Comparison of different constitutive models to characterize the viscoelastic properties of human abdominal adipose tissue. A pilot study

Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression

Subcutaneous tissue mechanics are important for drug delivery. Yet, even though this material is poroelastic, its mechanical characterization has focused on its hyperelastic response. Moreover, advancement in subcutaneous drug delivery requires effective tissue mimics such as hydrogels for which similar gaps of poroelastic data exist. Porcine subcutaneous samples and gelatin hydrogels were tested under confined compression at physiological conditions and strain rates of 0.01%/s in 5% strain steps with 2600 s of stress relaxation between loading steps. Force-time data were used in an inverse finite element approach to obtain material parameters. Tissues and gels were modeled as porous neo-Hookean materials with properties specified via shear modulus, effective solid volume fraction, initial hydraulic permeability, permeability exponent, and normalized viscous relaxation moduli. The constitutive model was implemented into an isogeometric analysis (IGA) framework to study subcutaneous injection. Subcutaneous tissue exhibited an initial spike in stress due to compression of the solid and fluid pressure buildup, with rapid relaxation explained by fluid drainage, and longer time-scale relaxation explained by viscous dissipation. The inferred parameters aligned with the ranges reported in the literature. Hydraulic permeability, the most important parameter for drug delivery, was in the rangek 0 ∈ [ 0.142 , 0.203 ] mm4 /(N s). With these parameters, IGA simulations showed peak stresses due to a 1-mL injection to reach 48.8 kPa at the site of injection, decaying after drug volume disperses into the tissue. The poro-hyper-viscoelastic neo-Hookean model captures the confined compression response of subcutaneous tissue and gelatin hydrogels. IGA implementation enables predictive simulations of drug delivery.

Geometry of adipocyte packing in subcutaneous tissue contributes to nonlinear tissue properties captured through a Gaussian process surrogate model

Subcutaneous tissue mechanical response is governed by the geometry and mechanical properties at the microscale and drives physiological and clinical processes such as drug delivery. Even though adipocyte packing is known to change with age, disease, and from one individual to another, the link between the geometry of the packing and the overall mechanical response of adipose tissue remains poorly understood. Here we create 1200 periodic representative volume elements (RVEs) that sample the possible space of Laguerre packings describing adipose tissue. RVE mechanics are modeled under tri-axial loading. Equilibrium configuration of RVEs is solved by minimizing an energetic potential that includes volume change contributions from adipocyte expansion, and area change contributions from collagen foam stretching. The resulting mechanical response across all RVE samples is interpolated with the aid of a Gaussian process (GP), revealing how the microscale geometry dictates the overall RVE mechanics. For example, increase in adipocyte size and increase in sphericity lead to adipose tissue softening. We showcase the use of the homogenized model in finite element simulations of drug injection by implementing a Blatz-Ko model, informed by the GP, as a custom material in the popular open-source package FEBio. These simulations show how microscale geometry can lead to vastly different injection dynamics even if the constituent parameters are held constant, highlighting the importance of characterizing individual's adipose tissue structure in the development of personalized therapies.

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

Mechanical characterisation of commercial artificial skin models

Understanding of the mechanical properties of skin is crucial in evaluating the performance of skin-interfacing medical devices. Artificial skin models (ASMs) have rapidly gained attention as they are able to overcome the challenges in ethically sourcing consistent and representative ex vivo animal or human tissue models. Although some ASMs have become commercialised, a thorough understanding of the mechanical properties of the skin models is crucial to ensure that they are suitable for the purpose of the study. In the present study, skin and fat layers of ASMs (Simulab®, LifeLike®, SynDaver® and Parafilm®) were mechanically characterised through hardness, needle insertion, tensile and compression testing. Different boundary constraint conditions (minimally and highly constrained) were investigated for needle insertion testing, while anisotropic properties of the skin models were investigated through different specimen orientations during tensile testing. Analysis of variance (ANOVA) tests were performed to compare the mechanical properties between the skin models. Properties of the skin models were compared against literature to determine the suitability of the skin models based on the material property of interest. All skin models offer relatively consistent mechanical performance, providing a solid basis for benchtop evaluation of skin-interfacing medical device performance. Through prioritising models with mechanical properties that are consistent with human skin data, and with limited variance, researchers can use the data presented here as a toolbox to select the most appropriate ASM for their particular application.

