An inverse finite-element model of heel-pad indentation

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

Subject-specific material properties of the heel pad: An inverse finite element analysis

Individuals with diabetes are at a higher risk of developing foot ulcers. To better understand internal soft tissue loading and potential treatment options, subject-specific finite element (FE) foot models have been used. However, existing models typically lack subject-specific soft tissue material properties and only utilize subject-specific anatomy. Therefore, this study determined subject-specific hindfoot soft tissue material properties from one non-diabetic and one diabetic subject using inverse FE analysis. Each subject underwent cyclic MRI experiments to simulate physiological gait and to obtain compressive force and three-dimensional soft tissue imaging data at 16 phases along the loading-unloading cycles. The FE models consisted of rigid bones and nearly-incompressible first-order Ogden hyperelastic skin, fat, and muscle (resulting in six independent material parameters). Then, calcaneus and loading platen kinematics were computed from imaging data and prescribed to the FE model. Two analyses were performed for each subject. First, the skin, fat, and muscle layers were lumped into a single generic soft tissue material and optimized to the platen force. Second, the skin, fat, and muscle material properties were individually determined by simultaneously optimizing for platen force, muscle vertical displacement, and skin mediolateral bulging. Our results indicated that compared to the individual without diabetes, the individual with diabetes had stiffer generic soft tissue behavior at high strain and that the only substantially stiffer multi-material layer was fat tissue. Thus, we suggest that this protocol serves as a guideline for exploring differences in non-diabetic and diabetic soft tissue material properties in a larger population.

Reliability and Validity of Shore Hardness in Plantar Soft Tissue Biomechanics

Shore hardness (SH) is a cost-effective and easy-to-use method to assess soft tissue biomechanics. Its use for the plantar soft tissue could enhance the clinical management of conditions such as diabetic foot complications, but its validity and reliability remain unclear. Twenty healthy adults were recruited for this study. Validity and reliability were assessed across six different plantar sites. The validity was assessed against shear wave (SW) elastography (the gold standard). SH was measured by two examiners to assess inter-rater reliability. Testing was repeated following a test/retest study design to assess intra-rater reliability. SH was significantly correlated with SW speed measured in the skin or in the microchamber layer of the first metatarsal head (MetHead), third MetHead and rearfoot. Intraclass correlation coefficients and Bland-Altman plots of limits of agreement indicated satisfactory levels of reliability for these sites. No significant correlation between SH and SW elastography was found for the hallux, 5th MetHead or midfoot. Reliability for these sites was also compromised. SH is a valid and reliable measurement for plantar soft tissue biomechanics in the first MetHead, the third MetHead and the rearfoot. Our results do not support the use of SH for the hallux, 5th MetHead or midfoot.

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.

Finite Element Parametric Design of Hallux Valgus Orthosis Based on Orthogonal Analysis

OBJECTIVE

To design appropriate orthosis for hallux valgus, a difficult foot condition that affects a quarter of the body's bones, we need to clarify the numerical biomechanical features, which have not been established in previous biomechanical studies. Therefore, we constructed a finite element model of the bunion foot to investigate the orthopaedic force compensation mechanism.

METHODS

A patient with moderate hallux valgus was recruited. CT imaging data in DICOM format were extracted for three-dimensional foot model reconstruction. In conjunction with the need for rapid design of bunion orthosis, a metatarsal force application sizing method based on an orthogonal test design was investigated. The orthogonal test design was used to obtain the hallux valgus angle (HVA) and the inter metatarsal angle (IMA) data for different force combinations. Based on the extreme difference analysis and analysis of variance of the test results, the influence of different force combinations on the bunion angle was quickly determined.

RESULTS

The results showed that the stress concentration occurred mainly in the first metatarsal bone. The distribution trend was in the medial and lateral middle of the bone and gradually decreased to the dorsal base of the bone body. The greatest stress occurs in the cartilage between the phalanges and metatarsals. In 25 groups of simulation experiments, HVA was reduced from 27.7° to 13°, and IMA was reduced from 12.5° to 7.3°.

CONCLUSION

Applying detailed orthopaedic force collocation to the first metatarsal column can effectively restore the mechanics and kinematics of hallux valgus, and provide a reference for the treatment of bunion valgus and the design of orthopaedic devices.

