Effects of internal stress concentrations in plantar soft-tissue—A preliminary three-dimensional finite element analysis

Quantifying Dynamic Changes in Plantar Pressure Gradient in Diabetics with Peripheral Neuropathy

Diabetic foot ulcers remain one of the most serious complications of diabetes. Peak plantar pressure (PPP) and peak pressure gradient (PPG) during walking have been shown to be associated with the development of diabetic foot ulcers. To gain further insight into the mechanical etiology of diabetic foot ulcers, examination of the pressure gradient angle (PGA) has been recently proposed. The PGA quantifies directional variation or orientation of the pressure gradient during walking and provides a measure of whether pressure gradient patterns are concentrated or dispersed along the plantar surface. We hypothesized that diabetics at risk of foot ulceration would have smaller PGA in key plantar regions, suggesting less movement of the pressure gradient over time. A total of 27 participants were studied, including 19 diabetics with peripheral neuropathy and 8 non-diabetic control subjects. A foot pressure measurement system was used to measure plantar pressures during walking. PPP, PPG, and PGA were calculated for four foot regions – first toe (T1), first metatarsal head (M1), second metatarsal head (M2), and heel (HL). Consistent with prior studies, PPP and PPG were significantly larger in the diabetic group compared with non-diabetic controls in the T1 and M1 regions, but not M2 or HL. For example, PPP was 165% (P = 0.02) and PPG was 214% (P < 0.001) larger in T1. PGA was found to be significantly smaller in the diabetic group in T1 (46%, P = 0.04), suggesting a more concentrated pressure gradient pattern under the toe. The proposed PGA may improve our understanding of the role of pressure gradient on the risk of diabetic foot ulcers.

Towards the generation of a parametric foot model using principal component analysis: A pilot study

There have been many recent developments in patient-specific models with their potential to provide more information on the human pathophysiology and the increase in computational power. However they are not yet successfully applied in a clinical setting. One of the main challenges is the time required for mesh creation, which is difficult to automate. The development of parametric models by means of the Principle Component Analysis (PCA) represents an appealing solution. In this study PCA has been applied to the feet of a small cohort of diabetic and healthy subjects, in order to evaluate the possibility of developing parametric foot models, and to use them to identify variations and similarities between the two populations. Both the skin and the first metatarsal bones have been examined. Besides the reduced sample of subjects considered in the analysis, results demonstrated that the method adopted herein constitutes a first step towards the realization of a parametric foot models for biomechanical analysis. Furthermore the study showed that the methodology can successfully describe features in the foot, and evaluate differences in the shape of healthy and diabetic subjects.

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%).

Simplified versus geometrically accurate models of forefoot anatomy to predict plantar pressures: A finite element study

Integration of patient-specific biomechanical measurements into the design of therapeutic footwear has been shown to improve clinical outcomes in patients with diabetic foot disease. The addition of numerical simulations intended to optimise intervention design may help to build on these advances, however at present the time and labour required to generate and run personalised models of foot anatomy restrict their routine clinical utility. In this study we developed second-generation personalised simple finite element (FE) models of the forefoot with varying geometric fidelities. Plantar pressure predictions from barefoot, shod, and shod with insole simulations using simplified models were compared to those obtained from CT-based FE models incorporating more detailed representations of bone and tissue geometry. A simplified model including representations of metatarsals based on simple geometric shapes, embedded within a contoured soft tissue block with outer geometry acquired from a 3D surface scan was found to provide pressure predictions closest to the more complex model, with mean differences of 13.3kPa (SD 13.4), 12.52kPa (SD 11.9) and 9.6kPa (SD 9.3) for barefoot, shod, and insole conditions respectively. The simplified model design could be produced in <1h compared to >3h in the case of the more detailed model, and solved on average 24% faster. FE models of the forefoot based on simplified geometric representations of the metatarsal bones and soft tissue surface geometry from 3D surface scans may potentially provide a simulation approach with improved clinical utility, however further validity testing around a range of therapeutic footwear types is required.