Damage and Fracture Mechanics of Porcine Subcutaneous Tissue Under Tensile Loading

Subcutaneous injection, which is a preferred delivery method for many drugs, causes deformation, damage, and fracture of the subcutaneous tissue. Yet, experimental data and constitutive modeling of these dissipation mechanisms in subcutaneous tissue remain limited. Here we show that subcutaneous tissue from the belly and breast anatomical regions in the swine show nonlinear stress-strain response with the characteristic J-shaped behavior of collagenous tissue. Additionally, subcutaneous tissue experiences damage, defined as a decrease in the strain energy capacity, as a function of the previously experienced maximum deformation. The elastic and damage response of the tissue are accurately described by a microstructure-driven constitutive model that relies on the convolution of a neo-Hookean material of individual fibers with a fiber orientation distribution and a fiber recruitment distribution. The model fit revealed that subcutaneous tissue can be treated as initially isotropic, and that changes in the fiber recruitment distribution with loading are enough to explain the dissipation of energy due to damage. When tested until failure, subcutaneous tissue that has undergone damage fails at the same peak stress as virgin samples, but at a much larger stretch, overall increasing the tissue toughness. Together with a finite element implementation, these data and constitutive model may enable improved drug delivery strategies and other applications for which subcutaneous tissue biomechanics are relevant.

Strain-dependent shear properties of human adipose tissue in vivo

INTRODUCTION

Human adipose tissue (fat) deforms substantially under normal physiological loading and during impact. Thus, accurate data on strain-dependent stiffness of fat is essential for the creation of accurate biomechanical models. Previous studies on ex vivo samples reported human fat to be nonlinear and viscoelastic. When static compression is combined with magnetic resonance (MR) elastography (an imaging technique used to measure viscoelasticity in vivo), the large deformation properties of tissues can be determined. Here, we use magnetic resonance elastography to quantify fat shear modulus in vivo under increasing compressive strain and compare it to the underlying passive gluteal muscle.

METHODS

The right buttocks of ten female participants were incrementally compressed at four levels while MR elastography (50 Hz) and mDixon images were acquired. Maps of tissue shear modulus (G*) were reconstructed from the MR elastography phase images. Tissue strain was estimated from registration of deformed and undeformed mDixon images. Linear mixed models were fit to the natural logarithm of the compressive strain and shear modulus data for each tissue.

RESULTS

Shear modulus increased in an exponential relationship with compressive strain in fat: Gfat*=748.5*Cyy-1.18Pa, and to a lesser extent in muscle: Gmuscle*=956.4*Cyy-0.36Pa. The baseline (undeformed) stiffness of fat was significantly lower than that of muscle (mean G*fat = 752 Pa, mean G*muscle = 1000 Pa, paired samples t-test, t = -4.24, p = 0.001). However, fat exhibited a significantly higher degree of strain dependence (characterised by the exponent of the curve, t = -6.47, p = 0.0001).

CONCLUSION

Static compression of human adipose tissue results in an increase in apparent viscoelastic shear modulus (stiffness), in an exponentially increasing relationship. The relationships defined here can be used in the development of physiologically realistic computational models for impact, injury and biomechanical modelling.

Mechanical Behavior of Subcutaneous and Visceral Abdominal Adipose Tissue in Patients with Obesity

The mechanical characterization of adipose tissues is important for various medical purposes, including plastic surgery and biomechanical applications, such as computational human body models for the simulation of surgical procedures or injury prediction, for example, in the evaluation of vehicle crashworthiness. In this context, the measurement of human subcutaneous adipose tissue (SAT) and visceral adipose tissue (VAT) mechanical properties in relation to subject characteristics may be really relevant. The aim of this work was to properly characterize the mechanical response of adipose tissues in patients with obesity. Then, the data were exploited to develop a reliable finite element model of the adipose tissues characterized by a constitutive material model that accounted for nonlinear elasticity and time dependence. Mechanical tests have been performed on both SAT and VAT specimens, which have been harvested from patients with severe obesity during standard laparoscopic sleeve gastrectomy intervention. The experimental campaign included indentation tests, which permitted us to obtain the initial/final indentation stiffnesses for each specimen. Statistical results revealed a higher statistical stiffness in SAT than in VAT, with an initial/final indentation stiffness of 1.65 (SD ± 0.29) N/30.30 (SD ± 20) N compared to 1.29 (SD ± 0.30) N/21.00 (SD ± 16) N. Moreover, the results showed that gender, BMI, and age did not significantly affect the stiffness. The experimental results were used in the identification of the constitutive parameters to be inserted in the constitutive material model. Such constitutive characterization of VAT and SAT mechanics can be the starting point for the future development of more accurate computational models of the human adipose tissue and, in general, of the human body for the optimization of numerous medical and biomechanical procedures and applications.

