A multi-layered computational model of coupled elastin degradation, vasoactive dysfunction, and collagenous stiffening in aortic aging

An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta

The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.

A multiscale computational model of arterial growth and remodeling including Notch signaling

Blood vessels grow and remodel in response to mechanical stimuli. Many computational models capture this process phenomenologically, by assuming stress homeostasis, but this approach cannot unravel the underlying cellular mechanisms. Mechano-sensitive Notch signaling is well-known to be key in vascular development and homeostasis. Here, we present a multiscale framework coupling a constrained mixture model, capturing the mechanics and turnover of arterial constituents, to a cell-cell signaling model, describing Notch signaling dynamics among vascular smooth muscle cells (SMCs) as influenced by mechanical stimuli. Tissue turnover was regulated by both Notch activity, informed by in vitro data, and a phenomenological contribution, accounting for mechanisms other than Notch. This novel framework predicted changes in wall thickness and arterial composition in response to hypertension similar to previous in vivo data. The simulations suggested that Notch contributes to arterial growth in hypertension mainly by promoting SMC proliferation, while other mechanisms are needed to fully capture remodeling. The results also indicated that interventions to Notch, such as external Jagged ligands, can alter both the geometry and composition of hypertensive vessels, especially in the short term. Overall, our model enables a deeper analysis of the role of Notch and Notch interventions in arterial growth and remodeling and could be adopted to investigate therapeutic strategies and optimize vascular regeneration protocols.

Global and local stiffening of ex vivo-perfused stented human thoracic aortas: A mock circulation study

The effects of thoracic endovascular repair (TEVAR) on the biomechanical properties of aortic tissue have not been adequately studied. Understanding these features is important for the management of endograft-triggered complications of a biomechanical nature. This study aims to examine how stent-graft implantation affects the elastomechanical behavior of the aorta. Non-pathological human thoracic aortas (n=10) were subjected to long-standing perfusion (8h) within a mock circulation loop under physiological conditions. To quantify compliance and its mismatch in the test periods without and with a stent, the aortic pressure and the proximal cyclic circumferential displacement were measured. After perfusion, biaxial tension tests (stress-stretch) were carried out to examine the stiffness profiles between non-stented and stented tissue, followed by a histological assessment. Experimental evidence shows: (i) a significant reduction in aortic distensibility after TEVAR, indicating aortic stiffening and compliance mismatch, (ii) a stiffer behavior of the stented samples compared to the non-stented samples with an earlier entry into the nonlinear part of the stress-stretch curve and (iii) strut-induced histological remodeling of the aortic wall. The biomechanical and histological comparison of the non-stented and stented aortas provides new insights into the interaction between the stent-graft and the aortic wall. The knowledge gained could refine the stent-graft design to minimize the stent-induced impacts on the aortic wall and the resulting complications. STATEMENT OF SIGNIFICANCE: Stent-related cardiovascular complications occur the moment the stent-graft expands on the human aortic wall. Clinicians base their diagnosis on the anatomical morphology of CT scans while neglecting the endograft-triggered biomechanical events that compromise aortic compliance and wall mechanotransduction. Experimental replication of endovascular repair in cadaver aortas within a mock circulation loop may have a catalytic effect on biomechanical and histological findings without an ethical barrier. Demonstrating interactions between the stent and the wall can help clinicians make a broader diagnosis such as ECG-triggered oversizing and stent-graft characteristics based on patient-specific anatomical location and age. In addition, the results can be used to optimize towards more aortophilic stent grafts.

Intracellular signaling control of mechanical homeostasis in the aorta

Mature arteries exhibit a preferred biomechanical state in health evidenced by a narrow range of intramural and wall shear stresses. When stresses are perturbed by changes in blood pressure or flow, homeostatic mechanisms tend to restore target values via altered contractility and/or cell and matrix turnover. In contrast, vascular disease associates with compromised homeostasis, hence we must understand mechanisms underlying mechanical homeostasis and its robustness. Here, we use a multiscale computational model wherein mechanosensitive intracellular signaling pathways drive arterial growth and remodeling. First, we identify an ensemble of cell-level parameterizations where tissue-level responses are well-regulated and adaptive to hemodynamic perturbations. The responsible mechanism is persistent multiscale negative feedback whereby mechanosensitive signaling drives mass turnover until homeostatic target stresses are reached. This demonstrates how robustness emerges despite inevitable cell and individual heterogeneity. Second, we investigate tissue-level effects of signaling node knockdowns (ATIR, ROCK, TGF[Formula: see text]RII, PDGFR, ERK1/2) and find general agreement with experimental reports of fault tolerance. Robustness against structural changes manifests via low engagement of the node under baseline stresses or compensatory multiscale feedback via upregulation of additional pathways. Third, we show how knockdowns affect collagen and smooth muscle turnover at baseline and with perturbed stresses. In several cases, basal production is not remarkably affected, but sensitivities to stress deviations, which influence feedback strength, are reduced. Such reductions can impair adaptive responses, consistent with previously reported aortic vulnerability despite grossly normal appearances. Reduced stress sensitivities thus form a candidate mechanism for how robustness is lost, enabling transitions from health towards disease.

