Mechanics of the foot Part 1: a continuum framework for evaluating soft tissue stiffening in the pathologic foot

Toward improved understanding of foot shape, foot posture, and foot biomechanics during running: A narrative review

The current narrative review has explored known associations between foot shape, foot posture, and foot conditions during running. The artificial intelligence was found to be a useful metric of foot posture but was less useful in developing and obese individuals. Care should be taken when using the foot posture index to associate pronation with injury risk, and the Achilles tendon and longitudinal arch angles are required to elucidate the risk. The statistical shape modeling (SSM) may derive learnt information from population-based inference and fill in missing data from personalized information. Bone shapes and tissue morphology have been associated with pathology, gender, age, and height and may develop rapid population-specific foot classifiers. Based on this review, future studies are suggested for 1) tracking the internal multi-segmental foot motion and mapping the biplanar 2D motion to 3D shape motion using the SSM; 2) implementing multivariate machine learning or convolutional neural network to address nonlinear correlations in foot mechanics with shape or posture; 3) standardizing wearable data for rapid prediction of instant mechanics, load accumulation, injury risks and adaptation in foot tissue and bones, and correlation with shapes; 4) analyzing dynamic shape and posture via marker-less and real-time techniques under real-life scenarios for precise evaluation of clinical foot conditions and performance-fit footwear development.

A combined functional dorsal nerve model of the foot

The nerves in the skin surface of the foot are comprised of unmyelinated smaller somatic nerves and larger myelinated sensory nerves. Current diagnostic methods are unable to evaluate combined nerve conduction velocity (NCV) from both unmyelinated smaller somatic nerve (USSN) and myelinated larger nerves (MLN) respectively. Computational models may provide an alternative tool to determine the NCV of the combined nerve. Therefore, a combined functional dorsal nerve model (CFDNM) of the various dorsal nerves along with its associated nerve ending of the human foot is proposed and constructed. The combined dorsal nerve model consists of synthetic USSN (SUSSN) and dorsal MLN of the foot. The unmyelinated as well as myelinated electrophysiological nerve models were used to simulate selected SUSSN and MLN of the foot by injecting an external stimulus at the most distal part of SUSSN of the foot through the use of bidomain model. Results from our work demonstrated that the action potential propagated from the most distal part to proximal part of distinct dorsal nerves of the foot, e.g., the simulated NCV of the combined intermediate dorsal cutaneous nerve (IDCN) of the foot was 28.4 m s^-1. The CFDNM will provide a vital tool for diagnosis initially small fibre neuropathy (SFN) by computing NCV in the prospective studies.

The Structural Effects of Diabetes on Soft Tissues: A Systematic Review

Hyperglycemia, which is associated with diabetes, increases the production of advanced glycation end products. Advanced glycation end products lead to the structural degradation of soft tissues. The structural degradation of diabetic soft tissues has been investigated in humans, rodents, and canines. Therefore, the objective of this review is to unify the various contributions to diabetes research through the mechanical properties and geometric characteristics of soft tissues. A systematic review was performed and identified the effects of diabetes on mechanical and geometric properties of soft tissues via experimental testing or in vivo - driven finite element analysis. The literature concludes that diabetes contributes to major structural changes in soft tissues but does not cause the same structural changes in all soft tissues (e.g., diabetic tendons are weaker and diabetic plantar tissues are tougher). Diabetes stiffens and toughens soft tissues, thus altering viscoelastic behavior (e.g., poor strain and stress response). However, diabetes management routines can prevent or minimize the effects of diabetes on the mechanical and geometric properties of soft tissues. Unification of the structural effects of diabetes on soft tissues will contribute to the pathophysiology of diabetes.

Implication of obesity on motion, posture and internal stress of the foot: an experimental and finite element analysis

Obesity causes increased loading on the foot which can damage the soft tissue and bone ultimately leading to foot problems. Experimental and computational methods were used to analyse the chain of biomechanical changes in the lower limb due to obesity. The experimental study shows some changes in foot posture and gait where obese subjects were more likely to have pronated feet, smaller joint angles in the sagittal and frontal planes, smaller cadence, and smaller stride length. Anatomically correct finite element models generated on obese subjects showed increased and altered internal and plantar stress.  Altered foot posture was identified as a key indicator of increased internal stress indicating the importance of foot posture correction.

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.

