A robust anisotropic hyperelastic formulation for the modelling of soft tissue

A new method for determining the ogden parameters of soft materials using indentation experiments

A full understanding of the material properties of skin tissue is crucial for exploring its tribo-mechanical behaviour. It has been widely accepted that the mechanical behaviour of skin tissue for both small and large deformations can be accurately described using a hyperelastic model, such as the one developed by Ogden. However, obtaining these Ogden parameters for in-vivo skin by in-vivo experiments no matter the indentation or suction tests is a significant challenge. The mathematical model used to describe the material behaviour during the test should consider not only the material nonlinearity but also the geometrical confinement of the tissue, the large deformations induced, and the fact that the specimens are relatively thin. A range of contact models is available to describe the contact behaviour during the indentation test. However, none of them can be used for hyperelastic materials with small thickness under large deformations. Simultaneously explaining material nonlinearity and geometric nonlinearity, either through theoretical equations or numerical calculations, poses a significant challenge. In this research, we propose a pragmatic method to obtain Ogden parameters for in-vivo skin tissue by combining experimental indentation results and numerical simulations. The indentation tests were used to obtain the force-indentation depth curves, while the numerical simulations were used to obtain the strain fields. The method assumes the material behaviour of specimens can be linearized in each small deformation increment, and the contact model developed by Hayes can be applied to accommodate each increment. Then, the linear elastic behaviour in each increment can be described by the elastic modulus E which were obtained using Hayes model, and the principal stresses in each increment were subsequently obtained using Hooke's law. By combining all stress fields, overall stress-strain curves can be constructed, from which the hyperelastic Ogden parameters can be obtained. A second numerical simulation of the hyperelastic indentation was then performed using the obtained Ogden parameters, allowing a comparison of the experimental and simulated relationships between force and indentation.

A computationally efficient gradient-enhanced healing model for soft biological tissues

Soft biological tissues, such as arterial tissue, have the ability to grow and remodel in response to damage. Computational method plays a critical role in understanding the underlying mechanisms of tissue damage and healing. However, the existing healing model often requires huge computation time and it is inconvenient to implement finite element simulation. In this paper, we propose a computationally efficient gradient-enhanced healing model that combines the advantages of the gradient-enhanced damage model, the homeostatic-driven turnover remodeling model, and the damage-induced growth model. In the proposed model, the evolution of healing-related parameters can be solved explicitly. Additionally, an adaptive time increment method is used to further reduce computation time. The proposed model can be easily implemented in Abaqus, requiring only a user subroutine UMAT. The effectiveness of proposed model is verified through a semi-analytical example, and the influence of the variables in the proposed model is investigated using uniaxial tension and open-hole plate tests. Finally, the long-term development of aneurysms is simulated to demonstrate the potential applications of the proposed model in real biomechanical problems.

Shape or size matters? Towards standard reporting of tensile testing parameters for human soft tissues: systematic review and finite element analysis

Material properties of soft-tissue samples are often derived through uniaxial tensile testing. For engineering materials, testing parameters (e.g., sample geometries and clamping conditions) are described by international standards; for biological tissues, such standards do not exist. To investigate what testing parameters have been reported for tensile testing of human soft-tissue samples, a systematic review of the literature was performed using PRISMA guidelines. Soft tissues are described as anisotropic and/or hyperelastic. Thus, we explored how the retrieved parameters compared against standards for engineering materials of similar characteristics. All research articles published in English, with an Abstract, and before 1 January 2023 were retrieved from databases of PubMed, Web of Science, and BASE. After screening of articles based on search terms and exclusion criteria, a total 1,096 articles were assessed for eligibility, from which 361 studies were retrieved and included in this review. We found that a non-tapered shape is most common (209 of 361), followed by a tapered sample shape (92 of 361). However, clamping conditions varied and were underreported (156 of 361). As a preliminary attempt to explore how the retrieved parameters might influence the stress distribution under tensile loading, a pilot study was performed using finite element analysis (FEA) and constitutive modeling for a clamped sample of little or no fiber dispersion. The preliminary FE simulation results might suggest the hypothesis that different sample geometries could have a profound influence on the stress-distribution under tensile loading. However, no conclusions can be drawn from these simulations, and future studies should involve exploring different sample geometries under different computational models and sample parameters (such as fiber dispersion and clamping effects). Taken together, reporting and choice of testing parameters remain as challenges, and as such, recommendations towards standard reporting of uniaxial tensile testing parameters for human soft tissues are proposed.

Need for transverse strain data for fitting constitutive models of arterial tissue to uniaxial tests

The study deals with the process of estimation of material parameters from uniaxial test data of arterial tissue and focuses on the role of transverse strains. Two fitting strategies are analyzed and their impact on the predictive and descriptive capabilities of the resulting model is evaluated. The standard fitting procedure (strategy A) based on longitudinal stress-strain curves is compared with the enhanced approach (strategy B) taking also the transverse strain test data into account. The study is performed on a large set of material data adopted from literature and for a variety of constitutive models developed for fibrous soft tissues. The standard procedure (A) ignoring the transverse strain test data is found rather hazardous, leading often to unrealistic predictions of the model exhibiting auxetic behaviour. In contrast, the alternative fitting method (B) ensures a realistic strain response of the model and is proved to be superior since it does not require any significant demands of computational effort or additional testing. The results presented in this paper show that even the artificial transverse strain data (i.e., not measured during testing but generated ex post based on assumed Poisson's ratio) are much less hazardous than total disregard of the transverse strain response.

A data-driven computational model for engineered cardiac microtissues

Engineered heart tissues (EHTs) present a potential solution to some of the current challenges in the treatment of heart disease; however, the development of mature, adult-like cardiac tissues remains elusive. Mechanical stimuli have been observed to improve whole-tissue function and cardiomyocyte (CM) maturation, although our ability to fully utilize these mechanisms is hampered, in part, by our incomplete understanding of the mechanobiology of EHTs. In this work, we leverage experimental data, produced by a mechanically tunable experimental setup, to introduce a tissue-specific computational modeling pipeline of EHTs. Our new modeling pipeline generates simulated, image-based EHTs, capturing ECM and myofibrillar structure as well as functional parameters estimated directly from experimental data. This approach enables the unique estimation of EHT function by data-based estimation of CM active stresses. We use this experimental and modeling pipeline to study different mechanical environments, where we contrast the force output of the tissue with the computed active stress of CMs. We show that the significant differences in measured experimental forces can largely be explained by the levels of myofibril formation achieved by the CMs in the distinct mechanical environments, with active stress showing more muted variations across conditions. The presented model also enables us to dissect the relative contributions of myofibrils and extracellular matrix to tissue force output, a task difficult to address experimentally. These results highlight the importance of tissue-specific modeling to augment EHT experiments, providing deeper insights into the mechanobiology driving EHT function. STATEMENT OF SIGNIFICANCE: Engineered heart tissues (EHTs) have the potential to revolutionize the way heart disease is treated. However, developing mature cardiomyocytes (CM) in these tissues remains a challenge due, in part, to our incomplete understanding of the fundamental biomechanical mechanisms that drive EHT development. This work integrates the experimental data of an EHT platform developed to study the influence of mechanics in CM maturation with computational biomechanical models. This approach is used to augment conclusions obtained in-vitro - by measuring quantities such as cell stress and strain - and to dissect the relevance of each component in the whole tissue performance. Our results show how a combination of specialized in-silico and in-vitro approaches can help us better understand the mechanobiology of EHTs.