A fluoroscopic imaging-guided computational analyses to inform internal tissue loads within fat pad of the diabetic foot during gait

To accurately predict internal tissue loads for early diagnostics of diabetic foot ulcerations, a novel data-driven computational analysis was conducted. A dedicated dual fluoroscopic system was combined with a pressure mat to simultaneously characterize foot motions and soft tissue's material properties during gait. Finite element (FE) models of the heel pad of a diabetic patient were constructed with 3D trajectories of the calcaneus applied as boundary conditions to simulate gait events. The tensile and compressive stresses occurring in the plantar tissue were computed. Predictions of the layered tissue FE model with anatomically-accurate heel pad structures (i.e., fat and skin) were compared with those of the traditional lumped tissue (i.e., homogeneous) models. The influence of different material properties (patient-specific versus generic) on internal tissue stresses was also investigated. The results showed the peak tensile stresses in the layered tissue model were predominantly found in the skin and distributed towards the circumferential regions of the heel, while peak compressive stresses in the fat tissue-bone interface were up to 51.4% lower than those seen in the lumped models. Performing FE analyses at four different phases of walking revealed that ignorance of layered tissue structures resulted in an unphysiological increase of peak-to-peak value of stress fluctuation in the fat and skin tissue components. Thus, to produce more clinical-relevant predictions, foot FE models are suggested to include layered tissue structures of the plantar tissue for an improved estimation of internal stresses in the diabetic foot in gait.

Definition and evaluation of a finite element model of the human heel for diabetic foot ulcer prevention under shearing loads

Diabetic foot ulcers are triggered by mechanical loadings applied to the surface of the plantar skin. Strain is considered to play a crucial role in relation to ulcer etiology and can be assessed by Finite Element (FE) modeling. A difficulty in the generation of these models is the choice of the soft tissue material properties. In the literature, many studies attempt to model the behavior of the heel soft tissues by implementing constitutive laws that can differ significantly in terms of mechanical response. Moreover, current FE models lack of proper evaluation techniques that could estimate their ability to simulate realistic strains. In this article, we propose and evaluate a FE model of the human heel for diabetic foot ulcer prevention. Soft tissue constitutive laws are defined through the fitting of experimental stretch-stress curves published in the literature. The model is then evaluated through Digital Volume Correlation (DVC) based on non-rigid 3D Magnetic Resonance Image Registration. The results from FE analysis and DVC show similar strain locations in the fat pad and strain intensities according to the type of applied loads. For additional comparisons, different sets of constitutive models published in the literature are applied into the proposed FE mesh and simulated with the same boundary conditions. In this case, the results in terms of strains show great diversity in locations and intensities, suggesting that more research should be developed to gain insight into the mechanical properties of these tissues.

Identifiability of soft tissue constitutive parameters from in-vivo macro-indentation

Reliable identification of soft tissue material parameters is frequently required in a variety of applications, particularly for biomechanical simulations using finite element analysis (FEA). However, determining representative constitutive laws and material parameters is challenging and often comprises a bottleneck that hinders the successful implementation of FEA. Soft tissues exhibit a nonlinear response and are commonly modeled using hyperelastic constitutive laws. In-vivo material parameter identification, for which standard mechanical tests (e.g., uniaxial tension and compression) are inapplicable, is commonly achieved using finite macro-indentation test. Due to the lack of analytical solutions, the parameters are commonly identified using inverse FEA (iFEA), in which simulated results and experimental data are iteratively compared. However, determining what data must be collected to accurately identify a unique parameter set remains unclear. This work investigates the sensitivities of two types of measurements: indentation force-depth data (e.g., measured using an instrumented indenter) and full-field surface displacements (e.g., using digital image correlation). To eliminate model fidelity and measurement-related errors, we employed an axisymmetric indentation FE model to produce synthetic data for four 2-parameter hyperelastic constitutive laws: compressible Neo-Hookean, and nearly incompressible Mooney-Rivlin, Ogden, and Ogden-Moerman models. For each constitutive law, we computed the objective functions representing the discrepancies in the reaction force, the surface displacement, and their combination, and visualized them for hundreds of parameter sets, spanning a representative range as found in the literature for the bulk soft tissue complex in human lower limbs. Moreover, we quantified three identifiability metrics, which provided insights into the uniqueness (or lack thereof) and the sensitivities. This approach provides a clear and systematic evaluation of the parameter identifiability, which is independent of the selection of the optimization algorithm and initial guesses required in iFEA. Our analysis indicated that the indenter's force-depth data, despite being commonly used for parameter identification, was insufficient for reliably and accurately identifying both parameters for all the investigated material models and that the surface displacement data improved the parameter identifiability in all cases, although the Mooney-Rivlin parameters remained poorly identifiable. Informed by the results, we then discuss several identification strategies for each constitutive model. Finally, we openly provide the codes used in this study, to allow others to further investigate the indentation problem according to their specifications (e.g., by modifying the geometries, dimensions, mesh, material models, boundary conditions, contact parameters, or objective functions).

