Determination of elastomeric foam parameters for simulations of complex loading

Machine Learning Algorithms for Predicting Mechanical Stiffness of Lattice Structure-Based Polymer Foam

Polymer foams are extensively utilized because of their superior mechanical and energy-absorbing capabilities; however, foam materials of consistent geometry are difficult to produce because of their random microstructure and stochastic nature. Alternatively, lattice structures provide greater design freedom to achieve desired material properties by replicating mesoscale unit cells. Such complex lattice structures can only be manufactured effectively by additive manufacturing or 3D printing. The mechanical properties of lattice parts are greatly influenced by the lattice parameters that define the lattice geometries. To study the effect of lattice parameters on the mechanical stiffness of lattice parts, 360 lattice parts were designed by varying five lattice parameters, namely, lattice type, cell length along the X, Y, and Z axes, and cell wall thickness. Computational analyses were performed by applying the same loading condition on these lattice parts and recording corresponding strain deformations. To effectively capture the correlation between these lattice parameters and parts' stiffness, five machine learning (ML) algorithms were compared. These are Linear Regression (LR), Polynomial Regression (PR), Decision Tree (DT), Random Forest (RF), and Artificial Neural Network (ANN). Using evaluation metrics such as mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE), all ML algorithms exhibited significantly low prediction errors during the training and testing phases; however, the Taylor diagram demonstrated that ANN surpassed other algorithms, with a correlation coefficient of 0.93. That finding was further supported by the relative error box plot and by comparing actual vs. predicted values plots. This study revealed the accurate prediction of the mechanical stiffness of lattice parts for the desired set of lattice parameters.

Effective and clinically relevant optimisation of cushioning stiffness to maximise the offloading capacity of diabetic footwear

INTRODUCTION

Optimising the cushioning stiffness of diabetic footwear/orthoses can significantly enhance their offloading capacity. This study explores whether optimum cushioning stiffness can be predicted using simple demographic and anthropometric parameters.

METHODS

Sixty-nine adults with diabetes and loss of protective sensation in their feet were recruited for this cross-sectional observational study. In-shoe plantar pressure was measured using Pedar® for a neutral diabetic shoe (baseline) and after adding cushioning footbeds of varying stiffness. The cushioning stiffness that achieved maximum offloading was identified for each participant. The link between optimum cushioning stiffness and plantar loading or demographic/anthropometric parameters was assessed using multinomial regression.

RESULTS

People with higher baseline plantar loading required stiffer cushioning materials for maximum offloading. Using sex, age, weight, height, and shoe-size as covariates correctly predicted the cushioning stiffness that minimised peak pressure across the entire foot, or specifically in the metatarsal heads, midfoot and heel regions in 70%, 72%, 83% and 66% of participants respectively.

CONCLUSIONS

Increased plantar loading is associated with the need for stiffer cushioning materials for maximum offloading. Patient-specific optimum cushioning stiffness can be predicted using five simple demographic/anthropometric parameters. These results open the way for methods to optimise cushioning stiffness as part of clinical practice.

Predicting Forefoot-Orthosis Interactions in Rheumatoid Arthritis Using Computational Modelling

Foot orthoses are prescribed to reduce forefoot plantar pressures and pain in people with rheumatoid arthritis. Computational modelling can assess how the orthoses affect internal tissue stresses, but previous studies have focused on a single healthy individual. This study aimed to ascertain whether simplified forefoot models would produce differing biomechanical predictions at the orthotic interface between people with rheumatoid arthritis of varying severity, and in comparison to a healthy control. The forefoot models were developed from magnetic resonance data of 13 participants with rheumatoid arthritis and one healthy individual. Measurements of bony morphology and soft tissue thickness were taken to assess deformity. These were compared to model predictions (99th% shear strain and plantar pressure, max. pressure gradient, volume of soft tissue over 10% shear strain), alongside clinical data including body mass index and Leeds Foot Impact Scale–Impairment/Footwear score (LFIS-IF). The predicted pressure and shear strain for the healthy participant fell at the lower end of the rheumatoid models’ range. Medial first metatarsal head curvature moderately correlated to all model predicted outcomes (0.529 < r < 0.574, 0.040 < p < 0.063). BMI strongly correlated to all model predictions except pressure gradients (0.600 < r < 0.652, p < 0.05). There were no apparent relationships between model predictions and instances of bursae, erosion and synovial hypertrophy or LFIS-IF score. The forefoot models produced differing biomechanical predictions between a healthy individual and participants with rheumatoid arthritis, and between individuals with rheumatoid arthritis. Models capable of predicting subject specific biomechanical orthotic interactions could be used in the future to inform more personalised devices to protect skin and soft tissue health. While the model results did not clearly correlate with all clinical measures, there was a wide range in model predictions and morphological measures across the participants. Thus, the need for assessment of foot orthoses across a population, rather than for one individual, is clear.

