Constitutive formulation and analysis of heel pad tissues mechanics

A novel in-situ dynamic mechanical analysis for human plantar soft tissue: The device design, definition of characteristics, test protocol, and preliminary results

The in-situ mechanical characterization of elastomers is not highly regarded due to the existence of a well-established set of sample-based standard tests for research and industry. However, there are certain situations or materials, like biological soft tissue, where an in-situ approach is necessary due to the impossibility of sampling from a living body. We have developed a dynamic mechanical analysis (DMA)-like device to approach in-vivo and in-situ multidimensional stress-strain properties of human plantar soft tissues. This work elucidates the operational mechanism of the novel measurement, with the definition of a new set of moduli, test standardization and protocol. Exploratory results of a volunteer's living plantar, silica rubber samples are presented with well preciseness and consistence as expected.

Mechanical Behaviour of Plantar Adipose Tissue: From Experimental Tests to Constitutive Analysis

Plantar adipose tissue is a connective tissue whose structural configuration changes according to the foot region (rare or forefoot) and is related to its mechanical role, providing a damping system able to adsorb foot impact and bear the body weight. Considering this, the present work aims at fully describing the plantar adipose tissue's behaviour and developing a proper constitutive formulation. Unconfined compression tests and indentation tests have been performed on samples harvested from human donors and cadavers. Experimental results provided the initial/final elastic modulus for each specimen and assessed the non-linear and time-dependent behaviour of the tissue. The different foot regions were investigated, and the main differences were observed when comparing the elastic moduli, especially the final elastic ones. It resulted in a higher level for the medial region (89 ± 77 MPa) compared to the others (from 51 ± 29 MPa for the heel pad to 11 ± 7 for the metatarsal). Finally, results have been used to define a visco-hyperelastic constitutive model, whose hyperelastic component, which describes tissue non-linear behaviour, was described using an Ogden formulation. The identified and validated tissue constitutive parameters could serve, in the early future, for the computational model of the healthy foot.

Description of the Pliocene marsupial Ambulator keanei gen. nov. (Marsupialia: Diprotodontidae) from inland Australia and its locomotory adaptations

Diprotodontids were the largest marsupials to exist and an integral part of Australian terrestrial ecosystems until the last members of the group became extinct approximately 40 000 years ago. Despite the frequency with which diprotodontid remains are encountered, key aspects of their morphology, systematics, ecology and evolutionary history remain poorly understood. Here we describe new skeletal remains of the Pliocene taxon Zygomaturus keanei from northern South Australia. This is only the third partial skeleton of a late Cenozoic diprotodontid described in the last century, and the first displaying soft tissue structures associated with footpad impressions. Whereas it is difficult to distinguish Z. keanei and the type species of the genus, Z. trilobus, on dental grounds, the marked cranial and postcranial differences suggest that Z. keanei warrants genus-level distinction. Accordingly, we place it in the monotypic Ambulator gen. nov. We, also recognize the late Miocene Z. gilli as a nomen dubium. Features of the forelimb, manus and pes reveal that Ambulator keanei was more graviportal with greater adaptation to quadrupedal walking than earlier diprotodontids. These adaptations may have been driven by a need to travel longer distances to obtain resources as open habitats expanded in the late Pliocene of inland Australia.

Optimization Design of the Inner Structure for a Bioinspired Heel Pad with Distinct Cushioning Property

In the existing research on prosthetic footplates, rehabilitation insoles, and robot feet, the cushioning parts are basically based on simple mechanisms and elastic pads. Most of them are unable to provide adequate impact resistance especially during contact with the ground. This paper developed a bioinspired heel pad by optimizing the inner structures inspired from human heel pad which has great cushioning performance. The distinct structures of the human heel pad were determined through magnetic resonance imaging (MRI) technology and related literatures. Five-layer pads with and without inner structures by using two materials (soft rubber and resin) were obtained, resulting in four bionic heel pads. Three finite element simulations (static, impact, and walking) were conducted to compare the cushioning effects in terms of deformations, ground reactions, and principal stress. The optimal pad with bionic structures and soft rubber material reduced 28.0% peak vertical ground reaction force (GRF) during walking compared with the unstructured resin pad. Human walking tests by a healthy subject wearing the 3D printed bionic pads also showed similar findings, with an almost 20% decrease in peak vertical GRF at normal speed. The soft rubber heel pad with bionic structures has the best cushioning performance, while the unstructured resin pad depicts the poorest. This study proves that with proper design of the inner structures and materials, the bionic pads will demonstrate distinct cushioning properties, which could be applied to the engineering fields, including lower limb prosthesis, robotics, and rehabilitations.