Computational modeling of the effect of skin pinch and stretch on subcutaneous injection of monoclonal antibodies using autoinjector devices

Subcutaneous injection of monoclonal antibodies (mAbs) has experienced unprecedented growth in the pharmaceutical industry due to its benefits in patient compliance and cost-effectiveness. However, the impact of different injection techniques and autoinjector devices on the drug's transport and uptake is poorly understood. Here, we develop a biphasic large-deformation chemomechanical model that accounts for the components of the extracellular matrix that govern solid deformation and fluid flow within the subcutaneous tissue: interstitial fluid, collagen fibers and negatively charged proteoglycan aggregates. We use this model to build a high-fidelity representation of a virtual patient performing a subcutaneous injection of mAbs. We analyze the impact of the pinch and stretch methods on the injection dynamics and the use of different handheld autoinjector devices. The results suggest that autoinjector base plates with a larger device-skin contact area cause significantly lower tissue mechanical stress, fluid pressure and fluid velocity during the injection process. Our simulations indicate that the stretch technique presents a higher risk of intramuscular injection for autoinjectors with a relatively long needle insertion depth.

Fiber orientation and crimp level might control the auxetic effect of biological tissues

We propose an analytical micromechanical model for studying the lamellar-composite-like structure of fibrous soft tissue. The tissue under consideration is made up of several lamellae, and is designed to resemble the annulus fibrosus (AF) tissue or media layer of arterial tissue, for example. The collagen fibers are arranged in parallel in each lamella and the fiber orientation differs from one lamella to its neighbors. The parallel fibers in each lamella of AF tissue, for example, have been observed to have a crimped microstructure. The proposed model incorporates this quality, considering fiber waviness as a sinusoidal shape and taking into account the fiber dispersion in different layers, where both fiber and matrix are considered as solid phases. We find that collagen-fiber waviness and layer orientation have a significant influence on Poisson's ratio. The effective Poisson's ratio predicted by the proposed model demonstrates that the crimped collagen fiber microstructure might weaken the auxetic effect of fibrous soft tissue, which might explain why, as the literature suggests, the auxetic behavior is more difficult to observe than large Poisson's ratios. As opposed to the many studies that use the well-known hyperelastic fiber-based constitutive model, in which out-of-plane expansion is often observed, the present work explains the auxetic response found in modeling and in experimental data from the perspective of collagen fiber microstructure.

On a three-dimensional model for the description of the passive characteristics of skeletal muscle tissue

In this work, a three-dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation-dependent axial ([Formula: see text], [Formula: see text], [Formula: see text]) and semi-confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at [Formula: see text] (mode I), fibre elongation at [Formula: see text] (mode II) and a neutral state of the fibres at [Formula: see text] where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation-dependent axial compression ([Formula: see text] kPa) occurs when the fibres are oriented perpendicular to the loading direction ([Formula: see text]) and are thus stretched during loading. Semi-confined compression experiments yielded the stiffest tissue ([Formula: see text] kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

Uncertainty Quantification in the In Vivo Image-Based Estimation of Local Elastic Properties of Vascular Walls

Introduction: Patient-specific computational models are a powerful tool for planning cardiovascular interventions. However, the in vivo patient-specific mechanical properties of vessels represent a major source of uncertainty. In this study, we investigated the effect of uncertainty in the elastic module (E) on a Fluid–Structure Interaction (FSI) model of a patient-specific aorta. Methods: The image-based χ-method was used to compute the initial E value of the vascular wall. The uncertainty quantification was carried out using the generalized Polynomial Chaos (gPC) expansion technique. The stochastic analysis was based on four deterministic simulations considering four quadrature points. A deviation of about ±20% on the estimation of the E value was assumed. Results: The influence of the uncertain E parameter was evaluated along the cardiac cycle on area and flow variations extracted from five cross-sections of the aortic FSI model. Results of stochastic analysis showed the impact of E in the ascending aorta while an insignificant effect was observed in the descending tract. Conclusions: This study demonstrated the importance of the image-based methodology for inferring E, highlighting the feasibility of retrieving useful additional data and enhancing the reliability of in silico models in clinical practice.

Biomechanics of keratoconus: Two numerical studies

BACKGROUND

The steep cornea in keratoconus can greatly impair eyesight. The etiology of keratoconus remains unclear but early injury that weakens the corneal stromal architecture has been implicated. To explore keratoconus mechanics, we conducted two numerical simulation studies.

METHODS

A finite-element model describing the five corneal layers and the heterogeneous mechanical behaviors of the ground substance and lamellar collagen-fiber architecture in the anterior and posterior stroma was developed using the Holzapfel-Gasser-Ogden constitutive model. The geometry was from a healthy subject. Its stroma was divided into anterior, middle, and posterior layers to assess the effect of changing regional mechanical parameters on corneal displacement and maximum principal stress under intraocular pressure. Specifically, the effect of softening an inferocentral corneal button, the collagen-based tissues throughout the whole cornea, or specific stromal layers in the button was examined. The effect of simply disorganizing the orthogonally-oriented posterior stromal fibers in the button was also assessed. The healthy cornea was also subjected to eye rubbing-like loading to identify the corneal layer(s) that experienced the most tensional stress.

RESULTS

Conical deformation and corneal thinning emerged when the corneal button or the mid-posterior stroma of the button underwent gradual softening or when the collagen fibers in the mid-posterior stroma of the button were dispersed. Softening the anterior layers of the button or the whole cornea did not evoke conical deformation. Button softening greatly increased and disrupted the stress on Bowman's membrane while mid-posterior stromal softening increased stress in the anterior layers. Eye rubbing profoundly stressed the deep posterior stroma while other layers were negligibly affected.

DISCUSSION

These observations suggest that keratoconus could be initiated, at least partly, by mechanical instability/damage in the mid-posterior stroma that then imposes stress on the anterior layers. This may explain why subclinical keratoconus is marked by posterior but not anterior elevation on videokeratoscopy.