Role of multi-layer tissue composition of musculoskeletal extremities for prediction of in vivo surface indentation response and layer deformations

Emergent mechanics of musculoskeletal extremities (surface indentation stiffness and tissue deformation characteristics) depend on the underlying composition and mechanics of each soft tissue layer (i.e. skin, fat, and muscle). Limited experimental studies have been performed to explore the layer specific relationships that contribute to the surface indentation response. The goal of this study was to examine through statistical modeling how the soft tissue architecture contributed to the aggregate mechanical surface response across 8 different sites of the upper and lower extremities. A publicly available dataset was used to examine the relationship of soft tissue thickness (fat and muscle) to bulk tissue surface compliance. Models required only initial tissue layer thicknesses, making them usable in the future with only a static ultrasound image. Two physics inspired models (series of linear springs), which allowed reduced statistical representations (combined locations and location specific), were explored to determine the best predictability of surface compliance and later individual layer deformations. When considering the predictability of the experimental surface compliance, the physics inspired combined locations model showed an improvement over the location specific model (percent difference of 25.4 +/- 27.9% and 29.7 +/- 31.8% for the combined locations and location specific models, respectively). While the statistical models presented in this study show that tissue compliance relies on the individual layer thicknesses, it is clear that there are other variables that need to be accounted for to improve the model. In addition, the individual layer deformations of fat and muscle tissues can be predicted reasonably well with the physics inspired models, however additional parameters may improve the robustness of the model outcomes, specifically in regard to capturing subject specificity.

Template models for simulation of surface manipulation of musculoskeletal extremities

Capturing the surface mechanics of musculoskeletal extremities would enhance the realism of life-like mechanics imposed on the limbs within surgical simulations haptics. Other fields that rely on surface manipulation, such as garment or prosthetic design, would also benefit from characterization of tissue surface mechanics. Eight homogeneous tissue models were developed for the upper and lower legs and arms of two donors. Ultrasound indentation data was used to drive an inverse finite element analysis for individualized determination of region-specific material coefficients for the lumped tissue. A novel calibration strategy was implemented by using a ratio based adjustment of tissue properties from linear regression of model predicted and experimental responses. This strategy reduced requirement of simulations to an average of under four iterations. These free and open-source specimen-specific models can serve as templates for simulations focused on mechanical manipulations of limb surfaces.

Increased exposure to loading is associated with decreased plantar soft tissue hardness in people with diabetes and neuropathy

AIMS

Literature indicates that altered plantar loading in people with diabetes could trigger changes in plantar soft tissue biomechanics which, in turn, could affect the risk for ulceration. To stimulate more research in this area, this study uses in vivo testing to investigate the link between plantar loading and tissue hardness.

METHODS

Tissue hardness and plantar pressure distribution were measured for six plantar areas in 39 people with diabetes and peripheral neuropathy.

RESULTS

Spearman correlation analysis revealed that increased pressure time integral at the 1st metatarsal-head region (r = -0.354, n = 39, P = 0.027) or at the heel (r = -0.378, n = 39, P = 0.018) was associated with reduced hardness in the same regions. After accounting for confounding parameters, generalised estimating equations analysis also showed that 10% increase in pressure time integral at the heel was associated with ≈ 1 unit reduction in hardness in the same region.

CONCLUSIONS

For the first time, this study reveals that people with diabetes and neuropathy who tend to load their feet more heavily also tend to have plantar soft tissues with lower hardness. The observed difference in tissue hardness is likely to affect the tissue's vulnerability to overload injury. More research will be needed to explore the implications of the observed association for the risk of ulceration.

Mechanical behavior of infrapatellar fat pad of patients affected by osteoarthritis

The infrapatellar fat pad (IFP) is an adipose tissue present in the knee that lies between the patella, femur, meniscus and tibia, filling the space between these structures. IFP facilitates the distribution of the synovial fluid and may act to absorb impulsive actions generated through the joint. IFP in osteoarthritis (OA) pathology undergoes structural changes characterized by inflammation, hypertrophy and fibrosis. The aim of the present study is to analyze the mechanical behavior of the IFP in patients affected by end-stage OA. A specific test fixture was designed and indentation tests were performed on IFP specimens harvested from OA patients who underwent total knee arthroplasty. Experiments allowed to assess the typical features of mechanical response, such as non-linear stress-strain behavior and time-dependent effects. Results from mechanical experimentations were implemented within the framework of a visco-hyperelastic constitutive theory, with the aim to provide data for computational modelling of OA IFP role in knee mechanics. Initial and final indentation stiffness were calculated for all subjects and statistical results reveled that OA IFP mechanics was not significantly influenced by gender, BMI and sample preparation. OA IFP mechanical behavior was also compared to that of other adipose tissues. OA IFP appeared to be a stiffer adipose tissue compared to subcutaneous, visceral adipose tissues and heel fat pads. It is reasonable that fibrosis induces a modification of the tissue destabilizing the normal distribution of forces in the joint during movement, causing a worsening of the disease.

