Biomechanical analysis of foot with different foot arch heights: a finite element analysis

Clinically, different foot arch heights are associated with different tissue injuries to the foot. To investigate the possible factors contributing to the difference in foot arch heights, previous studies have mostly measured foot pressure in either low-arched or high-arched feet. However, little information exists on stress variation inside the foot with different arch heights. Therefore, this study aimed to implement the finite element (FE) method to analyse the influence of different foot arches. This study established a 3D foot FE model using software ANSYS 11.0. After validating the FE model, this study created low-arched, high-arched and normal-arched foot FE models. The FE analysis found that both the stress and strain on the plantar fascia and metatarsal were higher in the high-arched foot, whereas the stress and strain on the calcaneous, navicular and cuboid were higher in low-arched foot. Additionally, forefoot pressure was increased with an increase in arch height.     

Effects of vertical loading on arch characteristics and intersegmental foot motions

The medial longitudinal arch plays a major role in determining lower extremity kinematics. Thus, it is necessary to understand the dynamics of the arch structure in response to load. The purpose of this study was to examine arch function in high- and low-arched feet during a vertical loading condition. Ten high- and ten low-arched females performed five trials in a sit-to-stand exercise. Ground reaction force (1200 Hz) and three-dimensional kinematics (240 Hz) were collected simultaneously. The high-and low-arched athletes had no differences in vertical deformation of the arch. High-arched participants were less everted than the low-arched athletes; furthermore, the high-arched athletes had smaller mid-forefoot eversion excursions. Differences between the high-arched and low-arched athletes occur through and motion at the mid-forefoot joint.     

Deformation and stress distribution of the human foot after plantar ligaments release: A cadaveric study and finite element analysis

The majority of foot deformities are related to arch collapse or instability, especially the longitudinal arch. Although the relationship between the plantar fascia and arch height has been previously investigated, the stress distribution remains unclear. The aim of this study was to explore the role of the plantar ligaments in foot arch biomechanics. We constructed a geometrical detailed three-dimensional (3-D) finite element (FE) model of the human foot and ankle from computer tomography images. The model comprised the majority of joints in the foot as well as bone segments, major ligaments, and plantar soft tissue. Release of the plantar fascia and other ligaments was simulated to evaluate the corresponding biomechanical effects on load distribution of the bony and ligamentous structures. These intrinsic ligaments of the foot arch were sectioned to simulate different pathologic situations of injury to the plantar ligaments, and to explore bone segment displacement and stress distribution. The validity of the 3-D FE model was verified by comparing results with experimentally measured data via the displacement and von Mise stress of each bone segment. Plantar fascia release decreased arch height, but did not cause total collapse of the foot arch. The longitudinal foot arch was lost when all the four major plantar ligaments were sectioned simultaneously. Plantar fascia release was compromised by increased strain applied to the plantar ligaments and intensified stress in the midfoot and metatarsal bones. Load redistribution among the centralized metatarsal bones and focal stress relief at the calcaneal insertion were predicted. The 3-D FE model indicated that plantar fascia release may provide relief of focal stress and associated heel pain. However, these operative procedures may pose a risk to arch stability and clinically may produce dorsolateral midfoot pain. The initial strategy for treating plantar fasciitis should be non-operative.     

Parametric study of orthopedic insole of valgus foot on partial foot amputation

Orthopedic insole was important for partial foot amputation (PFA) to achieve foot balance and avoid foot deformity. The inapposite insole orthosis was thought to be one of the risk factors of reamputation for foot valgus patient, but biomechanical effects of internal tissues on valgus foot had not been clearly addressed. In this study, plantar pressure on heel and metatarsal regions of PFA was measured using F-Scan. The three-dimensional finite element (FE) model of partial foot evaluated different medial wedge angles (MWAs) (0.0°–10.0°) of orthopedic insole on valgus foot. The effect of orthopedic insole on the internal bone stress, the medial ligament tension of ankle, plantar fascia tension, and plantar pressure was investigated. Plantar pressure on medial heel region was about 2.5 times higher than that of lateral region based on the F-Scan measurements. FE-predicted results showed that the tension of medial ankle ligaments was the lowest, and the plantar pressure was redistributed around the heel, the first metatarsal, and the lateral longitudinal arch regions when MWA of orthopedic insole ranged from 7.5° to 8.0°. The plantar fascias maintained about 3.5% of the total load bearing on foot. However, the internal stresses from foot bones increased. The simulation in this study would provide the suggestion of guiding optimal design of orthopedic insole and therapeutic planning to pedorthist.     

