An anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue

Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

Strain rate-dependent failure mechanics of the intervertebral disc under tension/compression and constitutive analysis

BACKGROUND

The intervertebral disc exhibits not only strain rate dependence (viscoelasticity), but also significant asymmetry under tensile and compressive loads, which is of great significance for understanding the mechanism of lumbar disc injury under physiological loads.

OBJECTIVE

In this study, the strain rate sensitive and tension-compression asymmetry of the intervertebral disc were analyzed by experiments and constitutive equation.

METHOD

The Sheep intervertebral disc samples were divided into three groups, in order to test the strain rate sensitive mechanical behavior, and the internal displacement as well as pressure distribution.

RESULTS

The tensile stiffness is one order of magnitude smaller than the compression stiffness, and the logarithm of the elastic modulus is approximately linear with the logarithm of the strain rate, showing obvious tension-compression asymmetry and rate-related characteristics. In addition, the sensitivity to the strain rate is the same under these two loading conditions. The stress-strain curves of unloading and loading usually do not coincide, and form a Mullins effect hysteresis loop. The radial displacement distribution is opposite between the anterior and posterior region, which is consistent with the stress distribution. By introducing the damage factor into ZWT constitutive equation, the rate-dependent viscoelastic and weakening behavior of the intervertebral disc can be well described.

A parametric study assessing Implicit Solver limits for a generic FEM Simulation of PTA without stent deployment

This study focuses on the robustness of a generic Finite Element Model (FEM) of Percutaneous Transluminal Angioplasty (PTA) procedure with permanent set. The influence of three different parameters on simulation robustness were investigated: the stenosis percent, the stenosis offset and the arterial caliber. Five arterial calibers are modeled by adapting the ratio between the inner diameter and the wall thickness. Overall, forty configurations were tested with the same simulation settings and boundary conditions. Results shows convergence issues caused by excessive deformations of elements for stenosis above 65% blockage. Moreover, an increasing stenosis offset tends to decrease convergence. Simulation of PTA on small calibers and large calibers are less robust than intermediate e.g., iliac calibers.Clinical Relevance- PTA can benefit from numerical tools to improve the procedure outcomes. A FEM simulation of PTA without stent deployment can predict the permanent strain induced by this surgery for various configurations. However, robustness of the simulation is required to consider its transfer to clinics. This work aims to determine the robustness boundaries of an implicit solver for PTA simulation. It shows that an implicit solver is robust for all artery calibers with a stenosis below 50% blockage. Moreover medium-caliber arteries exhibit better robustness with converging solutions for stenosis reaching 60% blockage.

Hyperelastic and damage properties of the hypoxic aorta treated with Cinaciguat

Chronic hypoxia during gestation and postnatal period induces pulmonary hypertension, aorta stiffening and vascular remodeling. In this study, we hypothesized that a postnatal treatment with Cinaciguat, a guanylate cyclase activator, may improve the vascular function by enhancing NO-sGC pathways that induce vasodilation. To assess this, we collected aortas from six lambs gestated, born and raised at 3600 masl. Half of these lambs received a Cinaciguat postnatal treatment, while the other half was used as control (vehicle). Uniaxial tension was applied on samples of each group of aortas (control and Cinaciguat-treated) through cyclic loading. The obtained stress-stretch curves were used to identify constitutive parameters of a hyperelastic damage model. These material constants allowed us to assess the softening/dissipation behavior and to characterize the treatment effects. Results showed that Cinaciguat has an effect on the damage behavior at large strains, altering the damage onset under uniaxial tension. We conclude that Cinaciguat, as a vasodilator, can prevent the very early effects of vascular remodeling caused by perinatal hypoxia, and improve the aortic-tissue damage properties of hypoxic lambs.