Computational methods for the investigation of ski boots ergonomics

Ski boots are known to cause vasoconstriction in the wearer’s lower limbs and, thus, cause a “cold leg” phenomenon. To address this problem, this work provides a computational framework for analysing interactions between the ski boot and the lower limb. The geometry of the lower limb was derived from magnetic resonance imaging and computed tomography techniques and anthropometric data. The geometry of the ski boot shell was obtained by means of three-dimensional computer aided design models from a manufacturer. Concerning the ski boot liner, laser scanning techniques were implemented to capture the geometry of each layer. The mechanical models of the ski boot and the lower limb were identified and validated by means of coupled experimental investigations and computational analyses. The computational models were exploited to simulate the buckling process and to investigate interaction phenomena between the boot and the lower limb. Similarly, experimental activities were performed to further analyse the buckling phenomena. The obtained computational and experimental results were compared regarding both interaction pressure and displacements between the buckle and the corresponding buckle hooks. These comparisons provided reasonable agreement (mean value of discrepancy between the model and mean experimental results in the tibial region: 20%), underlining the model’s capability to correctly interpret results from experimental measurements. Results identified the critical areas of the leg, such as the tibial region, the calcaneal region of the foot and the anterior sole, which may suffer the most due to the hydrostatic pressure and compressive strain exerted on them. The results highlight that computational methods allow investigation of the interaction phenomena between the lower leg and ski boot, potentially providing an effective framework for a more comfortable and ergonomic design of ski boots.

Identification of potential plantar ulceration among diabetes patients using plantar soft tissue stiffness

This study investigates the relationship between plantar tissue stiffness and selected parameters, including age, diabetes mellitus (DM) duration, body mass index (BMI), and HbA_1c level. 70 diabetes patients with no foot problems were recruited. The plantar soft tissue at the 2nd sub-metatarsal head (MTH) pad was examined using the novel indentation system developed. The stiffness constant, K, was used to describe the tissue stiffness. The four factors (age, DM duration, BMI, and HbA_1c level) were plotted against the plantar tissue stiffness. The scatter plots revealed that a higher plantar tissue stiffness was usually associated with (1) BMI>25  kgm^-2, (2) HbA_1c score >10% (86 mmol/mol), and (3) DM duration >10 years. The three risk criteria were further evaluated using the binary classification test. The predictions were reported to be fairly accurate and reliable in detecting stiffened tissues. The study has successfully identified the strong association of BMI, HbA_1c, and DM duration with the plantar tissue properties. Special attention should be given to the high risk group with BMI>25 kgm^-2, HbA_1c score >10% (86 mmol/mol), and DM duration >10 years. The high diagnostic odds ratio attained suggests its potential usefulness in helping clinicians to diagnose diabetic foot more efficiently.

Comprehensive Biomechanism of Impact Resistance in the Cat's Paw Pad

Cats are able to jump from a high-rise without any sign of injury, which is attributed in large part to their impact-resistant paw pads. The biomechanical study of paw pads may therefore contribute to improving the impact resistance of specific biomimetic materials. The present study is aimed at investigating the mechanics of the paw pads, revealing their impact-resistant biomechanism from macro- and microscopic perspectives. Histological and micro-CT scanning methods were exploited to analyze the microstructure of the pads, and mechanical testing was conducted to observe the macroscopic mechanical properties at different loading frequencies. Numerical micromodels of the ellipsoidal and cylindrical adipose compartments were developed to evaluate the mechanical functionality as compressive actions. The results show that the stiffness of the pad increases roughly in proportion to strain and mechanical properties are almost impervious to strain rate. Furthermore, the adipose compartment, which comprises adipose tissue enclosed within collagen septa, in the subcutaneous tissue presents an ellipsoid-like structure, with a decreasing area from the middle to the two ends. Additionally, the finite element results show that the ellipsoidal structure has larger displacement in the early stage of impact, which can absorb more energy and prevent instability at touchdown, while the cylindrical structure is more resistant to deformation. Moreover, the Von Mises of the ellipsoidal compartment decrease gradually from both ends to the middle, making it change to a cylindrical shape, and this may be the reason why the macroscopic stiffness increases with increasing time after contact. This preliminary investigation represents the basis for biomechanical interpretation and can accordingly provide new inspirations of shock-absorbing composite materials in engineering.