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.     

Natural gaits of the non-pathological flat foot and high-arched foot

There has been a controversy as to whether or not the non-pathological flat foot and high-arched foot have an effect on human walking activities. The 3D foot scanning system was employed to obtain static footprints from subjects adopting a half-weight-bearing stance. Based upon their footprints, the subjects were divided into two groups: the flat-footed and the high-arched. The plantar pressure measurement system was used to measure and record the subjects' successive natural gaits. Two indices were proposed: distribution of vertical ground reaction force (VGRF) of plantar and the rate of change of footprint areas. Using these two indices to compare the natural gaits of the two subject groups, we found that (1) in stance phase, there is a significant difference (p<0.01) in the distributions of VGRF of plantar; (2) in a stride cycle, there is also a significant difference (p<0.01) in the rate of change of footprint area. Our analysis suggests that when walking, the VGRF of the plantar brings greater muscle tension to the flat-footed while a smaller rate of change of footprint area brings greater stability to the high-arched.     

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.     

Development of a patient-specific anatomical foot model from structured light scan data

The use of anatomically accurate finite element (FE) models of the human foot in research studies has increased rapidly in recent years. Uses for FE foot models include advancing knowledge of orthotic design, shoe design, ankle–foot orthoses, pathomechanics, locomotion, plantar pressure, tissue mechanics, plantar fasciitis, joint stress and surgical interventions. Similar applications but for clinical use on a per-patient basis would also be on the rise if it were not for the high costs associated with developing patient-specific anatomical foot models. High costs arise primarily from the expense and challenges of acquiring anatomical data via magnetic resonance imaging (MRI) or computed tomography (CT) and reconstructing the three-dimensional models. The proposed solution morphs detailed anatomy from skin surface geometry and anatomical landmarks of a generic foot model (developed from CT or MRI) to surface geometry and anatomical landmarks acquired from an inexpensive structured light scan of a foot. The method yields a patient-specific anatomical foot model at a fraction of the cost of standard methods. Average error for bone surfaces was 2.53 mm for the six experiments completed. Highest accuracy occurred in the mid-foot and lowest in the forefoot due to the small, irregular bones of the toes. The method must be validated in the intended application to determine if the resulting errors are acceptable.     

The Relationships between Foot Arch Volumes and Dynamic Plantar Pressure during Midstance of Walking in Preschool Children

Objectives

The purpose of this study was to examine the correlation between the foot arch volume measured from static positions and the plantar pressure distribution during walking.

Methods

A total of 27 children, two to six years of age, were included in this study. Measurements of static foot posture were obtained, including navicular height and foot arch volume in sitting and standing positions. Plantar pressure, force and contact areas under ten different regions of the foot were obtained during walking.

Results

The foot arch index was correlated (r = 0.32) with the pressure difference under the midfoot during the foot flat phase. The navicular heights and foot arch volumes in sitting and standing positions were correlated with the mean forces and pressures under the first (r = −0.296∼−0.355) and second metatarsals (r = −0.335∼−0.504) and midfoot (r = −0.331∼−0.496) during the stance phase of walking. The contact areas under the foot were correlated with the foot arch parameters, except for the area under the midfoot.

Conclusions

The foot arch index measured in a static position could be a functional index to predict the dynamic foot functions when walking. The foot arch is a factor which will influence the pressure distribution under the foot. Children with a lower foot arch demonstrated higher mean pressure and force under the medial forefoot and midfoot, and lower contact areas under the foot, except for the midfoot region. Therefore, children with flatfoot may shift their body weight to a more medial foot position when walking, and could be at a higher risk of soft tissue injury in this area.     

Structural components of the arch of the foot analyzed by radiogrammetric and multivariate statistical methods

The structural component of the arches of the human foot were analyzed by a radiogrammetric method and multivariate statistical procedures. The right feet of 101 male university students were radiographed in the standing position from a lateromedial direction. 6 joint heights were measured directly on the radiographs. Factor analysis with varimax rotation showed 3 basic underlying factors for arch heights: (1) calcaneonavicular joint, cuneonavicular joint and first tarsometatarsal joint; (2) calcaneocuboidal joint and 5th tarsometatarsal joint and (3) subtalar joint. The first factor represented the medial longitudinal arch height, the second was associated with the lateral longitudinal arch height. No transverse factor indicating tarsometatarsal or transverse tarsal joints was found. Cluster analysis showed a similar configuration to that in factor analysis. Analysis suggested a key role of the subtalar joint which integrated both the medial and lateral longitudinal arch heights.     

