The quasi-linear viscoelastic properties of diabetic and non-diabetic plantar soft tissue

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.

The effect of diabetes and tissue depth on adipose chamber size and plantar soft tissue features

BACKGROUND

Plantar ulceration is a serious complication of diabetes. However, the mechanism of injury initiating ulceration remains unclear. The unique structure of the plantar soft tissue includes superficial and deep layers of adipocytes contained in septal chambers, however, the size of these chambers has not been quantified in diabetic or non-diabetic tissue. Computer-aided methods can be leveraged to guide microstructural measurements and differences with disease status.

METHODS

Adipose chambers in whole slide images of diabetic and non-diabetic plantar soft tissue were segmented with a pre-trained U-Net and area, perimeter, and minimum and maximum diameter of adipose chambers were measured. Whole slide images were classified as diabetic or non-diabetic using the Axial-DeepLab network, and the attention layer was overlaid on the input image for interpretation.

RESULTS

Non-diabetic deep chambers were 90 %, 41 %, 34 %, and 39 % larger in area (26,954 ± 2428 µm2 vs 14,157 ± 1153 µm2), maximum (277 ± 13 µm vs 197 ± 8 µm) and minimum (140 ± 6 µm vs 104 ± 4 µm) diameter, and perimeter (405 ± 19 µm vs 291 ± 12 µm), respectively, than the superficial (p < 0.001). However, there was no significant difference in these parameters in diabetic specimens (area 18,695 ± 2576 µm2 vs 16627 ± 130 µm2, maximum diameter 221 ± 16 µm vs 210 ± 14 µm, minimum diameter 121 ± 8 µm vs 114 ± 7 µm, perimeter 341 ± 24 µm vs 320 ± 21 µm). Between diabetic and non-diabetic chambers, only the maximum diameter of the deep chambers differed (221 ± 16 µm vs 277 ± 13 µm). The attention network achieved 82 % accuracy on validation, but the attention resolution was too coarse to identify meaningful additional measurements.

CONCLUSIONS

Adipose chamber size differences may provide a basis for plantar soft tissue mechanical changes with diabetes. Attention networks are promising tools for classification, but additional care is required when designing networks for identifying novel features.

DATA AVAILABILITY

All images, analysis code, data, and/or other resources required to replicate this work are available from the corresponding author upon reasonable request.

Does the Heel’s Dissipative Energetic Behavior Affect Its Thermodynamic Responses During Walking?

Most of the terrestrial legged locomotion gaits, like human walking, necessitate energy dissipation upon ground collision. In humans, the heel mostly performs net-negative work during collisions, and it is currently unclear how it dissipates that energy. Based on the laws of thermodynamics, one possibility is that the net-negative collision work may be dissipated as heat. If supported, such a finding would inform the thermoregulation capacity of human feet, which may have implications for understanding foot complications and tissue damage. Here, we examined the correlation between energy dissipation and thermal responses by experimentally increasing the heel’s collisional forces. Twenty healthy young adults walked overground on force plates and for 10 min on a treadmill (both at 1.25 ms−1) while wearing a vest with three different levels of added mass (+0%, +15%, &amp; +30% of their body mass). We estimated the heel’s work using a unified deformable segment analysis during overground walking. We measured the heel’s temperature immediately before and after each treadmill trial. We hypothesized that the heel’s temperature and net-negative work would increase when walking with added mass, and the temperature change is correlated with the increased net-negative work. We found that walking with +30% added mass significantly increased the heel’s temperature change by 0.72 ± 1.91 ℃ (p = 0.009) and the magnitude of net-negative work (extrapolated to 10 min of walking) by 326.94 ± 379.92 J (p = 0.005). However, we found no correlation between the heel’s net-negative work and temperature changes (p = 0.277). While this result refuted our second hypothesis, our findings likely demonstrate the heel’s dynamic thermoregulatory capacity. If all the negative work were dissipated as heat, we would expect excessive skin temperature elevation during prolonged walking, which may cause skin complications. Therefore, our results likely indicate that various heat dissipation mechanisms control the heel’s thermodynamic responses, which may protect the health and integrity of the surrounding tissue. Also, our results indicate that additional mechanical factors, besides energy dissipation, explain the heel’s temperature rise. Therefore, future experiments may explore alternative factors affecting thermodynamic responses, including mechanical (e.g., sound &amp; shear-stress) and physiological mechanisms (e.g., sweating, local metabolic rate, &amp; blood flow).

Which plantar region can predict peripheral arterial disease by using laser speckleflowgraphy?