Mechano-regulated cell-cell signaling in the context of cardiovascular tissue engineering

Cardiovascular tissue engineering (CVTE) aims to create living tissues, with the ability to grow and remodel, as replacements for diseased blood vessels and heart valves. Despite promising results, the (long-term) functionality of these engineered tissues still needs improvement to reach broad clinical application. The functionality of native tissues is ensured by their specific mechanical properties directly arising from tissue organization. We therefore hypothesize that establishing a native-like tissue organization is vital to overcome the limitations of current CVTE approaches. To achieve this aim, a better understanding of the growth and remodeling (G&R) mechanisms of cardiovascular tissues is necessary. Cells are the main mediators of tissue G&R, and their behavior is strongly influenced by both mechanical stimuli and cell-cell signaling. An increasing number of signaling pathways has also been identified as mechanosensitive. As such, they may have a key underlying role in regulating the G&R of tissues in response to mechanical stimuli. A more detailed understanding of mechano-regulated cell-cell signaling may thus be crucial to advance CVTE, as it could inspire new methods to control tissue G&R and improve the organization and functionality of engineered tissues, thereby accelerating clinical translation. In this review, we discuss the organization and biomechanics of native cardiovascular tissues; recent CVTE studies emphasizing the obtained engineered tissue organization; and the interplay between mechanical stimuli, cell behavior, and cell-cell signaling. In addition, we review past contributions of computational models in understanding and predicting mechano-regulated tissue G&R and cell-cell signaling to highlight their potential role in future CVTE strategies.

Constrained Mixture Models of Soft Tissue Growth and Remodeling - Twenty Years After

Soft biological tissues compromise diverse cell types and extracellular matrix constituents, each of which can possess individual natural configurations, material properties, and rates of turnover. For this reason, mixture-based models of growth (changes in mass) and remodeling (change in microstructure) are well-suited for studying tissue adaptations, disease progression, and responses to injury or clinical intervention. Such approaches also can be used to design improved tissue engineered constructs to repair, replace, or regenerate tissues. Focusing on blood vessels as archetypes of soft tissues, this paper reviews a constrained mixture theory introduced twenty years ago and explores its usage since by contrasting simulations of diverse vascular conditions. The discussion is framed within the concept of mechanical homeostasis, with consideration of solid-fluid interactions, inflammation, and cell signaling highlighting both past accomplishments and future opportunities as we seek to understand better the evolving composition, geometry, and material behaviors of soft tissues under complex conditions.

Glomerular filtration and podocyte tensional homeostasis: importance of the minor type IV collagen network

The minor type IV collagen chain, which is a significant component of the glomerular basement membrane in healthy individuals, is known to assemble into large structures (supercoils) that may contribute to the mechanical stability of the collagen network and the glomerular basement membrane as a whole. The absence of the minor chain, as in Alport syndrome, leads to glomerular capillary demise and eventually to kidney failure. An important consideration in this problem is that the glomerular capillary wall must be strong enough to withstand the filtration pressure and porous enough to permit filtration at reasonable pressures. In this work, we propose a coupled feedback loop driven by filtration demand and tensional homeostasis of the podocytes forming the outer portion of the glomerular capillary wall. Briefly, the deposition of new collagen increases the stiffness of basement membrane, helping to stress shield the podocytes, but the new collagen also decreases the permeability of the basement membrane, requiring an increase in capillary transmural pressure drop to maintain filtration; the resulting increased pressure outweighs the increased glomerular basement membrane stiffness and puts a net greater stress demand on the podocytes. This idea is explored by developing a multiscale simulation of the capillary wall, in which a macroscopic (µm scale) continuum model is connected to a set of microscopic (nm scale) fiber network models representing the collagen network and the podocyte cytoskeleton. The model considers two cases: healthy remodeling, in which the presence of the minor chain allows the collagen volume fraction to be increased by thickening fibers, and Alport syndrome remodeling, in which the absence of the minor chain allows collagen volume fraction to be increased only by adding new fibers to the network. The permeability of the network is calculated based on previous models of flow through a fiber network, and it is updated for different fiber radii and volume fractions. The analysis shows that the minor chain allows a homeostatic balance to be achieved in terms of both filtration and cell tension. Absent the minor chain, there is a fundamental change in the relation between the two effects, and the system becomes unstable. This result suggests that mechanobiological or mechanoregulatory therapies may be possible for Alport syndrome and other minor chain collagen diseases of the kidney.

