Growth and Remodeling of Load-Bearing Biological Soft Tissues

Evaluation of the Stress-Growth Hypothesis in Saphenous Vein Perfusion Culture

The great saphenous vein (GSV) has served as a coronary artery bypass graft (CABG) conduit for over 50 years. Despite prevalent use, first-year failure rates remain high compared to arterial autograft options. Amongst other factors, vein graft failure can be attributed to material and mechanical mismatching that lead to apoptosis, inflammation, and intimal-medial hyperplasia. Through the implementation of the continuum mechanical-based theory of "stress-mediated growth and remodeling," we hypothesize that the mechanical properties of porcine GSV grafts can be favorably tuned for CABG applications prior to implantation using a prolonged but gradual transition from venous to arterial loading conditions in an inflammatory and thrombogenic deficient environment. To test this hypothesis, we used a hemodynamic-mimetic perfusion bioreactor to guide remodeling through stepwise incremental changes in pressure and flow over the course of 21-day cultures. Biaxial mechanical testing of vessels pre- and post-remodeling was performed, with results fit to structurally-motivated constitutive models using non-parametric bootstrapping. The theory of "small-on-large" was used to describe appropriate stiffness moduli, while histology and viability assays confirmed microstructural adaptations and vessel viability. Results suggest that stepwise transition from venous-to-arterial conditions results in a partial restoration of circumferential stretch and circumferential, but not axial, stress through vessel dilation and wall thickening in a primarily outward remodeling process. These remodeled tissues also exhibited decreased mechanical isotropy and circumferential, but not axial, stiffening. In contrast, only increases in axial stiffness were observed using culture under venous perfusion conditions and those tissues experienced moderate intimal resorption.

A pilot in silico modeling-based study of the pathological effects on the biomechanical function of tricuspid valves

Current clinical assessment of functional tricuspid valve regurgitation relies on metrics quantified from medical imaging modalities. Although these clinical methodologies are generally successful, the lack of detailed information about the mechanical environment of the valve presents inherent challenges for assessing tricuspid valve regurgitation. In the present study, we have developed a finite element-based in silico model of one porcine tricuspid valve (TV) geometry to investigate how various pathological conditions affect the overall biomechanical function of the TV. There were three primary observations from our results. Firstly, the results of the papillary muscle (PM) displacement study scenario indicated more pronounced changes in the TV biomechanical function. Secondly, compared to uniform annulus dilation, nonuniform dilation scenario induced more evident changes in the von Mises stresses (83.8-125.3 kPa vs 65.1-84.0 kPa) and the Green-Lagrange strains (0.52-0.58 vs 0.47-0.53) for the three TV leaflets. Finally, results from the pulmonary hypertension study scenario showed opposite trends compared to the PM displacement and annulus dilation scenarios. Furthermore, various chordae rupture scenarios were simulated, and the results showed that the chordae tendineae attached to the TV anterior and septal leaflets may be more critical to proper TV function. This in silico modeling-based study has provided a deeper insight into the tricuspid valve pathologies that may be useful, with moderate extensions, for guiding clinical decisions. NOVELTY STATEMENT: The novelties of the research are summarized below: A comprehensive in silico pilot study of how isolated functional tricuspid regurgitation pathologies and ruptured chordae tendineae would alter the tricuspid valve function; An extensive analysis of the tricuspid valve function, including mechanical quantities (eg, the von Mises stress and the Green-Lagrange strain) and clinically-relevant geometry metrics (eg, the tenting area and the coaptation height); and A developed computational modeling pipeline that can be extended to evaluate patient-specific tricuspid valve geometries and enhance the current clinical diagnosis and treatment of tricuspid regurgitation.

A Pilot Study on Linking Tissue Mechanics with Load-Dependent Collagen Microstructures in Porcine Tricuspid Valve Leaflets