Laser speckle flowgraphy (LSFG) is a new device that can measure skin blood flow and capture the movement of erythrocytes. However, there are a few reports on the use of LSFG to estimate skin blood flow, especially in the lower extremities. We aimed to compare plantar skin blood flow between patients with and without peripheral arterial disease (PAD) to discern the extent to which LSFG could accurately predict PAD. We prospectively measured the plantar skin blood flow in 28 patients with PAD and 37 participants without PAD at two hospitals from 2017 to 2021, using the ankle-brachial index (ABI) and LSFG. We partitioned the plantar into 12 parts: digits 1-5, medial metatarsal, middle metatarsal, lateral metatarsal, medial arch, middle arch, lateral arch, and heel, and compared the difference between the two groups and the area under the curve (AUC) of each point. Statistical analyses were performed to determine the sensitivity, specificity, false-positive rate, and false-negative rate at high accuracy points of AUC and ABI. There was a significant difference among the 12 points between the two groups, and the ratio using toe 1 and toe 5 was highly accurate. The ratio using toe 1 indicated higher sensitivity (89 vs. 82%), higher false-positive rate (22 vs. 4%), lower specificity (81 vs. 97%), and an equivalent false-negative rate (9 vs. 12%) to that of the ABI. These findings could facilitate the use of LSFG to estimate the skin blood flow condition in the plantar skin. Our results indicate that measuring toe 1 using LSFG could be used to somewhat assess PAD.

The compressive, shear, biochemical, and histological characteristics of diabetic and non-diabetic plantar skin are minimally different

Diabetes is associated with lower limb co-morbidities, including ulceration and subsequent amputation. As a systemic disease, diabetes affects the microstructure of soft tissues, and material microstructural changes are known to affect the macroscale mechanics. However, the associations between diabetes-related disruptions to essential microstructural components and mechanical changes in plantar skin with diabetes has not been thoroughly characterized. Plantar skin specimens were collected from four diabetic and eight non-diabetic donors at six plantar locations (hallux; first, third, and fifth metatarsals; lateral midfoot; calcaneus) from matched pairs. Mechanical testing was performed on fresh frozen specimens from one foot, and histomorphological measurement and biochemical quantification were performed on specimens from the other foot. Mechanical (compressive and shear moduli and viscoelastic slopes) and biochemical/histological (total quantity of collagen and elastin; dermal and epidermal thickness) parameters were correlated using linear mixed effects regression. There were no significant differences by disease state. Skin thicknesses were positively correlated with initial compression modulus and all three shear moduli. The final compressive modulus was significantly lower at the third metatarsal than the fifth metatarsal, lateral midfoot, and calcaneus, while the final shear modulus was significantly higher at the calcaneus than at the hallux, first, and third metatarsals. Epidermal thickness was significantly higher at the calcaneus compared to all other locations. While differences were not significant by disease state, the strong differences by locations and significant but weak correlations between skin thickness and mechanics can inform future research to understand the mechanism of ulcer formation in the diabetic foot.

The Structural Effects of Diabetes on Soft Tissues: A Systematic Review

Hyperglycemia, which is associated with diabetes, increases the production of advanced glycation end products. Advanced glycation end products lead to the structural degradation of soft tissues. The structural degradation of diabetic soft tissues has been investigated in humans, rodents, and canines. Therefore, the objective of this review is to unify the various contributions to diabetes research through the mechanical properties and geometric characteristics of soft tissues. A systematic review was performed and identified the effects of diabetes on mechanical and geometric properties of soft tissues via experimental testing or in vivo - driven finite element analysis. The literature concludes that diabetes contributes to major structural changes in soft tissues but does not cause the same structural changes in all soft tissues (e.g., diabetic tendons are weaker and diabetic plantar tissues are tougher). Diabetes stiffens and toughens soft tissues, thus altering viscoelastic behavior (e.g., poor strain and stress response). However, diabetes management routines can prevent or minimize the effects of diabetes on the mechanical and geometric properties of soft tissues. Unification of the structural effects of diabetes on soft tissues will contribute to the pathophysiology of diabetes.

Histomorphological and biochemical properties of plantar soft tissue in diabetes

BACKGROUND

Diabetes results in pathophysiological changes, leading to tissue that is unable to withstand and adapt to the same loads, resulting in breakdown. Certain locations are more susceptible to breakdown, yet differences between locations are largely not well understood. The authors performed a histological and biochemical analysis of isolated plantar adipose tissue at six relevant locations.

METHODS

Tissue from six plantar locations (hallux, first, third and fifth metatarsal heads, lateral midfoot and calcaneus) was taken from fresh cadaveric feet of older diabetic and older non-diabetic intact donors. Histomorphological and biochemical analysis of isolated plantar tissue from both diabetic and non-diabetic feet at six relevant locations was performed.