Vascular adaptation in the presence of external support - A modeling study

Vascular grafts have long been used to replace damaged or diseased vessels with considerable success, but a new approach is emerging where native vessels are merely supported, not replaced. Although external supports have been evaluated in diverse situations - ranging from aneurysmal disease to vein grafts or the Ross operation - optimal supports and procedures remain wanting. In this paper, we present a novel application of a growth and remodeling model well suited for parametrically exploring multiple designs of external supports while accounting for mechanobiological and immunobiological responses of the supported native vessel. These results suggest that a load bearing external support can reduce vessel thickening in response to pressure elevation. Results also suggest that the final adaptive state of the vessel depends on the structural stiffness of the support via a mechano-driven adaptation, although luminal encroachment may be a complication in the presence of chronic inflammation. Finally, the supported vessel can stiffen (structurally and materially) along circumferential and axial directions, which could have implications on overall hemodynamics and thus subsequent vascular remodeling. The proposed framework can provide valuable insights into vascular adaptation in the presence of external support, accelerate rational design, and aid translation of this emerging approach.

A Two-Dimensional Model of Hypertension-Induced Arterial Remodeling With Account for Stress Interaction Between Elastin and Collagen

We propose a novel structure-based two-dimensional (2D) mathematical model of hypertension-induced arterial remodeling. The model is built in the framework of the constrained mixture theory and global growth approach, utilizing a recently proposed structure-based constitutive model of arterial tissue that accounts for the individual natural configurations of and stress interaction between elastin and collagen. The basic novel predictive result is that provided remodeling causes a change in the elastin/collagen mass fraction ratio, it leads to a structural reorganization of collagen that manifests as an altered fiber undulation and a change in direction of the helically oriented fibers in the tissue natural state. Results obtained from the illustrative simulations for a porcine renal artery show that when remodeling is complete the collagen reorganization might have significant effects on the initial arterial geometry and mechanical properties of the arterial tissue. The proposed model has potential to describe and advance mechanistic understanding of adaptive arterial remodeling, promote the continual refinement of mathematical models of arterial remodeling, and provide motivation for new avenues of experimental investigation.

A new finite-element shell model for arterial growth and remodeling after stent implantation

The goal of this paper is to study computationally how blood vessels adapt when they are exposed to a mechanobiological insult, namely, a sudden change of their biomechanical conditions such as proteolytic injuries or implantation. Adaptation occurs through growth and remodeling (G&R), consisting of mass production or removal of structural proteins, such as collagen, until restoring the initial homeostatic biomechanical conditions. In some circumstances, the initial conditions can never be recovered, and arteries evolve towards unstable pathological conditions, such as aneurysms, which are responsible for significant morbidity and mortality. Therefore, computational predictions of G&R under different circumstances can be helpful in understanding fundamentally how arterial pathologies progress. For that, we have developed a low-cost open-source finite-element 2D axisymmetric shell model (FEM) of the arterial wall. The constitutive equations for static equilibrium used to model the stress-strain behavior and the G&R response are expressed within the homogenized constrained mixture theory. The originality is to integrate the layer-specific behavior of both arterial layers (media and adventitia) into the model. Considering different mechanobiological insults, our results show that the resulting arterial dilatation is strongly correlated with the media thickness. The adaptation to stent implantation is particularly interesting. For large stent oversizing ratios, the artery cannot recover from the mechanobiological insult and dilates forever, whereas dilatation stabilizes after a transient period for more moderate oversizing ratios. We also show that stent implantation induces a different response in an aneurysm or in a healthy artery, the latter yielding more unstable G&R. Finally, our G&R model can efficiently predict, with very low computational cost, fundamental aspects of arterial adaptation induced by clinical procedures.

Elastic Fibers and Large Artery Mechanics in Animal Models of Development and Disease

Development of a closed circulatory system requires that large arteries adapt to the mechanical demands of high, pulsatile pressure. Elastin and collagen uniquely address these design criteria in the low and high stress regimes, resulting in a nonlinear mechanical response. Elastin is the core component of elastic fibers, which provide the artery wall with energy storage and recoil. The integrity of the elastic fiber network is affected by component insufficiency or disorganization, leading to an array of vascular pathologies and compromised mechanical behavior. In this review, we discuss how elastic fibers are formed and how they adapt in development and disease. We discuss elastic fiber contributions to arterial mechanical behavior and remodeling. We primarily present data from mouse models with elastic fiber deficiencies, but suggest that alternate small animal models may have unique experimental advantages and the potential to provide new insights. Advanced ultrastructural and biomechanical data are constantly being used to update computational models of arterial mechanics. We discuss the progression from early phenomenological models to microstructurally motivated strain energy functions for both collagen and elastic fiber networks. Although many current models individually account for arterial adaptation, complex geometries, and fluid-solid interactions (FSIs), future models will need to include an even greater number of factors and interactions in the complex system. Among these factors, we identify the need to revisit the role of time dependence and axial growth and remodeling in large artery mechanics, especially in cardiovascular diseases that affect the mechanical integrity of the elastic fibers.