A review of foot finite element modelling for pressure ulcer prevention in bedrest: Current perspectives and future recommendations

Pressure ulcers (PUs) are a major public health challenge, having a significant impact on healthcare service and patient quality of life. Computational biomechanical modelling has enhanced PU research by facilitating the investigation of pressure responses in subcutaneous tissue and skeletal muscle. Extensive work has been undertaken on PUs on patients in the seated posture, but research into heel ulcers has been relatively neglected. The aim of this review was to address the key challenges that exist in developing an effective FE foot model for PU prevention and the confusion surrounding the wide range of outputs reported. Nine FE foot studies investigating heel ulcers in bedrest were identified and reviewed. Six studies modelled the posterior part of the heel, two included the calf and foot, and one modelled the whole body. Due to the complexity of the foot anatomy, all studies involved simplification or assumptions regarding parts of the foot structure, boundary conditions and material parameters. Simulations aimed to understand better the stresses and strains exhibited in the heel soft tissues of the healthy foot. The biomechanical properties of soft tissue derived from experimental measurements are critical for developing a realistic model and consequently guiding clinical decisions. Yet, little to no validation was reported in each of the studies. If FE models are to address future research questions and clinical applications, then sound verification and validation of these models is required to ensure accurate conclusions and prediction of patient outcomes. Recommendations and considerations for future FE studies are therefore proposed.

Real-Time Analysis of the Dynamic Foot Function: A Machine Learning and Finite Element Approach

Finite element analysis (FEA) has been widely used to study foot biomechanics and pathological functions or effects of therapeutic solutions. However, development and analysis of such foot modeling is complex and time-consuming. The purpose of this study was therefore to propose a method coupling a FE foot model with a model order reduction (MOR) technique to provide real-time analysis of the dynamic foot function. A generic and parametric FE foot model was developed and dynamically validated during stance phase of gait. Based on a design of experiment of 30 FE simulations including four parameters related to foot function, the MOR method was employed to create a prediction model of the center of pressure (COP) path that was validated with four more random simulations. The four predicted COP paths were obtained with a 3% root-mean-square-error (RMSE) in less than 1 s. The time-dependent analysis demonstrated that the subtalar joint position and the midtarsal joint laxity are the most influential factors on the foot functions. These results provide additionally insight into the use of MOR technique to significantly improve speed and power of the FE analysis of the foot function and may support the development of real-time decision support tools based on this method.

Risk factors for developing heel ulcers for bedridden patients: A finite element study

BACKGROUND

The heel is one of the most common sites of pressure ulcers and the anatomical location with the highest prevalence of deep tissue injury. Several finite element modeling studies investigate heel ulcers for bedridden patients. In the current study we have added the implementation of the calf structure to the current heel models. We tested the effect of foot posture, mattress stiffness, and a lateral calcaneus displacement to the contact pressure and internal maximum shear strain occurring at the heel.

METHODS

A new 3D finite element model is created which includes the heel and calf structure. Sensitivity analyses are performed for the foot orientation relative to the mattress, the Young's modulus of the mattress, and a lateral displacement of the calcaneus relative to the other soft tissues in the heel.

FINDINGS

The models predict that a stiffer mattress results in higher contact pressures and internal maximum shear strains at the heel as well as the calf. An abducted foot posture reduces the internal strains in the heel and a lateral calcaneus displacement increases the internal maximum shear strains. A parameter study with different mattress-skin friction coefficients showed that a coefficient below 0.4 decreases the maximum internal shear strains in all of the used loading conditions.

INTERPRETATION

In clinical practice, it is advised to avoid internal shearing of the calcaneus of patients, and it could be taken into consideration by medical experts and nurses that a more abducted foot position may reduce the strains in the heel.

Increase of stiffness in plantar fat tissue in diabetic patients

Plantar soft tissue stiffening in diabetes leads to a risk of developing ulcers. There are relatively few studies providing methods for quantifying the mechanical properties of skin and fat in the plantar tissue of diabetic patients. Previous studies used linear or non-linear single layer deformable models or linear multi-layer models. This study aimed to investigate the mechanical properties of plantar soft tissue using multi-layer, non-linear models to estimate more accurate mechanical properties in the plantar tissues of diabetic patients. Ten healthy young (HY) subjects, ten healthy old (HO) subjects, and ten old diabetic patients (DB) volunteered for the study. Indentation tests were performed at two sites in the heel. The subjects underwent computed tomography (CT) to measure the respective thicknesses of the skin and fat at the indentation sites. Subject-specific finite element models were created to estimate the parameters of the first-order Ogden forms of the skin and fat. The initial shear modulus for the fat layer μ_F in DB, HO, and HY were 4.68 MPa (±0.87), 2.71 MPa (±1.25), and 2.27 MPa (±0.87), respectively. The initial shear modulus for the skin layer (μ_S) in DB, HO, and HY were 5.86 MPa (±2.51), 7.05 MPa (±1.94), and 14.58 MPa (±1.98), respectively. The DB had stiffer fat tissue than the normal subjects in the same age group but had the same soft skin. These aspects can cause different mechanical stress conditions in a diabetic foot than in a normal foot under the same mechanical loading, making the diabetic foot vulnerable to the initiation of mechanical breakdowns such as ulcers.