NUMERICAL ANALYSIS OF THE FOOT IN HEALTHY AND DEGENERATIVE CONDITIONS

The aim of this work is the development of a 3D numerical model of the foot that allows evaluating the influence of degenerative phenomena on the foot mechanical functionality. Such degenerative phenomena induce histo-morphological alterations and significant modification of the plantar soft tissue mechanical properties, as stiffening and lower damping capabilities. The finite element model of the foot is developed starting from the analysis of biomedical images. Different constitutive models define the mechanical response of the biological tissues. Because of the major role of plantar soft tissue in the here proposed analysis, a specific visco-hyperelastic constitutive formulation is provided considering the typical features of the tissue mechanics, as geometric and material non linearity, almost incompressible behavior and time-dependent phenomena. Constitutive parameters are identified by the analysis of experimental data from in vitro and in vivo mechanical tests, leading to the identification of a range of constitutive parameters for healthy and degenerative conditions. Numerical analyses are developed to investigate the influence of the progression of the degeneration on the distribution of stress and of strain within foot tissues during static standing. Numerical results show the increase of stress values with the appearance of degenerative conditions, showing the typical stiffening phenomenon. The mechanical response of the plantar soft tissue during specific loading condition and the influence of degenerative phenomena on foot mechanics can be evaluated with numerical analysis.

GAIT ANALYSIS DRIVEN 2D FINITE ELEMENT MODEL OF THE NEUROPATHIC HINDFOOT

The diabetic foot is one of the most serious complications of diabetes mellitus and it can lead to foot ulcerations and amputations. Finite element analysis quantifies the loads developed in the different anatomical structures and describes how these affect foot tissue during foot–floor interaction. This approach for the diabetic subjects’ foot could provide valuable information in the process of plantar orthosis fabrication and fit. The purpose of this study was to develop two finite element models of the hindfoot, of healthy and diabetic neuropathic subjects. These models accounts for in vivo kinematics, kinetics, plantar pressure (PP) data and magnetic resonance images. These were acquired during gait analysis on 10 diabetic neuropathics and 10 healthy subjects. Validity of the models has been assessed through comparison between the peak PPs of simulated and experimental data: root mean square error (RMSE) in percentage of the experimental peak value was evaluated. Two different finite elements analysis were performed: subject-specific simulations in terms of both geometry and gait analysis, and by adopting the complete gait analysis dataset as boundary conditions. Model predicted plantar pressures were in good agreement with those experimentally measured. Best agreement was obtained in the subject-specific case (RMSE of 13%).

Relationship between tissue stress during gait in healthy volunteers and patterns of urate deposition and bone erosion in gout: a biomechanical computational modelling study

Objectives

To determine whether patterns of high internal tissue stress during gait are associated with patterns of monosodium urate crystal deposition and bone erosion in gout.

Methods

We compared patterns of foot von Mises stress predicted computationally during gait in volunteers of normal and high body mass index (BMI) with patterns of urate deposition in gout and asymptomatic hyperuricaemia, and bone erosion in gout using dual-energy and conventional CT data.

Results

The highest average and peak von Mises stress during gait was observed at the third metatarsal (MT) head. Similar stress patterns were observed for high and low BMI groups. In contrast, for both urate deposition and bone erosion, the first MT head was most frequently affected, with very infrequent involvement of the third MT head. There was no clear relationship between average or peak von Mises stress patterns with patterns of urate deposition or bone erosion (−0.29>r<0.16). Addition of BMI into linear regression models did not alter the findings.

Conclusions

These data do not support the concept that elevated internal tissue stress during biomechanical loading plays an important role in patterns of monosodium urate crystal deposition or structural damage in gout.

What has finite element analysis taught us about diabetic foot disease and its management? A systematic review

Background

Over the past two decades finite element (FE) analysis has become a popular tool for researchers seeking to simulate the biomechanics of the healthy and diabetic foot. The primary aims of these simulations have been to improve our understanding of the foot’s complicated mechanical loading in health and disease and to inform interventions designed to prevent plantar ulceration, a major complication of diabetes. This article provides a systematic review and summary of the findings from FE analysis-based computational simulations of the diabetic foot.

Methods

A systematic literature search was carried out and 31 relevant articles were identified covering three primary themes: methodological aspects relevant to modelling the diabetic foot; investigations of the pathomechanics of the diabetic foot; and simulation-based design of interventions to reduce ulceration risk.

Results

Methodological studies illustrated appropriate use of FE analysis for simulation of foot mechanics, incorporating nonlinear tissue mechanics, contact and rigid body movements. FE studies of pathomechanics have provided estimates of internal soft tissue stresses, and suggest that such stresses may often be considerably larger than those measured at the plantar surface and are proportionally greater in the diabetic foot compared to controls. FE analysis allowed evaluation of insole performance and development of new insole designs, footwear and corrective surgery to effectively provide intervention strategies. The technique also presents the opportunity to simulate the effect of changes associated with the diabetic foot on non-mechanical factors such as blood supply to local tissues.

Discussion

While significant advancement in diabetic foot research has been made possible by the use of FE analysis, translational utility of this powerful tool for routine clinical care at the patient level requires adoption of cost-effective (both in terms of labour and computation) and reliable approaches with clear clinical validity for decision making.

Mechanics of the foot Part 2: A coupled solid-fluid model to investigate blood transport in the pathologic foot

A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region.