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed mucosa–submucosa layer under large deformation

Mechanical characterisation of the layer-specific, viscoelastic properties of the human oesophagus is crucial in furthering the development of devices emerging in the field, such as robotic endoscopic biopsy devices, as well as in enhancing the realism, and therefore effectiveness, of surgical simulations. In this study, the viscoelastic and stress-softening behaviour of the passive human oesophagus was investigated through ex vivo cyclic mechanical tests. Due to restrictions placed on the laboratory as a result of COVID-19, only oesophagi from cadavers fixed in formalin were allowed for testing. Three oesophagi in total were separated into their two main layers and the mucosa–submucosa layer was investigated. A series of uniaxial tensile tests were conducted in the form of increasing stretch level cyclic tests at two different strain rates: 1% s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1 and 10% s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1. Rectangular samples in both the longitudinal and circumferential directions were tested to observe any anisotropy. Histological analysis was also performed through a variety of staining methods. Overall, the longitudinal direction was found to be much stiffer than the circumferential direction. Stress-softening was observed in both directions, as well as permanent set and hysteresis. Strain rate-dependent behaviour was also apparent in the two directions, with an increase in strain rate resulting in an increase in stiffness. This strain rate dependency was more pronounced in the longitudinal direction than the circumferential direction. Finally, the results were discussed in regard to the histological content of the layer, and the behaviour was modelled and validated using a visco-hyperelastic matrix-fibre model.

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed muscular layer under large deformation

The oesophagus is a primarily mechanical organ whose material characterisation would aid in the investigation of its pathophysiology, help in the field of tissue engineering, and improve surgical simulations and the design of medical devices. However, the layer-dependent, anisotropic properties of the organ have not been investigated using human tissue, particularly in regard to its viscoelastic and stress-softening behaviour. Restrictions caused by the COVID-19 pandemic meant that fresh human tissue was not available for dissection. Therefore, in this study, the layer-specific material properties of the human oesophagus were investigated through ex vivo experimentation of the embalmed muscularis propria layer. For this, a series of uniaxial tension cyclic tests with increasing stretch levels were conducted at two different strain rates. The muscular layers from three different cadaveric specimens were tested in both the longitudinal and circumferential directions. The results displayed highly nonlinear and anisotropic behaviour, with both time- and history-dependent stress-softening. The longitudinal direction was found to be stiffer than the circumferential direction at both strain rates. Strain rate-dependent behaviour was apparent, with an increase in strain rate resulting in an increase in stiffness in both directions. Histological analysis was carried out via various staining methods; the results of which were discussed with regard to the experimentally observed stress-stretch response. Finally, the behaviour of the muscularis propria was simulated using a matrix-fibre model able to capture the various mechanical phenomena exhibited, the fibre orientation of which was driven by the histological findings of the study.

Cerebral vascular strains in dynamic head impact using an upgraded model with brain material property heterogeneity

Cerebral vascular injury (CVI) is a frequent consequence of traumatic brain injury but has often been neglected. Substantial experimental work exists on vascular material properties and failure/subfailure thresholds. However, little is known about vascular in vivo loading conditions in dynamic head impact, which is necessary to investigate the risk, severity, and extent of CVI. In this study, we resort to the Worcester Head Injury Model (WHIM) V2.1 for investigation. The model embeds the cerebral vasculature network and is further upgraded to incorporate brain material property heterogeneity based on magnetic resonance elastography. The brain material property is calibrated to match with the previously validated anisotropic V1.0 version in terms of whole-brain strains against six experimental datasets of a wide range of blunt impact conditions. The upgraded WHIM is finally used to simulate five representative real-world head impacts drawn from contact sports and automotive crashes. We find that peak strains in veins are considerably higher than those in arteries and that peak circumferential strains are also higher than peak axial strains. For a typical concussive head impact, cerebral vascular axial strains reach the lowest reported yield strain of ∼7-8%. For severe automotive impacts, axial strains could reach ∼20%, which is on the order of the lowest reported ultimate failure strain of ∼24%. These results suggest in vivo mechanical loading conditions of the cerebral vasculature (excluding bridging veins not assessed here) due to rapid head rotation are at the lower end of failure/subfailure thresholds established from ex vivo experiments. This study provides some first insight into the risk, severity, and extent of CVI in real-world head impacts.