Modeling large-volume subcutaneous injection of monoclonal antibodies with anisotropic porohyperelastic models and data-driven tissue layer geometries

Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has become one of the fastest-growing fields in the pharmaceutical industry. The transport and mechanical processes behind large volume injections are poorly understood. Here, we leverage a large-deformation poroelastic model to study high-dose, high-speed subcutaneous injection. We account for the anisotropy of subcutaneous tissue using of a fibril-reinforced porohyperelastic model. We also incorporate the multi-layer structure of the skin tissue, generating data-driven geometrical models of the tissue layers using histological data. We analyze the impact of handheld autoinjectors on the injection dynamics for different patient forces. Our simulations show the importance of considering the large deformation approach to model large injection volumes. This work opens opportunities to better understand the mechanics and transport processes that occur in large-volume subcutaneous injections of mAbs.

On the structural origin of the anisotropy in the myocardium: Multiscale modeling and analysis

Due to structural heterogeneities within the tissue, the myocardium displays an orthotropic material behavior. However, the link between the microstructure and the macroscopic mechanical properties is still not fully established. In particular, if it is admitted that the cardiomyocyte organization induces a transversely isotropic symmetry, the relative role in the observed orthotropic symmetry of cardiomyocyte orientation variation and perimysium collagen "sheetlet" structure, two mechanisms occurring at different scales, is still a matter of debate. In order to shed light on this question, we designed a multiscale model of the myocardium, bridging the cell, sheetlet and tissue scales. More precisely, we compared the macroscopic anisotropy obtained by homogenization of different mesostructures consisting in cardiomyocytes and extracellular collageneous layers, also taking into account the variation of cardiomyocyte and sheetlet orientations on the macroscale, to available experimental data. This study confirms the importance of sheetlets layers in assuring the tissue's anisotropic response, as cardiomyocytes-only mesostructures cannot reproduce the observed anisotropy. Moreover, our model shows the existence of a size effect in the myocardial tissue shear properties, which will require further experimental analysis.

Effect of balloon pre-dilation on performance of self-expandable nitinol stent in femoropopliteal artery

Balloon pre-dilation is usually performed before implantation of a nitinol stent in a femoropopliteal artery in a case of severe blockage or calcified plaque. However, its effect on performance of the nitinol stent in a diseased femoropopliteal artery has not been studied yet. This study compares the outcomes of stenting with pre-dilation and without it by modelling the entire processes of stent deployment. Fatigue deformation of the implanted stent is also modelled under diastolic-systolic blood pressure, repetitive bending, torsion, axial compression and their combination. Reduced level of stress in the stent occurs after stenting with pre-dilation, but causing the increased damage in the media layer, i.e. the middle layer of the arterial wall. Generally, pre-dilation increases the risk of nitinol stent's fatigue failure. Additionally, the development of in-stent restenosis is predicted based on the stenting-induced tissue damage in the media layer, and no severe mechanical irritation is induced to the media layer by pre-dilation, stent deployment or fatigue loading.

Computer simulation of the wound process (review of literature)

Relevance. Computer simulation is a mathematical modeling process performed on a computer that is designed to predict the behavior or results of a real or physical system. Computer simulation has a number of advantages over classical models of animal experiments: the cheapness of the method (the need to acquire and maintain animals disappears by itself), the speed of obtaining results, the absence of bioethical problems, the ability to change the conditions of the experiment, etc.

he purpose of this study is to review the methods of computer simulation of the wound process, to identify the shortcomings of the models and propose ways to solve them, as well as to select the best existing model for describing wound regeneration.

Material and methods. In the course of this work, an analysis was made of foreign and domestic literature on the problem of computer modeling of the wound process.

Results. After analyzing the relevant literature on this topic, the problem is seen precisely in the insufficiently studied process of wound regeneration, since many different cells, cytokines, growth factors, enzymes, fibrillar proteins, etc. take part in it. The models that currently exist describe wound regeneration only in an extremely generalized way, which does not allow us to apply them in clinical situations. Analyzing literature sources, we came to the conclusion that both numerical approaches, both cellular-biochemical (the first type of models) and phenomenological (the second type) are applicable in the case of wound modeling and can be used very successfully. The problem is that on the basis of one approach it is impossible to display a complete picture of wound healing, in this way it is possible to predict only individual regeneration parameters necessary for certain purposes due to the complexity and versatility of this typical pathophysiological process.

Conclusion. Computer modeling of wounds is still a controversial and complex topic. Existing models are not intended to describe all the processes occurring in a healing wound. It is much more productive to describe the various phenomena during healing separately. This is due to the fact that many elements are involved in the regeneration of the skin, which are almost impossible to take into account in full. The available models are of exclusively scientific value, consisting in attempts to understand all complex processes and interactions. Practical application is difficult, since existing models require specific input data that require highly specialized equipment. If we abstract from all this, then the best existing model of the first type is the model of the authors Yangyang Wang, Christian F. Guerrero-Juarez, Yuchi Qiu and co-authors, in addition to it, any of the described phenomenological models will do. 

Three-Dimensional Anisotropic Hyperelastic Constitutive Model Describing the Mechanical Response of Human and Mouse Cervix

The mechanical function of the uterine cervix is critical for a healthy pregnancy. During pregnancy, the cervix undergoes significant softening to allow for a successful delivery. Abnormal cervical remodeling is suspected to contribute to preterm birth. Material constitutive models describing known biological shifts in pregnancy are essential to predict the mechanical integrity of the cervix. In this work, the material response of human cervical tissue under spherical indentation and uniaxial tensile tests loaded along different anatomical directions is experimentally measured. A deep-learning segmentation tool is applied to capture the tissue deformation during the uniaxial tensile tests. A 3-dimensional, equilibrium anisotropic continuous fiber constitutive model is formulated, considering collagen fiber directionality, fiber bundle dispersion, and the entropic nature of wavy cross-linked collagen molecules. Additionally, the universality of the material model is demonstrated by characterizing previously published mouse cervix mechanical data. Overall, the proposed material model captures the tension-compression asymmetric material responses and the remodeling characteristics of both human and mouse cervical tissue. The pregnant (PG) human cervix (mean locking stretch ζ=2.4, mean initial stiffness ξ=12 kPa, mean bulk modulus κ=0.26 kPa, mean dispersion b=1.0) is more compliant compared with the nonpregnant (NP) cervix (mean ζ=1.3, mean ξ=32 kPa, mean κ=1.4 kPa, mean b=1.4). Creating a validated material model, which describes the role of collagen fiber directionality, dispersion, and crosslinking, enables tissue-level biomechanical simulations to determine which material and anatomical factors drive the cervix to open prematurely. STATEMENT OF SIGNIFICANCE: In this study, we report a 3D anisotropic hyperelastic constitutive model based on Langevin statistic mechanics and successfully describe the material behavior of both human and mouse cervical tissue using this model. This model bridges the connection between the extracellular matrix (ECM) microstructure remodeling and the macro mechanical properties change of the cervix during pregnancy via microstructure-associated material parameters. This is the first model, to our knowledge, to connect the the entropic nature of wavy cross-linked collagen molecules with the mechanical behavior of the cervix. Inspired by microstructure, this model provides a foundation to understand further the relationship between abnormal cervical ECM remodeling and preterm birth. Furthermore, with a relatively simple form, the proposed model can be applied to other fibrous tissues in the future.