The characteristics of the lobular arrangement indicate the dynamic role played by the infrapatellar fat pad in knee kinematics

The infrapatellar fat pad (IFP) is an intracapsular but extrasynovial structure, located between the patellar tendon, the femoral condyles and the tibial plateau. It consists of white adipose tissue, organised in lobules defined by thin connective septa. The aim of this study is the morphometric and ultrasonographic analysis of IFP in subjects without knee pathology during flexion-extension movements. The morphometric study was conducted on 20 cadavers (15M, 5F, mean age 80.2 years). Ultrasound was performed on 24 volunteers with no history of knee diseases (5M, 19F, mean age: 45 years). The characteristics of the adipose lobules near the patellar tendon and in the deep portion of the IFP were evaluated. Numerical models were provided, according to the size of the lobules. At histological examination, the adipose lobules located near the patellar tendon were larger (mean area 12.2 mm²  ± 5.3) than those at a deeper level (mean area 1.34 mm²  ± 0.7, P < 0.001) and the thickness of the septa of the deepest adipose lobules (mean value 0.35 mm ± 0.32) was greater than that of the superficial one (mean value 0.29 mm ± 0.25, P < 0.001). At ultrasound, the IFP was seen to be composed of very large lobules in the superficial part (mean area 0.29 cm²  ± 0.17 in extension), with a significant reduction in flexion (mean area 0.12 cm²  ± 0.07, P < 0.01). The deep lobules were smaller (mean area 0.11 cm²  ± 0.08 in extension) and did not change their values (mean area 0.19 cm²  ± 0.52 in flexion, P > 0.05). In the sagittal plane, the reduction of thickness of the superficial layer (with large adipose lobules) during flexion was 20.6%, whereas that of the deep layer (with small adipose lobules) was 1.3%. Numerical simulation of vertical loads, corresponding to flexion of the knee, showed that stress mainly developed within the interlobular septa and opposed bulging of the lobules. The characteristics of the lobular arrangement of the IFP (large lobules with superficial septa in the superficial part and small lobules with thick septa in the deep one), significant changes in the areas and perimeters of the superficial lobules, and the reduced thickness of the superficial layer during flexion all indicate the dynamic role played by the IFP in knee kinematics.

Mechanical Modeling of Healthy and Diseased Calcaneal Fat Pad Surrogates

The calcaneal fat pad is a major load bearing component of the human foot due to daily gait activities such as standing, walking, and running. Heel and arch pain pathologies such as plantar fasciitis, which over one third of the world population suffers from, is a consequent effect of calcaneal fat pad damage. Also, fat pad stiffening and ulceration has been observed due to diabetes mellitus. To date, the biomechanics of fat pad damage is poorly understood due to the unavailability of live human models (because of ethical and biosafety issues) or biofidelic surrogates for testing. This also precludes the study of the effectiveness of preventive custom orthotics for foot pain pathologies caused due to fat pad damage. The current work addresses this key gap in the literature with the development of novel biofidelic surrogates， which simulate the in vivo and in vitro compressive mechanical properties of a healthy calcaneal fat pad. Also, surrogates were developed to simulate the in vivo mechanical behavior of the fat pad due to plantar fasciitis and diabetes. A four-part elastomeric material system was used to fabricate the surrogates, and their mechanical properties were characterized using dynamic and cyclic load testing. Different strain (or displacement) rates were tested to understand surrogate behavior due to high impact loads. These surrogates can be integrated with a prosthetic foot model and mechanically tested to characterize the shock absorption in different simulated gait activities, and due to varying fat pad material property in foot pain pathologies (i.e., plantar fasciitis, diabetes, and injury). Additionally, such a foot surrogate model, fitted with a custom orthotic and footwear, can be used for the experimental testing of shock absorption characteristics of preventive orthoses.

How does the canine paw pad attenuate ground impacts? A multi-layer cushion system

Macroscopic mechanical properties of digitigrade paw pads, such as non-linear elastic and variable stiffness, have been investigated in previous studies; however, little is known about the micro-scale structural characteristics of digitigrade paw pads, or the relationship between these characteristics and the exceptional cushioning of the pads. The digitigrade paw pad consists of a multi-layered structure, which is mainly comprised of a stratified epithelium layer, a dermis layer and a subcutaneous layer. The stratified epithelium layer and dermal papillae constitute the epidermis layer. Finite element analyses were carried out and showed that the epidermis layer effectively attenuated the ground impact across impact velocities of 0.05–0.4 m/s, and that the von Mises stresses were uniformly distributed in this layer. The dermis layer encompassing the subcutaneous layer can be viewed as a hydrostatic system, which can store, release and dissipate impact energy. All three layers in the paw pad work as a whole to meet the biomechanical requirements of animal locomotion. These findings provide insights into the biomechanical functioning of digitigrade paw pads and could be used to facilitate bio-inspired, ground-contacting component development for robots and machines, as well as contribute to footwear design.