Biomechanical insights into the role of foot pads during locomotion in camelid species

From the camel’s toes to the horse’s hooves, the diversity in foot morphology among mammals is striking. One distinguishing feature is the presence of fat pads, which may play a role in reducing foot pressures, or may be related to habitat specialization. The camelid family provides a useful paradigm to explore this as within this phylogenetically constrained group we see prominent (camels) and greatly reduced (alpacas) fat pads. We found similar scaling of vertical ground reaction force with body mass, but camels had larger foot contact areas, which increased with velocity, unlike alpacas, meaning camels had relatively lower foot pressures. Further, variation between specific regions under the foot was greater in alpacas than camels. Together, these results provide strong evidence for the role of fat pads in reducing relative peak locomotor foot pressures, suggesting that the fat pad role in habitat specialization remains difficult to disentangle.

Material properties of human lumbar intervertebral discs across strain rates

BACKGROUND CONTEXT

The use of finite element (FE) methods to study the biomechanics of the intervertebral disc (IVD) has increased over recent decades due to their ability to quantify internal stresses and strains throughout the tissue. Their accuracy is dependent upon realistic, strain-rate dependent material properties, which are challenging to acquire.

PURPOSE

The aim of this study was to use the inverse FE technique to characterize the material properties of human lumbar IVDs across strain rates.

STUDY DESIGN

A human cadaveric experimental study coupled with an inverse finite element study.

METHODS

To predict the structural response of the IVD accurately, the material response of the constituent structures was required. Therefore, compressive experiments were conducted on 16 lumbar IVDs (39±19 years) to obtain the structural response. An FE model of each of these experiments was developed and then run through an inverse FE algorithm to obtain subject-specific constituent material properties, such that the structural response was accurate.

RESULTS

Experimentally, a log-linear relationship between IVD stiffness and strain rate was observed. The material properties obtained through the subject-specific inverse FE optimization of the annulus fibrosus (AF) fiber and AF fiber ground matrix allowed a good match between the experimental and FE response. This resulted in a Young modulus of AF fibers (-MPa) to strain rate (ε˙, /s) relationship of YMAF=31.5ln(ε˙)+435.5, and the C₁₀ parameter of the Neo-Hookean material model of the AF ground matrix was found to be strain-rate independent with an average value of 0.68 MPa.

CONCLUSIONS

These material properties can be used to improve the accuracy, and therefore predictive ability of FE models of the spine that are used in a wide range of research areas and clinical applications.

CLINICAL SIGNIFICANCE

Finite element models can be used for many applications including investigating low back pain, spinal deformities, injury biomechanics, implant design, design of protective systems, and degenerative disc disease. The accurate material properties obtained in this study will improve the predictive ability, and therefore clinical significance of these models.

Strain-rate dependence of viscous properties of the plantar soft tissue identified by a spherical indentation test

The mechanical properties of the plantar soft tissue are known to vary in diabetic patients, indicating that parameter identification of the mechanical properties of the foot tissue using an indentation test is clinically important for possible early diagnosis and interventions of diabetic foot. However, accurate mechanical characterization of the viscous properties of the plantar soft tissue has been difficult, as measured force-relaxation curves of the same soft tissue differ depending on how the material is loaded. In the present study, we attempted to clarify how the indentation rate of the plantar soft tissue affects the measured force-relaxation curves, which is necessary in order to identify the viscoelastic properties. The force-relaxation curves of the heel pads were obtained from the indentation experiment in vivo at indentation rates of 15, 25, 50, 75, and 100 mm/s. The curves were fit to an analytical contact model of spherical indentation incorporating a five-element Maxwell model. The results of the present study demonstrated that, although experimentally obtained force-relaxation curves were actually variable depending on the indentation rate, similar viscous parameters could be identified for the same heel if the effects of (1) the underestimation of the peak force due to the energy dissipation occurring during indentation and (2) the deceleration of the indenter at the target position were incorporated in the parameter identification process. The indentation-rate-independent viscous properties could therefore be estimated using the proposed method.

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.