Evolution of relaxation properties of callus tissue during bone transport

Callus tissue exhibits a viscoelastic behavior that has a strong influence on the distribution of stresses and their evolution with time and, thus, it can affect tissue differentiation during distraction procedures. For this reason, a deep knowledge of that viscoelastic behavior can be very useful to improve current protocols of bone distraction and bone transport. Monitoring stress relaxation of the callus during distraction osteogenesis allows characterizing its viscoelastic behavior. Different procedures have been used in the literature to fit the response of a given viscoelastic model to the force relaxation curve. However, these procedures do not ensure the uniqueness of that fit, which is of the utmost importance for statistical purposes. This work uses a fitting procedure already validated for other tissues that ensures that uniqueness. Very importantly too, the procedure presented here allows obtaining more information from the stress relaxation tests, distinguishing relaxation in different time scales, which provides a deeper insight into the viscoelastic behavior and its evolution over time. As it was observed in the results, relaxation is faster at the first days after osteotomy and becomes slower and more gradual with time. This fact can be directly linked to the temporal evolution of the callus composition (water, organic phase, and mineral content) and also to the progression of tissue differentiation, with a prevalence of hard tissues as time passes.

Cavitation in a soft porous material

We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equation that extends the Rayleigh-Plesset equation to bubbles in soft porous media. The extended Rayleigh-Plesset equation reveals that finite-size effects lead to the breakdown of the universal scaling relation between bubble radius and time that holds in the infinite-size limit. Our data indicate that the deformability of the porous medium slows down the collapse and expansion processes, a result with important consequences for wide-ranging phenomena, from drug delivery to spore dispersion.

The effects of gravity and compression on interstitial fluid transport in the lower limb

Edema in the limbs can arise from pathologies such as elevated capillary pressures due to failure of venous valves, elevated capillary permeability from local inflammation, and insufficient fluid clearance by the lymphatic system. The most common treatments include elevation of the limb, compression wraps and manual lymphatic drainage therapy. To better understand these clinical situations, we have developed a comprehensive model of the solid and fluid mechanics of a lower limb that includes the effects of gravity. The local fluid balance in the interstitial space includes a source from the capillaries, a sink due to lymphatic clearance, and movement through the interstitial space due to both gravity and gradients in interstitial fluid pressure (IFP). From dimensional analysis and numerical solutions of the governing equations we have identified several parameter groups that determine the essential length and time scales involved. We find that gravity can have dramatic effects on the fluid balance in the limb with the possibility that a positive feedback loop can develop that facilitates chronic edema. This process involves localized tissue swelling which increases the hydraulic conductivity, thus allowing the movement of interstitial fluid vertically throughout the limb due to gravity and causing further swelling. The presence of a compression wrap can interrupt this feedback loop. We find that only by modeling the complex interplay between the solid and fluid mechanics can we adequately investigate edema development and treatment in a gravity dependent limb.

Experimental characterisation of porcine subcutaneous adipose tissue under blunt impact up to irreversible deformation

A deeper understanding of the mechanical characteristics of adipose tissue under large deformation is important for the analysis of blunt force trauma, as adipose tissue alters the stresses and strains that are transferred to subjacent tissues. Hence, results from drop tower tests of subcutaneous adipose tissue are presented (i) to characterise adipose tissue behaviour up to irreversible deformation, (ii) to relate this to the microstructural configuration, (iii) to quantify this deformation and (iv) to provide an analytical basis for computational modelling of adipose tissue under blunt impact. The drop tower experiments are performed exemplarily on porcine subcutaneous adipose tissue specimens for three different impact velocities and two impactor geometries. An approach based on photogrammetry is used to derive 3D representations of the deformation patterns directly after the impact. Median values for maximum impactor acceleration for tests with a flat cylindrical impactor geometry at impact velocities of 886 mm/s, 1253 mm/s and 2426 mm/s amount to 61.1 g, 121.6 g and 264.2 g, respectively, whereas thickness reduction of the specimens after impact amount to 16.7%, 30.5% and 39.3%, respectively. The according values for tests with a spherically shaped impactor at an impact velocity of 1253 mm/s are 184.2 g and 78.7%. Based on these results, it is hypothesised that, in the initial phase of a blunt impact, adipose tissue behaviour is mainly governed by the behaviour of the lipid inside the adipocytes, whereas for further loading, contribution of the extracellular collagen fibre network becomes more dominant.