RESULTS

The main differences found between diabetic and non-diabetic tissue were in the thickness of the septal walls and the elastin content. Diabetic tissue had significantly thicker septal walls and an increased elastin concentration. When comparing the calcaneus to other locations, although there were no differences found in the thickness of the septal walls of diabetic tissue, elastin content was lower in the calcaneous tissue compared to the non-calcaneus sites.

CONCLUSIONS

Modifications in the structural and biochemical properties could translate to changes in the mechanical properties. This information could lead to an understanding of how the structural and biochemical changes result in an increase in susceptibility of tissue to breakdown with load at the different locations of the foot.

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.

NUMERICAL ANALYSIS OF THE FOOT IN HEALTHY AND DEGENERATIVE CONDITIONS

The aim of this work is the development of a 3D numerical model of the foot that allows evaluating the influence of degenerative phenomena on the foot mechanical functionality. Such degenerative phenomena induce histo-morphological alterations and significant modification of the plantar soft tissue mechanical properties, as stiffening and lower damping capabilities. The finite element model of the foot is developed starting from the analysis of biomedical images. Different constitutive models define the mechanical response of the biological tissues. Because of the major role of plantar soft tissue in the here proposed analysis, a specific visco-hyperelastic constitutive formulation is provided considering the typical features of the tissue mechanics, as geometric and material non linearity, almost incompressible behavior and time-dependent phenomena. Constitutive parameters are identified by the analysis of experimental data from in vitro and in vivo mechanical tests, leading to the identification of a range of constitutive parameters for healthy and degenerative conditions. Numerical analyses are developed to investigate the influence of the progression of the degeneration on the distribution of stress and of strain within foot tissues during static standing. Numerical results show the increase of stress values with the appearance of degenerative conditions, showing the typical stiffening phenomenon. The mechanical response of the plantar soft tissue during specific loading condition and the influence of degenerative phenomena on foot mechanics can be evaluated with numerical analysis.

STUDY ON MECHANICAL CHARACTERIZATION OF LIVER TISSUE BASED ON HAPTIC DEVICES FOR VIRTUAL SURGICAL SIMULATION

In recent years, virtual surgical simulation has been one of the hot direction of digital medical research, it is mainly used in teaching, training, diagnosis, preoperative planning, rehabilitation and modeling and analysis of surgical instruments. The modeling of soft tissue of human organs is the basis to realize the virtual surgical simulation. The quasi-linear viscoelastic (QLV) theory has been proposed by Fung, and it was widely used for modeling the constitutive equation of soft tissues. The purpose of this study is to determine the mechanical characterization of the liver soft tissue based on the PHANTOM Omni Haptic devices. Five parameters are included in the constitutive equation with QLV theory, which must be determined experimentally. The specimens were obtained from fresh porcine liver tissues in vitro. The liver tissues were cut into 14[Formula: see text]mm[Formula: see text][Formula: see text][Formula: see text]14[Formula: see text]mm[Formula: see text][Formula: see text][Formula: see text]14[Formula: see text]mm cubes. Two types of unconfined compression tests were performed on cube liver specimens. Puncture tests were performed on the complete liver. The material parameters of the QLV constitutive equation were obtained by fitting the experimental data. These parameters will provide the references for the computational modeling of the liver in the virtual surgical simulation.

The association between mechanical and biochemical/histological characteristics in diabetic and non-diabetic plantar soft tissue

Diabetes, and the subsequent complication of lower limb ulcers leading to potential amputation, remains an important health care problem in United States, even with declining amputation rates. It has been well documented that diabetes can alter the mechanical properties (i.e., increased stiffness) of the plantar soft tissue, although this finding is not universal. Similarly, biochemical, and histological changes have been found in the plantar soft tissue, but, as with the mechanical changes, these findings are not consistent across all studies. Our group׳s work has demonstrated that diabetes increases plantar soft tissue modulus and increases elastic septal thickness. The purpose of the current study was to explore the association between mechanical, biochemical and histological properties. Using previously collected data, a linear mixed effects regression was conducted. The correlations were weak; of the 32 that were tested, only 3 (modulus to septal thickness when location was accounted for, energy loss to total collagen, and energy loss to collagen/elastin ratio) were statistically significant, none with an R2 greater than 0.10. The main differences in the means were increased tissue stiffness and increased septal wall thickness, both trends were supported in the literature. However, as the correlations were weak, it is likely that another unexamined biochemical factor (perhaps collagen crosslinking) is associated with the mechanical tissue changes.

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot.