Development of a simplified, reproducible, parametric 3D model of the talus

Computational foot models have significant application in surgical decision making, injury and disease diagnosis and prevention, sports performance analysis and footwear engineering. However, due to the substantial time in model building and the heavy computational costs from the complexity of the models, daily clinical application of these foot models has yet to be achieved. Much of the previous research adopted a detailed-geometry approach in modeling bones that potentially contributed to the heavy computational costs. In this research, we developed a computational talus model based on CT section image data, image reconstruction and segmentation, contact surface identification, standard shape fitting, and finite element auto meshing algorithms. Modeling the bones as rigid is common, and modeling the contact surfaces only for the rigid body saves additional computational resources. Priority, therefore, in the shape fitting with optimization is given to the contact surfaces of the talus. Thirteen sets (9 males and 4 females) of CT section data were obtained. Image reconstruction, segmentation and bone labeling were conducted on each set of CT data to identify talus and its adjacent bones. Contact surfaces of the talus were then identified based on bone spatial relationships. Apart from the talar dome surface which was fitted by a 3rd-order polynomial, standard shapes such as ellipsoids and planes were used to fit the selected contact surfaces so that the geometrical parameters maintain physical significance. Based on these parameters, we automatically recreated and meshed the least-squares fitted shapes rapidly with limited elements. Last, mean major contact surfaces of the talus were obtained and fitted by standard shapes. Although the number of samples in this study was relatively small, our method provides sufficient and accurate geometric parameters of these contact surfaces to completely describe and reproduce the talus, on both a subject specific and average basis. The method for describing the talus here helps to parametrize computational models using planes and ellipsoids, improves surgical decision making and implants with a more precise and physically significant measures, and the description provides bone geometric parameters which can later be used to relate risk analysis for bone shape specific injury rates.

In Vivo Measurement of Plantar Tissue Characteristics and Its Indication for Foot Modeling

Plantar heel pain is one of the most common musculoskeletal disorders and generally causing long term discomfort of the patients. The objective of the present study is to combine in vivo experimental measurements and finite element modelling of the foot to investigate the influences of stiffness and thickness variation of individual plantar tissues especially the heel pad on deformation behaviours of the human foot. The stiffness and thickness variance of individuals were measured through supersonic shear wave elastography considering detailed heel pad layers refered to in literature as: dermis, stiffer micro-chamber layer, softer macro-chamber layer. A corresponding foot model with separated heel pad layers was established and used to a sensitivity analysis related to the variance of above-mentioned tissue characteristics. The experimental results show that the average stiffness of the micro-chamber layer ranged from 24.7 (SD 2.4) kPa to 18.8 (SD 3.5) kPa with the age group increasing from 20-29 years old to 60-69 years old, while the average macro-chamber stiffness is 10.6 (SD 1.5) kPa that appears to slightly decrease with the increasing age. Both plantar soft tissue stiffness and thickness of male were generally larger than that of female. The numerical simulation results show that the variance of heel pad strain level can reach 27.5% due to the effects of stiffness and thickness change of the plantar tissues. Their influences on the calcaneus stress and plantar pressure were also significant. This indicates that the most appreciate way to establish a personalized foot model needs to consider the difference of both individual foot anatomic geometry and plantar soft tissue material properties.

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.

Foot internal stress distribution during impact in barefoot running as function of the strike pattern

The aim of the present study is to examine the impact absorption mechanism of the foot for different strike patterns (rearfoot, midfoot and forefoot) using a continuum mechanics approach. A three-dimensional finite element model of the foot was employed to estimate the stress distribution in the foot at the moment of impact during barefoot running. The effects of stress attenuating factors such as the landing angle and the surface stiffness were also analyzed. We characterized rear and forefoot plantar sole behavior in an experimental test, which allowed for refined modeling of plantar pressures for the different strike patterns. Modeling results on the internal stress distributions allow predictions of the susceptibility to injury for particular anatomical structures in the foot.

Finite element analysis of the effect of high tibial osteotomy correction angle on articular cartilage loading

Osteoarthritis is a globally common disease that imposes a considerable ongoing health and economic burden on the socioeconomic system. As more and more biomechanical factors have been explored, malalignment of the lower limb has been found to influence the load distribution across the articular surface of the knee joint substantially. In this work, a three-dimensional finite element analysis was carried out to investigate the effect of varying the high tibial osteotomy correction angle on the stress distribution in both compartments of the human knee joint. Thereafter, determine the optimal correction angle to achieve a balanced loading between these two compartments. The developed finite element model was validated against experimental and numerical results. The findings of this work suggest that by changing the correction angle from 0° to 10° valgus, high tibial osteotomy shifted the mechanical load from the affected medial compartment to the lateral compartment with intact cartilage. The Von Mises and the shear stresses decreased in the medial compartment and increased in the lateral compartment. Moreover, a balanced stress distribution between the two compartments as well as the desired alignment were achieved under a valgus hypercorrection of 4.5° that significantly unloads the medial compartment, loads the lateral compartment and arrests the progression of osteoarthritis. After comparing the achieved results against the ones of previous studies that explored the effects of the high tibial osteotomy correction angle on either clinical outcomes or biomechanical outcomes, one can conclude that the findings of this study agree well with the related clinical data and recommendations found in the literature.