Multidirectional mechanical properties and constitutive modeling of human adipose tissue under dynamic loading

The mechanical behavior of subcutaneous adipose tissue (SAT) affects the interaction between vehicle occupants and restraint systems in motor vehicle crashes (MVCs). To enhance future restraints, injury countermeasures, and other vehicle safety systems, computational simulations are often used to augment experiments because of their relative efficiency for parametric analysis. How well finite element human body models (FE-HBMs), which are often used in such simulations, predict human response has been limited by the absence of material models for human SAT that are applicable to the MVC environment. In this study, for the first time, dynamic multidirectional unconfined compression and simple shear loading tests were performed on human abdominal SAT specimens under conditions similar to MVCs. We also performed multiple ramp-hold tests to evaluate the quasilinear viscoelasticity (QLV) assumption and capture the stress relaxation behavior under both compression and shear. Our mechanical characterization was supplemented with scanning electron microscopy (SEM) performed in different orientations to investigate whether the macrostructural response can be related to the underlying microstructure. While the overall structure was shown to be visually different in different anatomical planes, a preferred orientation of any fibrous structures could not be identified. We showed that the nonlinear, viscoelastic, and direction-dependent responses under compression and shear tests could be captured by incorporating QLV in an Ogden-type hyperelastic model. Our comprehensive approach will lead to more accurate computational simulations and support the collective effort on the research of future occupant protection systems. STATEMENT OF SIGNIFICANCE: There is an urgent need to characterize the mechanical behavior of human adipose tissue under multiple dynamic loading conditions, and to identify constitutive models that are able to capture the tissue response under these conditions. We performed the first series of experiments on human adipose tissue specimens to characterize the multi-directional compression and shear behavior at impact loading rates and obtained scanning electron microscope images to investigate whether the macrostructural response can be related to the underlying microstructure. The results showed that human adipose tissue is nonlinear, viscoelastic and direction dependent, and its mechanical response under compression and shear tests at different loading rates can be captured by incorporating quasi-linear viscoelasticity in an Ogden-type hyperelastic model.

Quasi-Linear Viscoelastic Characterization of Soft Tissue-Mimicking Materials

We present a novel method based on the quasi-linear viscoelastic (QLV) theory to describe the time-dependent behavior of soft materials. Unlike previous methods for deriving QLV parameters, we characterize the elastic and viscous behavior of materials separately by using two different sets of experiments. To model the nonlinear elastic behavior, we fit the elastic stress response with a one-term Ogden model. Then, we model the relaxation behavior with a Prony series to compare the stress relaxation of the material at different timescales. This new method allows us to characterize materials with narrow confidence intervals (high accuracy), independently from the loading conditions. We validate our model using samples made of phantom materials that mimic normal and cancerous prostate tissues in terms of Young's modulus. Our model is shown to distinguish materials with similar elastic (viscous) properties but different viscous (elastic) properties. Drawing a precise distinction between the phantoms, this method could be useful for prostate cancer (PCa) diagnosis; but significant clinical studies will be needed in the future.

In Vitro Mechanical Characterization and Modeling of Subcutaneous Adipose Tissue: A Comprehensive Review

Mechanical models of adipose tissue are important for various medical applications including cosmetics, injuries, implantable drug delivery systems, plastic surgeries, biomechanical applications such as computational human body models for surgery simulation, and blunt impact trauma prediction. This article presents a comprehensive review of in vivo experimental approaches that aimed to characterize the mechanical properties of adipose tissue, and the resulting constitutive models and model parameters identified. In particular, this study examines the material behavior of adipose tissue, including its nonlinear stress-strain relationship, viscoelasticity, strain hardening and softening, rate-sensitivity, anisotropy, preconditioning, failure behavior, and temperature dependency.

Comparison of porcine and human adipose tissue loading responses under dynamic compression and shear: A pilot study

Understanding the mechanical properties of human adipose tissue, and its influence on seat belt-pelvis interaction is beneficial for computational human body models that are developed for injury prediction in the vehicle crashworthiness simulations. While various studies have characterized adipose tissue, most of the studies used porcine adipose tissue as a surrogate, and none of the studies were performed at loading rates relevant for motor vehicle collisions. In this work, the mechanical response of human and porcine adipose tissue was studied. Two dynamic loading modes (compression and simple shear) were tested in adipose tissue extracted from the human abdomen and porcine back. An Ogden hyperelastic model was used to fit the loading response, and specific material parameters were obtained for each specimen. Two-sample t-tests were performed to compare the effective shear moduli and peak stresses from porcine and human samples. The material response of the human adipose tissue was consistent with previous studies. Porcine adipose tissue was found to be significantly stiffer than human adipose tissue under compression and shear loading. Also, when material model parameters were fit to only one loading mode, the predicted response in the other mode showed a poor fit.