Minimum indentation depth for characterization of 2nd sub-metatarsal head and heel pad tissue properties

Most in-vivo indentation techniques are limited by the lack of adequate indentation into the plantar soft tissue. The purpose of this study is therefore to assess the effect of deformation depth on plantar soft tissue behavior and to establish a guideline for the minimum indentation depth that is sufficient to quantify critical plantar soft tissue behavior. Twenty young subjects (20-25 years) participated in this study. The test was conducted with equal weight borne on each of the participants׳ feet to mimic the static stance of the gait cycle. During the experiment, the indenter probed the 2nd sub-metatarsal head (MTH) and heel pad tissue at a constant rate of 12.3 mm/s. The maximum tissue deformation induced was varied from 1.2 mm to 6.0 mm, in steps of 1.2 mm. The tissue stiffness obtained from the tissue response curves was compared and fitted to the proposed viscoelastic model. As the probe tip indents deeper into the plantar soft tissue beyond a threshold depth, Xs, the force gradient increases notably. The absolute value of Xs was approximately 2.23 mm and 2.14 mm at the heel and 2nd sub-MTH respectively. Indentation depths which were less than this threshold depth might not be representative of the nature of plantar soft tissue nor reflect the critical deformation it experiences during physical activities that expose the tissue to risk of ulceration. Our study indicated the necessity to induce a minimum tissue indentation depth in order to describe its actual characteristics. By doing so, additional useful parameters can be obtained to identify potentially abnormal soft tissue.

Influence of first proximal phalanx geometry on hallux valgus deformity: a finite element analysis

Hallux abducto valgus (HAV), one of the most common forefoot deformities, occurs primarily in elderly women. HAV is a complex disease without a clearly identifiable cause for its higher prevalence in women compared with men. Several studies have reported various skeletal parameters related to HAV. This study examined the geometry of the proximal phalanx of the hallux (PPH) as a potential etiologic factor in this deformity. A total of 43 cadaver feet (22 males and 21 females) were examined by means of cadaveric dissection. From these data, ten representative PPHs for both genders were selected, corresponding to five percentiles for males (0, 25, 50, 75, and 100%) and five for females. These ten different PPHs were modeled and inserted in ten foot models. Stress distribution patterns within these ten PPH models were qualitatively compared using finite element analysis. In the ten cases analyzed, tensile stresses were larger on the lateral side, whereas compressive stresses were larger on the medial side. The bones of males were larger than female bones for each of the parameters examined; however, the mean difference between lateral and medial sides of the PPH (mean ± SD) was larger in women. Also the shallower the concavity at the base of the PPH, the larger the compressive stresses predicted. Internal forces on the PPH, due to differences in length between its medial and lateral sides, may force the PPH into a less-stressful position. The geometry of the PPH is a significant factor in HAV development influencing the other reported skeletal parameters and, thus, should be considered during preoperative evaluation. Clinical assessment should evaluate the first ray as a whole and not as isolated factors.

Plantar pressure relief under the metatarsal heads: therapeutic insole design using three-dimensional finite element model of the foot

Therapeutic footwear with specially-made insoles is often used in people with diabetes and rheumatoid arthritis to relieve ulcer risks and pain due to high pressures from areas beneath bony prominences of the foot, in particular to the metatarsal heads (MTHs). In a three-dimensional finite element study of the foot and footwear with sensitivity analysis, effects of geometrical variations of a therapeutic insole, in terms of insole thicknesses and metatarsal pad (MP) placements, on local peak plantar pressure under MTHs and stress/strain states within various forefoot tissues, were determined. A validated musculoskeletal finite element model of the human foot was employed. Analyses were performed in a simulated muscle-demanding instant in gait. For many design combinations, increasing insole thicknesses consistently reduce peak pressures and internal tissue strain under MTHs, but the effects reach a plateau when insole becomes very thick (e.g., a value of 12.7mm or greater). Altering MP placements, however, showed a proximally- and a distally-placed MP could result in reverse effects on MTH pressure-relief. The unsuccessful outcome due to a distally-placed MP may attribute to the way it interacts with plantar tissue (e.g., plantar fascia) adjacent to the MTH. A uniform pattern of tissue compression under metatarsal shaft is necessary for a most favorable pressure-relief under MTHs. The designated functions of an insole design can best be achieved when the insole is very thick, and when the MP can achieve a uniform tissue compression pattern adjacent to the MTH.

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot.

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.