Introduction of a Novel Image-Based and Non-Invasive Method for the Estimation of Local Elastic Properties of Great Vessels

Background: In the context of a growing demand for the use of in silico models to meet clinical requests, image-based methods play a crucial role. In this study, we present a parametric equation able to estimate the elasticity of vessel walls, non-invasively and indirectly, from information uniquely retrievable from imaging. Methods: A custom equation was iteratively refined and tuned from the simulations of a wide range of different vessel models, leading to the definition of an indirect method able to estimate the elastic modulus E of a vessel wall. To test the effectiveness of the predictive capability to infer the E value, two models with increasing complexity were used: a U-shaped vessel and a patient-specific aorta. Results: The original formulation was demonstrated to deviate from the ground truth, with a difference of 89.6%. However, the adoption of our proposed equation was found to significantly increase the reliability of the estimated E value for a vessel wall, with a mean percentage error of 9.3% with respect to the reference values. Conclusion: This study provides a strong basis for the definition of a method able to estimate local mechanical information of vessels from data easily retrievable from imaging, thus potentially increasing the reliability of in silico cardiovascular models.

Understanding the deformation gradient in Abaqus and key guidelines for anisotropic hyperelastic user material subroutines (UMATs)

This tutorial paper provides a step-by-step guide to developing a comprehensive understanding of the different forms of the deformation gradient used in Abaqus, and outlines a number of key issues that must be considered when developing an Abaqus user defined material subroutine (UMAT) in which the Cauchy stress is computed from the deformation gradient. Firstly, we examine the "classical" forms of global and local deformation gradients. We then show that Abaqus/Standard does not use the classical form of the local deformation gradient when continuum elements are used, and we highlight the important implications for UMAT development. We outline the key steps that must be implemented in developing an anisotropic fibre-reinforced hyperelastic UMAT for use with continuum elements and local orientation systems. We also demonstrate that a classical local deformation gradient is provided by Abaqus/Standard if structural (shell and membrane) elements are used, and by Abaqus/Explicit for all element types. We emphasise, however, that the majority of biomechanical simulations rely on the use of continuum elements with a local coordinate system in Abaqus/Standard, and therefore the development of a hyperelastic UMAT requires an in-depth and precise understanding of the form of the non-classical deformation gradient provided as input by Abaqus. Several worked examples and case studies are provided for each section, so that the details and implications of the form of the deformation gradient can be fully understood. For each worked example in this tutorial paper the source files and code (Abaqus input files, UMATs, and Matlab script files) are provided, allowing the reader to efficiently explore the implications of the form of the deformation gradient in the development of a UMAT.

A new constitutive model for permanent deformation of blood clots with application to simulation of aspiration thrombectomy

As a first line option in the treatment of acute ischemic stroke (AIS), direct aspiration is a fast and effective technique with promising outcomes. In silico models are widely used for design and preclinical assessment of new developed devices and therapeutic methods. Accurate modelling of the mechanical behaviour of blood clot is a key factor in the design and simulation of aspiration devices. In this study we develop a new constitutive model which incorporates the unrecoverable plastic deformation of clots. The model is developed based on the deformation-induced microstructural changes in fibrin network, including the formation and dissociation of the cross-links between fibrin fibres. The model is calibrated using previously reported experimentally measured permanent clot deformation following uniaxial stretching. The calibrated plasticity model is then used to simulate aspiration thrombectomy. Results reveal that inclusion of permanent plastic deformation results in ∼ 15 % increase in clot aspiration length at an applied aspiration pressure of 100 mmHg. The constitutive law developed in this study provides a basis for improved design and evaluation of novel aspiration catheters leading to increased first-pass revascularization rate.

A viscoelastic model for human myocardium

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena. STATEMENT OF SIGNIFICANCE: The viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.

Mechanical properties of whole-body soft human tissues: a review

The mechanical properties of soft tissues play a key role in studying human injuries and their mitigation strategies. While such properties are indispensable for computational modelling of biological systems, they serve as important references in loading and failure experiments, and also for the development of tissue simulants. To date, experimental studies have measured the mechanical properties of peripheral tissues (e.g. skin)in-vivoand limited internal tissuesex-vivoin cadavers (e.g. brain and the heart). The lack of knowledge on a majority of human tissues inhibit their study for applications ranging from surgical planning, ballistic testing, implantable medical device development, and the assessment of traumatic injuries. The purpose of this work is to overcome such challenges through an extensive review of the literature reporting the mechanical properties of whole-body soft tissues from head to toe. Specifically, the available linear mechanical properties of all human tissues were compiled. Non-linear biomechanical models were also introduced, and the soft human tissues characterized using such models were summarized. The literature gaps identified from this work will help future biomechanical studies on soft human tissue characterization and the development of accurate medical models for the study and mitigation of injuries.

Influence of shape-memory stent grafts on local aortic compliance

The effect of repair techniques on the biomechanics of the aorta is poorly understood, resulting in significant levels of postoperative complications for patients worldwide. This study presents a computational analysis of the influence of Nitinol-based devices on the biomechanical performance of a healthy patient-specific human aorta. Simulations reveal that Nitinol stent-grafts stretch the artery wall so that collagen is stretched to a straightened high-stiffness configuration. The high-compliance regime (HCR) associated with low diastolic lumen pressure is eliminated, and the artery operates in a low-compliance regime (LCR) throughout the entire cardiac cycle. The slope of the lumen pressure–area curve for the LCR post-implantation is almost identical to that of the native vessel during systole. This negligible change from the native LCR slope occurs because the stent-graft increases its diameter from the crimped configuration during deployment so that it reaches a low-stiffness unloading plateau. The effective radial stiffness of the implant along this unloading plateau is negligible compared to the stiffness of the artery wall. Provided the Nitinol device unloads sufficiently during deployment to the unloading plateau, the degree of oversizing has a negligible effect on the pressure–area response of the vessel, as each device exerts approximately the same radial force, the slope of which is negligible compared to the LCR slope of the native artery. We show that 10% oversizing based on the observed diastolic diameter in the mid descending thoracic aorta results in a complete loss of contact between the device and the wall during systole, which could lead to an endoleak and stent migration. 20% oversizing reaches the Dacron enforced area limit (DEAL) during the pulse pressure and results in an effective zero-compliance in the later portion of systole.

