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.     

Finite element analysis as a tool for parametric prosthetic foot design and evaluation. Technique development in the solid ankle cushioned heel (SACH) foot

In this study, we developed an approach for prosthetic foot design incorporating motion analysis, mechanical testing and computer analysis. Using computer modeling and finite element analysis, a three-dimensional (3D), numerical foot model of the solid ankle cushioned heel (SACH) foot was constructed and analyzed based upon loading conditions obtained from the gait analysis of an amputee and validated experimentally using mechanical testing. The model was then used to address effects of viscoelastic heel performance numerically. This is just one example of the type of parametric analysis and design enabled by this approach. More importantly, by incorporating the unique gait characteristics of the amputee, these parametric analyses may lead to prosthetic feet more appropriately representing a particular user's needs, comfort and activity level.     

Finite Element Analysis as a Tool for Parametric Prosthetic Foot Design and Evaluation. Technique Development in the Solid Ankle Cushioned Heel (SACH) Foot

In this study, we developed an approach for prosthetic foot design incorporating motion analysis, mechanical testing and computer analysis. Using computer modeling and finite element analysis, a three-dimensional (3D), numerical foot model of the solid ankle cushioned heel (SACH) foot was constructed and analyzed based upon loading conditions obtained from the gait analysis of an amputee and validated experimentally using mechanical testing. The model was then used to address effects of viscoelastic heel performance numerically. This is just one example of the type of parametric analysis and design enabled by this approach. More importantly, by incorporating the unique gait characteristics of the amputee, these parametric analyses may lead to prosthetic feet more appropriately representing a particular user's needs, comfort and activity level.     

A Coupling Analysis of the Biomechanical Functions of Human Foot Complex during Locomotion

This study represents a functional analysis of the human foot complex based on in-vivo gait measurements, finite element (FE) modeling and biological coupling theory, with the objective of achieving a comprehensive understanding of the impact attenuation and energy absorption functions of the human foot complex. A simplified heel pad FE model comprising reticular fiber structure and fat cells was constructed based on the foot pad Magnetic Resonance (MR) images. The model was then used to investigate the foot pad behaviors under impact during locomotion. Three-dimensional (3D) gait measurement and a 3D FE foot model comprising 29 bones, 85 ligaments and the plantar soft tissues were used to investigate the foot arch and plantar fascia deformations in mid-stance phase. The heel pad simulation results show that the pad model with fat cells (coupling model) has much stronger capacity in impact attenuation and energy storage than the model without fat cells (structure model). Furthermore, the FE simulation reproduced the deformations of the foot arch structure and the plantar fascia extension observed in the gait measurements, which reinforces the postulation that the foot arch structure also plays an important role in energy absorption during locomotion. Finally, the coupling mechanism of the human foot functions in impact attenuation and energy absorption was proposed.     

A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking

A multi-segment kinematic model of the foot was developed for use in a gait analysis laboratory. The foot was divided into hindfoot, talus, midfoot and medial and lateral forefoot segments. Six functional joints were defined: ankle and subtalar joints, frontal and transverse plane motions of the hindfoot relative to midfoot, supination/pronation twist of the forefoot relative to midfoot and medial longitudinal arch height-to-length ratio. Twelve asymptomatic subjects were tested during barefoot walking with a six-camera optical stereometric system and auto-reflective markers organized in triads. Repeatability of the joint motions was tested using coefficients of multiple correlation. Ankle and subtalar joint motions and twisting of the forefoot were most repeatable. Hindfoot motions were least repeatable both within-subjects and between-subjects. Hindfoot and forefoot pronation in the frontal plane was found to coincide with dropping of the medial longitudinal arch between early to mid-stance, followed by supination and rising of the arch in late stance and swing phase. This multi-segment foot model addresses an unfortunate shortcoming in current gait analysis practice-the inability to measure motion within the foot. Such measurements are crucial if gait analysis is to remain relevant in the orthopaedic and rehabilitative treatment of the foot and ankle.     