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.     

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.     

Biomechanical model of the diabetic foot

In this work, a two dimensional (2D) finite element foot model was established from magnetic resonance imaging (MRI) of a male subject. The model comprises first medial planar cross-section through the foot, representing the foot in standing posture. For specified external load, the stress and strain distribution field under foot structure are determined. The material characterization of foot structure components are stronger related to diabetic phenomena. The new material model for soft tissue based on mixture theory is proposed. The linear finite element model replaced by nonlinear counterpart with segment-to-segment contact element.     

Biomechanical analysis of the three-dimensional foot structure during gait: a basic tool for clinical applications

A novel three-dimensional numerical model of the foot, incorporating, for the first time in the literature, realistic geometric and material properties of both skeletal and soft tissue components of the foot, was developed for biomechanical analysis of its structural behavior during gait. A system of experimental methods, integrating the optical Contact Pressure Display (CPD) method for plantar pressure measurements and a Digital Radiographic Fluoroscopy (DRF) instrument for acquisition of skeletal motion during gait, was also developed in this study and subsequently used to build the foot model and validate its predictions. Using a Finite Element solver, the stress distribution within the foot structure was obtained and regions of elevated stresses for six subphases of the stance (initial-contact, heel-strike, midstance, forefoot-contact, push-off, and toe-off) were located. For each of these subphases, the model was adapted according to the corresponding fluoroscopic data, skeletal dynamics, and active muscle force loading. Validation of the stress state was achieved by comparing model predictions of contact stress distribution with respective CPD measurements. The presently developed measurement and numerical analysis tools open new approaches for clinical applications, from simulation of the development mechanisms of common foot disorders to pre- and post-interventional evaluation of their treatment.     

Stress analysis of the standing foot following surgical plantar fascia release

Plantar fascia release is a surgical alternative for patients who suffer chronic heel pain due to plantar fasciitis and are unaffected by conservative treatment. A computational (finite element) model for analysis of the structural behavior of the human foot during standing was utilized to investigate the biomechanical effects of releasing the plantar fascia. The model integrates a system of five planar structures in the directions of the foot rays. It was built according to accurate geometric data of MRI, and includes linear and non-linear elements that represent bony, cartilaginous, ligamentous and fatty tissues. The model was successfully validated by comparing its resultant ground reactions with foot-ground pressure measurements and its predicted displacements with those observed in radiological tests. Simulation of plantar fascia release (partial or total) was accomplished by gradually removing parts of the fascia in the model. The results showed that total fascia release causes extensive arch deformation during standing, which is greater than normal deformation by more than 2.5mm. Tension stresses carried by the long plantar ligaments increased significantly, and may exceed the normal average stress by more than 200%. Since the contribution of the plantar fascia to the foot's load-bearing ability is of major importance, its release must be very carefully considered, and the present model may be used to help surgeons decide upon the desired degree of release.     

Foot arch deformation and plantar fascia loading during running with rearfoot strike and forefoot strike: A dynamic finite element analysis

Forefoot strike becomes popular among runners because it facilitates better impact attenuation. However, forefoot strike may overload the plantar fascia and impose risk of plantar fasciitis. This study aimed to examine and compare the foot arch deformation and plantar fascia tension between different foot strike techniques in running using a computational modelling approach. A three-dimensional finite element foot model was reconstructed from the MRI of a healthy runner. The foot model included twenty bones, bulk soft tissue, ligaments, tendons, and plantar fascia. The time-series data of segmental kinematics, foot muscle force, and ankle joint reaction force were derived from a musculoskeletal model of the same participant based on the motion capture analysis and input as the boundary conditions for the finite element analysis. Rearfoot strike and forefoot strike running were simulated using a dynamic explicit solver. The results showed that, compared to rearfoot strike, forefoot strike reduced the foot arch height by 9.12% and increased the medial longitudinal arch angle by 2.06%. Forefoot strike also increased the plantar connective tissues stress by 18.28–200.11% and increased the plantar fascia tensile force by 18.71–109.10%. Although it is currently difficult to estimate the threshold value of stress or force that results in injury, forefoot strike runners appeared to be more vulnerable to plantar fasciitis.     