An Implementation of Patient-Specific Biventricular Mechanics Simulations With a Deep Learning and Computational Pipeline

Parameterised patient-specific models of the heart enable quantitative analysis of cardiac function as well as estimation of regional stress and intrinsic tissue stiffness. However, the development of personalised models and subsequent simulations have often required lengthy manual setup, from image labelling through to generating the finite element model and assigning boundary conditions. Recently, rapid patient-specific finite element modelling has been made possible through the use of machine learning techniques. In this paper, utilising multiple neural networks for image labelling and detection of valve landmarks, together with streamlined data integration, a pipeline for generating patient-specific biventricular models is applied to clinically-acquired data from a diverse cohort of individuals, including hypertrophic and dilated cardiomyopathy patients and healthy volunteers. Valve motion from tracked landmarks as well as cavity volumes measured from labelled images are used to drive realistic motion and estimate passive tissue stiffness values. The neural networks are shown to accurately label cardiac regions and features for these diverse morphologies. Furthermore, differences in global intrinsic parameters, such as tissue anisotropy and normalised active tension, between groups illustrate respective underlying changes in tissue composition and/or structure as a result of pathology. This study shows the successful application of a generic pipeline for biventricular modelling, incorporating artificial intelligence solutions, within a diverse cohort.

A Review of Biomechanics Analysis of the Umbilical-Placenta System With Regards to Diseases

Placenta is an important organ that is crucial for both fetal and maternal health. Abnormalities of the placenta, such as during intrauterine growth restriction (IUGR) and pre-eclampsia (PE) are common, and an improved understanding of these diseases is needed to improve medical care. Biomechanics analysis of the placenta is an under-explored area of investigation, which has demonstrated usefulness in contributing to our understanding of the placenta physiology. In this review, we introduce fundamental biomechanics concepts and discuss the findings of biomechanical analysis of the placenta and umbilical cord, including both tissue biomechanics and biofluid mechanics. The biomechanics of placenta ultrasound elastography and its potential in improving clinical detection of placenta diseases are also discussed. Finally, potential future work is listed.

Growth-profile configuration for specific deformations of tubular organs: A study of growth-induced thinning and dilation of the human cervix

Growth is a significant factor that results in deformations of tubular organs, and particular deformations associated with growth enable tubular organs to perform certain physiological functions. Configuring growth profiles that achieve particular deformation patterns is critical for analyzing potential pathological conditions and for developing corresponding clinical treatments for tubular organ dysfunctions. However, deformation-targeted growth is rarely studied. In this article, the human cervix during pregnancy is studied as an example to show how cervical thinning and dilation are generated by growth. An advanced hyperelasticity theory called morphoelasticity is employed to model the deformations, and a growth tensor is used to represent growth in three principle directions. The computational results demonstrate that both negative radial growth and positive circumferential growth facilitate thinning and dilation. Modeling such mixed growth represents an advancement beyond commonly used uniform growth inside tissues to study tubular deformations. The results reveal that complex growth may occur inside tissues to achieve certain tubular deformations. Integration of further biochemical and cellular activities that initiate and mediate such complex growth remains to be explored.

A literature review on large intestinal hyperelastic constitutive modeling

Impacts, traumas and strokes are spontaneously life-threatening, but chronic symptoms strangle patient every day. Colorectal tissue mechanics in such chronic situations not only regulates the physio-psychological well-being of the patient, but also confirms the level of comfort and post-operative clinical outcomes. Numerous uniaxial and multiaxial tensile experiments on healthy and affected samples have evidenced significant differences in tissue mechanical behavior and strong colorectal anisotropy across each layer in thickness direction and along the length. Furthermore, this study reviewed various forms of passive constitutive models for the highly fibrous colorectal tissue ranging from the simplest linearly elastic and the conventional isotropic hyperelastic to the most sophisticated second harmonic generation image based anisotropic mathematical formulation. Under large deformation, the isotropic description of tissue mechanics is unequivocally ineffective which demands a microstructural based tissue definition. Therefore, the information collected in this review paper would present the current state-of-the-art in colorectal biomechanics and profoundly serve as updated computational resources to develop a sophisticated characterization of colorectal tissues.

A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model [1, 2] to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

Linear elastic and hyperelastic studies of equine hoof mechanical response at different hydration levels

Most simulation studies on equine hoof biomechanics employed linear elastic (LE) material models. However, the equine hoof wall's stress-strain relationship is nonlinear and varies with hydration level. Therefore, it is essential to investigate the accuracy of the LE model compared to more advanced material models, such as hyperelastic (HE) or viscoelastic models. The current research investigated performances of LE and three HE models (Mooney-Rivlin, Neo-Hookean, and Marlow) in describing equine hoof's mechanical behavior using finite element (FE) analysis. In the first attempt, a rectangular tissue specimen was simulated using the previously published experimental data. The Marlow HE model predicted the hoof wall stress-strain curve more accurately than the LE, Mooney-Rivlin, and Neo-Hookean models. The LE model accuracy, compared with the experimental results, varied within the reported range of the strain. However, the Marlow HE model perfectly matched the experimental data for a wide range of strains. In the second attempt, the entire hoof, including nine associated tissues, was modeled from computed tomography (CT) scans of an equine forelimb, and analyzed at trotting and standing modes of locomotion. The effect of environmental humidity on the hoof wall material properties was incorporated at four hydration levels; 0%, 53%, 75%, and 100%. The simulation results of the LE and HE models indicated that the minimum principal strain distribution on the hoof wall remained under 2% for various hydration levels and gait conditions. The numerical results of the Marlow HE model demonstrated better agreement with published experimental data compared to the LE, Mooney-Rivlin, and Neo-Hookean models. Higher hydration levels significantly increased the strains - a potential explanation could be the fact that the higher hydration levels decreased stiffness of the hoof wall tissues and ultimately increased strains. Higher ground reaction forces increased the von Mises stress at various points in the hoof wall, especially in the quarter regions and close to the coronet, where cracks and fractures are found more often in the physiological conditions.

A homogenized constrained mixture model of restenosis and vascular remodelling after balloon angioplasty

Restenosis is one of the main adverse effects of the treatment of atherosclerosis through balloon angioplasty or stenting. During the intervention, the arterial wall is overstretched, causing a cascade of cellular events and subsequent neointima formation. This mechanical stimulus and its mechanobiological effects can be reproduced in biomechanical simulations. The aim of these models is to predict the long-term outcome of these procedures, to help increase the understanding of restenosis formation and to allow for in silico optimization of the treatment. We propose a predictive finite-element model of restenosis, using the homogenized constrained mixture modelling framework designed to model growth and remodelling in soft tissues. We compare the results with clinical observations in human coronary arteries and experimental findings in non-human primate models. We also explore the model's clinical relevance by testing its response to different balloon loads and to the use of drug-eluting balloons. The comparison of the results with experimental data shows the relevance of the model. We show its ability to predict both inward and outward remodelling as observed in vivo and we show the importance of an improved understanding of restenosis formation from a biomechanical point of view.