A Novel Nonlinear Parameter Estimation Method of Soft Tissues

The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine (WCFM_SVM). Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young's modulus and Poisson's ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg-Marquardt (LM) algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.

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.

Development of the CAVEMAN Human Body Model: Validation of Lower Extremity Sub-Injurious Response to Vertical Accelerative Loading

Improving injury prediction accuracy and fidelity for mounted Warfighters has become an area of focus for the U.S. military in response to improvised explosive device (IED) use in both Iraq and Afghanistan. Although the Hybrid III anthropomorphic test device (ATD) has historically been used for crew injury analysis, it is only capable of predicting a few select skeletal injuries. The Computational Anthropomorphic Virtual Experiment Man (CAVEMAN) human body model is being developed to expand the injury analysis capability to both skeletal and soft tissues. The CAVEMAN model is built upon the Zygote 50^th percentile male human CAD model and uses a finite element modeling approach developed for high performance computing (HPC). The lower extremity subset of the CAVEMAN human body model presented herein includes: 28 bones, 26 muscles, 40 ligaments, fascia, cartilage and skin. Sensitivity studies have been conducted with the CAVEMAN lower extremity model to determine the structures critical for load transmission through the leg in the underbody blast (UBB) environment. An evaluation of the CAVEMAN lower extremity biofidelity was also carried out using 14 unique data sets derived by the Warrior Injury Assessment Manikin (WIAMan) program cadaveric lower leg testing. Extension of the CAVEMAN lower extremity model into anatomical tissue failure will provide additional injury prediction capabilities, beyond what is currently achievable using ATDs, to improve occupant survivability analyses within military vehicles.

In-vivo viscous properties of the heel pad by stress-relaxation experiment based on a spherical indentation

Identifying the viscous properties of the plantar soft tissue is crucial not only for understanding the dynamic interaction of the foot with the ground during locomotion, but also for development of improved footwear products and therapeutic footwear interventions. In the present study, the viscous and hyperelastic material properties of the plantar soft tissue were experimentally identified using a spherical indentation test and an analytical contact model of the spherical indentation test. Force-relaxation curves of the heel pads were obtained from the indentation experiment. The curves were fit to the contact model incorporating a five-element Maxwell model to identify the viscous material parameters. The finite element method with the experimentally identified viscoelastic parameters could successfully reproduce the measured force-relaxation curves, indicating the material parameters were correctly estimated using the proposed method. Although there are some methodological limitations, the proposed framework to identify the viscous material properties may facilitate the development of subject-specific finite element modeling of the foot and other biological materials.

Validation of plantar pressure simulations using finite and discrete element modelling in healthy and diabetic subjects

Plantar pressure simulation driven by integrated 3D motion capture data, using both a finite element and a discrete element model, is compared for ten healthy and ten diabetic neuropathic subjects. The simulated peak pressure deviated on average between 16.7 and 34.2% from the measured peak pressure. The error in the position of the peak pressure was on average smaller than 4.2 cm. No method was more accurate than the other although statistical differences were found between them. Both techniques are thus complementary and useful tools to better understand the alteration of diabetic foot biomechanics during gait.

A preliminary study of patient-specific mechanical properties of diabetic and healthy plantar soft tissue from gated magnetic resonance imaging

Foot loading rate, load magnitude, and the presence of diseases such as diabetes can all affect the mechanical properties of the plantar soft tissues of the human foot. The hydraulic plantar soft tissue reducer instrument was designed to gain insight into which variables are the most significant in determining these properties. It was used with gated magnetic resonance imaging to capture three-dimensional images of feet under dynamic loading conditions. Custom electronics controlled by LabVIEW software simultaneously recorded system pressure, which was then translated to applied force values based on calibration curves. Data were collected for two subjects, one without diabetes (Subject A) and one with diabetes (Subject B). For a 0.2-Hz loading rate, and strains 0.16, 0.18, 0.20, and 0.22, Subject A's average tangential heel pad stiffness was 10 N/mm and Subject B's was 24 N/mm. Maximum test loads were approximately 200 N. Loading rate and load magnitude limitations (both were lower than physiologic values) will continue to be addressed in the next version of the instrument. However, the current hydraulic plantar soft tissue reducer did produce a data set for healthy versus diabetic tissue stiffness that agrees with previous trends. These data are also being used to improve finite element analysis models of the foot as part of a related project.

