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.     

Explicit finite element modelling of heel pad mechanics in running: inclusion of body dynamics and application of physiological impact loads

Many heel pathologies including plantar heel pain may result from micro tears/trauma in the subcutaneous tissues, in which internal tissue deformation/stresses within the heel pad play an important role. Previously, many finite element models have been proposed to evaluate stresses inside the heel pad, but the majority of these models only focus on static loading boundary conditions. This study explored a dynamics modelling approach to the heel pad subjected to realistic impact loads during running. In this model, the inertial property and action of the body are described by a lumped parameter model, while the heel/shoe interactions are modelled using a viscoelastic heel pad model with contact properties. The impact force pattern, dynamic heel pad deformation and stress states predicted by the model were compared with published experimental data. Further parametrical studies revealed the model responses, in terms of internal stresses in the skin and fatty tissue, change nonlinearly when body dynamics changes. A reduction in foot's touchdown velocity resulted in a less severe impact landing and stress relief inside the heel pad, for example peak von-Mises stress in fatty tissue, was reduced by 11.3%. Applications of the model may be extendable to perform iterative analyses to further understand the complex relationships between body dynamics and stress distributions in the soft tissue of heel pad during running. This may open new opportunities to study the mechanical aetiology of plantar heel pain in runners.     

The potential influence of the heel counter on internal stress during static standing: a combined finite element and positional MRI investigation

Confinement of the heel due to the counter of the shoe is believed to influence heel pad biomechanics. Using a two-dimensional finite element model of the heel pad and shoe during a simulation of static standing, the aim of this study was to quantify the potential effect of confinement on internal heel pad stress. Non-weightbearing MRI and weightbearing MRI with plantar pressure and ground reaction force data were recorded for a single subject. The non-weightbearing MRI was used to create two FE models of the heel pad, using either homogeneous or composite material properties. The composite model included a distinction in material properties between fat pad and skin. Vertical and medial-lateral forces, as measured on the subject's heel, were applied to the models and vertical compressive strains for both models were comparable with those observed by weightbearing MRI. However, only for the composite model was the predicted plantar pressure distribution comparable with measured data. The composite model was therefore used in further analyses. In this composite model, the internal stresses were located mainly in the skin and were predominantly tensile in nature, whereas the stress state in the fat pad approached hydrostatic conditions. A representation of a running shoe, including an insole, midsole and heel counter was then added to the composite heel pad to form the shod model. In order to investigate the counter effect, the load was applied to the shod model with and without the heel counter. The effect of the counter on peak stress was to elevate compression (0-50%), reduce tension (22-34%) and reduce shear (22-28%) in the skin. In addition, the counter reduced both compressive (20-40%) and shear (58-80%) stress in the fat pad and tension in the fat pad remained negligible. Taken together the results indicate that a well-fitted counter works in sympathy with the internal structure of the heel pad and could be an effective reducer of heel pad stress. However, further research needs to be undertaken to assess the long-term effects on the soft-tissues, practicalities of achieving good fit and behavior under dynamic events.     

The damping properties of the venous plexus of the heel region of the foot during simulated heelstrike

The damping mechanisms that are operational in the heel pad during the impact phase of locomotion have the important function to protect the musculo-skeletal system from injuries. How this is achieved is still not fully understood, as is for instance illustrated by the ‘heel pad paradox’, the observation that in vivo and in vitro experiments yielded widely different results. This paradox could so far only partially be explained. In the light of this paradox, and a previous study by our group, we conjectured that the venous plexus might contribute as a hydraulic shock absorber to the damping properties of the heel pad. To investigate this hypothesis in vivo, heel pads of 11 volunteers were subjected to pendulum impact tests, using velocities of 0.2, 0.4, and 0.6 m/s, and three physiologically different, consecutive conditions: (i) a relatively empty venous plexus, (ii) a congested venous plexus, and (iii) a decongested venous plexus. At congestion, the maximum impact force decreased slightly but significantly by 2.6% at 0.2 m/s and 1.8% at 0.4 m/s. This effect was no longer found at 0.6 m/s. Although these effects are rather small, they confirm the fundamental hypothesis that the venous plexus contributes to the damping properties of the heel pad during walking. It is likely that some underestimation of the effect has occurred.     