The in vivo plantar soft tissue mechanical property under the metatarsal head: implications of tissues׳ joint-angle dependent response in foot finite element modeling

Material properties of the plantar soft tissue have not been well quantified in vivo (i.e., from life subjects) nor for areas other than the heel pad. This study explored an in vivo investigation of the plantar soft tissue material behavior under the metatarsal head (MTH). We used a novel device collecting indentation data at controlled metatarsophalangeal joint angles. Combined with inverse analysis, tissues׳ joint-angle dependent material properties were identified. The results showed that the soft tissue under MTH exhibited joint-angle dependent material responses, and the computed parameters using the Ogden material model were 51.3% and 30.9% larger in the dorsiflexed than in the neutral positions, respectively. Using derived parameters in subject-specific foot finite element models revealed only those models that used tissues׳ joint-dependent responses could reproduce the known plantar pressure pattern under the MTH. It is suggested that, to further improve specificity of the personalized foot finite element models, quantitative mechanical properties of the tissue inclusive of the effects of metatarsophalangeal joint dorsiflexion are needed.

Quantification of plantar soft tissue changes due to aging in various metatarsophalangeal joint angles with realistic tissue deformation

The nonlinearity of plantar soft tissue is seldom examined because of the small extent of deformation induced during indentation for measurement purposes. Furthermore, in most indentation experiments, the metatarsophalangeal joint (MTPJ) angle is not well controlled, although it has been proven to have a significant stiffening effect on sub-metatarsal head (MTH) pads. Hence, the study aims to quantify changes in the mechanical properties of plantar soft tissue due to aging under an experimental condition which is similar to walking. This is done by subjecting the tissue to an appropriate level of deformation at various MTPJ angles. A custom-made in vivo tissue indenter was used to measure directly the force-indentation response of the plantar tissue of two healthy groups: "Young" (n=25, mean age 22) and "Elderly" (n=25, mean age 67) subjects. Tests were performed on the 2nd sub-MTH pad at angles of 0°, 20°, 40° MTPJ dorsiflexion, as well as at the hallux and heel pad at 0° MTPJ angle. At all three plantar sites tested, elderly subjects showed significantly higher tissue stiffness than the young (p<0.05). However, the stiffening effect of MTPJ angle was not notably influenced by aging. In this work, tissue stiffness is quantified in stiffness constant (K) based on the proposed indentation technique. It is hypothesized that the increase in stiffness with age observed is probably due to compositional change in the plantar soft tissue.

Plantar pressures, plantar forces, and their influence on the pathogenesis of diabetic foot ulcers: a review

BACKGROUND

Clinical recommendations for the prevention and healing of diabetic foot ulcers (DFUs) are somewhat clear. However, assessment and quantification of the mechanical stress responsible for DFU remain complex. Different pressure variables have been described in the literature to better understand plantar tissue stress exposure. This article reviews the role of pressure and shear forces in the pathogenesis of plantar DFU.

METHODS

We performed systematic searches of the PubMed and Embase databases, completed by a manual search of the selected studies. From 535 potentially relevant references, 70 studies were included in the full-text review.

RESULTS

Variables of plantar mechanical stress relate to vertical pressure, shear stress, and temporality of loading. At this time, in-shoe peak plantar pressure (PPP) is the only reliable variable that can be used to prevent DFU. Although it is a poor predictor of in-shoe PPP, barefoot PPP seems complementary and may be more suitable when evaluating patients with diabetes mellitus and peripheral neuropathy who seem noncompliant with footwear. An in-shoe PPP threshold value of 200 kPa has been suggested to prevent DFU. Other variables, such as peak pressure gradient and peak maximal subsurface shear stress and its depth, seem to be of additional utility.

CONCLUSIONS

To better assess the at-risk foot and to prevent ulceration, the practitioner should integrate quantitative models of dynamic foot plantar pressures, such as in-shoe and barefoot PPPs, with the regular clinical screening examination. Prospective studies are needed to evaluate causality between other variables of mechanical stress and DFUs.

Investigation of the biomechanical effect of variable stiffness shoe on external knee adduction moment in various dynamic exercises

Background

The growing ageing population and high prevalence of knee osteoarthritis (OA) in athletes across nations have created a strong demand for improved non-invasive therapeutic alternatives for knee OA. The aim of this study is to investigate the effect of the variable stiffness shoe (VSS), a new non-invasive therapeutic approach, on external knee adduction moment (EKAM) in various dynamic exercises. EKAM is believed to have positive correlation with the progression and development of knee OA.

Methods

Thirty young participants (16 male and 14 female; age 22.6 ± 1.9 years) from National University of Singapore were enrolled in this study. The tested activities were walking, running, drop-landing, and lateral hopping. All the dynamic exercises were recorded simultaneously by the 8-camera VICON Motion Systems (Oxford Metric, UK) with a sampling rate of 100 Hz.