Biomechanical Investigation of Disturbed Hemodynamics-Induced Tissue Degeneration in Abdominal Aortic Aneurysms Using Computational and Experimental Techniques

Abdominal aortic aneurysm (AAA) is the dilatation of the aorta beyond 50% of the normal vessel diameter. It is reported that 4-8% of men and 0.5-1% of women above 50 years of age bear an AAA and it accounts for ~15,000 deaths per year in the United States alone. If left untreated, AAA might gradually expand until rupture; the most catastrophic complication of the aneurysmal disease that is accompanied by a striking overall mortality of 80%. The precise mechanisms leading to AAA rupture remains unclear. Therefore, characterization of disturbed hemodynamics within AAAs will help to understand the mechanobiological development of the condition which will contribute to novel therapies for the condition. Due to geometrical complexities, it is challenging to directly quantify disturbed flows for AAAs clinically. Two other approaches for this investigation are computational modeling and experimental flow measurement. In computational modeling, the problem is first defined mathematically, and the solution is approximated with numerical techniques to get characteristics of flow. In experimental flow measurement, once the setup providing physiological flow pattern in a phantom geometry is constructed, velocity measurement system such as particle image velocimetry (PIV) enables characterization of the flow. We witness increasing number of applications of these complimentary approaches for AAA investigations in recent years. In this paper, we outline the details of computational modeling procedures and experimental settings and summarize important findings from recent studies, which will help researchers for AAA investigations and rupture mechanics.

Mechanical stresses associated with flattening of human femoropopliteal artery specimens during planar biaxial testing and their effects on the calculated physiologic stress-stretch state

Planar biaxial testing is commonly used to characterize the mechanical properties of arteries, but stresses associated with specimen flattening during this test are unknown. We quantified flattening effects in human femoropopliteal arteries (FPAs) of different ages and determined how they affect the calculated arterial physiologic stress-stretch state. Human FPAs from 472 tissue donors (age 12-82 years, mean 53 ± 16 years) were tested using planar biaxial extension, and morphometric and mechanical characteristics were used to assess the flattening effects. Constitutive parameters for the invariant-based model were adjusted to account for specimen flattening and used to calculate the physiologic stresses, stretches, axial force, circumferential stiffness, and stored energy for the FPAs in seven age groups. Flattened specimens were overall 12 ± 4% stiffer longitudinally and 19 ± 11% stiffer circumferentially when biaxially tested. Differences between the stress-stretch curves adjusted and non-adjusted for the effects of flattening were relatively constant across all age groups longitudinally, but increased with age circumferentially. In all age groups, these differences were smaller than the intersubject variability. Physiologic stresses, stretches, axial force, circumferential stiffness, and stored energy were all qualitatively and quantitatively similar when calculated with and without the flattening effects. Stresses, stretches, axial force, and stored energy reduced with age, but circumferential stiffness remained relatively constant between 25 and 65 years of age suggesting a homeostatic target of 0.75 ± 0.02 MPa. Flattening effects associated with planar biaxial testing are smaller than the intersubject variability and have little influence on the calculated physiologic stress-stretch state of human FPAs.

A Mechanobiologically Equilibrated Constrained Mixture Model for Growth and Remodeling of Soft Tissues

Growth and remodeling of soft tissues is a dynamic process and several theoretical frameworks have been developed to analyze the time-dependent, mechanobiological and/or biomechanical responses of these tissues to changes in external loads. Importantly, general processes can often be conveniently separated into truly non-steady contributions and steady-state ones. Depending on characteristic times over which the external loads are applied, time-dependent models can sometimes be specialized to respective time-independent formulations that simplify the mathematical treatment without compromising the goodness of the particularized solutions. Very few studies have analyzed the long-term, steady-state responses of soft tissue growth and remodeling following a direct approach. Here, we derive a mechanobiologically equilibrated formulation that arises from a general constrained mixture model. We see that integral-type evolution equations that characterize these general models can be written in terms of an equivalent set of time-independent, nonlinear algebraic equations that can be solved efficiently to yield long-term outcomes of growth and remodeling processes in response to sustained external stimuli. We discuss the mathematical conditions, in terms of orders of magnitude, that yield the particularized equations and illustrate results numerically for general arterial mechano-adaptations.

Critical roles of time-scales in soft tissue growth and remodeling

Most soft biological tissues exhibit a remarkable ability to adapt to sustained changes in mechanical loads. These macroscale adaptations, resulting from mechanobiological cellular responses, are important determinants of physiological behaviors and thus clinical outcomes. Given the complexity of such adaptations, computational models can significantly increase our understanding of how contributions of different cell types or matrix constituents, and their rates of turnover and evolving properties, ultimately change the geometry and biomechanical behavior at the tissue level. In this paper, we examine relative roles of the rates of tissue responses and external loading and present a new rate-independent approach for modeling the evolution of soft tissue growth and remodeling. For illustrative purposes, we also present numerical results for arterial adaptations. In particular, we show that, for problems defined by particular characteristic times, this approximate theory captures well the predictions of a fully general constrained mixture theory at a fraction of the computational cost.

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.