The tricuspid valve (TV) is composed of three leaflets that coapt during systole to prevent deoxygenated blood from re-entering the right atrium. The connection between the TV leaflets’ microstructure and the tissue-level mechanical responses has yet to be fully understood in the TV biomechanics society. This pilot study sought to examine the load-dependent collagen fiber architecture of the three TV leaflets, by employing a multiscale, combined experimental approach that utilizes tissue-level biaxial mechanical characterizations, micro-level collagen fiber quantification, and histological analysis. Our results showed that the three TV leaflets displayed greater extensibility in the tissues’ radial direction than in the circumferential direction, consistently under different applied biaxial tensions. Additionally, collagen fibers reoriented towards the direction of the larger applied load, with the largest changes in the alignment of the collagen fibers under radially-dominant loading. Moreover, collagen fibers in the belly region of the TV leaflets were found to experience greater reorientations compared to the tissue region closer to the TV annulus. Furthermore, histological examinations of the TV leaflets displayed significant regional variation in constituent mass fraction, highlighting the heterogeneous collagen microstructure. The combined experimental approach presented in this work enables the connection of tissue mechanics, collagen fiber microstructure, and morphology for the TV leaflets. This experimental methodology also provides a new research platform for future developments, such as multiscale models for the TVs, and the design of bioprosthetic heart valves that could better mimic the mechanical, microstructural, and morphological characteristics of the native tricuspid valve leaflets.

Biological cells and coupled electro-mechanical effects: The role of organelles, microtubules, and nonlocal contributions

Biological cells are exposed to a variety of mechanical loads throughout their life cycles that eventually play an important role in a wide range of cellular processes. The understanding of cell mechanics under the application of external stimuli is important for capturing the nuances of physiological and pathological events. Such critical knowledge will play an increasingly vital role in modern medical therapies such as tissue engineering and regenerative medicine, as well as in the development of new remedial treatments. At present, it is well known that the biological molecules exhibit piezoelectric properties that are of great interest for medical applications ranging from sensing to surgery. In the current study, a coupled electro-mechanical model of a biological cell has been developed to better understand the complex behaviour of biological cells subjected to piezoelectric and flexoelectric properties of their constituent organelles under the application of external forces. Importantly, a more accurate modelling paradigm has been presented to capture the nonlocal flexoelectric effect in addition to the linear piezoelectric effect based on the finite element method. Major cellular organelles considered in the developed computational model of the biological cell are the nucleus, mitochondria, microtubules, cell membrane and cytoplasm. The effects of variations in the applied forces on the intrinsic piezoelectric and flexoelectric contributions to the electro-elastic response have been systematically investigated along with accounting for the variation in the coupling coefficients. In addition, the effect of mechanical degradation of the cytoskeleton on the electro-elastic response has also been quantified. The present studies suggest that flexoelectricity could be a dominant electro-elastic coupling phenomenon, exhibiting electric fields that are four orders of magnitude higher than those generated by piezoelectric effects alone. Further, the output of the coupled electro-mechanical model is significantly dependent on the variation of flexoelectric coefficients. We have found that the mechanical degradation of the cytoskeleton results in the enhancement of both the piezo and flexoelectric responses associated with electro-mechanical coupling. In general, our study provides a framework for more accurate quantification of the mechanical/electrical transduction within the biological cells that can be critical for capturing the complex mechanisms at cellular length scales.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Mechano-biological adaptation of the pulmonary artery exposed to systemic conditions

Cardiac surgeries may expose pulmonary arterial tissue to systemic conditions, potentially resulting in failure of that tissue. Our goal was to quantitatively assess pulmonary artery adaptation due to changes in mechanical environment. In 17 sheep, we placed a pulmonary autograft in aortic position, with or without macroporous mesh reinforcement. It was exposed to systemic conditions for 6 months. All sheep underwent 3 ECG-gated MRI’s. Explanted tissue was subjected to mechanical and histological analysis. Results showed progressive dilatation of the unreinforced autograft, while reinforced autografts stabilized after two months. Some unreinforced pulmonary autograft samples displayed more aorta-like mechanical behavior with increased collagen deposition. The mechanical behavior of reinforced autografts was dominated by the mesh. The decrease in media thickness and loss of vascular smooth muscle cells was more pronounced in reinforced than in unreinforced autografts. In conclusion, altering the mechanical environment of a pulmonary artery causes changes in its mechano-biological properties.

Connective Tissue Remodeling in Myopia and its Potential Role in Increasing Risk of Glaucoma

Myopia and glaucoma are both increasing in prevalence and are linked by an unknown mechanism as many epidemiologic studies have identified moderate to high myopia as an independent risk factor for glaucoma. Myopia and glaucoma are both chronic conditions that lead to connective tissue remodeling within the sclera and optic nerve head. The mechanobiology underlying connective tissue remodeling differs substantially between both diseases, with different homeostatic control mechanisms. In this article, we discuss similarities and differences between connective tissue remodeling in myopia and glaucoma; selected multi-scale mechanisms that are thought to underlie connective tissue remodeling in both conditions; how asymmetric remodeling of the optic nerve head may predispose a myopic eye for pathological remodeling and glaucoma; and how neural tissue deformations may accumulate throughout both pathologies and increase the risk for mechanical insult of retinal ganglion cell axons.

