Parameter identification of hyperelastic material properties of the heel pad based on an analytical contact mechanics model of a spherical indentation

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.

Effects of extreme cyclic loading on the cushioning performance of human heel pads under engineering test condition

Human heel pads commonly undergo cyclic loading during daily activities. Low cyclic loadings such as daily human walking tend to have less effect on the mechanical properties of heel pads. However, the impact of cyclic loading on cushion performance, a vital biomechanical property of heel pads, under engineering test condition remains unexplored. Herein, dynamic mechanical measurements and finite element (FE) simulations were employed to explore this phenomenon. It was found that the wavy collagen fibers in the heel pad will be straightened under cycle compression loading, which resulted in increased stiffness of the heel pad. The stiffness of the heel pads demonstrated an inclination to escalate over a span of 50,000 loading cycles, consequently resulting in a corresponding increase in peak impact force over the same loading cycles. Sustained cyclic loading has the potential to result in the fracturing of the straightened collagen fibers, this collagen breakage may diminish the stiffness of the heel pad, leading to a reduction in peak impact force. This work enhances understanding of the biomechanical functions of human heel pad and may provide potential inspirations for the innovative development of healthcare devices for foot complex.

A review of the characterizations of soft tissues used in human body modeling: Scope, limitations, and the path forward

Soft tissue material properties are vital to human body models that evaluate interactions between the human body and its environment. Such models evaluate internal stress/strain responses in soft tissues to investigate issues like pressure injuries. Numerous constitutive models and parameters have been used to represent mechanical behavior of soft tissues in biomechanical models under quasi-static loading. However, researchers reported that generic material properties cannot accurately represent specific target populations due to large inter-individual variability. Two challenges that exist are experimental mechanical characterization and constitutive modeling of biological soft tissues and personalization of constitutive parameters using non-invasive, non-destructive bedside testing methods. It is imperative to understand the scope and appropriate applications for reported material properties. Thus, the goal of this paper was to compile studies from which soft tissue material properties were obtained and categorize them by source of tissue samples, methods used to quantify deformation, and material models used to describe tissues. The collected studies displayed wide ranges of material properties, and factors that affected the properties included whether tissue samples were in vivo or ex vivo, from humans or animals, the body region tested, body position during in vivo studies, deformation measurements, and material models used to describe tissues. Because of the factors that affected reported material properties, it is clear that much progress has been made in understanding soft tissue responses to loading, yet there is a need to broaden the scope of reported soft tissue material properties and better match reported properties to appropriate human body models.

Comparative Functional Morphology of Human and Chimpanzee Feet Based on Three-Dimensional Finite Element Analysis

To comparatively investigate the morphological adaptation of the human foot for achieving robust and efficient bipedal locomotion, we develop three-dimensional finite element models of the human and chimpanzee feet. Foot bones and the outer surface of the foot are extracted from computer tomography images and meshed with tetrahedral elements. The ligaments and plantar fascia are represented by tension-only spring elements. The contacts between the bones and between the foot and ground are solved using frictionless and Coulomb friction contact algorithms, respectively. Physiologically realistic loading conditions of the feet during quiet bipedal standing are simulated. Our results indicate that the center of pressure (COP) is located more anteriorly in the human foot than in the chimpanzee foot, indicating a larger stability margin in bipedal posture in humans. Furthermore, the vertical free moment generated by the coupling motion of the calcaneus and tibia during axial loading is larger in the human foot, which can facilitate the compensation of the net yaw moment of the body around the COP during bipedal locomotion. Furthermore, the human foot can store elastic energy more effectively during axial loading for the effective generation of propulsive force in the late stance phase. This computational framework for a comparative investigation of the causal relationship among the morphology, kinematics, and kinetics of the foot may provide a better understanding regarding the functional significance of the morphological features of the human foot.

In vivo soft tissue compressive properties of the human hand

Background/Purpose

Falls onto outstretched hands are the second most common sports injury and one of the leading causes of upper extremity injury. Injury risk and severity depends on forces being transmitted through the palmar surface to the upper extremity. Although the magnitude and distribution of forces depend on the soft tissue response of the palm, the in vivo properties of palmar tissue have not been characterized. The purpose of this study was to characterize the large deformation palmar soft tissue properties.

Methods

In vivo dynamic indentations were conducted on 15 young adults (21–29 years) to quantify the soft tissue characteristics of over the trapezium. The effects of loading rate, joint position, tissue thickness and sex on soft tissue responses were assessed.

Results

Energy absorbed by the soft tissue and peak force were affected by loading rate and joint angle. Energy absorbed was 1.7–2.8 times higher and the peak force was 2–2.75 times higher at high rate loading than quasistatic rates. Males had greater energy absorbed than females but not at all wrist positions. Damping characteristics were the highest in the group with the thickest soft tissue while damping characteristics were the lowest in group with the thinnest soft tissues.

Conclusion

Palmar tissue response changes with joint position, loading rate, sex, and tissue thickness. Accurately capturing these tissue responses is important for developing effective simulations of fall and injury biomechanics and assessing the effectiveness of injury prevention strategies.

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.

Investigation of the relationship between localized cumulative stress and plantar tissue stiffness in healthy individuals using the in-vivo indentation technique

This study was conducted to determine whether prolonged and repetitive exercise stiffens the plantar soft tissue. Healthy female subjects in their early 20s with a similar body mass index but different majors (13 engineers (controls) and 13 ballet dancers) were recruited. Tissue thickness was measured using ultrasound, while peak stress, stress distribution, and center of pressure were obtained Zebris^® pressure mat. Stiffness was evaluated using a custom-made tissue indentation system. F-test and independent sample T-test were used to determine significant differences between the two groups. No significance was found in the thickness of the second sub-metatarsal head (MTH) and heel between the two groups. In the second sub-MTH, the ballet group showed higher peak stress, loading rate, and stiffness than the control group. Conversely, in the heel region, all the results were higher for the control group. The results of this study quantify the impact of exercise on the stiffness of plantar soft tissue and confirm that even healthy individuals who do prolonged and repetitive exercise have stiffer plantar soft tissue.

Phenomenological tissue fracture modeling for an Endoscopic Sinus and Skull Base Surgery training system based on experimental data

The ideal simulator for Endoscopic Sinus and Skull Base Surgery (ESSS) training must be supported by a physical model and provide repetitive behavior in a controlled environment. Development of realistic tissue models is a key part of ESSS virtual reality (VR)-based surgical simulation. Considerable research has been conducted to address haptic or force feedback and propose a phenomenological tissue fracture model for sino-nasal tissue during surgical tool indentation. Mechanical properties of specific sino-nasal regions of the sheep head have been studied in various indentation and relaxation experiments. Tool insertion at different indentation rates into coronal orbital floor (COF) tissue is modeled as a sequence of three events: deformation, fracture, and cutting. The behavior in the deformation phase can be characterized using a non-linear, rate-dependent modified Kelvin-Voigt model. A non-linear model for tissue behavior prior to the fracture point is presented. The overall model shows a non-positive dependency of maximum force on tool indentation rate, which indicates faster tool insertion velocity decreases the maximum final fracture force. The tissue cutting phase has been modeled to characterize the force necessary to slice through the COF. The proposed model in this study can help develop VR-based ESSS base simulators in otolaryngology and ophthalmology surgeries. Such simulators are useful in preoperative planning, accurate surgical simulation, intelligent robotic assistance, and treatment applications.

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.