Optimization of nonlinear hyperelastic coefficients for foot tissues using a magnetic resonance imaging deformation experiment

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).

Evaluation of novel plantar pressure-based 3-dimensional printed accommodative insoles - A feasibility study

BACKGROUND

Custom insoles are commonly prescribed to patients with diabetes to redistribute plantar pressure and decrease the risk of ulceration. Advances in 3D printing have enabled the creation of 3D-printed personalized metamaterials whose properties are derived not only from the base material but also the lattice microstructures within the metamaterial. Insoles manufactured using personalized metamaterials have both patient-specific geometry and stiffnesses. However, the safety and biomechanical effect of the novel insoles have not yet been tested clinically.

METHODS

Individuals without ulcer, neuropathy, or deformity were recruited for this study. In-shoe walking plantar pressure at baseline visit was taken and sensels with pressure over 200 kPa was used to define offloading region(s). Three pairs of custom insoles (two 3D printed insoles with personalized metamaterials (Hybrid and Full) designed based on foot shape and plantar pressure mapping and one standard-of-care diabetic insole as a comparator). In-shoe plantar pressure measurements during walking were recorded in a standardized research shoe and the three insoles and compared across all four conditions.

FINDINGS

Twelve individuals were included in the final analysis. No adverse events occurred during testing. Maximum peak plantar pressure and the pressure time integral were reduced in the offloading regions in the Hybrid and Full but not in the standard-of-care compared to the research shoe.

INTERPRETATION

This feasibility study confirms our ability to manufacture the 3D printed personalized metamaterials insoles and demonstrates their ability to reduce plantar pressure. We have demonstrated the ability to modify the 3D printed design to offload certain parts of the foot using plantar pressure data and a patient-specific metamaterials in the 3D printed insole design. The advance in 3D printed technology has shown its potential to improve current care.

MR-compatible loading device for assessment of heel pad internal tissue displacements under shearing load

In the last decade, the role of shearing loads has been increasingly suspected to play a determinant impact in the formation of deep pressure ulcers. In vivo observations of such deformations are complex to obtain. Previous studies only provide global measurements of such deformations without getting the quantitative values of the loads that generate these deformations. To study the role that shearing loads have in the etiology of heel pressure ulcers, an MR-compatible device for the application of shearing and normal loads was designed. Magnetic resonance imaging is a key feature that allows to monitor deformations of soft tissues after loading in a non-invasive way. Measuring applied forces in an MR-environment is challenging due to the impossibility to use magnetic materials. In our device, forces are applied through the compression of springs made of polylactide. Shearing and normal loads were applied on the plantar skin of the human heel through a flat plate while acquiring MR images. The device materials did not introduce any imaging artifact and allowed for high quality MR deformation measurements of the internal components of the heel. The obtained subject-specific results are an original data set that can be used in validations for Finite Element analysis and therefore contribute to a better understanding of the factors involved in pressure ulcer development.

OPTIMAL MESH CRITERIA IN FINITE ELEMENT MODELING OF HUMAN FOOT: THE DEPENDENCE FOR MULTIPLE MODEL OUTPUTS ON MESH DENSITY AND LOADING BOUNDARY CONDITIONS

The use of finite element models has gained popularity in the field of foot and footwear biomechanics to predict the stress–strain distribution and the treatment effectiveness of therapeutic insoles for pathological foot conditions. However, a comprehensive evaluation of mesh quality is often ignored, meanwhile no golden standard exists for the mesh density and selection of element size at an acceptable accuracy. Here, we make a convergence test and established anatomically-realistic foot models at different mesh densities. The study compared the discrepancy in output variables to the changes of element type and mesh density under barefoot and footwear conditions with compressive and shear loads, which are commonly encountered in foot and footwear biomechanics simulations. For a range of loading conditions simulated in 125 finite element models, the peak plantar pressure consistently converged with optimal mesh size determined at 2.5[Formula: see text]mm. The convergence variable of principal strains and stress tensors, however, varies significantly. The max von-Mises stress showed strong sensitive behavior to the changes of the mesh density. The pattern for contact pressure distribution became less accurate when the element sizes increase to 6.0[Formula: see text]mm; in particular, the locations of the pressure peak do not show remarkable changes, but the size of the area of contact still changes. The current study could offer a general guideline when generating a reasonable accurate finite element models for the analysis of plantar pressure distributions and stress/strain states employed for foot and footwear biomechanics evaluations.