IDENTIFICATION OF UNIAXIAL DEFORMATION BEHAVIOR AND ITS INITIAL TANGENT MODULUS FOR ATHEROMATOUS INTIMA IN THE HUMAN CAROTID ARTERY AND THORACIC AORTA USING THREE-PARAMETER ISOTROPIC HYPERELASTIC MODELS

Uniaxial stretching tests are used for mechanical identification of small fibrous regions of atheromatous arteries. Material constants in isotropic hyperelastic models are determined to minimize the fitting error for the stress–strain curve. We developed a novel method to better characterize the material constants in typical forms of Yeoh, Ogden, Chuong–Fung (CF) and Gasser–Ogden–Holzapfel (GOH) isotropic hyperelastic models for fibrous caps and normal intimal layers from human carotid artery and thoracic aorta by incorporating Young’s modulus, i.e., the initial tangent modulus of uniaxial stress–strain relationships, as one of three material constants. We derived a unified, isotropic form for the anisotropic exponential-type strain energy density functions of CF and GOH models. The uniaxial stress–strain relationship equations were expanded to Maclaurin series to identify Young’s modulus as a coefficient of the linear term of the strain and to examine the roles of the material constants in the nonlinear function. The remaining two material constants were determined by curvefitting. The incorporation of Young’s modulus into the CF and GOH models gave reasonable curvefitting, with errors [Formula: see text], whereas large errors ([Formula: see text]) were observed in one case for the Yeoh model and in two cases for the Ogden model.

Comparison of the viscoelastic properties of human abdominal and breast adipose tissue and its incidence on breast reconstruction surgery. A pilot study

BACKGROUND

Breast cancer is the leading malignant tumor in women in the world. Reconstruction after mastectomy plays a key role in the physical and psychological recuperation, being the abdominal skin and adipose tissue the best current option for the DIEP surgery. The aim of the surgery is to obtain a reconstructed breast which looks and behaves naturally. Therefore, it would be useful to characterize the mechanical behaviour of the adipose tissue in the abdomen and breast to compare their mechanical properties, also investigating possible regional differences.

METHODS

Experimental tests have been carried out in breast and abdominal adipose tissue samples, obtaining their viscoelastic properties. The specimens have been subjected to uniaxial compression relaxation tests and a mechanical behaviour model has been fitted to the experimental curves. Afterwards, statistical analyses have been used to detect differences between different individuals' abdominal fat tissue and finally between different areas of the same individual's breast and abdominal adipose tissue.

FINDINGS

Several conclusions could be extracted from the results: 1) inter-individual differences may exist in the abdominal adipose tissue; 2) the breast fat could be regarded as a unique tissue from the mechanical point of view; 3) significant differences were detected between the superficial breast and all the locations of the abdomen, except for the superficial lateral one and 4) the mechanical properties of the abdominal adipose tissue seem to change with the depth. These conclusions can be of great value for DIEP surgeries and other surgeries in which the adipose tissue is involved.

Effect of axial prestretch and adipose tissue on the inflation-extension behavior of the human abdominal aorta

Our study aims to show that perivascular adipose tissue may significantly change the mechanical state of the abdominal aorta. To this end, uniaxial tensile tests with perivascular fat tissue were carried out. In the subsequent regression analysis, stress-strain data were fitted by the polynomial strain energy density. A constitutive model of adipose tissue was used in the analytical simulation of the inflation-extension behavior of the human abdominal aorta. The computational model was based on the theory of the bi-layered thick-walled tube. In addition to the effect of perivascular tissue, the effect of axial prestretch was also studied. It was found that the presence of perivascular tissue reduces the distensibility of the aorta. Axial prestretch applied to the aorta embedded in adipose tissue had an effect opposite to that of adipose tissue. Axially prestrained aorta exhibited higher distensiblity than non-prestrained aorta. It was also shown that the perivascular envelope bears some portion of the pressure loading and thus reduces the mechanical stresses inside the wall of aorta. A similar effect was found for axial prestretch.