Smart Diabetic Socks: Embedded device for diabetic foot prevention

ObjectivesMost foot ulcers are the consequence of a trauma (repetitive high stress, ill-fitting footwear, or an object inside the shoe) associated to diabetes. They are often followed by amputation and shorten life expectancy. This paper describes the prototype of the Smart Diabetic Socks that has been developed in the context of the French ANR TecSan project. The objective is to prevent pressure foot ulcers for diabetic persons.Material and methodsA fully wireless, customizable and washable “smart sock” has been designed. It is made of a textile which fibers are knitted in a way they provide measurements of the pressure exerted under and all around the foot in real-life conditions. This device is coupled with a subject-specific Finite Element foot model that simulates the internal strains within the soft tissues of the foot.ResultsA number of derived stress indicators can be computed based on that analysis, such as the accumulated stress dose, high internal strains or peak pressures near bony prominences during gait. In case of risks for pressure ulcer, an alert is sent to the person and/or to the clinician. A watch, a smart-phone or a distant laptop can be used for providing such alert.     

Foot internal stress distribution during impact in barefoot running as function of the strike pattern

The aim of the present study is to examine the impact absorption mechanism of the foot for different strike patterns (rearfoot, midfoot and forefoot) using a continuum mechanics approach. A three-dimensional finite element model of the foot was employed to estimate the stress distribution in the foot at the moment of impact during barefoot running. The effects of stress attenuating factors such as the landing angle and the surface stiffness were also analyzed. We characterized rear and forefoot plantar sole behavior in an experimental test, which allowed for refined modeling of plantar pressures for the different strike patterns. Modeling results on the internal stress distributions allow predictions of the susceptibility to injury for particular anatomical structures in the foot.     

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.     

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.     

Simulation of the double limb support phase of human gait

Dynamic mechanical models of the double limb support phase of human gait were developed for both two-dimensional (sagittal plane) and three-dimensional motion. A "foot" model with a curved plantar surface was also developed such that the model foot motion was kinematically equivalent to that of a walking subject. This foot model was incorporated into the planar model for double limb support. The dynamic formulations were based on Kane's method and were implemented symbolically using MACSYMA. The development of the formulations for the constrained systems, application of these formulations to the study of normal gait, the sensitivity of the simulation to the frequency content of the input data, the sensitivity of limb displacements to changes in joint moments and the application of a nonlinear feedback controller to correct for perturbations in limb trajectories were investigated.     

Direct comparison of measured and calculated total knee replacement force envelopes during walking in the presence of normal and abnormal gait patterns

Knee joint forces measured from instrumented implants provide important information for testing the validity of computational models that predict knee joint forces. The purpose of this study was to validate a parametric numerical model for predicting knee joint contact forces against measurements from four subjects with instrumented TKRs during the stance phase of gait. Model sensitivity to abnormal gait patterns was also investigated. The results demonstrated good agreement for three subjects with relatively normal gait patterns, where the difference between the mean measured and calculated forces ranged from 0.05 to 0.45 body weights, and the envelopes of measured and calculated forces (from three walking trials) overlapped. The fourth subject, who had a "quadriceps avoidance" external moment pattern, initially had little overlap between the measured and calculated force envelopes. When additional constraints were added, tailored to the subject's gait pattern, the model predictions improved to complete force envelope overlap. Coefficient of multiple determination analysis indicated that the shape of the measured and calculated force waveforms were similar for all subjects (adjusted coefficient of multiple correlation values between 0.88 and 0.92). The parametric model was accurate in predicting both the magnitude and waveform of the contact force, and the accuracy of model predictions was affected by deviations from normal gait patterns. Equally important, the envelope of forces generated by the range of solutions substantially overlapped with the corresponding measured envelope from multiple gait trials for a given subject, suggesting that the variable strategic processes of in vivo force generation are covered by the solution range of this parametric model.     

3D finite element model of the diabetic neuropathic foot: A gait analysis driven approach

Diabetic foot is an invalidating complication of diabetes that can lead to foot ulcers. Three-dimensional (3D) finite element analysis (FEA) allows characterizing the loads developed in the different anatomical structures of the foot in dynamic conditions. The aim of this study was to develop a subject specific 3D foot FE model (FEM) of a diabetic neuropathic (DNS) and a healthy (HS) subject, whose subject specificity can be found in term of foot geometry and boundary conditions. Kinematics, kinetics and plantar pressure (PP) data were extracted from the gait analysis trials of the two subjects with this purpose. The FEM were developed segmenting bones, cartilage and skin from MRI and drawing a horizontal plate as ground support. Materials properties were adopted from previous literature. FE simulations were run with the kinematics and kinetics data of four different phases of the stance phase of gait (heel strike, loading response, midstance and push off). FEMs were then driven by group gait data of 10 neuropathic and 10 healthy subjects. Model validation focused on agreement between FEM-simulated and experimental PP.     