Spatial-dependent mechanical properties of the heel pad by shear wave elastography

The heel pad plays an important role in gait, and its biomechanical behavior and functionality are determined by its specialized architecture and mechanical properties. The purpose of this study was to apply supersonic shear wave elastography, an ultrasound-based noninvasive modality that can quantitatively estimate the shear stiffness of the tissue, to investigate the spatial-dependent mechanical properties of the heel pad. Measurements were conducted in 40 heel pads of 20 normal participants aged between 20 and 30 years by shear wave elastography. The continuous change in local shear stiffness of the heel pad along the depth direction of the heel pad was measured. The result showed that the mechanical properties of the heel pad were highly heterogeneous but followed a simple and specific pattern that local heel pad shear stiffness was highest beneath the plantar skin and decreased continuously with increasing depth. This finding provides a better understanding of the heel pad biomechanics and basis for further investigation of the heterogeneous properties of the heel pad.     

In vivo biomechanical behavior of the human heel pad during the stance phase of gait

A technique is introduced for simultaneous measurements of the heel pad tissue deformation and the heel–ground contact stresses developing during the stance phase of gait. Subjects walked upon a gait platform integrating the contact pressure display optical method for plantar pressure measurements and a digital radiographic fluoroscopy system for skeletal and soft tissue motion recording. Clear images of the posterior-plantar aspect of the calcaneus and enveloping soft tissues were obtained simultaneously with the pressure distribution under the heel region throughout the stance phase of gait. The heel pad was shown to undergo a rapid compression during initial contact and heel strike, reaching a strain of 0.39±0.05 in about 150 ms. The stress–strain relation of the heel pad was shown to be highly non-linear, with a compression modulus of 105±11 kPa initially and 306±16 kPa at 30% strain. The energy dissipation during heel strike was evaluated to be 17.8±0.8%. The present technique is useful for biomechanical as well as clinical evaluation of the stress–strain and energy absorption characteristics of the heel pad in vivo, during natural gait.     

Constitutive formulation and numerical analysis of the heel pad region

The aim of this work is to provide a numerical approach for the investigation of the mechanical behaviour of the heel pad region. A visco-hyperelastic model is formulated with regard to fat pad tissue, while a fibre-reinforced hyperelastic model is considered for the heel skin tissue. Bone components are defined by means of an orthotropic linear elastic model. Particular attention is paid to the evaluation of constitutive parameters within different models adopted in consideration of experimental tests data. Preliminarily, indentation tests on a skinless cadaveric foot are considered with regard to fat pad tissue. Indentation tests on an intact heel pad of a cadaveric foot are subsequently adopted for the final identification of constitutive parameters of fat pad and skin tissues. A numerical model of the rear foot is defined and different loading conditions are assumed according to experimental data. A comparison between experimental and numerical data leads to the evaluation of the real capability of the procedure to interpret the actual response of the rear foot.     

Constitutive formulation and numerical analysis of the heel pad region

The aim of this work is to provide a numerical approach for the investigation of the mechanical behaviour of the heel pad region. A visco-hyperelastic model is formulated with regard to fat pad tissue, while a fibre-reinforced hyperelastic model is considered for the heel skin tissue. Bone components are defined by means of an orthotropic linear elastic model. Particular attention is paid to the evaluation of constitutive parameters within different models adopted in consideration of experimental tests data. Preliminarily, indentation tests on a skinless cadaveric foot are considered with regard to fat pad tissue. Indentation tests on an intact heel pad of a cadaveric foot are subsequently adopted for the final identification of constitutive parameters of fat pad and skin tissues. A numerical model of the rear foot is defined and different loading conditions are assumed according to experimental data. A comparison between experimental and numerical data leads to the evaluation of the real capability of the procedure to interpret the actual response of the rear foot.     