The effect of prior compression tests on the plantar soft tissue compressive and shear properties

Changes in the shear plantar soft tissue properties with diabetes are believed to play a role in plantar ulceration, yet little is known about these properties. Our group recently conducted shear tests on specimens previously tested in compression to fully characterize the tissue under both these loading modes. However, previously tested specimens may not necessarily provide representative mechanical properties as prior testing may have altered the tissue to an unknown extent. Thus, the purpose of this study was to test the effect of prior compression testing on both the plantar soft tissue shear and compressive properties using paired specimens. First, one specimen from each pair was subject to compression using our standard protocol with modifications to compare compressive properties before and after the protocol while the other specimen from each pair was left untested. Then, both specimens (i.e., one previously compression tested and one previously untested) were subject to shear testing. The results indicate that prior compression testing may affect the tissue compressive properties by reducing peak stress and modulus; however, additional testing is needed since these results were likely confounded by stress softening effects. In contrast, neither the elastic nor the viscoelastic plantar soft tissue shear properties were affected by prior testing in compression, indicating that previously compression tested specimens should be viable for use in future shear tests. However, these results are limited given the small sample size of the study and the fact that only nondiabetic specimens were examined.

A progressive rupture model of soft tissue stress relaxation

A striking feature of stress relaxation in biological soft tissue is that it frequently follows a power law in time with an exponent that is independent of strain even when the elastic properties of the tissue are highly nonlinear. This kind of behavior is an example of quasi-linear viscoelasticity, and is usually modeled in a purely empirical fashion. The goal of the present study was to account for quasi-linear viscoelasticity in mechanistic terms based on our previously developed hypothesis that it arises as a result of isolated micro-yield events occurring in sequence throughout the tissue, each event passing the stress it was sustaining on to other regions of the tissue until they themselves yield. We modeled stress relaxation computationally in a collection of stress-bearing elements. Each element experiences a stochastic sequence of either increases in elastic equilibrium length or decreases in stiffness according to the stress imposed upon it. This successfully predicts quasi-linear viscoelastic behavior, and in addition predicts power-law stress relaxation that proceeds at the same slow rate as observed in real biological soft tissue.

Investigations on the viscoelastic behaviour of a human healthy heel pad: In vivo compression tests and numerical analysis

The aim of this study was to investigate the viscoelastic behaviour of the human heel pad by comparing the stress–relaxation curves obtained from a compression device used on an in vivo heel pad with those obtained from a three-dimensional computer-based subject-specific heel pad model subjected to external compression. The three-dimensional model was based on the anatomy revealed by magnetic resonance imaging of a 31-year-old healthy female. The calcaneal fat pad tissue was described with a viscohyperelastic model, while a fibre-reinforced hyperelastic model was formulated for the skin. All numerical analyses were performed to interpret the mechanical response of heel tissues, with loading conditions and displacement rate in agreement with experimental tests. The heel tissues showed a non-linear, viscoelastic behaviour described by characteristic hysteretic curves, stress–relaxation and viscous recovery phenomena. The reliability of the investigations was validated by the interpretation of the mechanical response of heel tissues under the application of three pistons with diameter of 15, 20 and 40 mm, at the same displacement rate of about 1.7 mm/s. The maximum and minimum relative errors were found to be less than 0.95 and 0.064, respectively.

The shear mechanical properties of diabetic and non-diabetic plantar soft tissue

Changes in the plantar soft tissue shear properties may contribute to ulceration in diabetic patients, however, little is known about these shear parameters. This study examines the elastic and viscoelastic shear behavior of both diabetic and non-diabetic plantar tissue. Previously compression tested plantar tissue specimens (n=54) at six relevant plantar locations (hallux, first, third, and fifth metatarsal heads, lateral midfoot, and calcaneus) from four cadaveric diabetic feet and five non-diabetic feet were utilized. Per in vivo data (i.e., combined deformation patterns of compression followed by shear), an initial static compressive strain (36-38%) was applied to the tissue followed by target shear strains of 50% and 85% of initial thickness. Triangle waves were used to quantify elastic parameters at both strain levels and a stress relaxation test (0.25 s ramp and 300 s hold) was used to quantify the viscoelastic parameters at the upper strain level. Several differences were found between test groups including a 52-62% increase in peak shear stress, a 63% increase in toe shear modulus, a 47% increase in final shear modulus, and a 67% increase in middle slope magnitude (sharper drop in relaxation) in the diabetic tissue. Beyond a 54% greater peak compressive stress in the third metatarsal compared to the lateral midfoot, there were no differences in shear properties between plantar locations. Notably, this study demonstrates that plantar soft tissue with diabetes is stiffer than healthy tissue, thereby compromising its ability to dissipate shear stresses borne by the foot that may increase ulceration risk.