Evaluation of microstructurally motivated constitutive models to describe age-dependent tendon healing

Tendon injuries are common to all ages. Injured tendons typically do not recover full functionality. The amount and organization of tendon constituents dictate their mechanical properties. The impact of changes in these constituents during (patho)physiologic processes (e.g., aging and healing) are not fully understood. Toward this end, microstructurally motivated strain energy functions (SEFs) offer insight into underlying mechanisms of age-dependent healing. Several SEFs have been adapted for tendon; however, most are phenomenological. Therefore, the aims of this study are: (1) evaluate the descriptive capability of SEFs in age-dependent murine patellar tendon healing and (2) identify a SEF for implementation in a growth and remodeling (G&R) model. To accomplish these aims, models were fitted to patellar tendon tensile data from multiple age groups and post-injury timepoints. Model sensitivity to parameters and the determinability of the parameters were assessed. A two-way analysis of variance was used to identify changes in parameters and the feasibility of implementing each model into a G&R model is discussed. The evaluated SEFs exhibited adequate descriptive capability. Parameter determinability and sensitivity analysis, however, highlighted the need for additional data to inform and validate the models to increase physiologic relevance and enable G&R model formulation to determine underlying mechanisms of age-dependent healing. This work, as a first, evaluated changes in tendon mechanical properties both as functions of age and injury in an age-dependent manner using microstructurally motivated models, highlights inherent dependencies between parameters of widely used hyperelastic models, and identified unique post-injury behavior by the aging group compared to the mature and aged groups.

Potential biomechanical roles of risk factors in the evolution of thrombus-laden abdominal aortic aneurysms

Abdominal aortic aneurysms (AAAs) typically harbour an intraluminal thrombus (ILT), yet most prior computational models neglect biochemomechanical effects of thrombus on lesion evolution. We recently proposed a growth and remodelling model of thrombus-laden AAAs that introduced a number of new constitutive relations and associated model parameters. Because values of several of these parameters have yet to be elucidated by clinical data and could vary significantly from patient to patient, the aim of this study was to investigate the possible extent to which these parameters influence AAA evolution. Given that some of these parameters model potential effects of factors that influence the risk of rupture, this study also provides insight into possible roles of common risk factors on the natural history of AAAs. Despite geometrical limitations of a cylindrical domain, findings support current thought that smoking, hypertension, and female sex likely increase the risk of rupture. Although thrombus thickness is not a reliable risk factor for rupture, the model suggests that the presence of ILT may have a destabilizing effect on AAA evolution, consistent with histological findings from human samples. Finally, simulations support two hypotheses that should be tested on patient-specific geometries in the future. First, ILT is a potential source of the staccato enlargement observed in many AAAs. Second, ILT can influence rupture risk, positively or negatively, via competing biomechanical (eg, stress shielding) and biochemical (ie, proteolytic) effects. Although further computational and experimental studies are needed, the present findings highlight the importance of considering ILT when predicting aneurysmal enlargement and rupture risk.

Vascular smooth muscle cells in Marfan syndrome aneurysm: the broken bricks in the aortic wall

Marfan syndrome (MFS) is a connective tissue disorder with multiple organ manifestations. The genetic cause of this syndrome is the mutation of the FBN1 gene, encoding the extracellular matrix (ECM) protein fibrillin-1. This genetic alteration leads to the degeneration of microfibril structures and ECM integrity in the tunica media of the aorta. Indeed, thoracic aortic aneurysm and dissection represent the leading cause of death in MFS patients. To date, the most effective treatment option for this pathology is the surgical substitution of the damaged aorta. To highlight novel therapeutic targets, we review the molecular mechanisms related to MFS etiology in vascular smooth muscle cells, the foremost cellular type involved in MFS pathogenesis.

Disturbed Cyclical Stretch of Endothelial Cells Promotes Nuclear Expression of the Pro-Atherogenic Transcription Factor NF-κB

Exposure of endothelial cells to low and multidirectional blood flow is known to promote a pro-atherogenic phenotype. The mechanics of the vessel wall is another important mechano-stimulus within the endothelial cell environment, but no study has examined whether changes in the magnitude and direction of cell stretch can be pro-atherogenic. Herein, we developed a custom cell stretching device to replicate the in vivo stretch environment of the endothelial cell and examined whether low and multidirectional stretch promote nuclear translocation of NF-κB. A fluid–structure interaction model of the device demonstrated a nearly uniform strain within the region of cell attachment and a negligible magnitude of shear stress due to cyclical stretching of the cells in media. Compared to normal cyclical stretch, a low magnitude of cyclical stretch or no stretch caused increased expression of nuclear NF-κB (p = 0.09 and p < 0.001, respectively). Multidirectional stretch also promoted significant nuclear NF-κB expression, comparable to the no stretch condition, which was statistically higher than the low (p < 0.001) and normal (p < 0.001) stretch conditions. This is the first study to show that stretch conditions analogous to atherogenic blood flow profiles can similarly promote a pro-atherogenic endothelial cell phenotype, which supports a role for disturbed vessel wall mechanics as a pathological cell stimulus in the development of advanced atherosclerotic plaques.

