Estimating the material properties of heel pad sub-layers using inverse Finite Element Analysis

Identification of constitutive materials of bi-layer soft tissues from multimodal indentations

The personalisation of finite element models is an important problem in the biomechanical fields where subject-specific analyses are fundamental, particularly in studying soft tissue mechanics. The personalisation includes the choice of the constitutive law of the model's material, as well as the choice of the material parameters. In vivo identification of the material properties of soft tissues is challenging considering the complex behaviour of soft tissues that are, among other things, non-linear hyperelastic and heterogeneous. Hybrid experimental-numerical methods combining in vivo indentations and inverse finite element analyses are common to identify these material parameters. Yet, the uniqueness and the uncertainty of the multi-material hyperelastic model have not been evaluated. This study presents a sensitivity analysis performed on synthetic indentation data to investigate the identification uncertainties of the material parameters in a bi-material thigh phantom. Synthetic numerical data, used to replace experimental measurements, considered several measurement modalities: indenter force and displacement, stereo-camera 3D digital image correlation of the indented surface, and ultrasound B-mode images. A finite element model of the indentation was designed with either Ogden-Moerman or Mooney-Rivlin constitutive laws for both materials. The parameters' identifiability (i.e. the possibility of converging to a unique parameter set within an acceptable margin of error) was assessed with various cost functions formulated using the different synthetic data sets. The results underline the need for multiple experimental modalities to reduce the uncertainty of the identified parameters. Additionally, the experimental error can impede the identification of a unique parameter set, and the cost function depends on the constitutive law. This study highlights the need for sensitivity analyses before the design of the experimental protocol. Such studies can also be used to define the acceptable range of errors in the experimental measurement. Eventually, the impact of the evaluated uncertainty of the identified parameters should be further investigated according to the purpose of the finite element modelling.

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 Parameters of Leather in Relation to Technological Processing of the Footwear Uppers

This paper aimed to define two critical mechanical properties of leather—Young’s modulus and Poisson ratio—essential to the virtual simulation of the behaviour of the footwear uppers against the manufacturing operations of stitching and perforating. The following technological aspects were considered to analyse the materials from manufacturing conditions point of view: the number of layers (one layer and two layers), the nature of the materials used for uppers subgroups (calfskin-outer upper, sheep leather-lining, polyester knitted fabric-lining), the overlapping width in the stitching area, the number of parallel stitches (single stitch and double stitch), the punching interval and the type of perforations (simple and with eyelets), resulting in nine kinds of samples. Furthermore, the elasticity (Young’s modulus) and lateral contraction (Poisson’s ratio) were calculated during the tensile strength analysis performed on the SATRA STM 466 equipment. Both mechanical parameters are essential to simulate the behaviour of the virtual footwear prototypes in various conditions.

3D printed auxetic heel pads for patients with diabetic mellitus

More than 422 million people worldwide suffered from diabetes mellitus (DM) in 2021. Diabetic foot is one the most critical complications resultant of DM. Foot ulceration and infection are frequently arisen, which are associated with changes in the mechanical properties of the plantar soft tissues, peripheral arterial disease, and sensory neuropathy. Diabetic insoles are currently the mainstay in reducing the risk of foot ulcers by reducing the magnitude of the pressure on the plantar Here, we propose a novel pressure relieving heel pad based on a circular auxetic re-entrant honeycomb structure by using three-dimensional (3D) printing technology to minimize the pressure on the heel, thus reducing the occurrence of foot ulcers. Finite element models (FEMs) are developed to evaluate the structural changes of the developed circular auxetic structure upon exertion of compressive forces. Moreover, the effects of the internal angle of the re-entrant structure on the peak contact force and the mean pressure acting on the heel as well as the contact area between the heel and the pads are investigated through a finite element analysis (FEA). Based on the result from the validated FEMs, the proposed heel pad with an auxetic structure demonstrates a distinct reduction in the peak contact force (∼10%) and the mean pressure (∼14%) in comparison to a conventional diabetic insole (PU foam). The characterized result of the designed circular auxetic structure not only provides new insights into diabetic foot protection, but also the design and development of various impact resistance products.

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.