Summary: This study examines the micro-scale structural characteristics of the digitigrade paw pad and analyses how these structures work together to further clarify the paw pad cushioning mechanism.

Urethral lumen occlusion by artificial sphincteric device: Evaluation of degraded tissues effects

Urinary incontinence can be surgically treated by means of artificial sphincters, based on a cuff that provides a pressure around the urethra to occlude the lumen. Considering the frequent access of elderly patients to this surgical practice, tissue degradation phenomena must be investigated, since they could affect treatment reliability and durability. The potential degradation can be interpreted considering a variation within soft tissue constitutive formulation, by means of a correlation between mechanical properties and tissues ageing. The overall compressibility varies, as characteristics aspect of soft tissue mechanical response with age, as well as the stiffness. The investigation is performed by means of a three dimensional numerical model of the urethral duct. The effects of the interaction phenomenon with a cuff is interpreted considering the changes, within the constitutive models, of the basic parameters that define the potential degradation process. The deformation related to compressibility is recalled, ranging between ten and fifty percent in dependence on the degradation level considered. This parameter, reported mostly as representative of the aging effect, shows a large variation that confirms the relevance of the investigation performed toward a sensitivity of the mechanical response of the urethral duct referred to the lumen occlusion.

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.

Dynamic material characterization of the human heel pad based on in vivo experimental tests and numerical analysis

A numerical-experimental, proof-of-concept approach is described to characterize the mechanical material behavior of the human heel pad under impact conditions similar to a heel strike while running. A 3D finite-element model of the right foot of a healthy female subject was generated using magnetic resonance imaging. Based on quasi-static experimental testing of the subject's heel pad, force-displacement data was obtained. Using this experimental data as well as a numerical optimization algorithm, an inverse finite-element analysis and the 3D model, heel pad hyperelastic (long-term) material parameters were determined. Applying the same methodology, based on the dynamic experimental data from the impact test and obtained long-term parameters, linear viscoelastic parameters were established with a Prony series. Model validation was performed employing quasi-static and dynamic force-displacement data. Coefficients of determination when comparing model to experimental data during quasi-static and dynamic (initial velocity: 1480mm/s) procedure were R(2) = 0.999 and R(2) = 0.990, respectively. Knowledge of these heel pad material parameters enables realistic numerical analysis to evaluate internal stress and strain in the heel pad during different quasi-static or dynamic load conditions.

Investigation of the mechanical behaviour of the plantar soft tissue during gait cycle: Experimental and numerical activities

The aim of this work is to investigate the mechanical response of the plantar soft tissue from the heel strike to the midstance, developing both experimental and numerical activities. Using force plates and motion tracking system, the dynamic and kinematic data of 10 subjects are evaluated. The average kinematics data obtained from the experimental tests are assumed as boundary and loading conditions for the computational analyses. A three-dimensional virtual solid model of the foot is developed from the analysis of Digital Imaging and Communications in Medicine images from computed tomography and magnetic resonance. Constitutive formulations that interpret the mechanical response of the biological tissues are defined. Because of the major role of plantar soft tissue in the proposed analysis, a specific visco-hyperelastic constitutive formulation is provided considering the typical features of the tissue mechanics. The three-dimensional numerical model permits to evaluate the capability of the plantar soft tissue to redistribute the deformations, especially during the midstance, and to define quantitative aspects related to the energy absorption. The numerical results highlight the stress distribution from the heel strike to the midstance. The values of stress and strain reached are more intensive during the midstance, when there is a single support of the foot.