Mechanisms of Vascular Smooth Muscle Contraction and the Basis for Pharmacologic Treatment of Smooth Muscle Disorders

The smooth muscle cell directly drives the contraction of the vascular wall and hence regulates the size of the blood vessel lumen. We review here the current understanding of the molecular mechanisms by which agonists, therapeutics, and diseases regulate contractility of the vascular smooth muscle cell and we place this within the context of whole body function. We also discuss the implications for personalized medicine and highlight specific potential target molecules that may provide opportunities for the future development of new therapeutics to regulate vascular function.

The conundrum of arterial stiffness, elevated blood pressure, and aging

Isolated systolic hypertension is a major health burden that is expanding with the aging of our population. There is evidence that central arterial stiffness contributes to the rise in systolic blood pressure (SBP); at the same time, central arterial stiffening is accelerated in patients with increased SBP. This bidirectional relationship created a controversy in the field on whether arterial stiffness leads to hypertension or vice versa. Given the profound interdependency of arterial stiffness and blood pressure, this question seems intrinsically challenging, or probably naïve. The aorta's function of dampening the pulsatile flow generated by the left ventricle is optimal within a physiological range of distending pressure that secures the required distal flow, keeps the aorta in an optimal mechanical conformation, and minimizes cardiac work. This homeostasis is disturbed by age-associated, minute alterations in aortic hemodynamic and mechanical properties that induce short- and long-term alterations in each other. Hence, it is impossible to detect an "initial insult" at an epidemiological level. Earlier manifestations of these alterations are observed in young adulthood with a sharp decline in aortic strain and distensibility accompanied by an increase in diastolic blood pressure. Subsequently, aortic mechanical reserve is exhausted, and aortic remodeling with wall stiffening and dilatation ensue. These two phenomena affect pulse pressure in opposite directions and different magnitudes. With early remodeling, there is an increase in pulse pressure, due to the dominance of arterial wall stiffness, which in turn accelerates aortic wall stiffness and dilation. With advanced remodeling, which appears to be greater in men, the effect of diameter becomes more pronounced and partially offsets the effect of wall stiffness leading to plateauing in pulse pressure in men and slower increase in pulse pressure (PP) than that of wall stiffness in women. The complex nature of the hemodynamic changes with aging makes the "one-size-fits-all" approach suboptimal and urges for therapies that address the vascular profile that underlies a given blood pressure, rather than the blood pressure values themselves.

Theory and application of arterial tissue in-host remodelling

A central therapeutic goal in many applications of modern Biomedicine is the reconstruction of the diseased arterial sections via robust and viable tissue equivalents. In-host remodelling is an emerging technology that exploits the remodelling ability of the host to regenerate tissue. We develop a general theoretical framework of growth and remodeling of arterial tissue starting from a synthetic, degradable, acellularized graft and we demonstrate the potential of mechanistic models to guide the development and assisting in the design of arterial tissue engineered constructs.

Growth and hemodynamics after early embryonic aortic arch occlusion

The majority of severe clinically significant forms of congenital heart disease (CHD) are associated with great artery lesions, including hypoplastic, double, right or interrupted aortic arch morphologies. While fetal and neonatal interventions are advancing, their potential ability to restore cardiac function, optimal timing, location, and intensity required for intervention remain largely unknown. Here, we combine computational fluid dynamics (CFD) simulations with in vivo experiments to test how individual pharyngeal arch artery hemodynamics alter as a result of local interventions obstructing individual arch artery flow. Simulated isolated occlusions within each pharyngeal arch artery were created with image-derived three-dimensional (3D) reconstructions of normal chick pharyngeal arch anatomy at Hamburger-Hamilton (HH) developmental stages HH18 and HH24. Acute flow redistributions were then computed using in vivo measured subject-specific aortic sinus inflow velocity profiles. A kinematic vascular growth-rendering algorithm was then developed and implemented to test the role of changing local wall shear stress patterns in downstream 3D morphogenesis of arch arteries. CFD simulations predicted that altered pressure gradients and flow redistributions were most sensitive to occlusion of the IVth arches. To evaluate these simulations experimentally, a novel in vivo experimental model of pharyngeal arch occlusion was developed and implemented using two-photon microscopy-guided femtosecond laser-based photodisruption surgery. The right IVth arch was occluded at HH18, and resulting diameter changes were followed for up to 24 h. Pharyngeal arch diameter responses to acute hemodynamic changes were predicted qualitatively but poorly quantitatively. Chronic growth and adaptation to hemodynamic changes, however, were predicted in a subset of arches. Our findings suggest that this complex biodynamic process is governed through more complex forms of mechanobiological vascular growth rules. Other factors in addition to wall shear stress or more complex WSS rules are likely important in the long-term arterial growth and patterning. Combination in silico/experimental platforms are essential for accelerating our understanding and prediction of consequences from embryonic/fetal cardiovascular occlusions and lay the foundation for noninvasive methods to guide CHD diagnosis and fetal intervention.