Intervertebral Disc Mechanics With Nucleotomy: Differences Between Simple and Dual Loading

Painful herniated discs are treated surgically by removing extruded nucleus pulposus (NP) material (nucleotomy). NP removal through enzymatic digestion is also commonly performed to initiate degenerative changes to study potential biological repair strategies. Experimental and computational studies have shown a decrease in disc stiffness with nucleotomy under single loading modalities, such as compression-only or bending-only loading. However, studies that apply more physiologically relevant loading conditions, such as compression in combination with bending or torsion, have shown contradicting results. We used a previously validated bone-disc-bone finite element model (Control) to create a Nucleotomy model to evaluate the effect of dual loading conditions (compression with torsion or bending) on intradiscal deformations. While disc joint stiffness decreased with nucleotomy under single loading conditions, as commonly reported in the literature, dual loading resulted in an increase in bending stiffness. More specifically, dual loading resulted in a 40% increase in bending stiffness under flexion and extension and a 25% increase in stiffness under lateral bending. The increase in bending stiffness was due to an increase and shift in compressive stress, where peak stresses migrated from the NP-annulus interface to the outer annulus. In contrast, the decrease in torsional stiffness was due to greater fiber reorientation during compression. In general, large radial strains were observed with nucleotomy, suggesting an increased risk for delamination or degenerative remodeling. In conclusion, the effect of nucleotomy on disc mechanics depends on the type and complexity of applied loads.

Image-derived modeling of nucleus strain amplification associated with chromatin heterogeneity

Beyond the critical role of cell nuclei in gene expression and DNA replication, they also have a significant influence on cell mechanosensation and migration. Nuclear stiffness can impact force transmission and, furthermore, act as a physical barrier to translocation across tight spaces. As such, it is of wide interest to accurately characterize nucleus mechanical behavior. In this study, we present a computational investigation of the in situ deformation of a heterogeneous chondrocyte nucleus. A methodology is developed to accurately reconstruct a three-dimensional finite-element model of a cell nucleus from confocal microscopy. By incorporating the reconstructed nucleus into a chondrocyte model embedded in pericellular and extracellular matrix, we explore the relationship between spatially heterogeneous nuclear DNA content, shear stiffness, and resultant shear strain. We simulate an externally applied extracellular matrix shear deformation and compute intranuclear strain distributions, which are directly compared with corresponding experimentally measured distributions. Simulations suggest that the mechanical behavior of the nucleus is highly heterogeneous, with a nonlinear relationship between experimentally measured grayscale values and corresponding local shear moduli (μn). Three distinct phases are identified within the nucleus: a low-stiffness mRNA-rich interchromatin phase (0.17 kPa ≤ μn ≤ 0.63 kPa), an intermediate-stiffness euchromatin phase (1.48 kPa ≤ μn ≤ 2.7 kPa), and a high-stiffness heterochromatin phase (3.58 kPa ≤ μn ≤ 4.0 kPa). Our simulations also indicate that disruption of the nuclear envelope associated with lamin A/C depletion significantly increases nuclear strain in regions of low DNA concentration. We further investigate a phenotypic shift of chondrocytes to fibroblast-like cells, a signature for osteoarthritic cartilage, by increasing the contractility of the actin cytoskeleton to a level associated with fibroblasts. Peak nucleus strains increase by 35% compared to control, with the nucleus becoming more ellipsoidal. Our findings may have broad implications for current understanding of how local DNA concentrations and associated strain amplification can impact cell mechanotransduction and drive cell behavior in development, migration, and tumorigenesis.

Development of an FEA framework for analysis of subject-specific aortic compliance based on 4D flow MRI

This paper presents a subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel during the cardiac cycle uncovered through our MRI investigations. A microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle cell stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle cell contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin digestion and SMC activation experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower distally. The analyses presented in this paper provide new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. Furthermore, this subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development. STATEMENT OF SIGNIFICANCE: This study provides a significant advance in in-silico medicine by capturing the structure/function relationship of the subject-specific human aorta presented in our previous MRI analyses. A physiologically based aortic constitutive model is developed, and simulations reveal that internal vessel contractility must be incorporated, along with collagen strain stiffening, to accurately predict the in-vivo non-linear pressure-area relationship. Furthermore, this is the first subject-specific model to predict spatial variation in the volume fractions of aortic wall constituents. Previous studies perform phenomenological hyperelastic curve fits to medical imaging data and ignore the prestress contribution of elastin, collagen, and SMCs and the associated zero-pressure reference state of the vessel. This novel MRI/FEA framework can be used as an in-silico diagnostic tool for the early stage detection of aortic pathologies.

A computational study of fatigue resistance of nitinol stents subjected to walk-induced femoropopliteal artery motion

Fatigue resistance of nitinol stents implanted in femoropopliteal arteries is a critical issue because of their harsh biomechanical environment. Limb flexions due to daily walk expose the femoropopliteal arteries and, subsequently, the implanted stents to large cyclic deformations, which may lead to fatigue failure of the smart self-expandable stents. For the first time, this paper utilised the up-to-date measurements of walk-induced motion of a human femoropopliteal artery to investigate the fatigue behaviour of nitinol stent after implantation. The study was carried out by modelling the processes of angioplasty, stent crimping, self-expansion and deformation under diastolic-systolic blood pressure, repetitive bending, torsion and axial compression as well as their combination. The highest risk of fatigue failure of the nitinol stent occurs under a combined loading condition, with the bending contributing the most, followed by compression and torsion. The pulsatile blood pressure alone hardly causes any fatigue failure of the stent. The work is significant for understanding and improving the fatigue performance of nitinol stents through innovative design and procedural optimisation.

Development of a test method to investigate mode II fracture and dissection of arteries

The current study presents the development and implementation of a bespoke experimental technique to generate and characterise mode II crack initiation and propagation in arterial tissue. The current study begins with a demonstration that lap-shear testing of arterial tissue results in mixed mode fracture, rather than mode II. We perform a detailed computational design of a bespoke experimental method (which we refer to as a shear fracture ring test (SFRT)) to robustly and repeatably generate mode II crack initiation and propagation in arteries. This method is based on generating a localised region of high shear adjacent to a cylindrical loading bar. Placement of a radial notch in this region of high shear stress is predicted to result in a kinking of the crack during a mode II initiation and propagation of the crack over a long distance in the circumferential (c)-direction along the circumferential-axial (c-a) plane. Fabrication and experimental implementation of the SFRT on excised ovine aorta specimens confirms that the bespoke test method results in pure mode II initiation and propagation. We demonstrate that the mode II fracture strength along the c-a plane is eight times higher than the corresponding mode I strength determined from a standard peel test. We also calibrate the mode II fracture energy based on our measurement of crack propagation rates. The mechanisms of fracture uncovered in the current study, along with our quantification of mode II fracture properties have significant implications for current understanding of the biomechanical conditions underlying aortic dissection.

