feedback, the nervous system must modulate reflex pathways to meet the mechanical requirements of gait. The purpose of this study was to quantify ankle joint mechanical output of the plantar flexor stretch reflex response during a novel unexpected gait perturbation. We used a robotic ankle exoskeleton to mechanically amplify the ankle torque output resulting from soleus muscle activation. We recorded lower-body kinematics, ground reaction forces, and electromyography during steady-state walking and during randomly perturbed steps when the exoskeleton assistance was unexpectedly turned off. We also measured soleus Hoffmann- (H-) reflexes at late stance during the two conditions. Subjects reacted to the unexpectedly decreased exoskeleton assistance by greatly increasing soleus muscle activity about 60 ms after ankle angle deviated from the control condition (p<0.001). There were large differences in ankle kinematic and electromyography patterns for the perturbed and control steps, but the total ankle moment was almost identical for the two conditions (p=0.13). The ratio of soleus H-reflex amplitude to background electromyography was not significantly different between the two conditions (p=0.4). This is the first study to show that the nervous system chooses reflex responses during human walking such that invariant ankle joint moment patterns are maintained during perturbations. Our findings are particularly useful for the development of neuromusculoskeletal computer simulations of human walking that need to adjust reflex gains appropriately for biomechanical analyses.     

Neuromuscular response of hip-spanning and low back muscles to medio-lateral foot center of pressure manipulation during gait

Background: Footwear-generated medio-lateral foot center of pressure manipulation has been shown to have potential positive effects on gait parameters of hip osteoarthritis patients, ultimately reducing maximum joint reaction forces. The objective of this study was to investigate effects of medio-lateral foot center of pressure manipulation on muscle activity of hip-spanning and back muscles during gait in bilateral hip osteoarthritis patients. Methods: Foot center of pressure was shifted along the medio-lateral foot axis using a foot-worn biomechanical device allowing controlled center of pressure manipulation. Sixteen female bilateral hip osteoarthritis patients underwent electromyography analysis while walking in the device set to three parasagittal configurations: neutral (control), medial, and lateral. Seven hip-spanning muscles (Gluteus Medius, Gluteus Maximus, Tensor Fascia Latae, Rectus Femoris, Semitendinosis, Biceps Femoris, Adductor Magnus) and one back muscle (Erector Spinae) were analyzed. Magnitude and temporal parameters were calculated. Results: The amplitude and temporal parameter varied significantly between foot center of pressure positions for 5 out of 8 muscles each for either the more or less symptomatic leg in at least one subphase of the gait cycle. Conclusion: Medio-lateral foot center of pressure manipulation significantly affects neuromuscular pattern of hip and back musculature during gait in female hip bilateral osteoarthritis patients.     

Effect of heel height on in-shoe localized triaxial stresses

Abnormal and excessive plantar pressure and shear are potential risk factors for high-heeled related foot problems, such as forefoot pain, hallux valgus deformity and calluses. Plantar shear stresses could be of particular importance with an inclined supporting surface of high-heeled shoe. This study aimed to investigate the contact pressures and shear stresses simultaneously between plantar foot and high-heeled shoe over five major weightbearing regions: hallux, heel, first, second and fourth metatarsal heads, using in-shoe triaxial force transducers. During both standing and walking, peak pressure and shear stress shifted from the lateral to the medial forefoot as the heel height increased from 30 to 70mm. Heel height elevation had a greater influence on peak shear than peak pressure. The increase in peak shear was up to 119% during walking, which was about five times that of peak pressure. With increasing heel height, peak posterolateral shear over the hallux at midstance increased, whereas peak pressure at push-off decreased. The increased posterolateral shear could be a contributing factor to hallux deformity. It was found that there were differences in the location and time of occurrence between in-shoe peak pressure and peak shear. In addition, there were significant differences in time of occurrence for the double-peak loading pattern between the resultant horizontal ground reaction force peaks and in-shoe localized peak shears. The abnormal and drastic increase of in-shoe shear stresses might be a critical risk factor for shoe-related foot disorders. In-shoe triaxial stresses should therefore be considered to help in designing proper footwear.     