The foot as a shock absorber

A mathematical analysis of the deformation of the foot is developed to determine the role that stretch of ligaments and tendons plays in absorbing shock following impact. Our analysis is based on an anatomical biomechanical model that includes each of the bones of the foot. We calculate the time course of the deflection of the joints and the elongation of the ligaments and tendons and determine the ground reaction force acting on the heel. Quasi-linear viscoelastic theory is used for soft tissue constitutive relationships. With biomechanical data selected from the literature, we obtain a vertical force impact peak of 8000 N, occurring at 16 ms following heel strike. This is of higher magnitude and shorter duration than is found experimentally, as is to be expected, since we did not include the heel pad in our model and we assumed that the impact surface was ideally rigid.     

The role of the heel pad and shank soft tissue during impacts: a further resolution of a paradox

The aim of this study was to test the hypothesis that the motion of the soft tissue of the lower leg contributes significantly to the attenuation of the forces during heel impacts. To examine this, a two-dimensional model of the shank and heel pad was developed using DADS. The model contained a heel pad element and a rigid skeleton to which was connected soft tissue which could move relative to the bone. Simulations permitted estimation of heel pad properties directly from heel pad deformations, and from the kinematics of an impacting pendulum. These two approaches paralleled those used in vitro and in vivo, respectively. Measurements from the pendulum indicated that heel pad properties changed from those found in vitro to those found in vivo as relative motion of the bone and soft tissue was allowed. This would indicate that pendulum measures of the in vivo heel pad properties are also measuring the properties of the whole lower leg. The ability of the wobbling mass of the shank to dissipate energy during an impact was found to be significant. These results demonstrate the important role of both the heel pad and soft tissue of the shank to the dissipation of mechanical energy during impacts. These results provide a further clarification of the paradox between the measurements of heel pad properties made in vivo and in vitro.     

Finite element analysis of heel pad with insoles

To design optimal insoles for reduction of pedal tissue trauma, experimental measurements and computational analyses were performed. To characterize the mechanical properties of the tissues, indentation tests were performed. Pedal tissue geometry and morphology were obtained from magnetic resonance scan of the subject's foot. Axisymmetrical finite element models of the heel of the foot were created with 1/4 of body weight load applied. The stress, strain and strain energy density (SED) fields produced in the pedal tissues were computed. The effects of various insole designs and materials on the resulting stress, strain, and SED in the soft pedal tissues were analyzed. The results showed: (a) Flat insoles made of soft material provide some reductions in the maximum stress, strain and SED produced in the pedal tissues. These maximum values were computed near the calcaneus. (b) Flat insoles, with conical/cylindrical reliefs, provided more reductions in these maximum values than without reliefs. (c) Custom insoles, contoured to match the pedal geometry provide most reductions in the maximum stress, strain and SED. Also note, the maximum stress, strain and SED computed near the calcaneus were found to be about 10 times the corresponding peak values computed on the skin surface. Based on the FEA analysis, it can be concluded that changing insole design and using different material can significantly redistribute the stress/strain inside the heel pad as well as on the skin surface.     

The significance of the heel process in anthropoids

The plantar process of the tuber calcanei among pongids and hominids serves as the origin for the superficial head of the flexor digitorum brevis muscle (FDB). In a survey of the soft tissues and osteology of the foot in a diverse number of anthropoid genera, it was found that a large superficial head of the FDB is associated with a large inflated plantar process (heel process). A large FDB with a separate calcaneal origin allows toe flexion independent of foot position. This type of movement allows an animal to reach and grasp or hang by its feet during slow deliberate climbing. The presence of á heel process in anthropoids and in nonprimate mammals is correlated with those animals which are slow climbers or are likely descended from slow-climbing forms. The presence of a heel process in humans and in pongids implies that the common pongid-hominid ancestor was most likely a slow climber. In fossil catarrhines the presence of a heel process can be interpreted either as evidence of slow-climbing behavior or as a heritage feature from a slow-climbing ancestor.     