Vimentin regulates Notch signaling strength and arterial remodeling in response to hemodynamic stress

The intermediate filament (IF) cytoskeleton has been proposed to regulate morphogenic processes by integrating the cell fate signaling machinery with mechanical cues. Signaling between endothelial cells (ECs) and vascular smooth muscle cells (VSMCs) through the Notch pathway regulates arterial remodeling in response to changes in blood flow. Here we show that the IF-protein vimentin regulates Notch signaling strength and arterial remodeling in response to hemodynamic forces. Vimentin is important for Notch transactivation by ECs and vimentin knockout mice (VimKO) display disrupted VSMC differentiation and adverse remodeling in aortic explants and in vivo. Shear stress increases Jagged1 levels and Notch activation in a vimentin-dependent manner. Shear stress induces phosphorylation of vimentin at serine 38 and phosphorylated vimentin interacts with Jagged1 and increases Notch activation potential. Reduced Jagged1-Notch transactivation strength disrupts lateral signal induction through the arterial wall leading to adverse remodeling. Taken together we demonstrate that vimentin forms a central part of a mechanochemical transduction pathway that regulates multilayer communication and structural homeostasis of the arterial wall.

Direct and inverse identification of constitutive parameters from the structure of soft tissues. Part 2: dispersed arrangement of collagen fibers

This paper investigates on the relationship between the arrangement of collagen fibers within soft tissues and parameters of constitutive models. Starting from numerical experiments based on biaxial loading conditions, the study addresses both the direct (from structure to mechanics) and the inverse (from mechanics to structure) problems, solved introducing optimization problems for model calibration and regression analysis. A campaign of parametric analyses is conducted in order to consider fibers distributions with different main orientation and angular dispersion. Different anisotropic constitutive models are employed, accounting for fibers dispersion either with a generalized structural approach or with an increasing number of strain energy terms. Benchmark data sets, toward which constitutive models are fitted, are built by employing a multiscale description of fiber nonlinearities and accounting for fibers dispersion with an angular integration method. Results show how the optimal values of constitutive parameters obtained from model calibration vary as a function of fibers arrangement and testing protocol. Moreover, the fitting capabilities of constitutive models are discussed. A novel strategy for model calibration is also proposed, in order to obtain a robust accuracy with respect to different loading conditions starting from a low number of mechanical tests. Furthermore, novel results useful for the inverse determination of the mean angle and the variance of fibers distribution are obtained. Therefore, the study contributes: to better design procedures for model calibration; to account for mechanical alterations due to remodeling mechanisms; and to gain structural information in a nondestructive way.

A microstructural model of cross-link interaction between collagen fibrils in the human cornea

We propose a simplified micromechanical model of the fibrous reinforcement of the corneal tissue. We restrict our consideration to the structural function of the collagen fibrils located in the stroma and disregard the other all-important components of the cornea. The reinforcing structure is modelled with two sets of parallel fibrils, connected by transversal bonds within the single fibril family (inter-cross-link) and across the two families (intra-cross-link). The particular design chosen for this ideal structure relies on the fact that its ability to sustain loads is dependent on the degree of the cross-link and, therefore, on the density and stiffness of the bonds. We analyse the mechanical response of the system according to the type of interlacing and on the stiffness of fibres and bonds. Results show that the weakening of transversal bonds is associated with a marked increase of the deformability of the system. In particular, the deterioration of transversal bonds due to mechanical, chemical or enzymatic reasons can justify the loss of stiffness of the stromal tissue resulting in localized thinning and bulging typically observed in keratoconus corneas. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

Molecular-level collagen damage explains softening and failure of arterial tissues: A quantitative interpretation of CHP data with a novel elasto-damage model