A novel concept for low-cost non-electronic detection of overloading in the foot during activities of daily living

Identifying areas in the sole of the foot which are routinely overloaded during daily living is extremely important for the management of the diabetic foot. This work showcases the feasibility of reliably detecting overloading using a low-cost non-electronic technique. This technique uses thin-wall structures that change their properties differently when they are repeatedly loaded above or below a tuneable threshold. Flexible hexagonal thin-wall structures were produced using three-dimensional printing, and their mechanical behaviour was assessed before and after repetitive loading at different magnitudes. These structures had an elastic mechanical behaviour until a critical pressure (P _crit = 252 kPa ± 17 kPa) beyond which they buckled. Assessing changes in stiffness after simulated use enabled the accurate detection of whether a sample was loaded above or below P _crit (sensitivity = 100%, specificity = 100%), with the overloaded samples becoming significantly softer. No specific P _crit value was targeted in this study. However, finite-element modelling showed that P _crit can be easily raised or lowered, through simple geometrical modifications, to become aligned with established thresholds for overloading (e.g. 200 kPa) or to assess overloading thresholds on a patient-specific basis. Although further research is needed, the results of this study indicate that clinically relevant overloading could indeed be reliably detected without the use of complex electronic in-shoe sensors.

Subject Specific Optimisation of the Stiffness of Footwear Material for Maximum Plantar Pressure Reduction

Current selection of cushioning materials for therapeutic footwear and orthoses is based on empirical and anecdotal evidence. The aim of this investigation is to assess the biomechanical properties of carefully selected cushioning materials and to establish the basis for patient-specific material optimisation. For this purpose, bespoke cushioning materials with qualitatively similar mechanical behaviour but different stiffness were produced. Healthy volunteers were asked to stand and walk on materials with varying stiffness and their capacity for pressure reduction was assessed. Mechanical testing using a surrogate heel model was employed to investigate the effect of loading on optimum stiffness. Results indicated that optimising the stiffness of cushioning materials improved pressure reduction during standing and walking by at least 16 and 19% respectively. Moreover, the optimum stiffness was strongly correlated to body mass (BM) and body mass index (BMI), with stiffer materials needed in the case of people with higher BM or BMI. Mechanical testing confirmed that optimum stiffness increases with the magnitude of compressive loading. For the first time, this study provides quantitative data to support the importance of stiffness optimisation in cushioning materials and sets the basis for methods to inform optimum material selection in the clinic.

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.

Effect of the skin layer on the overall behavior of closed-cell polyethylene foam sheets

This article presents an experimental investigation of the effect of the skin layer on the mechanical behavior of a closed-cell polymeric foam material. The skin layer is a thin layer with increased density due to the manufacturing processes, which results in inhomogeneity. The skin-layer effect is investigated by comparing the stretch-stress characteristics of specimens with and without this skin layer on a particular closed-cell polyethylene foam sheet. The characteristics were recorded via uniaxial tension and compression tests, respectively, in all principal manufacturing directions. Thus, the skin-layer effect can be obtained by analyzing the recorded data points, which are also presented. The skin-layer-free specimens are prepared with a particularly designed assembly in accordance with the ASTM standards.

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

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

Manufacturing and finite element assessment of a novel pressure reducing insole for Diabetic Neuropathic patients

Diabetes is one of the metabolic diseases. Uncontrolled diabetes can lead to diabetic foot ulcers and if it was not treated would lead to amputation. Foot ulcers can be prevented by using suitable insoles which are made of appropriate material and geometrically designed by constituent layers. In this study, single-layer and three-layer insoles have been compared during static and dynamic loading. The selected materials were silicone gel (SG), plastazote foam (PLZ), polyfoam (PF) and ethyl vinyl acetate foam (EVA). Four single-layer and 18 combinations of three-layer insoles were selected. Materials behaviors were determined by using a uniaxial pressure test. The description of stress and strain is obtained by using the model of three dimensional nonlinear Finite Element Method (FEM). Then samples were tested by using commercially available plantar pressure measurement system. The FEM results showed that the SG and PLZ insoles are more appropriate compared to single-layer insoles. The combinations of PLZ, SG and EVA (from top to bottom) are recognized as the best between three-layer insoles. Also the best three-layer insole is more effective in promoting a favourable stress and strain distribution than single-layer insoles, especially in dynamic mode. According to simulation results, three-layer insole decreases stress concentration by 9%. Also experimental tests showed that using three-layer insole decreases plantar pressure by 63% compared to barefoot condition bare foot.

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

Accurate prediction of plantar shear stress and internal stress in the soft tissue layers of the foot using finite element models would provide valuable insight into the mechanical etiology of neuropathic foot ulcers. Accurate prediction of the internal stress distribution using finite element models requires that realistic descriptions of the material properties of the soft tissues are incorporated into the model. Our investigation focused on the creation of a novel three-dimensional (3D) finite element model of the forefoot with multiple soft tissue layers (skin, fat pad, and muscle) and the development of an inverse finite element procedure that would allow for the optimization of the nonlinear elastic coefficients used to define the material properties of the skin muscle and fat pad tissue layers of the forefoot based on a Ogden hyperelastic constitutive model. Optimization was achieved by comparing deformations predicted by finite element models to those measured during an experiment in which magnetic resonance imaging (MRI) images were acquired while the plantar surface forefoot was compressed. The optimization procedure was performed for both a model incorporating all three soft tissue layers and one in which all soft tissue layers were modeled as a single layer. The results indicated that the inclusion of multiple tissue layers affected the deformation and stresses predicted by the model. Sensitivity analysis performed on the optimized coefficients indicated that small changes in the coefficient values (±10%) can have rather large impacts on the predicted nominal strain (differences up to 14%) in a given tissue layer.