A Computational Model of Biochemomechanical Effects of Intraluminal Thrombus on the Enlargement of Abdominal Aortic Aneurysms

Abdominal aortic aneurysms (AAAs) typically develop an intraluminal thrombus (ILT), yet most computational models of AAAs have focused on either the mechanics of the wall or the hemodynamics within the lesion, both in the absence of ILT. In the few cases wherein ILT has been modeled directly, as, for example, in static models that focus on the state of stress in the aortic wall and the associated rupture risk, thrombus has been modeled as an inert, homogeneous, load-bearing material. Given the biochemomechanical complexity of an ILT, there is a pressing need to consider its diverse effects on the evolving aneurysmal wall. Herein, we present the first growth and remodeling model that addresses together the biomechanics, mechanobiology, and biochemistry of thrombus-laden AAAs. Whereas it has been shown that aneurysmal enlargement in the absence of ILT depends primarily on the stiffness and turnover of fibrillar collagen, we show that the presence of a thrombus within lesions having otherwise the same initial wall composition and properties can lead to either arrest or rupture depending on the biochemical effects (e.g., release of proteases) and biomechanical properties (e.g., stiffness of fibrin) of the ILT. These computational results suggest that ILT should be accounted for when predicting the potential enlargement or rupture risk of AAAs and highlight specific needs for further experimental and computational research.

Biomechanical diversity despite mechanobiological stability in tissue engineered vascular grafts two years post-implantation

Recent advances in vascular tissue engineering have enabled a paradigm shift from ensuring short-term graft survival to focusing on long-term stability and growth potential. We present the first experimental-computational study of a tissue-engineered vascular graft (TEVG) effectively over the full lifespan of the recipient. We show that grafts implanted within the venous circulation of mice remained patent over 2 years without thrombus, stenosis, or aneurysmal dilatation. Moreover, the gross appearance and mechanical properties of the grafts evolved to be similar to the host vein within 24 weeks, with mean neovessel geometry and properties remaining unchanged thereafter despite a continued turnover of extracellular matrix. Biomechanical diversity manifested after 24 weeks, however, via two subsets of grafts despite all procedures being the same. Computational modeling and associated immunohistological analyses suggested that this diversity likely resulted from a differential ratio of collagen types I and III, with lower I to III ratios promoting grafts having a compliance similar to the native vein. We submit that TEVGs can exhibit the desired long-term mechanobiological stability; hence, we must now focus on evaluating growth potential and optimizing scaffold properties to achieve compliance matching throughout neovessel development.

Role of mechanotransduction in vascular biology: focus on thoracic aortic aneurysms and dissections

Thoracic aortic diseases that involve progressive enlargement, acute dissection, or rupture are influenced by the hemodynamic loads and mechanical properties of the wall. We have only limited understanding, however, of the mechanobiological processes that lead to these potentially lethal conditions. Homeostasis requires that intramural cells sense their local chemomechanical environment and establish, maintain, remodel, or repair the extracellular matrix to provide suitable compliance and yet sufficient strength. Proper sensing, in turn, necessitates both receptors that connect the extracellular matrix to intracellular actomyosin filaments and signaling molecules that transmit the related information to the nucleus. Thoracic aortic aneurysms and dissections are associated with poorly controlled hypertension and mutations in genes for extracellular matrix constituents, membrane receptors, contractile proteins, and associated signaling molecules. This grouping of factors suggests that these thoracic diseases result, in part, from dysfunctional mechanosensing and mechanoregulation of the extracellular matrix by the intramural cells, which leads to a compromised structural integrity of the wall. Thus, improved understanding of the mechanobiology of aortic cells could lead to new therapeutic strategies for thoracic aortic aneurysms and dissections.

Bio-Chemo-Mechanical Models of Vascular Mechanics

Models of vascular mechanics are necessary to predict the response of an artery under a variety of loads, for complex geometries, and in pathological adaptation. Classic constitutive models for arteries are phenomenological and the fitted parameters are not associated with physical components of the wall. Recently, microstructurally-linked models have been developed that associate structural information about the wall components with tissue-level mechanics. Microstructurally-linked models are useful for correlating changes in specific components with pathological outcomes, so that targeted treatments may be developed to prevent or reverse the physical changes. However, most treatments, and many causes, of vascular disease have chemical components. Chemical signaling within cells, between cells, and between cells and matrix constituents affects the biology and mechanics of the arterial wall in the short- and long-term. Hence, bio-chemo-mechanical models that include chemical signaling are critical for robust models of vascular mechanics. This review summarizes bio-mechanical and bio-chemo-mechanical models with a focus on large elastic arteries. We provide applications of these models and challenges for future work.