Spatial-Temporal Changes of Mechanical Microenvironment in Skin Wounds During Negative Pressure Wound Therapy

Cell migration, proliferation, and differentiation are regulated by mechanical cues during skin wound healing. Negative pressure wound therapy (NPWT) reduces the healing period by optimizing the mechanical microenvironment of the wound bed. Under NPWT, it remains elusive how the mechanical microenvironment (e.g., stiffness, strain gradients) changes both in time and space during wound healing. To illustrate this, the healing time of full-thickness skin wounds under NPWT, with pressure settings ranging from -50 to -150 mm Hg, were evaluated and compared with gauze dressing treatments (control group), and three-dimensional finite element models of full-thickness skin wounds on days 1 and 5 after treatment were developed on the basis of MR 3D imaging data. Shear wave elastography (SWE) was applied to detect the stiffness of wound soft tissue on days 1 and 5, and nonlinear finite element analysis (FEA) was used to represent the spatial-temporal environment of the 3D strain field of the wound under NPWT vs the control group. Compared with the control group, NPWT with -50, -80, and -125 mm Hg promoted wound healing. SWE showed that the elastic modulus of wounded skin increased during healing. Meanwhile, the elastic modulus in wounded skin under NPWT was significantly smaller than in the control group. Strain and its gradient decreased under NPWT during wound healing, while no significant change was observed in the control group. This study, which is based on MR 3D imaging, shear wave elastography, and nonlinear FEA, provides an in-depth understanding of changes of the skin mechanical microenvironment under NPWT in the time-space dimension and the associated wound healing.

Biomechanical evaluation of the first ray in pre-/post-operative hallux valgus: A comparative study

BACKGROUND

Deformity of the first ray in hallux valgus patient has been deemed to mainly contribute to instability of the metatarsophalangeal joint. However, it is not clear whether the fixation of the distal osteotomy fragment and transposition of the sesamoid represent the best method for hallux valgus treatment. The aim of this study was to examine how postoperative hallux valgus osteotomy affects the stability of the first ray.

METHODS

To accurately investigate the biomechanical behavior of the first ray in pre-/postoperative hallux valgus patients, we described the relative displacement and stress distribution of the first metatarsal bone and sesamoid by imageology, test measurement and foot finite element model.

FINDINGS

Compared with the preoperative hallux valgus, the plantar pressure decreased by 47.8% and was redistributed on second metatarsal region. The peak stress and relative displacement of the distal osteotomy fragment increased by +55.7% and -59.9%, respectively. The movement of this component shifted toward the positive sagittal axis direction. In addition, the relative displacement of sesamoid decreased by 87.4% (0.18 mm) in vertical axis direction and the stress was also redistributed on medial and lateral region. Moreover, the strain of the medial main ligament was more favorable to reconstruct function of the first ray.

INTERPRETATION

The findings showed that the osteotomy method was helpful for stability of the first ray. This would provide the stability suggestions for postoperative hallux valgus fixation and guide further rehabilitation.

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.

Quantification of Internal Stress-Strain Fields in Human Tendon: Unraveling the Mechanisms that Underlie Regional Tendon Adaptations and Mal-Adaptations to Mechanical Loading and the Effectiveness of Therapeutic Eccentric Exercise

By virtue of their anatomical location between muscles and bones, tendons make it possible to transform contractile force to joint rotation and locomotion. However, tendons do not behave as rigid links, but exhibit viscoelastic tensile properties, thereby affecting the length and contractile force in the in-series muscle, but also storing and releasing elastic stain energy as some tendons are stretched and recoiled in a cyclic manner during locomotion. In the late 90s, advancements were made in the application of ultrasound scanning that allowed quantifying the tensile deformability and mechanical properties of human tendons in vivo. Since then, the main principles of the ultrasound-based method have been applied by numerous research groups throughout the world and showed that tendons increase their tensile stiffness in response to exercise training and chronic mechanical loading, in general, by increasing their size and improving their intrinsic material. It is often assumed that these changes occur homogenously, in the entire body of the tendon, but recent findings indicate that the adaptations may in fact take place in some but not all tendon regions. The present review focuses on these regional adaptability features and highlights two paradigms where they are particularly evident: (a) Chronic mechanical loading in healthy tendons, and (b) tendinopathy. In the former loading paradigm, local tendon adaptations indicate that certain regions may “see,” and therefore adapt to, increased levels of stress. In the latter paradigm, local pathological features indicate that certain tendon regions may be “stress-shielded” and degenerate over time. Eccentric exercise protocols have successfully been used in the management of tendinopathy, without much sound understanding of the mechanisms underpinning their effectiveness. For insertional tendinopathy, in particular, it is possible that the effectiveness of a loading/rehabilitation protocol depends on the topography of the stress created by the exercise and is not only reliant upon the type of muscle contraction performed. To better understand the micromechanical behavior and regional adaptability/mal-adaptability of tendon tissue it is important to estimate its internal stress-strain fields. Recent relevant advancements in numerical techniques related to tendon loading are discussed.

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

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

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

Background

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

Methods

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

Results

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

Discussion

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