The present experimental-modelling study provides a quantitative interpretation of mechanical data and damage measurements obtained from collagen hybridizing peptide (CHP) techniques on overstretched sheep cerebral arterial tissues. To this aim, a structurally-motivated constitutive model is developed in the framework of continuum damage mechanics. The model includes two internal variables for describing the effects of collagen triple-helical unfolding via interstrand delamination: one governs plastic mechanisms in collagen fibers, leading to a stress softening response of the tissue at the macroscale; the other one describes the loss of fiber structural integrity, leading to tissue final failure. The proposed model is calibrated using the obtained mechanical experimental data, showing excellent fitting capabilities. The predicted evolution of internal variables agree well with independent measurements of molecular-level CHP-based damage data, obtaining an independent a posteriori validation of damage predictions. Moreover, available data on inelastic tissue elongation following supraphysiological loads are successfully reproduced. These outcomes further the hypothesis that the accumulation of interstrand delamination is a primary cause for the evolution of inelastic mechanisms in tissues, and in particular of stress softening up to failure.

Gradient-enhanced continuum models of healing in damaged soft tissues

Healing of soft biological tissue is the process of self-recovering or self-repairing the injured or damaged extracellular matrix (ECM). Healing is assumed to be stress-driven, with the objective of returning to a homeostatic stress metrics in the tissue after replacing the damaged ECM with new undamaged one. However, based on the existence of intrinsic length scales in soft tissues, it is thought that computational models of healing should be non-local. In the present study, we introduce for the first time two gradient-enhanced constitutive healing models for soft tissues including non-local variables. The first model combines a continuum damage model with a temporally homogenized growth model, where the growth direction is determined according to local principal stress directions. The second one is based on a gradient-enhanced healing model with continuously recoverable damage variable. Both models are implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three two-dimensional situations simulating the healing process of soft tissues are modeled numerically with both models, and their application for simulation of balloon angioplasty is provided by illustrating the change of damage field and geometry in the media layer throughout the healing process.

MicroRNA-dependent regulation of biomechanical genes establishes tissue stiffness homeostasis

Vertebrate tissues exhibit mechanical homeostasis, showing stable stiffness and tension over time and recovery after changes in mechanical stress. However, the regulatory pathways that mediate these effects are unknown. A comprehensive identification of Argonaute-2(AGO2)-associated microRNAs and mRNAs in endothelial cells identified a network of 122 microRNA families that target 73 mRNAs encoding cytoskeletal, contractile, adhesive and extracellular matrix (CAM) proteins. These microRNAs increased in cells plated on stiff vs. soft substrates, consistent with homeostasis, and suppressed targets via microRNA recognition elements (MREs) within the 3’UTRs of CAM mRNAs. Inhibition of DROSHA or AGO2, or disruption of MREs within individual target mRNAs such as Connective Tissue Growth Factor (CTGF), induced hyper-adhesive, hyper-contractile phenotypes in endothelial and fibroblast cells in vitro, and increased tissue stiffness, contractility and extracellular matrix (ECM) deposition in the zebrafish fin-fold in vivo. Thus, a network of microRNAs buffers CAM expression to mediate tissue mechanical homeostasis.

Mechanical behavior of metastatic femurs through patient-specific computational models accounting for bone-metastasis interaction

This paper proposes a computational model based on a finite-element formulation for describing the mechanical behavior of femurs affected by metastatic lesions. A novel geometric/constitutive description is introduced by modelling healthy bone and metastases via a linearly poroelastic constitutive approach. A Gaussian-shaped graded transition of material properties between healthy and metastatic tissues is prescribed, in order to account for the bone-metastasis interaction. Loading-induced failure processes are simulated by implementing a progressive damage procedure, formulated via a quasi-static displacement-driven incremental approach, and considering both a stress- and a strain-based failure criterion. By addressing a real clinical case, left and right patient-specific femur models are geometrically reconstructed via an ad-hoc imaging procedure and embedding multiple distributions of metastatic lesions along femurs. Significant differences in fracture loads, fracture mechanisms, and damage patterns, are highlighted by comparing the proposed constitutive description with a purely elastic formulation, where the metastasis is treated as a pseudo-healthy tissue or as a void region. Proposed constitutive description allows to capture stress/strain localization mechanisms within the metastatic tissue, revealing the model capability in describing possible strain-induced mechano-biological stimuli driving onset and evolution of the lesion. The proposed approach opens towards the definition of effective computational strategies for supporting clinical decision and treatments regarding metastatic femurs, contributing also to overcome some limitations of actual standards and procedures.

Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path

Surface growth by association or dissociation of material on the boundary of a body is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a single cell, and is increasingly applied in engineering processes for fabrication and self-assembly. A significant challenge in modelling such processes arises due to the inherent coupled interaction between the growth kinetics, the local stresses and the diffusing constituents needed to sustain the growth. Moreover, the volume of the body changes not only due to surface growth but also by variation in solvent concentration within the bulk. In this paper, we present a general theoretical framework that captures these phenomena and describes the kinetics of surface growth while accounting for coupled diffusion. Then, by the combination of analytical and numerical tools, applied to a simple growth geometry, we show that the evolution of such growth processes tends towards a universal path that is independent of initial conditions. This path, on which surface growth and diffusion act harmoniously, can be extended to analytically portray the evolution of a body from inception up to a treadmilling state, in which addition and removal of material are balanced.

Competing Mechanisms of Stress-Assisted Diffusivity and Stretch-Activated Currents in Cardiac Electromechanics

We numerically investigate the role of mechanical stress in modifying the conductivity properties of cardiac tissue, and also assess the impact of these effects in the solutions generated by computational models for cardiac electromechanics. We follow the recent theoretical framework from Cherubini et al. (2017), proposed in the context of general reaction-diffusion-mechanics systems emerging from multiphysics continuum mechanics and finite elasticity. In the present study, the adapted models are compared against preliminary experimental data of pig right ventricle fluorescence optical mapping. These data contribute to the characterization of the observed inhomogeneity and anisotropy properties that result from mechanical deformation. Our novel approach simultaneously incorporates two mechanisms for mechano-electric feedback (MEF): stretch-activated currents (SAC) and stress-assisted diffusion (SAD); and we also identify their influence into the nonlinear spatiotemporal dynamics. It is found that (i) only specific combinations of the two MEF effects allow proper conduction velocity measurement; (ii) expected heterogeneities and anisotropies are obtained via the novel stress-assisted diffusion mechanisms; (iii) spiral wave meandering and drifting is highly mediated by the applied mechanical loading. We provide an analysis of the intrinsic structure of the nonlinear coupling mechanisms using computational tests conducted with finite element methods. In particular, we compare static and dynamic deformation regimes in the onset of cardiac arrhythmias and address other potential biomedical applications.

Anisotropic stiffness and tensional homeostasis induce a natural anisotropy of volumetric growth and remodeling in soft biological tissues

Growth in soft biological tissues in general results in anisotropic changes of the tissue geometry. It remains a key challenge in biomechanics to understand, quantify, and predict this anisotropy. In this paper, we demonstrate that anisotropic tissue stiffness and the well-known mechanism of tensional homeostasis induce a natural anisotropy of the geometric changes resulting from volumetric growth in soft biological tissues. As a rule of thumb, this natural anisotropy makes differential tissue volume elements dilate mainly in the direction(s) of lowest stiffness. This simple principle is shown to explain the experimentally observed growth behavior in a host of different soft biological tissues without relying on any additional heuristic assumptions or quantities (such as ad hoc defined growth tensors).

Computational Fluid Dynamic Study for aTAA Hemodynamics: An Integrated Image-Based and Radial Basis Functions Mesh Morphing Approach

We present a novel framework for the fluid dynamics analysis of healthy subjects and patients affected by ascending thoracic aorta aneurysm (aTAA). Our aim is to obtain indications about the effect of a bulge on the hemodynamic environment at different enlargements. Three-dimensional (3D) surface models defined from healthy subjects and patients with aTAA, selected for surgical repair, were generated. A representative shape model for both healthy and pathological groups has been identified. A morphing technique based on radial basis functions (RBF) was applied to mold the shape relative to healthy patient into the representative shape of aTAA dataset to enable the parametric simulation of the aTAA formation. Computational fluid dynamics (CFD) simulations were performed by means of a finite volume solver using the mean boundary conditions obtained from three-dimensional (PC-MRI) acquisition. Blood flow helicity and flow descriptors were assessed for all the investigated models. The feasibility of the proposed integrated approach pertaining the coupling between an RBF morphing technique and CFD simulation for aTAA was demonstrated. Significant hemodynamic changes appear at the 60% of the bulge progression. An impingement of the flow toward the bulge was observed by analyzing the normalized flow eccentricity (NFE) index.