The effect of large deformation on Poisson's ratio of brain white matter: An experimental study

A more Accurate description of the mechanical behavior of brain tissue could improve the results of computational models. While most studies have assumed brain tissue as an incompressible material with constant Poisson's ratio of almost 0.5 and constructed their modeling approach according to this assumption, the relationship between this ratio and levels of applied strains has not yet been studied. Since the mechanical response of the tissue is highly sensitive to the value of Poisson's ratio, this study was designed to investigate the characteristics of the Poisson's ratio of brain tissue at different levels of applied strains. Samples were extracted from bovine brain tissue and tested under unconfined compression at strain values of 5%, 10%, and 30%. Using an image processing method, the axial and transverse strains were measured over a 60-s period to calculate the Poisson's ratio for each sample. The results of this study showed that the Poisson's ratio of brain tissue at strain levels of 5% and 10% was close to 0.5, and assuming brain tissue as an incompressible material is a valid assumption at these levels of strain. For samples under 30% compression, this ratio was higher than 0.5, which could suggest that under strains higher than the brain injury threshold (approximately 18%), tissue integrity was impaired. Based on these observations, it could be concluded that for strain levels higher than the injury threshold, brain tissue could not be assumed as an incompressible material, and new material models need to be proposed to predict the material behavior of the tissue. In addition, the results showed that brain tissue under unconfined compression uniformly stretched in the transverse direction, and the bulging in the samples is negligible.

A thermodynamic transient cross-bridge model for prediction of contractility and remodelling of the ventricle

Cardiac hypertrophy is an adaption of the heart to a change in cardiovascular loading conditions. The current understanding is that progression may be stress or strain driven, but the multi-scale nature of the cellular remodelling processes have yet to be uncovered. In this study, we develop a model of the contractile left ventricle, with the active cell tension described by a thermodynamically motivated cross-bridge cycling model. Simulation of the transient recruitment of myosin results in correct patterns of ventricular pressure predicted over a cardiac cycle. We investigate how changes in tissue loading and associated deviations in transient force generation can drive restructuring of cellular myofibrils in the heart wall. Our thermodynamic framework predicts in-series sarcomere addition (eccentric remodelling) in response to volume overload, and sarcomere addition in parallel (concentric remodelling) in response to valve and signalling disfunction. This framework provides a significant advance in the current understanding of the fundamental sub-sarcomere level biomechanisms underlying cardiac remodelling. Simulations reveal that pathological tissue loading conditions can significantly alter actin-myosin cross-bridge cycling over the course of the cardiac cycle. The resultant variation in sarcomere stress pushes an imbalance between the internal free energy of the myofibril and that of unbound contractile proteins, initiating remodelling. The link between cross-bridge thermodynamics and myofibril remodelling proposed in this study may significantly advance current understanding of cardiac disease onset.

An open source pipeline for design of experiments for hyperelastic models of the skin with applications to keloids

The aim of this work is to characterize the mechanical parameters governing the in-plane behavior of human skin and, in particular, of a keloid-scar. We consider 2D hyperelastic bi-material model of a keloid and the surrounding healthy skin. The problem of finding the optimal model parameters that minimize the misfit between the model observations and the in vivo experimental measurements is solved using our in-house developed inverse solver that is based on the FEniCS finite element computational platform. The paper focuses on the model parameter sensitivity quantification with respect to the experimental measurements, such as the displacement field and reaction force measurements. The developed tools quantify the significance of different measurements on different model parameters and, in turn, give insight into a given model's ability to capture experimental measurements. Finally, an a priori estimate for the model parameter sensitivity is proposed that is independent of the actual measurements and that is defined in the whole computational domain. This estimate is primarily useful for the design of experiments, specifically, in localizing the optimal displacement field measurement sites for the maximum impact on model parameter inference.

How to implement user-defined fiber-reinforced hyperelastic materials in finite element software

Finite element modeling is often used in biomechanical engineering to evaluate medical devices, treatments and diagnostic tools. Using an adequate material model that describes the mechanical behavior of biological tissues is essential for a reliable outcome of the simulation. Pre-programmed material models for biological tissues are available in many finite element software packages. However, since these pre-programmed models are presented to the user as a black box, without the possibility to modify the material description, many researchers turn to implementing their own material formulations. This is a complex undertaking, requiring extensive knowledge while documentation is limited. This paper provides a detailed description, at the level of the biomedical engineer, of the implementation of a nonlinear hyperelastic material model using user subroutines in Abaqus®, in casuUANISOHYPER_INV and UMAT. The Gasser-Ogden-Holzapfel material model is used as an example, resulting in four implementation variations: the built-in implementation, a UANISOHYPER_INV formulation, a UMAT with analytical tangent stiffness formulation and a UMAT with numerical tangent stiffness formulation. In addition, three different element formulations are used: a continuum compressible, a continuum incompressible and a plane stress incompressible. All cases are thoroughly verified by applying a series of deformations on a single cube element and by simulating an extension-inflation experiment with non-homogeneous deformations and multiple elements. In these test cases, stresses, displacements, reaction forces, the required number of iterations and the total CPU time were compared. The results show that the four implementation variations are very similar, with total relative errors between 10^-3 and 10^-15, number of iterations that varied by maximum one iteration, and a comparable CPU time. In addition to this detailed overview, the user subroutines are added as supplementary material to this tutorial, which can be used as the ideal starting point for biomechanical engineers to implement their own material models at different levels of complexity.

A compressible anisotropic hyperelastic model with I5 and I7 strain invariants

It is obvious that the mechanical properties of arterial tissue include compressibility, anisotropy, and the fact that the out-of-plane shear modulus is smaller than the shear modulus in the plane of the fibers. However, the last point is rarely considered when it comes to compressible anisotropic hyperelastic models. In order to acquire different shear moduli, we propose a modified hyperelastic model including the influence of strain invariants I5 and I7. The convergence and correctness of this model are verified through the hydrostatic tension test, uniaxial tension test, and shear deformation test. It turns out that our model correctly predicts an anisotropic response and volume change to hydrostatic tensile test and the fact that the out-of-plane shear modulus is always smaller than the shear modulus in the plane of the fibers in shear deformation test. We conclude that the influence of strain invariants I5 and I7 is great, especially in the shear deformation, so that it is necessary to include I5 and I7 in the compressible anisotropic hyperelastic model.