Biomechanical Effects of Plastic Heel Cup on Plantar Fasciitis Patients Evaluated by Ultrasound Shear Wave Elastography

The plastic heel cup has been adopted to treat plantar heel problems for years. However, its mechanisms and biomechanical effects are yet to be fully understood. The purpose of this study was to investigate the effects of the plastic heel cup on the microchamber and macrochamber layers of the heel pad by comparing the stiffness (in terms of the shear wave speed) and thickness of these two layers with and without a plastic heel cup during static standing. Fifteen patients with unilateral plantar fasciitis were recruited. The shear wave speed and thickness of the microchamber and microchamber layers of each symptomatic heel pad during standing measured by ultrasound shear wave elastography were compared between conditions with and without a plastic heel cup. It was found that a plastic heel cup reduced the shear wave speed of the microchamber layer to 55.5% and increased its thickness to 137.5% compared with the condition without a plastic heel cup. For the microchamber layer, the shear wave speed was reduced to 89.7%, and thickness was increased to 113.6% compared with the condition without a plastic heel cup. The findings demonstrate that a plastic heel cup can help to reduce the stiffness and increase the thickness for both layers of the heel pad during standing, suggesting that the mechanism of a plastic heel cup, and its resulting biomechanical effect, is to reduce the internal stress of the heel pad by increasing its thickness through confinement.

An in vivo model for overloading-induced soft tissue injury

This proof-of-concept study demonstrates that repetitive loading to the pain threshold can safely recreate overloading-induced soft tissue damage and that localised tissue stiffening can be a potential marker for injury. This concept was demonstrated here for the soft tissue of the sole of the foot where it was found that repeated loading to the pain threshold led to long-lasting statistically significant stiffening in the overloaded areas. Loading at lower magnitudes did not have the same effect. This method can shed new light on the aetiology of overloading injury in the foot to improve the management of conditions such as diabetic foot ulceration and heel pain syndrome. Moreover, the link between overloading and tissue stiffening, which was demonstrated here for the first time for the plantar soft tissue, opens the way for an assessment of overloading thresholds that is not based on the subjective measurement of pain thresholds.

Ultrasonic Evaluation of the Heel Fat Pad under Weight-Bearing Conditions Using a Polymethylpentene Resin Plate: Part 1

To evaluate the two-layer structure of the heel fat pad (HFP) from non-weight-bearing to full-weight-bearing conditions, we developed an instrument that assesses these changes from the sole through a polymethylpentene resin plate (PMP) with ultrasonography. For actual use, we investigated the influence on measured values and ultrasonogram appearance by interposing the PMP. Additionally, as the PMP may be bent under weight-bearing conditions, its influence on the measured values was investigated. First, two examiners measured the distances inside the phantom with and without a PMP. Second, ultrasonograms were obtained from 40 healthy adults with and without a PMP, and the thicknesses of the whole layer and the two layers of the HFP were measured using the same ultrasonogram. For each experiment, reproducibility was investigated. Third, the distances inside the phantom were measured and compared through the bent PMP, which models the weight-bearing condition, and the flat PMP. The reproducibility of the measurements was equivalent with and without the PMP interposed. Potential bias in measured values arising from deformation of PMP under weight-bearing conditions was not detected. Overall, the PMP's interposition and the bending of the PMP might not influence the measured values and reproducibility of the measurements.

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.

Finite element-based method for determining an optimal offloading design for treating and preventing heel ulcers

Diabetic heel ulceration, a serious, destructive, and costly complication of diabetes, is often treated by custom-made offloading footwear. One common offloading device is a custom-made insole designed with a hole under the damaged site that is intended to reduce local mechanical loads on the ulcer. However, current devices do not take into account the increasing loads at the wound peripheries, and quantitative assessments and scientific guidelines for the optimal design of the offloading hole are lacking. Here, we develop a novel method to determine the volumetric exposure to mechanical loading of a human heel, at two volume of interests (VOIs) during walking in 150 different finite-element footwear configurations. We defined the two VOIs as (1) the area of the heel soft tissues typically at high risk of ulceration, and (2) the soft tissues surrounding the high risk area. For all model variants, three hole-geometry parameters were defined: (1) radius, (2) radius of curvature (ROC) and (3) depth. We found two combinations of the offloading parameters which minimize heel loads in both VOIs. The first is with a large offloading radius, large ROC and large depth, whereas the second is with a large offloading radius, large depth but relatively small ROC. Our novel practical scientific analysis method, that takes into account the ulcer site as well as the peripheral area, has the potential to optimize development of offloading solutions by streamlining the examination of their biomechanical efficiency, and thus may revolutionize prevention and treatment of diabetic ulcers at any foot location.

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.

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.

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.