A Review on Damage and Rupture Modelling for Soft Tissues

Computational modelling of damage and rupture of non-connective and connective soft tissues due to pathological and supra-physiological mechanisms is vital in the fundamental understanding of failures. Recent advancements in soft tissue damage models play an essential role in developing artificial tissues, medical devices/implants, and surgical intervention practices. The current article reviews the recently developed damage models and rupture models that considered the microstructure of the tissues. Earlier review works presented damage and rupture separately, wherein this work reviews both damage and rupture in soft tissues. Wherein the present article provides a detailed review of various models on the damage evolution and tear in soft tissues focusing on key conceptual ideas, advantages, limitations, and challenges. Some key challenges of damage and rupture models are outlined in the article, which helps extend the present damage and rupture models to various soft tissues.

In Vivo Based Fluid-Structure Interaction Biomechanics of the Left Anterior Descending Coronary Artery

A fluid-structure interaction-based biomechanical model of the entire left anterior descending coronary artery is developed from in vivo imaging via the finite element method in this paper. Included in this investigation is ventricle contraction, three-dimensional motion, all angiographically visible side branches, hyper/viscoelastic artery layers, non-Newtonian and pulsatile blood flow, and the out-of-phase nature of blood velocity and pressure. The fluid-structure interaction model is based on in vivo angiography of an elite athlete's entire left anterior descending coronary artery where the influence of including all alternating side branches and the dynamical contraction of the ventricle is investigated for the first time. Results show the omission of side branches result in a 350% increase in peak wall shear stress and a 54% decrease in von Mises stress. Peak von Mises stress is underestimated by up to 80% when excluding ventricle contraction and further alterations in oscillatory shear indices are seen, which provide an indication of flow reversal and has been linked to atherosclerosis localization. Animations of key results are also provided within a video abstract. We anticipate that this model and results can be used as a basis for our understanding of the interaction between coronary and myocardium biomechanics. It is hoped that further investigations could include the passive and active components of the myocardium to further replicate in vivo mechanics and lead to an understanding of the influence of cardiac abnormalities, such as arrythmia, on coronary biomechanical responses.

Biaxial softening of isolated cerebral arteries following axial overstretch

Arteries play a critical role in carrying essential nutrients and oxygen throughout the brain; however, vessels can become damaged in traumatic brain injury (TBI), putting neural tissue at risk. Even in the absence of hemorrhage, large deformations can disrupt both the physiological and mechanical behavior of the cerebral vessels. Our group recently reported the effect of vessel overstretch on axial mechanics; however, that work did not address possible changes in circumferential mechanics that are critical to the regulation of blood flow. In order to address this in the present work, ovine middle cerebral arteries were isolated and overstretched axially to 10, 20, or 40% beyond the in vivo configuration. Results showed a statistically significant decrease in circumferential stiffness and strain energy, as well as an increase in vessel diameter following 40% overstretch (p < 0.05). These passive changes would lead to a decrease in vascular resistance and likely play a role in previous reports of cellular dysfunction. We anticipate that our findings will both increase understanding of vessel softening phenomena and also promote improved modeling of cerebrovascular mechanics following head trauma.

Influence of a Biocompatible Hydrophilic Needle Surface Coating on a Puncture Biopsy Process for Biomedical Applications

A puncture biopsy is a widely used, minimally invasive surgery process. During the needle insertion process, the needle body is always in direct contact with a biological soft tissue. Tissue adhesion and different degrees of tissue damage occur frequently. Optimization of the needle surface, and especially the lubrication of the needle surface, can deal with these problems efficiently. Therefore, in this paper, a biocompatible hydrophilic coating was applied onto the surface of a needle to improve the surface quality of the needle surface. Further, a simplified finite element model of insertion was established, and extracorporeal insertion experiments were used to verify the accuracy of the model. Then, by analyzing a simulation model of a coated needle and a conventional needle, the influence of the application of the coated needle on the insertion process was obtained. It can be seen from the results that the coating application relieved the force on the needle and the soft tissue during the insertion process and could significantly reduce friction during the insertion process. At the same time, the deformation of biological soft tissue was reduced, and the adhesion situation between the needle and tissue improved, which optimized the puncture needle.