Analysis of the structural behaviour of colonic segments by inflation tests: Experimental activity and physio-mechanical model

A coupled experimental and computational approach is provided for the identification of the structural behaviour of gastrointestinal regions, accounting for both elastic and visco-elastic properties. The developed procedure is applied to characterize the mechanics of gastrointestinal samples from pig colons. Experimental data about the structural behaviour of colonic segments are provided by inflation tests. Different inflation processes are performed according to progressively increasing top pressure conditions. Each inflation test consists of an air in-flow, according to an almost constant increasing pressure rate, such as 3.5 mmHg/s, up to a prescribed top pressure, which is held constant for about 300 s to allow the development of creep phenomena. Different tests are interspersed by 600 s of rest to allow the recovery of the tissues' mechanical condition. Data from structural tests are post-processed by a physio-mechanical model in order to identify the mechanical parameters that interpret both the non-linear elastic behaviour of the sample, as the instantaneous pressure-stretch trend, and the time-dependent response, as the stretch increase during the creep processes. The parameters are identified by minimizing the discrepancy between experimental and model results. Different sets of parameters are evaluated for different specimens from different pigs. A statistical analysis is performed to evaluate the distribution of the parameters and to assess the reliability of the experimental and computational activities.

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.

Constitutive formulation and numerical analysis of the biomechanical behaviour of forefoot plantar soft tissue

The aim of this work is to provide a numerical approach for the investigation of the mechanical behaviour of the forefoot soft tissues. The development of reliable numerical models of biological structures requires the definition of constitutive formulations that actually interpret the mechanical response of the constituent biological tissues and their structural arrangement. A specific visco-hyperelastic constitutive model is provided to account for the typical features of soft plantar tissue mechanics, as geometric and material non-linearity, almost-incompressible behaviour and time-dependent phenomena. Constitutive parameters are evaluated by the analysis of experimental data from compression and stress relaxation tests on tissue samples. A three-dimensional finite element model of the forefoot region is developed starting from the analysis of biomedical images, leading to the evaluation of overall structural response. The reliability of model and analyses is assessed by the comparison of experimental and numerical results pertaining to indentation tests. The numerical model developed allows to evaluate the mechanical response of plantar soft tissue in terms of stress and strain distribution.

Characterization of the anisotropic mechanical behaviour of colonic tissues: experimental activity and constitutive formulation

The aim was to investigate the biomechanical behaviour of colonic tissues by a coupled experimental and numerical approach. The wall of the colon is composed of different tissue layers. Within each layer, different fibre families are distributed according to specific spatial orientations, which lead to a strongly anisotropic configuration. Accounting for the complex histology of the tissues, mechanical tests must be planned and designed to evaluate the behaviour of the colonic wall in different directions. Uni-axial tensile tests were performed on tissue specimens from 15 fresh pig colons, accounting for six different loading directions (five specimens for each loading direction). The next step of the investigation was to define an appropriate constitutive framework and develop a procedure for identification of the constitutive parameters. A specific hyperelastic formulation was developed that accounted for the multilayered conformation of the colonic wall and the fibre-reinforced configuration of the tissues. The parameters were identified by inverse analyses of the mechanical tests. The comparison of model results with experimental data, together with the evaluation of satisfaction of material thermomechanics principles, confirmed the reliability of the analysis developed. This work forms the basis for more comprehensive activities that aim to provide computational tools for the interpretation of surgical procedures that involve the gastrointestinal tract, considering the specific biomedical devices adopted.

Analysis of the biomechanical behaviour of gastrointestinal regions adopting an experimental and computational approach

An integrated experimental and computational procedure is provided for the evaluation of the biomechanical behaviour that characterizes the pressure-volume response of gastrointestinal regions. The experimental activity pertains to inflation tests performed on specific gastrointestinal conduct segments. Different inflation processes are performed according to progressively increasing volumes. Each inflation test is performed by a rapid liquid in-flaw, up to a prescribed volume, which is held constant for about 300s to allow the development of relaxation processes. The different tests are interspersed by 600s of rest to allow the recovery of the specimen mechanical condition. A physio-mechanical model is developed to interpret both the elastic behaviour of the sample, as the pressure-volume trend during the rapid liquid in-flaw, and the time-dependent response, as the pressure drop during the relaxation processes. The minimization of discrepancy between experimental data and model results entails the identification of the parameters that characterize the viscoelastic model adopted for the definition of the behaviour of the gastrointestinal regions. The reliability of the procedure is assessed by the characterization of the response of samples from rat small intestine.