A biomimetic microfluidic model to study signalling between endothelial and vascular smooth muscle cells under hemodynamic conditions

Cell signalling and mechanics influence vascular pathophysiology and there is an increasing demand for in vitro model systems that enable examination of signalling between vascular cells under hemodynamic conditions. Current 3D vessel wall constructs do not recapitulate the mechanical conditions of the native tissue nor do they allow examination of cell-cell interactions under relevant hemodynamic conditions. Here, we describe a 3D microfluidic chip model of arterial endothelial and smooth muscle cells where cellular organization, composition and interactions, as well as the mechanical environment of the arterial wall are mimicked. The hemodynamic EC-VSMC-signalling-on-a-chip consists of two parallel polydimethylsiloxane (PDMS) cell culture channels, separated by a flexible, porous PDMS membrane, mimicking the porosity of the internal elastic lamina. The hemodynamic EC-VSMC-signalling-on-a-chip allows co-culturing of human aortic endothelial cells (ECs) and human aortic vascular smooth muscle cells (VSMCs), separated by a porous membrane, which enables EC-VSMC interaction and signalling, crucial for the development and homeostasis of the vessel wall. The device allows real time cell imaging and control of hemodynamic conditions. The culture channels are surrounded on either side by vacuum channels to induce cyclic strain by applying cyclic suction, resulting in mechanical stretching and relaxation of the membrane in the cell culture channels. The blood flow is mimicked by creating a flow of medium at the EC side. Vascular cells remain viable during prolonged culturing, exhibit physiological morphology and organization and make cell-cell contact. During dynamic culturing of the device with a shear stress of 1-1.5 Pa and strain of 5-8%, VSMCs align perpendicular to the given strain in the direction of the flow and EC adopt a cobblestone morphology. To our knowledge, this is the first report on the development of a microfluidic device, which enables a co-culture of interacting ECs and VSMCs under hemodynamic conditions and presents a novel approach to systematically study the biological and mechanical components of the intimal-medial vascular unit.

Fatigue of soft fibrous tissues: Multi-scale mechanics and constitutive modeling

In recent experimental studies a possible damage mechanism of collagenous tissues mainly caused by fatigue was disclosed. In this contribution, a multi-scale constitutive model ranging from the tropocollagen (TC) molecule level up to bundles of collagen fibers is proposed and utilized to predict the elastic and inelastic long-term tissue response. Material failure of collagen fibrils is elucidated by a permanent opening of the triple helical collagen molecule conformation, triggered either by overstretching or reaction kinetics of non-covalent bonds. This kinetics is described within a probabilistic framework of adhesive detachments of molecular linkages providing collagen fiber integrity. Both intramolecular and interfibrillar linkages are considered. The final constitutive equations are validated against recent experimental data available in literature for both uniaxial tension to failure and the evolution of fatigue in subsequent loading cycles. All material parameters of the proposed model have a clear physical interpretation.

STATEMENT OF SIGNIFICANCE

Irreversible changes take place at different length scales of soft fibrous tissues under supra-physiological loading and alter their macroscopic mechanical properties. Understanding the evolution of those histologic pathologies under loading and incorporating them into a continuum mechanical framework appears to be crucial in order to predict long-term evolution of various diseases and to support the development of tissue engineering.

Mechanosensitivity of Jagged-Notch signaling can induce a switch-type behavior in vascular homeostasis

Hemodynamic forces and Notch signaling are both known as key regulators of arterial remodeling and homeostasis. However, how these two factors integrate in vascular morphogenesis and homeostasis is unclear. Here, we combined experiments and modeling to evaluate the impact of the integration of mechanics and Notch signaling on vascular homeostasis. Vascular smooth muscle cells (VSMCs) were cyclically stretched on flexible membranes, as quantified via video tracking, demonstrating that the expression of Jagged1, Notch3, and target genes was down-regulated with strain. The data were incorporated in a computational framework of Notch signaling in the vascular wall, where the mechanical load was defined by the vascular geometry and blood pressure. Upon increasing wall thickness, the model predicted a switch-type behavior of the Notch signaling state with a steep transition of synthetic toward contractile VSMCs at a certain transition thickness. These thicknesses varied per investigated arterial location and were in good agreement with human anatomical data, thereby suggesting that the Notch response to hemodynamics plays an important role in the establishment of vascular homeostasis.