Quantitative assessment of gait determinants during single stance via a three-dimensional model--Part 1. Normal gait

In this two-part paper, a variety of three-dimensional, dynamical models are constructed for simulating the single support phases of normal and pathological human gait. A major objective of this work is to quantify the influence of individual gait determinants on the ground reaction forces generated during normal, level walking. To this end, Part 1 presents a three-dimensional, seven degree-of-freedom model incorporating five of the six fundamental determinants of gait. On the basis of crude muscle-force and/or joint-moment trajectories, body-segmental motions and ground reaction forces are synthesized open loop. Through a quantitative comparison with experimental gait data, the model's predictions are evaluated. Our simulation results suggest that pelvic list is not as dominant a dynamical determinant as either stance knee flexion-extension or foot and knee interaction. Transverse pelvic rotation, however, makes an important contribution by limiting the magnitude of the horizontal ground reaction prior to opposite heel-strike.     

Structural and functional predictors of regional peak pressures under the foot during walking

The objective of this study was to identify structural and functional factors which are predictors of peak pressure underneath the human foot during walking. Peak plantar pressure during walking and eight data sets of structural and functional measures were collected on 55 asymptomatic subjects between 20 and 70 yr. A best subset regression approach was used to establish models which predicted peak regional pressure under the foot. Potential predictor variables were chosen from physical characteristics, anthropometric data, passive range of motion (PROM), measurements from standardized weight bearing foot radiographs, mechanical properties of the plantar soft tissue, stride parameters, foot motion in 3D, and EMG during walking. Peak pressure values under the rearfoot, midfoot, MTH1, and hallux were measured. Heel pressure was a function of linear kinematics, longitudinal arch structure, thickness of plantar soft tissue, and age. Midfoot pressure prediction was dominated by arch structure, while MTH1 pressure was a function of radiographic measurements, talo-crural joint motion, and gastrocnemius activity. Hallux pressure was a function of structural measures and MTP1 joint motion. Foot structure and function predicted only approximately 50% of the variance in peak pressure, although the relative contributions in different anatomical regions varied dramatically. Structure was dominant in predicting peak pressure under the midfoot and MTH1, while both structure and function were important at the heel and hallux. The predictive models developed in this study give insight into potential etiological factors associated with elevated plantar pressure. They also provide direction for future studies designed to reduce elevated pressure in "at-risk" patients.     

Walking with increased ankle pushoff decreases hip muscle moments

In a simple bipedal walking model, an impulsive push along the trailing limb (similar to ankle plantar flexion) or a torque at the hip can power level walking. This suggests a tradeoff between ankle and hip muscle requirements during human gait. People with anterior hip pain may benefit from walking with increased ankle pushoff if it reduces hip muscle forces. The purpose of our study was to determine if simple instructions to alter ankle pushoff can modify gait dynamics and if resulting changes in ankle pushoff have an effect on hip muscle requirements during gait. We hypothesized that changes in ankle kinetics would be inversely related to hip muscle kinetics. Ten healthy subjects walked on a custom split-belt force-measuring treadmill at 1.25m/s. We recorded ground reaction forces and lower extremity kinematic data to calculate joint angles and internal muscle moments, powers and angular impulses. Subjects walked under three conditions: natural pushoff, decreased pushoff and increased pushoff. For the decreased pushoff condition, subjects were instructed to push less with their feet as they walked. Conversely, for the increased pushoff condition, subjects were instructed to push more with their feet. As predicted, walking with increased ankle pushoff resulted in lower peak hip flexion moment, power and angular impulse as well as lower peak hip extension moment and angular impulse (p<0.05). Our results emphasize the interchange between hip and ankle kinetics in human walking and suggest that increased ankle pushoff during gait may help to compensate for hip muscle weakness or injury and reduce hip joint forces.     