Mechanical damage characterization in human femoropopliteal arteries of different ages

Endovascular treatment of Peripheral Arterial Disease (PAD) is notorious for high failure rates, and interaction between the arterial wall and the repair devices plays a significant role. Computational modeling can help improve clinical outcomes of these interventions, but it requires accurate inputs of elastic and damage characteristics of the femoropopliteal artery (FPA) which are currently not available. Fresh human FPAs from n = 104 tissue donors 14-80 years old were tested using planar biaxial extension to capture elastic and damage characteristics. Damage initiation stretches and stresses were determined for both longitudinal and circumferential directions, and their correlations with age and risk factors were assessed. Two and four-fiber-family invariant-based constitutive models augmented with damage functions were used to describe stress softening with accumulating damage. In FPAs younger than 50 years, damage began accumulating after 1.51 ± 0.13 and 1.49 ± 0.11 stretch, or 196 ± 110 kPa and 239 ± 79 kPa Cauchy stress in the longitudinal and circumferential directions, respectively. In FPAs older than 50 years, damage initiation stretches and stresses decreased to 1.27 ± 0.09 (106 ± 52 kPa) and 1.26 ± 0.09 (104 ± 59 kPa), respectively. Damage manifested primarily as tears at the internal and external elastic laminae and within the tunica media layer. Higher body mass index and presence of diabetes were associated with lower damage initiation stretches and higher stresses. The selected constitutive models were able to accurately portray the FPA behavior in both elastic and inelastic domains, and properties were derived for six age groups. Presented data can help improve fidelity of computational models simulating endovascular PAD repairs that involve arterial damage. STATEMENT OF SIGNIFICANCE: This manuscript describes inelastic, i.e. damage, behavior of human femoropopliteal arteries, and provides values for three constitutive models simulating this behavior computationally. Using a set of 104 human FPAs 14-80 years old, we have investigated stress and stretch levels corresponding to damage initiation, and have studied how these damage characteristics change across different age groups. Presented inelastic arterial characteristics are important for computational simulations modeling balloon angioplasty and stenting of peripheral arterial disease lesions.

Evaluating Plastic Deformation and Damage as Potential Mechanisms for Tendon Inelasticity using a Reactive Modeling Framework

Inelastic behaviors, such as softening, a progressive decrease in modulus before failure, occur in tendon and are important aspect in degeneration and tendinopathy. These inelastic behaviors are generally attributed to two potential mechanisms: plastic deformation and damage. However, it is not clear which is primarily responsible. In this study, we evaluated these potential mechanisms of tendon inelasticity by using a recently developed reactive inelasticity model (RIE), which is a structurally-inspired continuum mechanics framework that models tissue inelasticity based on the molecular bond kinetics. Using RIE, we formulated two material models, one specific to plastic deformation and the other to damage. The models were independently fit to published experimental tensile tests of rat tail tendons. We quantified the inelastic effects and compared the performance of the two models in fitting the mechanical response during loading, relaxation, unloading, and reloading phases. Additionally, we validated the models by using the resulting fit parameters to predict an independent set of experimental stress-strain curves from ramp-to-failure tests. Overall, the models were both successful in fitting the experiments and predicting the validation data. However, the results did not strongly favor one mechanism over the other. As a result, to distinguish between plastic deformation and damage, different experimental protocols will be needed. Nevertheless, these findings suggest the potential of RIE as a comprehensive framework for studying tendon inelastic behaviors.