Relaxation time constant based optical coherence elastography

This study aimed at visualizing relative relaxation time constant (RTC) in soft tissue by using optical coherence elastography (OCE). We proposed a forced vibration model as a theoretical base to express RTC using axial gradient of periodic vibration phase captured by phase sensitive optical coherence tomography (PhS-OCT). Validation of the model had been accomplished by experiments with isotropic and double-layered phantoms. A fresh chicken breast sample treated with focused ultrasound was prepared to test performance of the RTC-OCE in real tissue. All results were cross-validated with indentation test and traditional strain-based elastography. This study first utilized RTC mapping in 2D and 3D that covers the information of both elasticity and viscosity. The generated RTC mapping revealed the same mechanical difference internal sample which is correlated with conventional strain mapping. RTC mapping is potentially to be served as new biomarker for disease diagnosis in the future.

Constitutive modeling of menisci tissue: a critical review of analytical and numerical approaches

Menisci are fibrocartilaginous disks consisting of soft tissue with a complex biomechanical structure. They are critical determinants of the kinematics as well as the stability of the knee joint. Several studies have been carried out to formulate tissue mechanical behavior, leading to the development of a wide spectrum of constitutive laws. In addition to developing analytical tools, extensive numerical studies have been conducted on menisci modeling. This study reviews the developments of the most widely used continuum models of the meniscus mechanical properties in conjunction with emerging analytical and numerical models used to study the meniscus. The review presents relevant approaches and assumptions used to develop the models and includes discussions regarding strengths, weaknesses, and discrepancies involved in the presented models. The study presents a comprehensive coverage of relevant publications included in Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, Springer, and Scopus databases. This review aims at opening novel avenues for improving menisci modeling within the framework of constitutive modeling through highlighting the needs for further research directed toward determining key factors in gaining insight into the biomechanics of menisci which is crucial for the elaborate design of meniscal replacements.

Finite element models can reproduce the effect of nucleotomy on the multi-axial compliance of human intervertebral discs

Finite element (FE) models can unravel the link between intervertebral disc (IVD) degeneration and its mechanical behaviour. Nucleotomy may provide the data required for model verification. Three human IVDs were scanned with MRI and tested in multiple loading scenarios, prior and post nucleotomy. The resulting data was used to generate, calibrate, and verify the FE models. Nucleotomy increased the experimental range of motion by 26%, a result reproduced by the FE simulation within a 5% error. This work demonstrates the ability of FE models to reproduce the mechanical compliance of human IVDs prior and post nucleotomy.

Finite strain parametric HFGMC micromechanics of soft tissues

A micromechanical analysis is offered for the prediction of the global behavior of biological tissues. The analysis is based on the isotropic-hyperelastic behavior of the individual constituents (Collagen and Elastin), their volume fractions, and takes into account their detailed interactions. The present analysis predicts the instantaneous tensors from which the effective current first tangent tensor is established, thus providing the overall anisotropic constitutive behavior of the composite and the resulting field distribution in the composite. This is in contradistinction with the macroanalysis in which the composite internal energy, which involves unknown functions that depend on several strain invariants, must be proposed. The offered micromechanical analysis forms a generalization to the finite strain high-fidelity generalized method of cells (HFGMC) based on the homogenization technique for periodic composites to the parametric finite strain. This involves an arbitrary discretization of the repeating unit-cell of the periodic composites. Results are given for the response of the human abdominal aorta, which consists of three layered tissues: intima, media, and adventitia, all of which are composed out of the Collagen and Elastin. The isotropic-hyperelastic constituents (Mooney-Rivlin and Yeoh) of the composites are calibrated by utilizing available experimental data which describe the response of the tissue. Validation of the results is performed by comparison of the predicted Cauchy stress and stretches with the experimental measurements. In addition, results are given in the form of Cauchy stress and deformation gradient field distributions in the constituents of several tissues.

Sensitivity analysis of a strongly-coupled human-based electromechanical cardiac model: Effect of mechanical parameters on physiologically relevant biomarkers

The human heart beats as a result of multiscale nonlinear dynamics coupling subcellular to whole organ processes, achieving electrophysiologically-driven mechanical contraction. Computational cardiac modelling and simulation have achieved a great degree of maturity, both in terms of mathematical models of underlying biophysical processes and the development of simulation software. In this study, we present the detailed description of a human-based physiologically-based, and fully-coupled ventricular electromechanical modelling and simulation framework, and a sensitivity analysis focused on its mechanical properties. The biophysical detail of the model, from ionic to whole-organ, is crucial to enable future simulations of disease and drug action. Key novelties include the coupling of state-of-the-art human-based electrophysiology membrane kinetics, excitation-contraction and active contraction models, and the incorporation of a pre-stress model to allow for pre-stressing and pre-loading the ventricles in a dynamical regime. Through high performance computing simulations, we demonstrate that 50% to 200% - 1000% variations in key parameters result in changes in clinically-relevant mechanical biomarkers ranging from diseased to healthy values in clinical studies. Furthermore mechanical biomarkers are primarily affected by only one or two parameters. Specifically, ejection fraction is dominated by the scaling parameter of the active tension model and its scaling parameter in the normal direction ( k ort 2 ); the end systolic pressure is dominated by the pressure at which the ejection phase is triggered ( P ej ) and the compliance of the Windkessel fluid model ( C ); and the longitudinal fractional shortening is dominated by the fibre angle ( ϕ ) and k ort 2 . The wall thickening does not seem to be clearly dominated by any of the considered input parameters. In summary, this study presents in detail the description and implementation of a human-based coupled electromechanical modelling and simulation framework, and a high performance computing study on the sensitivity of mechanical biomarkers to key model parameters. The tools and knowledge generated enable future investigations into disease and drug action on human ventricles.

Assessment of mechanical indicators of carotid plaque vulnerability: Geometrical curvature metric, plaque stresses and damage in tissue fibres

Stroke is a major cause of death worldwide. The rupture of atherosclerotic carotid plaques is the leading single cause of stroke. Currently there is no accepted clinical measure to quantitatively assess the risk of carotid plaque rupture. Structural analyses of vulnerable plaques, using finite element (FE) analysis, have retrospectively found that regions of high stress tend to be the site of plaque rupture. The current study proposes a new clinical measure, based on plaque geometry, to assess the risk of carotid plaque rupture. This measure, named the weighted curvature difference, is based on the curvature of both the lumen and intima-media boundary, and the local plaque thickness. A series of idealized and realistic, 2-D and 3-D geometries are used to systematically assess this novel geometrical metric. The areas predicted to be at high risk of rupture using this geometrical metric are compared with areas of high stress, obtained from both isotropic and anisotropic material models. These results are also compared with areas in diseased carotid arteries that are predicted to have high damage accumulation in collagen fibres using a continuum damage model. Results show the new geometrical metric consistently predicts the locations of high stress in all of the vessel geometries examined. The drawbacks of using lumen curvature only as a risk measure are highlighted; particularly in the case of outward remodelled vessels. Weighted curvature difference shows great potential to be used as a metric to efficiently distinguish the rupture prone areas in a diseased vessels in a way that is independent of material properties.