Measured and estimated ground reaction forces for multi-segment foot models

Accurate measurement of ground reaction forces under discrete areas of the foot is important in the development of more advanced foot models, which can improve our understanding of foot and ankle function. To overcome current equipment limitations, a few investigators have proposed combining a pressure mat with a single force platform and using a proportionality assumption to estimate subarea shear forces and free moments. In this study, two adjacent force platforms were used to evaluate the accuracy of the proportionality assumption on a three segment foot model during normal gait. Seventeen right feet were tested using a targeted walking approach, isolating two separate joints: transverse tarsal and metatarsophalangeal. Root mean square (RMS) errors in shear forces up to 6% body weight (BW) were found using the proportionality assumption, with the highest errors (peak absolute errors up to 12% BW) occurring between the forefoot and toes in terminal stance. The hallux exerted a small braking force in opposition to the propulsive force of the forefoot, which was unaccounted for by the proportionality assumption. While the assumption may be suitable for specific applications (e.g. gait analysis models), it is important to understand that some information on foot function can be lost. The results help highlight possible limitations of the assumption. Measured ensemble average subarea shear forces during normal gait are also presented for the first time.     

Gait alterations in rats following attachment of a device and application of altered knee loading

Animal models are widely used to study cartilage degeneration. Experimental interventions to alter contact mechanics in articular joints may also affect the loads borne by the leg during gait and consequently affect the overall loading experienced in the joint. In this study, force plate analyses were utilized to measure parameters of gait in the rear legs of adult rats following application of a varus loading device that altered loading in the knee. Adult rats were assigned to Control, Sham, or Loaded groups (n≥4/each). Varus loading devices were surgically attached to rats in the Sham and Loaded groups. In the Loaded group, this device applied a controlled compressive overload to the medial compartment of the knee during periods of engagement. Peak ground reaction forces during walking were recorded for each rear leg of each group. Analyses of variance were used to compare outcomes across groups (Control, Sham, and Loaded), leg (contralateral, experimental) and device status (disengaged, engaged) to determine the effects of surgically attaching the device and applying a compressive overload to the joint with the device. The mean peak vertical force in the experimental leg was reduced to 30% in the Sham group in comparison to the contralateral leg and the Control group, indicating an effect of attaching the device to the leg (p<0.01). No differences were found in ground reaction forces between the Sham and Loaded groups with application of compressive overloads with the device. The significant reduction in vertical force due to the surgical attachment of the varus loading device must be considered and accounted for in future studies.     

Temporal characteristics of plantar shear distribution: relevance to diabetic patients

Diabetic foot ulcers are known to have a biomechanical etiology. Among the mechanical factors that cause foot lesions, shear stresses have been either neglected or underestimated. The purpose of this study was to determine various plantar pressure and shear variables in the diabetic and control groups and compare them. Fifteen diabetic patients with neuropathy and 20 non-diabetic subjects without foot symptoms were recruited. Subjects walked on a custom-built platform capable of measuring local normal and tangential forces simultaneously. Pressure-time integral quantities were increased by 54% (p=0.013) in the diabetic group. Peak AP and resultant shear magnitudes were found to be about 32% larger (p<0.05), even though diabetic subjects walked at a slower velocity. Lower AP and ML stress range (peak-to-peak) values were observed in the control subjects (p<0.05). Shear-time integral values were increased in the diabetic group by 61% and 132% for AP and resultant shear cases, respectively (p<0.05). Plantar shear is known to be a factor in callus formation and has previously been associated with higher ulcer incidence. During gait, shear stresses are induced with twice the frequency of pressure characteristically. Therefore, plantar shear should be investigated further from a broader perspective including the temporal specifications and fatigue failure characteristics of the affected plantar tissue.     

Effects of arm swing on mechanical parameters of human gait

The aim of this study was to investigate the influence of the upper limb swing on human gait. Measurements were performed on 52 subjects by using the Elite system with two cameras and a Kistler force platform. The recording of trajectories of characteristic body points on the subjects and the measurement of ground reaction forces have been performed at normal walking and at walking with emphasised rhythmic upper limb swing. The trajectory of the whole body mass centre, central dynamic moments of inertia and ground reaction forces have been calculated for every subject and mean curves of the entire group have been determined for walking with the natural and the emphasised upper limb swing. The determined mean values of normalised mechanical parameters have been compared and differences between the gait with the natural and the emphasised upper limb swing have been described.