Validation of a full body finite element model (THUMS) for running-type impacts to the lower extremity

The purpose of this study was to determine whether modifying an existing, highly biofidelic full body finite element model [total human model for safety (THUMS)] would produce valid amplitude and temporal shock wave characteristics as it travels proximally through the lower extremity. Modifying an existing model may be more feasible than developing a new model, in terms of cost, labour and expertise. The THUMS shoe was modified to more closely simulate the material properties of a heel pad. Relative errors in force and acceleration data from experimental human pendulum impacts and simulated THUMS impacts were 22% and 54%, respectively, across the time history studied. The THUMS peak acceleration was attenuated by 57.5% and took 19.7 ms to travel proximally along the lower extremity. Although refinements may be necessary to improve force and acceleration timing, the modified THUMS represented, to a certain extent, shock wave propagation and attenuation demonstrated by living humans under controlled impact conditions.     

Reduction of plantar heel pressures: Insole design using finite element analysis

Plantar heel pain is a common condition that is often exacerbated by the repetitive stresses of walking. Treatment usually includes an in-shoe intervention designed to reduce plantar pressure under the heel by using insoles and a variety of off-the-shelf products. The design process for these products is often intuitive in nature and does not always rely on scientifically derived guidelines. Finite element analysis provides an efficient computational framework to investigate the performance of a large number of designs for optimal plantar pressure reduction. In this study, we used two-dimensional plane strain finite element modeling to investigate 27 insole designs. Combinations of three insole conformity levels (flat, half conforming, full conforming), three insole thickness values (6.3, 9.5 and 12.7 mm) and three insole materials (Poron Cushioning, Microcel Puff Lite and Microcel Puff) were simulated during the early support phase of gait. Plantar pressures predicted by the model were validated by experimental trials conducted in the same subject whose heel was modeled by loading the bare foot on a rigid surface and on foam mats. Conformity of the insole was the most important design variable, whereas peak pressures were relatively insensitive to insole material selection. The model predicted a 24% relief in pressure compared to barefoot conditions when using flat insoles; the reduction increased up to 44% for full conforming insoles.     

An inverse finite-element model of heel-pad indentation

A numerical-experimental approach has been developed to characterize heel-pad deformation at the material level. Left and right heels of 20 diabetic subjects and 20 nondiabetic subjects matched for age, gender and body mass index were indented using force-controlled ultrasound. Initial tissue thickness and deformation were measured using M-mode ultrasound; indentation forces were recorded simultaneously. An inverse finite-element analysis of the indentation protocol using axisymmetric models adjusted to reflect individual heel thickness was used to extract nonlinear material properties describing the hyperelastic behavior of each heel. Student's t-tests revealed that heel pads of diabetic subjects were not significantly different in initial thickness nor were they stiffer than those from nondiabetic subjects. Another heel-pad model with anatomically realistic surface representations of the calcaneus and soft tissue was developed to estimate peak pressure prediction errors when average rather than individualized material properties were used. Root-mean-square errors of up to 7% were calculated, indicating the importance of subject-specific modeling of the nonlinear elastic behavior of the heel pad. Indentation systems combined with the presented numerical approach can provide this information for further analysis of patient-specific foot pathologies and therapeutic footwear designs.     

The first branch of the lateral plantar nerve and heel pain

The course and ramification pattern of the lateral plantar nerve was studied in serial sections from 4 fetal feet and in dissections from 34 adult feet with special reference to the so called first branch. This branch was found in all of the observed fetal and adult specimen. From its originating point the nerve runs immediately distally to the medial process of the calcaneal tuberosity in a lateral direction to the proximal part of the abductor digiti minimi muscle. During its course the FB gives two branches. One of them penetrates sometimes the insertion of the quadratus plantae muscle, whereas in adult feet it always sends fibres to the periosteum around the medial process of the calcaneal tuberosity and the long plantar ligament. The other innervates the flexor digitorum brevis muscle. The site of a possible entrapment is located between the abductor hallucis muscle and the medial head of the quadratus plantae muscle. There is strong indirect evidence that the nerve is of a mixed type consisting of sensory fibres for the calcaneal periosteum and the medial head of the quadratus plantae muscle. There is strong indirect evidence that the nerve is of a mixed type consisting of sensory fibres for the calcaneal periosteum and the long plantar ligament as well as motor fibres for the quadratus plantae, flexor digitorum brevis and abductor digiti minimi muscles, which may explain the characteristic pain complaints of the heel pain syndrome. The occurrence of a stiff fascia perforated by the nerve branch or a bursa around the insertion of the plantar aponeurosis as has been described by several authors and which was put forward as a possible aetiological factor could not be confirmed in our material.     