Gradual loading ameliorates maladaptation in computational simulations of vein graft growth and remodelling

Vein graft failure is a prevalent problem in vascular surgeries, including bypass grafting and arteriovenous fistula procedures in which veins are subjected to severe changes in pressure and flow. Animal and clinical studies provide significant insight, but understanding the complex underlying coupled mechanisms can be advanced using computational models. Towards this end, we propose a new model of venous growth and remodelling (G&R) based on a constrained mixture theory. First, we identify constitutive relations and parameters that enable venous adaptations to moderate perturbations in haemodynamics. We then fix these relations and parameters, and subject the vein to a range of combined loads (pressure and flow), from moderate to severe, and identify plausible mechanisms of adaptation versus maladaptation. We also explore the beneficial effects of gradual increases in load on adaptation. A gradual change in flow over 3 days plus an initial step change in pressure results in fewer maladaptations compared with step changes in both flow and pressure, or even a gradual change in pressure and flow over 3 days. A gradual change in flow and pressure over 8 days also enabled a successful venous adaptation for loads as severe as the arterial loads. Optimization is used to accelerate parameter estimation and the proposed framework is general enough to provide a good starting point for parameter estimations in G&R simulations.

Viscoelastic computational modeling of the human head-neck system: Eigenfrequencies and time-dependent analysis

A subject-specific 3-dimensional viscoelastic finite element model of the human head-neck system is presented and investigated based on computed tomography and magnetic resonance biomedical images. Ad hoc imaging processing tools are developed for the reconstruction of the simulation domain geometry and the internal distribution of bone and soft tissues. Material viscoelastic properties are characterized point-wise through an image-based interpolating function used then for assigning the constitutive prescriptions of a heterogenous viscoelastic continuum model. The numerical study is conducted both for modal and time-dependent analyses, compared with similar studies and validated against experimental evidences. Spatiotemporal analyses are performed upon different exponential swept-sine wave-localized stimulations. The modeling approach proposes a generalized, patient-specific investigation of sound wave transmission and attenuation within the human head-neck system comprising skull and brain tissues. Model extensions and applications are finally discussed.

Multi-Scale Modeling of Vision-Guided Remodeling and Age-Dependent Growth of the Tree Shrew Sclera During Eye Development and Lens-Induced Myopia

The sclera uses unknown mechanisms to match the eye's axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the eye's refractive error. We define growth as a mechanism that changes the tissue volume and mass while remodeling involves internal micro-deformations that are volume-preserving at the macroscale. The model was fitted against longitudinal refractive measurements in tree shrews of different ages and exposed to three different visual conditions: (i) normal development; (ii) negative lens wear to induce myopia; and (iii) recovery from myopia by removing the negative lens. The model was able to replicate the age- and vision-dependent response of the tree shrew experiments. Scleral growth ceased at younger age than scleral remodeling. The remodeling rate decreased as the eye emmetropized but increased at any age when a negative lens was put on. The predictive power of the model was investigated by calculating the susceptibility to scleral remodeling and the response to form deprivation myopia in tree shrews. Both predictions were in good agreement with experimental data that were not used to fit the model. We propose the first model that distinguishes scleral growth from remodeling. The good agreement of our results with experimental data supports the notion that scleral growth and scleral remodeling are two independently controlled mechanisms during eye development.

A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue

Most mathematical models of the growth and remodeling of load-bearing soft tissues are based on one of two major approaches: a kinematic theory that specifies an evolution equation for the stress-free configuration of the tissue as a whole or a constrained mixture theory that specifies rates of mass production and removal of individual constituents within stressed configurations. The former is popular because of its conceptual simplicity, but relies largely on heuristic definitions of growth; the latter is based on biologically motivated micromechanical models, but suffers from higher computational costs due to the need to track all past configurations. In this paper, we present a temporally homogenized constrained mixture model that combines advantages of both classical approaches, namely a biologically motivated micromechanical foundation, a simple computational implementation, and low computational cost. As illustrative examples, we show that this approach describes well both cell-mediated remodeling of tissue equivalents in vitro and the growth and remodeling of aneurysms in vivo. We also show that this homogenized constrained mixture model suggests an intimate relationship between models of growth and remodeling and viscoelasticity. That is, important aspects of tissue adaptation can be understood in terms of a simple mechanical analog model, a Maxwell fluid (i.e., spring and dashpot in series) in parallel with a "motor element" that represents cell-mediated mechanoregulation of extracellular matrix. This analogy allows a simple implementation of homogenized constrained mixture models within commercially available simulation codes by exploiting available models of viscoelasticity.

Mechanobiological modelling of tendons: Review and future opportunities

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.