Analysis of the main passive soft tissues associated with adult acquired flatfoot deformity development: A computational modeling approach

Adult acquired flatfoot deformity (AAFD) is a pathology with a wide range of treatment options. Physicians decide the best treatment based on their experience, so the process is entirely subjective. A better understanding of soft tissue stress and its contribution in supporting the plantar arch could help to guide the clinical decision. Traditional experimental trials cannot consistently evaluate the contribution of each tissue. Therefore, in this research a 3-Dimensional FE foot model was reconstructed from a normal patient in order to measure the stress of the passive stabilizers of the arch, and its variation in different scenarios related with intermediate stages of AAFD development. All bones, the plantar fascia (PF), cartilages, plantar ligaments and the spring ligament (SL) were included, respecting their anatomical distribution and biomechanical characteristics. An AAFD evaluation scenario was simulated. The relative contribution of each tissue was obtained comparing each result with a normal case. The results show that PF is the main tissue that prevents the arch elongation, while SL mainly reduces the foot pronation. Long and short plantar ligaments play a secondary role in this process. The stress increment on both PF and SL when one of two fails suggests that these tissues complement each other. These findings support the theory that regards the tibialis posterior tendon as a secondary actor in the arch maintenance, compared with the PF and the SL, because this tendon is overstretched by the hindfoot pronation around the talonavicular joint. This approach could help to improve the understanding of AAFD.     

Analysis of the human and ape foot during bipedal standing with implications for the evolution of the foot

The ratio of the power arm (the distance from the heel to the talocrural joint) to the load arm (that from the talocrural joint to the distal head of the metatarsals), or RPL, differs markedly between the human and ape foot. The arches are relatively higher in the human foot in comparison with those in apes. This study evaluates the effect of these two differences on biomechanical effectiveness during bipedal standing, estimating the forces acting across the talocrural and tarsometatarsal joints, and attempts to identify which type of foot is optimal for bipedal standing. A simple model of the foot musculoskeletal system was built to represent the geometric and force relationships in the foot during bipedal standing, and measurements for a variety of human and ape feet applied. The results show that: (1) an RPL of around 40% (as is the case in the human foot) minimizes required muscle force at the talocrural joint; (2) the presence of an high arch in the human foot reduces forces in the plantar musculature and aponeurosis; and (3) the human foot has a lower total of force in joints and muscles than do the ape feet. These results indicate that the proportions of the human foot, and the height of the medial arch are indeed better optimized for bipedal standing than those of apes, further suggesting that their current state is to some extent the product of positive selection for enhanced bipedal standing during the evolution of the foot.     

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.     

MRI-based finite-element analysis of left ventricular aneurysm

Tagged MRI and finite-element (FE) analysis are valuable tools in analyzing cardiac mechanics. To determine systolic material parameters in three-dimensional stress-strain relationships, we used tagged MRI to validate FE models of left ventricular (LV) aneurysm. Five sheep underwent anteroapical myocardial infarction (25% of LV mass) and 22 wk later underwent tagged MRI. Asymmetric FE models of the LV were formed to in vivo geometry from MRI and included aneurysm material properties measured with biaxial stretching, LV pressure measurements, and myofiber helix angles measured with diffusion tensor MRI. Systolic material parameters were determined that enabled FE models to reproduce midwall, systolic myocardial strains from tagged MRI (630 +/- 187 strain comparisons/animal). When contractile stress equal to 40% of the myofiber stress was added transverse to the muscle fiber, myocardial strain agreement improved by 27% between FE model predictions and experimental measurements (RMS error decreased from 0.074 +/- 0.016 to 0.054 +/- 0.011, P < 0.05). In infarct border zone (BZ), end-systolic midwall stress was elevated in both fiber (24.2 +/- 2.7 to 29.9 +/- 2.4 kPa, P < 0.01) and cross-fiber (5.5 +/- 0.7 to 11.7 +/- 1.3 kPa, P = 0.02) directions relative to noninfarct regions. Contrary to previous hypotheses but consistent with biaxial stretching experiments, active cross-fiber stress development is an integral part of LV systole; FE analysis with only uniaxial contracting stress is insufficient. Stress calculations from these validated models show 24% increase in fiber stress and 115% increase in cross-fiber stress at the BZ relative to remote regions, which may contribute to LV remodeling.