A porous fibrous hyperelastic damage model for human periodontal ligament: Application of a microcomputerized tomography finite element model

The periodontal ligament (PDL) is a soft biological tissue that connects the tooth with the trabecular bone of the mandible. It plays a key role in load transmission and is primarily responsible for bone resorption and most common periodontal diseases. Although several numerical studies have analysed the biomechanical response of the PDL, most did not consider its porous fibrous structure, and only a few analysed damage to the PDL. This study presents an innovative numerical formulation of a porous fibrous hyperelastic damage material model for the PDL. The model considers two separate softening phenomena: fibre alignment during loading and fibre rupture. The parameters for the material model characterization were fitted using experimental data from the literature. Furthermore, the experimental tests used for characterization were computationally modelled to verify the material parameters. A finite element model of a portion of a human mandible, obtained by microcomputerized tomography, was developed, and the proposed constitutive model was implemented for the PDL. Our results confirm that damage to the PDL may occur mainly because of overpressure of the interstitial fluid, while large forces must be applied to damage the PDL fibrous network. Moreover, this study clarifies some aspects of the relationship between PDL damage and the bone remodelling process.

A Reactive Inelasticity Theoretical Framework for Modeling Viscoelasticity, Plastic Deformation, and Damage in Fibrous Soft Tissue

Fibrous soft tissues are biopolymeric materials that are made of extracellular proteins, such as different types of collagen and proteoglycans, and have a high water content. These tissues have nonlinear, anisotropic, and inelastic mechanical behaviors that are often categorized into viscoelastic behavior, plastic deformation, and damage. While tissue's elastic and viscoelastic mechanical properties have been measured for decades, there is no comprehensive theoretical framework for modeling inelastic behaviors of these tissues that is based on their structure. To model the three major inelastic mechanical behaviors of tissue's fibrous matrix, we formulated a structurally inspired continuum mechanics framework based on the energy of molecular bonds that break and reform in response to external loading (reactive bonds). In this framework, we employed the theory of internal state variables (ISV) and kinetics of molecular bonds. The number fraction of bonds, their reference deformation gradient, and damage parameter were used as state variables that allowed for consistent modeling of all three of the inelastic behaviors of tissue by using the same sets of constitutive relations. Several numerical examples are provided that address practical problems in tissue mechanics, including the difference between plastic deformation and damage. This model can be used to identify relationships between tissue's mechanical response to external loading and its biopolymeric structure.

Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates

Modelling the viscoelastic behavior of rubber for use in component design remains a challenge. Most of the literature does not consider the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). Previous studies have either focused on the behaviour at small strains and small strain rates or in fast loading conditions that result in low cycle fatigue or tearing phenomena. There is a lack of understanding of the dynamic response of natural rubber suspension components when used in real vehicle applications. This paper presents a review of popular viscoelastic nonlinear constitutive models and their ability to model the mechanical behaviour of typical elastomer materials such as Natural Rubber (NR) incorporating different PHR (Parts per Hundred Rubber, XX) of carbon black. The range of strain and strain rate are typical for the materials used in rubber suspensions when operating in severe service operating conditions, such as over rough terrain or over pot-holes. The cyclic strain is applied at different amplitudes and different strain rates in this medium strain range. Despite the availability of many models in the literature, our study reports that none of the existing models can fit the data satisfactorily over a wide range of conditions.

An investigation into the role of different constituents in damage accumulation in arterial tissue and constitutive model development

Carotid atherosclerotic plaque rupture is one of the leading causes of stroke. Treatments for atherosclerosis can induce tissue damage during the deployment of an intravascular device or through external tissue clamping during surgery. In this paper, a constituent specific study was performed to investigate the role of the ground matrix and collagen fibres of arterial tissue in response to supra-physiological loads. Cyclic mechanical tests were conducted on intact and collagenase-digested strips of porcine common carotid arteries. Using these tests, four passive damage-relevant phenomena were studied, namely (i) Mullins effect, (ii) hysteresis, (iii) permanent set and (iv) matrix failure and fibre rupture. A constitutive model was also developed to capture all of these damage-relevant phenomena using a continuum damage mechanics approach. The implemented constitutive model was fit to experimental results for both intact and digested samples. The results of this work demonstrate the important role of the ground matrix in the permanent deformation of the arterial tissue under high loads. Supra-physiological load-induced tissue damage may play a key role in vascular remodelling in arteries with atherosclerosis or following interventional procedures.