An ultrasound based non-invasive method for the measurement of intrinsic foot kinematics during gait

Soft tissue artefact (STA) and marker placement variability are sources of error when measuring the intrinsic kinematics of the foot. This study aims to demonstrate a non-invasive, combined ultrasound and motion capture (US/MC) technique to directly measure foot skeletal motion. The novel approach is compared to a standard motion capture protocol. Fourteen participants underwent instrumented barefoot analysis of foot motion during gait. Markers were attached to foot allowing medial longitudinal arch angle and navicular height to be determined. For the US/MC technique, the navicular marker was replaced by an ultrasound transducer which was secured to the foot allowing the skeletal landmark to be imaged. Ultrasound cineloops showing the location of the navicular tuberosity during the walking trials were synchronised with motion capture measurements and markers mounted on the probe allowed the true position of the bony landmark to be determined throughout stance phase. Two discrete variables, minimum navicular height and maximum MLA angle, were compared between the standard and US/MC protocols. Significant differences between minimum navicular height (P=0.004, 95% CI (1.57, 6.54)) and maximum medial longitudinal arch angle (P=0.0034, 95% CI (13.8, 3.4)) were found between the measurement methods. The individual effects of STA and marker placement error were also assessed. US/MC is a non-invasive technique which may help to provide more accurate measurements of intrinsic foot kinematics.     

Active control of lateral balance in human walking

We measured variability of foot placement during gait to test whether lateral balance must be actively controlled against dynamic instability. The hypothesis was developed using a simple dynamical model that can walk down a slight incline with a periodic gait resembling that of humans. This gait is entirely passive except that it requires active control for a single unstable mode, confined mainly to lateral motion. An especially efficient means of controlling this instability is to adjust lateral foot placement. We hypothesized that similar active feedback control is performed by humans, with fore-aft dynamics stabilized either passively or by very low-level control. The model predicts that uncertainty within the active feedback loop should result in variability in foot placement that is larger laterally than fore-aft. In addition, loss of sensory information such as by closing the eyes should result in larger increases in lateral variability. The control model also predicts a slight coupling between step width and length. We tested 15 young normal human subjects and found that lateral variability was 79% larger than fore-aft variability with eyes open, and a larger increase in lateral variability (53% vs. 21%) with eyes closed, consistent with the model's predictions. We also found that the coupling between lateral and fore-aft foot placements was consistent with a value of 0.13 predicted by the control model. Our results imply that humans may harness passive dynamic properties of the limbs in the sagittal plane, but must provide significant active control in order to stabilize lateral motion.     

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.     

An MRI-compatible foot-loading device for assessment of internal tissue deformation

It is well known that mechanical forces acting within the soft tissues of the foot can contribute to the formation of neuropathic ulcers in people with diabetes. Presently, only surface measurements of plantar pressure are used clinically to estimate risk status due to mechanical loading. It is currently not known how surface measurements relate to the three-dimensional (3-D) internal stress/strain state of the foot. This article describes the development of a foot-loading device that allows for the direct observation of the internal deformation of foot tissues under known forces. Ground reaction forces and plantar pressure distributions during normal walking were measured in ten healthy young adults. One instant in the gait cycle, when pressure under the metatarsal heads reached a peak, was extracted for simulation in an MR imager. T1-weighted 3-D gradient echo MRI sets were collected as the simulated walking ground reaction force was incrementally applied to the foot by the novel foot-loading device. The sub-metatarsal head soft-tissue thickness decreased rapidly at first and then reached a plateau. Peak plantar pressure measurements collected within the loading device (161+/-75kPa) were lower in magnitude and less focal than pressures measured during walking (492+/-91kPa). This finding implies that although the device successfully applied full peak walking ground reaction forces to the foot, they were not distributed in the same manner as during walking. Although not representative of gait, the data collected from this in vivo mechanical test are suitable for determination of foot tissue material properties or, when combined with finite element modeling, to examine the relationship between surface loading and internal stress.     