Results

The results showed that the EKAM was reduced in all the dynamic exercises with the use of VSS. The VSS produced significant reductions in the peak EKAM during walking (4.97%, p = 0.039), running (11.15%, p = 0.011), drop-landing (11.18%, p = 0.038) and lateral hopping (17.34%, p = 0.023) as compared to the control shoe.

Conclusions

The reduction of EKAM with the use of VSS in various dynamic exercises demonstrates its potential in delaying the onset and the progression of knee OA in early stage of knee OA patients.

Finite element analysis of the foot: model validation and comparison between two common treatments of the clawed hallux deformity

BACKGROUND

Clawed hallux is defined by first metatarsophalangeal joint extension and first interphalangeal joint flexion; it can increase plantar pressures and ulceration risk. We investigated two corrective surgical techniques, the modified Jones and flexor hallucis longus tendon transfer.

METHODS

A finite element foot model was modified to generate muscle overpulls, including extensor hallucis longus, flexor hallucis longus and peroneus longus. Both corrective procedures were simulated, predicting joint angle and plantar pressure changes.

FINDINGS

The clawed hallux deformity was generated by overpulling: 1) extensor hallucis longus, 2) peroneus longus + extensor hallucis longus, 3) extensor hallucis longus + flexor hallucis longus and 4) all three together. The modified Jones reduced metatarsophalangeal joint angles, but acceptable hallux pressure was found only when there was no flexor hallucis longus overpull. The flexor hallucis longus tendon transfer reduced deformity at the metatarsophalangeal and interphalangeal joints but may extended the hallux due to the unopposed extensor hallucis longus. Additionally, metatarsal head pressure increased with overpulling of the extensor hallucis longus + flexor hallucis longus, and all three muscles together.

INTERPRETATION

The modified Jones was effective in correcting clawed hallux deformity involving extensor hallucis longus overpull without flexor hallucis longus overpull. The flexor hallucis longus tendon transfer was effective in correcting clawed hallux deformity resulting from the combined overpull of both extensor and flexor hallucis longus, but not with isolated extensor hallucis longus overpull. An additional procedure to reduce the metatarsal head pressure may be required concomitant to the flexor hallucis longus tendon transfer. However this procedure avoids interphalangeal joint fusion.

A three-dimensional inverse finite element analysis of the heel pad

Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir et al. ("An Elaborate Data Set Characterizing the Mechanical Response of the Foot," ASME J. Biomech. Eng., 131(9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson's ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization (<1.05% maximum tool force, 0.9% maximum tool displacement) and validation cases (6.5% maximum tool force, 15% maximum tool displacement). The inverse analysis successfully predicted the material properties for the given specimen-specific heel pad using the experimental data for the specimen. The modeling framework and results can be used for accurate predictions of the three-dimensional interaction of the heel pad with its surroundings.

Effects of foot posture on fifth metatarsal fracture healing: a finite element study

The goal of this study was to evaluate the effects of maintaining different foot postures during healing of proximal fifth metatarsal fractures for each of 3 common fracture types. A 3-dimensional (3D) finite element model of a human foot was developed and 3 loading situations were evaluated, including the following: (1) normal weightbearing, (2) standing with the affected foot in dorsiflexion at the ankle, and (3) standing with the affected foot in eversion. Three different stages of the fracture-healing process were studied, including: stage 1, wherein the material interposed between the fractured edges was the initial connective tissue; stage 2, wherein connective tissue had been replaced by soft callus; and stage 3, wherein soft callus was replaced by mature bone. Thus, 30 3D finite element models were analyzed that took into account fracture type, foot posture, and healing stage. Different foot postures did not statistically significantly affect the peak-developed strains on the fracture site. When the fractured foot was everted or dorsiflexed, it developed a slightly higher strain within the fracture than when it was in the normal weightbearing position. In Jones fractures, eversion of the foot caused further torsional strain and we believe that this position should be avoided during foot immobilization during the treatment of fifth metatarsal base fractures. Tuberosity avulsion fractures and Jones fractures seem to be biomechanically stable fractures, as compared with shaft fractures. Our understanding of the literature and experience indicate that current clinical observations and standard therapeutic options are in accordance with the results that we observed in this investigation, with the exception of Jones fractures.

Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.