Detection and characterization of molecular-level collagen damage in overstretched cerebral arteries

It is well established that overstretch of arteries alters their mechanics and compromises their function. However, the underlying structural mechanisms behind these changes are poorly understood. Utilizing a recently developed collagen hybridizing peptide (CHP), we demonstrate that a single mechanical overstretch of an artery produces molecular-level unfolding of collagen. In addition, imaging and quantification of CHP binding revealed that overstretch produces damage (unfolding) among fibers aligned with the direction of loading, that damage increases with overstretch severity, and that the onset of this damage is closely associated with tissue yielding. These findings held true for both axial and circumferential loading directions. Our results are the first to identify stretch-induced molecular damage to collagen in blood vessels. Furthermore, our approach is advantageous over existing methods of collagen damage detection as it is non-destructive, readily visualized, and objectively quantified. This work opens the door to revealing additional structure-function relationships in arteries. We anticipate that this approach can be used to better understand arterial damage in clinically relevant settings such as angioplasty and vascular trauma. Furthermore, CHP can be a tool for the development of microstructurally-based constitutive models and experimentally validated computational models of arterial damage and damage propagation across physical scales.

STATEMENT OF SIGNIFICANCE

Arteries play a critical role by carrying oxygen and essential nutrients throughout the body. However, trauma to the head and neck, as well as surgical interventions, can overstretch arteries and alter their mechanics. In order to better understand the cause of these changes, we employ a novel collagen hybridizing peptide (CHP) to study collagen damage in overstretched arteries. Our approach is unique in that we go beyond the fiber- and fibril-level and characterize molecular-level disruption. In addition, we image and quantify fluorescently-labeled CHP to reveal a new structure-property relationship in arterial damage. We anticipate that our approach can be used to better understand arterial damage in clinically relevant settings such as angioplasty and vascular trauma.

Experimental characterization and constitutive modeling of the biomechanical behavior of male human urethral tissues validated by histological observations

This work aims at observing the mechanical behavior of the membranous and spongy portions of urethrae sampled on male cadavers in compliance with French regulations on postmortem testing, in accordance with the Scientific Council of body donation center of Grenoble. In this perspective, a thermostatic water tank was designed to conduct ex vivo planar tension tests in a physiological environment, i.e., in a saline solution at a temperature of [Formula: see text] [Formula: see text]. In order to observe the anisotropy of the tissues, the samples were tested in two directions. Tests consisting of a series of load-unload cycles of increasing amplitudes were performed to highlight their viscous behavior. The results were then discussed according to the microstructure of tissue, which was investigated using different staining methods and histological analysis. The observed behaviors were then fitted using an anisotropic hyperelastic or a visco-hyperelastic matrix-fiber model.

Fatigue damage of collagenous tissues: experiment, modeling and simulation studies

Mechanical fatigue damage is a critical issue for soft tissues and tissue-derived materials, particularly for musculoskeletal and cardiovascular applications; yet, our understanding of the fatigue damage process is incomplete. Soft tissue fatigue experiments are often difficult and time-consuming to perform, which has hindered progress in this area. However, the recent development of soft-tissue fatigue-damage constitutive models has enabled simulation-based fatigue analyses of tissues under various conditions. Computational simulations facilitate highly controlled and quantitative analyses to study the distinct effects of various loading conditions and design features on tissue durability; thus, they are advantageous over complex fatigue experiments. Although significant work to calibrate the constitutive models from fatigue experiments and to validate predictability remains, further development in these areas will add to our knowledge of soft-tissue fatigue damage and will facilitate the design of durable treatments and devices. In this review, the experimental, modeling, and simulation efforts to study collagenous tissue fatigue damage are summarized and critically assessed.