Investigation of the biomechanical behaviour of hindfoot ligaments

The aim of this work is to provide a computational tool for the mechanical characterization of the hindfoot ligaments. The investigation is performed by a coupled numerical and experimental approach. For this purpose, a numerical model that represents the complex structural configuration of the hindfoot and the typical features of the mechanical behaviour of the ligament tissue is developed. The geometrical analysis of the anatomical site is performed starting from the processing of computed tomography and magnetic resonance images. Accounting for morphometric measurements, the virtual solid model provides an averaged configuration of the hindfoot structure. In order to specify the mechanical behaviour of the ligament tissue, a fibre-reinforced visco-hyperelastic model is adopted. The formulation accounts for the anisotropic configuration, geometric non-linearity, non-linear elasticity and time-dependent phenomena. Numerical analyses are performed to evaluate the biological tissues and structure mechanics with regard to physiological boundary conditions, accounting for dorsiflexion and plantarflexion movements. In order to evaluate the reliability of the numerical model developed, the experimental data are compared with the numerical results. The numerical results are in agreement with the range of values obtained by experimental test confirming the accuracy of the procedure adopted.

Investigations on the viscoelastic behaviour of a human healthy heel pad: In vivo compression tests and numerical analysis

The aim of this study was to investigate the viscoelastic behaviour of the human heel pad by comparing the stress–relaxation curves obtained from a compression device used on an in vivo heel pad with those obtained from a three-dimensional computer-based subject-specific heel pad model subjected to external compression. The three-dimensional model was based on the anatomy revealed by magnetic resonance imaging of a 31-year-old healthy female. The calcaneal fat pad tissue was described with a viscohyperelastic model, while a fibre-reinforced hyperelastic model was formulated for the skin. All numerical analyses were performed to interpret the mechanical response of heel tissues, with loading conditions and displacement rate in agreement with experimental tests. The heel tissues showed a non-linear, viscoelastic behaviour described by characteristic hysteretic curves, stress–relaxation and viscous recovery phenomena. The reliability of the investigations was validated by the interpretation of the mechanical response of heel tissues under the application of three pistons with diameter of 15, 20 and 40 mm, at the same displacement rate of about 1.7 mm/s. The maximum and minimum relative errors were found to be less than 0.95 and 0.064, respectively.

Biomechanical behaviour of heel pad tissue experimental testing, constitutive formulation, and numerical modelling

This paper deals with the constitutive formulation of heel pad tissue and presents a procedure for identifying constitutive parameters using experimental data, with the aim of developing a computational approach for investigating the actual biomechanical response. The preliminary definition of constitutive parameters was developed using a visco-hyperelastic formulation, considering experimental data from in vitro compression tests on specimens of fat pad tissue and data from in vivo tests to identify the actual trend of tissue stiffness. The discrepancy between model results and experimental data was evaluated on the basis of a specific cost function, adopting a stochastic/deterministic procedure. The parameter evaluation was upgraded by considering experimental tests performed on the fat pad tissues of a cadaveric foot using in situ indentation tests at 0.01 and 350 mm/s strain rates. The constitutive formulation was implemented in a numerical model. The comparison of data from in situ tests and numerical results led to an optimal domain of parameters based on an admissible discrepancy criterion. Numerical results evaluated for different sets of parameters inside the domain are reported and compared with experimental data for a reliability evaluation of the proposed procedure.

The quasi-linear viscoelastic properties of diabetic and non-diabetic plantar soft tissue

The purpose of this study was to characterize the viscoelastic behavior of diabetic and non-diabetic plantar soft tissue at six ulcer-prone/load-bearing locations beneath the foot to determine any changes that may play a role in diabetic ulcer formation and subsequent amputation in this predisposed population. Four older diabetic and four control fresh frozen cadaveric feet were each dissected to isolate plantar tissue specimens from the hallux, first, third, and fifth metatarsals, lateral midfoot, and calcaneus. Stress relaxation experiments were used to quantify the viscoelastic tissue properties by fitting the data to the quasi-linear viscoelastic (QLV) theory using two methods, a traditional frequency-insensitive approach and an indirect frequency-sensitive approach, and by measuring several additional parameters from the raw data including the rate and amount of overall relaxation. The stress relaxation response of both diabetic and non-diabetic specimens was unexpectedly similar and accordingly few of the QLV parameters for either fit approach and none of raw data parameters differed. Likewise, no differences were found between plantar locations. The accuracy of both fit methods was comparable, however, neither approach predicted the ramp behavior. Further, fit coefficients varied considerably from one method to the other, making it hard to discern meaningful trends. Future testing using alternate loading modes and intact feet may provide more insight into the role that time-dependent properties play in diabetic foot ulceration.