A Finite Element Model of the Foot/Ankle to Evaluate Injury Risk in Various Postures

The foot/ankle complex is frequently injured in many types of debilitating events, such as car crashes. Numerical models used to assess injury risk are typically minimally validated and do not account for ankle posture variations that frequently occur during these events. The purpose of this study was to evaluate a finite element model of the foot and ankle accounting for these positional changes. A model was constructed from computed tomography scans of a male cadaveric lower leg and was evaluated by comparing simulated bone positions and strain responses to experimental results at five postures in which fractures are commonly reported. The bone positions showed agreement typically within 6° or less in all anatomical directions, and strain matching was consistent with the range of errors observed in similar studies (typically within 50% of the average strains). Fracture thresholds and locations in each posture were also estimated to be similar to those reported in the literature (ranging from 6.3 kN in the neutral posture to 3.9 kN in combined eversion and external rotation). The least vulnerable posture was neutral, and all other postures had lower fracture thresholds, indicating that examination of the fracture threshold of the lower limb in the neutral posture alone may be an underestimation. This work presents an important step forward in the modeling of lower limb injury risk in altered ankle postures. Potential clinical applications of the model include the development of postural guidelines to minimize injury, as well as the evaluation of new protective systems.

Material properties of bovine intervertebral discs across strain rates

The intervertebral disc (IVD) is a complex structure responsible for distributing compressive loading to adjacent vertebrae and allowing the vertebral column to bend and twist. To study the mechanical behaviour of individual components of the IVD, it is common for specimens to be dissected away from their surrounding tissues for mechanical testing. However, disrupting the continuity of the IVD to obtain material properties of each component separately may result in erroneous values. In this study, an inverse finite element (FE) modelling optimisation algorithm has been used to obtain material properties of the IVD across strain rates, therefore bypassing the need to harvest individual samples of each component. Uniaxial compression was applied to ten fresh-frozen bovine intervertebral discs at strain rates of 10^-3-1/s. The experimental data were fed into the inverse FE optimisation algorithm and each experiment was simulated using the subject specific FE model of the respective specimen. A sensitivity analysis revealed that the IVD's response was most dependent upon the Young's modulus (YM) of the fibre bundles and therefore this was chosen to be the parameter to optimise. Based on the obtained YM values for each test corresponding to a different strain rate (ε̇), the following relationship was derived:YM=35.5lnε̇+527.5. These properties can be used in finite element models of the IVD that aim to simulate spinal biomechanics across loading rates.

Material properties of the heel fat pad across strain rates

The complex structural and material behaviour of the human heel fat pad determines the transmission of plantar loading to the lower limb across a wide range of loading scenarios; from locomotion to injurious incidents. The aim of this study was to quantify the hyper-viscoelastic material properties of the human heel fat pad across strains and strain rates. An inverse finite element (FE) optimisation algorithm was developed and used, in conjunction with quasi-static and dynamic tests performed to five cadaveric heel specimens, to derive specimen-specific and mean hyper-viscoelastic material models able to predict accurately the response of the tissue at compressive loading of strain rates up to 150 s⁻¹. The mean behaviour was expressed by the quasi-linear viscoelastic (QLV) material formulation, combining the Yeoh material model (C10=0.1MPa, C30=7MPa, K=2GPa) and Prony׳s terms (A1=0.06, A2=0.77, A3=0.02 for τ1=1ms, τ2=10ms, τ3=10s). These new data help to understand better the functional anatomy and pathophysiology of the foot and ankle, develop biomimetic materials for tissue reconstruction, design of shoe, insole, and foot and ankle orthoses, and improve the predictive ability of computational models of the foot and ankle used to simulate daily activities or predict injuries at high rate injurious incidents such as road traffic accidents and underbody blast.

Differences in the mechanical characteristics of plantar soft tissue between ulcerated and non-ulcerated foot

AIMS

The purpose of this study was to investigate the differences in mechanical properties of the plantar soft tissue between the ulcerated and non-ulcerated feet in patients with diabetic neuropathy.

METHODS

Thirty nine patients who met the inclusion criteria participated in this study. Ten out of 39 participants had an active ulcer at a site other than the plantar heel and the first metatarsal head. Real time ultrasound elastography was performed to measure the soft tissue thickness and stiffness of the heel pad and sub-metatarsal fat pad. To account for the qualitative nature of conventional real time elastography, relative tissue stiffness was assessed against that of a standardised ultrasound standoff material.

RESULTS

The results indicated that the ulcerated group had a significantly lower heel pad relative stiffness (t (37)=2.559, P=0.015, η2=0.150) in the left foot.

CONCLUSIONS

The observed difference in the stiffness of the heel pad between the ulcerated and non-ulcerated feet indicates a possible link between tissue mechanics and ulceration. Further analysis of the data proposed in this study provided a quantitative assessment of plantar fat pad deformability which can contribute to understanding the role of tissue biomechanics in ulceration.

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.

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%).