Biaxial rupture properties of ascending thoracic aortic aneurysms

Although hundreds of samples obtained from ascending thoracic aortic aneurysms (ATAA) of patients undergoing elective surgical repair have already been characterized biomechanically, their rupture properties were always derived from uniaxial tensile tests. Due to their bulge shape, ATAAs are stretched biaxially in vivo. In order to understand the biaxial rupture of ATAAs, our group developed a novel methodology based on bulge inflation and full-field optical measurements. The objective of the current paper is threefold. Firstly, we will review the failure properties (maximum stress, maximum stretch) obtained by bulge inflation testing on a cohort of 31 patients and compare them with failure properties obtained by uniaxial tension in a previously published study. Secondly, we will investigate the relationship between the failure properties and the age of patients, showing that patients below 55years of age display significantly higher strength. Thirdly, we will define a rupture risk based on the extensibility of the tissue and we will show that this rupture risk is strongly correlated with the physiological elastic modulus of the tissue independently of the age, ATAA diameter or the aortic valve phenotype of the patient.

STATEMENT OF SIGNIFICANCE

Despite their medical importance, rupture properties of ascending thoracic aortic aneurysms (ATAA) subjected to biaxial tension were inexistent in the literature. In order to address this lack, our group developed a novel methodology based on bulge inflation and full-field optical measurements. Here we report rupture properties obtained with this methodology on 31 patients. It is shown for the first time that rupture occurs when the stretch applied to ATAAs reaches the maximum extensibility of the tissue and that this maximum extensibility correlates strongly with the elastic properties. The outcome is a better detection of at-risk individuals for elective surgical repair.

Damage Models for Soft Tissues: A Survey

Damage to soft tissues in the human body has been investigated for applications in healthcare, sports, and biomedical engineering. This paper reviews and classifies damage models for soft tissues to summarize achievements, identify new directions, and facilitate finite element analysis. The main ideas of damage modeling methods are illustrated and interpreted. A few key issues related to damage models, such as experimental data curve-fitting, computational effort, connection between damage and fractures/cracks, damage model applications, and fracture/crack extension simulation, are discussed. Several new challenges in the field are identified and outlined. This review can be useful for developing more advanced damage models and extending damage modeling methods to a variety of soft tissues.

Logarithmic rate based elasto-viscoplastic cyclic constitutive model for soft biological tissues

Based on the logarithmic rate and piecewise linearization theory, a thermodynamically consistent elasto-viscoplastic constitutive model is developed in the framework of finite deformations to describe the nonlinear time-dependent biomechanical performances of soft biological tissues, such as nonlinear anisotropic monotonic stress-strain responses, stress relaxation, creep and ratchetting. In the proposed model, the soft biological tissue is assumed as a typical composites consisting of an isotropic matrix and anisotropic fiber aggregation. Accordingly, the free energy function and stress tensor are divided into two parts related to the matrix and fiber aggregation, respectively. The nonlinear biomechanical responses of the tissues are described by the piecewise linearization theory with hypo-elastic relations of fiber aggregation. The evolution equations of viscoplasticity are formulated from the dissipation inequalities by the co-directionality hypotheses. The anisotropy is considered in the hypo-elastic relations and viscoplastic flow rules by introducing some material parameters dependent on the loading direction. Then the capability of the proposed model to describe the nonlinear time-dependent deformation of soft biological tissues is verified by comparing the predictions with the corresponding experimental results of three tissues. It is seen that the predicted monotonic stress-strain responses, stress relaxation, creep and ratchetting of soft biological tissues are in good agreement with the corresponding experimental ones.