Reconstruction of soft-tissue defect of the posterior heel with a lateral calcaneal artery island flap

We obtained most favorable results in 11 patients with a lateral calcaneal artery island flap. It is a simple, stable, sensate, and yet safe and versatile flap to repair defects around the ankle and heel. We have also used this flap to cover defects around the medial malleolus without any delay (extended lateral calcaneal artery island flap).     

Material properties of the human calcaneal fat pad in compression: experiment and theory

The structural behaviour of the human heel pad has been studied extensively due to its ability to absorb shock, protect against excessive local stress, and reduce plantar pressures. However, the material properties of the tissue have not been adequately measured. These must be known in order to perform a finite element analysis of the effect of factors such as foot geometry and shoe/surface construction on heel pad function. Therefore, the purposes of this study were to (a) measure the viscoelastic behaviour of the fat pad in compression, and (b) to determine an appropriate constitutive equation to model the tissue. A series of unconfined compression tests were performed on 8 mm diameter cylinders of fat pad tissue, consisting of quasi-static, 175, 350 mm/s and stress-relaxation tests to 50% deformation. The tissue exhibited nonlinear, viscoelastic behaviour. No significant difference was found in the quasi-static behaviour between samples from different locations and orientations in the heel. The stress-relaxation tests were used to determine the time constant (τ₁=0.5 s), the 175 mm/s test to determine the relaxation coefficient (g₁=28), and the 350 mm/s compression test to determine the material constants (C₁₀₀=C₀₁₀=0.01, C₂₀₀=C₀₂₀=0.1 Pa) of a single-phase, hyperelastic, linear viscoelastic strain energy function (r²=0.98).     

Image-based midsole insert design and the material effects on heel plantar pressure distribution during simulated walking loads

The primary objective of this paper is to study the use of medical image-based finite element (FE) modelling in subject-specific midsole design and optimisation for heel pressure reduction using a midsole plug under the calcaneus area (UCA). Plugs with different relative dimensions to the size of the calcaneus of the subject have been incorporated in the heel region of the midsole. The FE foot model was validated by comparing the numerically predicted plantar pressure with biomechanical tests conducted on the same subject. For each UCA midsole plug design, the effect of material properties and plug thicknesses on the plantar pressure distribution and peak pressure level during the heel strike phase of normal walking was systematically studied. The results showed that the UCA midsole insert could effectively modify the pressure distribution, and its effect is directly associated with the ratio of the plug dimension to the size of the calcaneus bone of the subject. A medium hardness plug with a size of 95% of the calcaneus has achieved the best performance for relieving the peak pressure in comparison with the pressure level for a solid midsole without a plug, whereas a smaller plug with a size of 65% of the calcaneus insert with a very soft material showed minimum beneficial effect for the pressure relief.     

Image-based midsole insert design and the material effects on heel plantar pressure distribution during simulated walking loads

The primary objective of this paper is to study the use of medical image-based finite element (FE) modelling in subject-specific midsole design and optimisation for heel pressure reduction using a midsole plug under the calcaneus area (UCA). Plugs with different relative dimensions to the size of the calcaneus of the subject have been incorporated in the heel region of the midsole. The FE foot model was validated by comparing the numerically predicted plantar pressure with biomechanical tests conducted on the same subject. For each UCA midsole plug design, the effect of material properties and plug thicknesses on the plantar pressure distribution and peak pressure level during the heel strike phase of normal walking was systematically studied. The results showed that the UCA midsole insert could effectively modify the pressure distribution, and its effect is directly associated with the ratio of the plug dimension to the size of the calcaneus bone of the subject. A medium hardness plug with a size of 95% of the calcaneus has achieved the best performance for relieving the peak pressure in comparison with the pressure level for a solid midsole without a plug, whereas a smaller plug with a size of 65% of the calcaneus insert with a very soft material showed minimum beneficial effect for the pressure relief.