Principles of determination and verification of muscle forces in the human musculoskeletal system: Muscle forces to minimise bending stress

While there are a growing number of increasingly complex methodologies available to model geometry and material properties of bones, these models still cannot accurately describe physical behaviour of the skeletal system unless the boundary conditions, especially muscular loading, are correct. Available in vivo measurements of muscle forces are mostly highly invasive and offer no practical way to validate the outcome of any computational model that predicts muscle forces. However, muscle forces can be verified indirectly using the fundamental property of living tissue to functional adaptation and finite element (FE) analysis. Even though the mechanisms of the functional adaptation are not fully understood, its result is clearly seen in the shape and inner structure of bones. The FE method provides a precise tool for analysis of the stress/strain distribution in the bone under given loading conditions. The present work sets principles for the determination of the muscle forces on the basis of the widely accepted view that biological systems are optimized light-weight structures with minimised amount of unloaded/underloaded material and hence evenly distributed loading throughout the structure. Bending loading of bones is avoided/compensated in bones under physiological loading. Thus, bending minimisation provides the basis for the determination of the musculoskeletal system loading. As a result of our approach, the muscle forces for a human femur during normal gait and sitting down (peak hip joint force) are obtained such that the bone is loaded predominantly in compression and the stress distribution in proximal and diaphyseal femur corresponds to the material distribution in bone.     

Predicting timing of foot strike during running,independent of striking technique,using principal component analysis of joint angles

As 3-dimensional (3D) motion-capture for clinical gait analysis continues to evolve, new methods must be developed to improve the detection of gait cycle events based on kinematic data. Recently, the application of principal component analysis (PCA) to gait data has shown promise in detecting important biomechanical features. Therefore, the purpose of this study was to define a new foot strike detection method for a continuum of striking techniques, by applying PCA to joint angle waveforms. In accordance with Newtonian mechanics, it was hypothesized that transient features in the sagittal-plane accelerations of the lower extremity would be linked with the impulsive application of force to the foot at foot strike. Kinematic and kinetic data from treadmill running were selected for 154 subjects, from a database of gait biomechanics. Ankle, knee and hip sagittal plane angular acceleration kinematic curves were chained together to form a row input to a PCA matrix. A linear polynomial was calculated based on PCA scores, and a 10-fold cross-validation was performed to evaluate prediction accuracy against gold-standard foot strike as determined by a 10 N rise in the vertical ground reaction force. Results show 89–94% of all predicted foot strikes were within 4 frames (20 ms) of the gold standard with the largest error being 28 ms. It is concluded that this new foot strike detection is an improvement on existing methods and can be applied regardless of whether the runner exhibits a rearfoot, midfoot, or forefoot strike pattern.     

Design parameters dependences on contact stress distribution in gait and jogging phases after total hip arthroplasty

We have developed a mathematical model to calculate the contact stress distribution in total hip arthroplasty (THA) prosthesis between the articulating surfaces. The model uses the clearance between bearing surfaces as well as the inclination and thickness of the Ultra High Molecular Weight Poly-Ethylene (UHMWPE) cup to achieve this. We have used this mathematical model to contrast the maximal force during normal gait and during jogging. This is based on the assumption that the contact stress is proportional to the radial deformation of the cup. The results show that the magnitude of the maximal contact stress remains constant for inclination values in the range of [0-35 degrees ] and increase significantly with the cup clearance and liner thickness for inclination values in the range of [35-65 degrees ]. A major use for this model would be the calculation of spatial contact stress distribution during normal gait or jogging for different couples of bearing surfaces.     

Evaluation of a patient-specific cost function to predict the influence of foot path on the knee adduction torque during gait

A large external knee adduction torque during gait has been correlated with the progression of knee osteoarthritis (OA). Though foot path changes (e.g. toeing out) can reduce the adduction torque, no method currently exists to predict whether an optimal foot path exists for a specific patient. This study evaluates a patient-specific optimization cost function to predict how foot path changes influence both adduction torque peaks. Video motion and ground reaction data were collected from a patient with knee OA performing normal, toe out, and wide stance gait. Joint and inertial parameters in a dynamic, 27 degree-of-freedom, full-body gait model were calibrated to the patient's normal gait data. The model was then used in gait optimizations that predicted how the patient's adduction torque peaks would change due to changes in foot path. The cost function tracked the patient's normal gait data using weight factors calibrated to toe out gait and tested using wide stance gait. For both gait motions, the same cost function weights predicted the change in both adduction torque peaks to within 7% error. With further development, this approach may eventually permit the design of patient-specific rehabilitation procedures such as an optimal foot path for patients with knee OA.