A microstructurally inspired damage model for early venous thrombus

Accumulative damage may be an important contributor to many cases of thrombotic disease progression. Thus, a complete understanding of the pathological role of thrombus requires an understanding of its mechanics and in particular mechanical consequences of damage. In the current study, we introduce a novel microstructurally inspired constitutive model for thrombus that considers a non-uniform distribution of microstructural fibers at various crimp levels and employs one of the distribution parameters to incorporate stretch-driven damage on the microscopic level. To demonstrate its ability to represent the mechanical behavior of thrombus, including a recently reported Mullins type damage phenomenon, we fit our model to uniaxial tensile test data of early venous thrombus. Our model shows an agreement with these data comparable to previous models for damage in elastomers with the added advantages of a microstructural basis and fewer model parameters. We submit that our novel approach marks another important step toward modeling the evolving mechanics of intraluminal thrombus, specifically its damage, and hope it will aid in the study of physiological and pathological thrombotic events.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures.

Subfailure overstretch induces persistent changes in the passive mechanical response of cerebral arteries

Cerebral blood vessels are critical in maintaining the health of the brain, but their function can be disrupted by traumatic brain injury (TBI). Even in cases without hemorrhage, vessels are deformed with the surrounding brain tissue. This subfailure deformation could result in altered mechanical behavior. This study investigates the effect of overstretch on the passive behavior of isolated middle cerebral arteries (MCAs), with the hypothesis that axial stretch beyond the in vivo length alters this response. Twenty nine MCA sections from 11 ewes were tested. Vessels were subjected to a baseline test consisting of an axial stretch from a buckled state to 1.05* in vivo stretch (λIV) while pressurized at 13.3 kPa. Specimens were then subjected to a target level of axial overstretch between 1.05*λIV (λz = 1.15) and 1.52*λIV (λz = 1.63). Following overstretch, baseline tests were repeated immediately and then every 10 min, for 60 min, to investigate viscoelastic recovery. Injury was defined as an unrecoverable change in the passive mechanical response following overstretch. Finally, pressurized MCAs were pulled axially to failure. Post-overstretch response exhibited softening such that stress values at a given level of stretch were lower after injury. The observed softening also generally resulted in increased non-linearity of the stress-stretch curve, with toe region slope decreasing and large deformation slope increasing. There was no detectable change in reference configuration or failure values. As hypothesized, the magnitude of these alterations increased with overstretch severity, but only once overstretch exceeded 1.2*λIV (p < 0.001). These changes were persistent over 60 min. These changes may have significant implications in repeated TBI events and in increased susceptibility to stroke post-TBI.

Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.

A finite viscoelastic-plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress-strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress-strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.

Validation of an empirical damage model for aging and in vivo injury of the murine patellar tendon

While useful models have been proposed to predict the mechanical impact of damage in tendon and other soft tissues, the applicability of these models for describing in vivo injury and age-related degeneration has not been investigated. Therefore, the objective of this study was to develop and validate a simple damage model to predict mechanical alterations in mouse patellar tendons after aging, injury, or healing. To characterize baseline properties, uninjured controls at age 150 days were cyclically loaded across three strain levels and five frequencies. For comparison, damage was induced in mature (120 day-old) mice through either injury or aging. Injured mice were sacrificed at three or six weeks after surgery, while aged mice were sacrificed at either 300 or 570 days old. Changes in mechanical properties (relative to baseline) in the three week post-injury group were assessed and used to develop an empirical damage model based on a simple damage parameter related to the equilibrium stress at a prescribed strain (6%). From the derived model, the viscoelastic properties of the 300 day-old, 570 day-old, and six week post-injury groups were accurately predicted. Across testing conditions, nearly all correlations between predicted and measured parameters were statistically significant and coefficients of determination ranged from R² = 0.25 to 0.97. Results suggest that the proposed damage model could exploit simple in vivo mechanical measurements to predict how an injured or aged tendon will respond to complex physiological loading regimens.