Limiting extensibility constitutive model with distributed fibre orientations and ageing of abdominal aorta

The abdominal aorta is susceptible to age-related pathological changes (arteriosclerosis, atherosclerosis, aneurysm, and tortuosity). Computational biomechanics and mechanobiology provide models capable of predicting mutual interactions between a changing mechanical environment and patho-physiological processes in ageing. However, a key factor is a constitutive equation which should reflect the internal tissue architecture. Our study investigates three microstructurally-motivated invariant-based hyperelastic anisotropic models suitable for description of the passive mechanical behaviour of the human abdominal aorta at a multiaxial state of stress known from recent literature. The three adopted models have also been supplemented with a newly proposed constitutive model (limiting extensibility with fibre dispersion). All models additively decouple the mechanical response of the isotropic (elastin and smooth muscle cells represented by the neo-Hookean term) and the anisotropic (collagen) parts. Two models use exponential functions to capture large strain stiffening ascribed to the engagement of collagen fibres into the load-bearing process. The other two models are based on the concept of limiting extensibility. Perfect alignment of reinforcing fibres with two preferred directions as well as fibre dispersion are considered. Constitutive models are calibrated to the inflation-extension response adopted from the literature based on the computational model of the residually-stressed thick-walled tube. A correlation analysis of determined material parameters was performed to reveal dependence on the age. The results of the nonlinear regression suggest that limiting fibre extensibility is the concept which is suitable to be used for the constitutive description of the aorta at multiaxial stress states and is highly sensitive to ageing-induced changes in mechanical response.

Computational model of the in vivo development of a tissue engineered vein from an implanted polymeric construct

Advances in vascular tissue engineering have been tremendous over the past 15 years, yet there remains a need to optimize current constructs to achieve vessels having true growth potential. Toward this end, it has been suggested that computational models may help hasten this process by enabling time-efficient parametric studies that can reduce the experimental search space. In this paper, we present a first generation computational model for describing the in vivo development of a tissue engineered vein from an implanted polymeric scaffold. The model was motivated by our recent data on the evolution of mechanical properties and microstructural composition over 24 weeks in a mouse inferior vena cava interposition graft. It is shown that these data can be captured well by including both an early inflammatory-mediated and a subsequent mechano-mediated production of extracellular matrix. There remains a pressing need, however, for more data to inform the development of next generation models, particularly the precise transition from the inflammatory to the mechanobiological dominated production of matrix having functional capability.

A finite element-based constrained mixture implementation for arterial growth, remodeling, and adaptation: theory and numerical verification

We implemented a constrained mixture model of arterial growth and remodeling in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and nonhomogenous degradation of elastin or loss of smooth muscle function. The nonlinear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons with prior results for two special cases: uniform transmural changes in mass and differential growth and remodeling within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement.

Calculation of the outcomes of remodeling of arteries subjected to sustained hypertension using a 3D two-layered model

Arteries manifest a remodeling response to long-term alterations in arterial pressure and blood flow by changing geometry, structure, and composition through processes driven by perturbations of the local stresses in the vascular wall from their baseline values. The objective of this study is twofold--to develop a general method for calculating the remodeling responses of an artery considered as a two-layered tube; and to provide results for adaptive and maladaptive remodeling of a coronary artery. By formulating an inverse problem of vascular mechanics, the geometrical dimensions and mechanical properties of an artery are calculated from a prescribed deformed configuration, stress field, structural stiffness, and applied load. As an illustrative example we consider a human LAD coronary artery in both a perfect and incomplete adaptive response to a sustained step-wise change in pressure and a maladaptive response due to impaired remodeling of adventitia. The results obtained show that adventitia plays an important role in vascular mechanics when an artery is subjected to high arterial pressure. In addition to its well-known short term function of preventing over-inflation of an artery, it seems reasonable to accept that the manner by which adventitia remodels in response to a chronic increase in pressure is essential for preserving normal arterial function or may lead to an increased risk of developing vascular disorders.

An automated approach for three-dimensional quantification of fibrillar structures in optically cleared soft biological tissues

We present a novel approach allowing for a simple, fast and automated morphological analysis of three-dimensional image stacks (z-stacks) featuring fibrillar structures from optically cleared soft biological tissues. Five non-atherosclerotic tissue samples from human abdominal aortas were used to outline the multi-purpose methodology, applicable to various tissue types. It yields a three-dimensional orientational distribution of relative amplitudes, representing the original collagen fibre morphology, identifies regions of isotropy where no preferred fibre orientations are observed and determines structural parameters throughout anisotropic regions for the analysis and numerical modelling of biomechanical quantities such as stress and strain. Our method combines optical tissue clearing with second-harmonic generation imaging, Fourier-based image analysis and maximum-likelihood estimation for distribution fitting. With a new sample preparation method for arteries, we present, for the first time to our knowledge, a continuous three-dimensional distribution of collagen fibres throughout the entire thickness of the aortic wall, revealing novel structural and organizational insights into the three arterial layers.

Continuum mixture models of biological growth and remodeling: past successes and future opportunities

Biological growth processes involve mass exchanges that increase, decrease, or replace material that constitutes cells, tissues, and organs. In most cases, such exchanges alter the structural makeup of the material and consequently affect associated mechanobiological responses to applied loads. Given that the type and extent of changes in structural integrity depend on the different constituents involved (e.g., particular cytoskeletal or extracellular matrix proteins), the continuum theory of mixtures is ideally suited to model the mechanics of growth and remodeling. The goal of this review is twofold: first, to highlight a few illustrative examples that show diverse applications of mixture theory to describe biological growth and/or remodeling; second, to identify some open problems in the fields of modeling soft-tissue growth and remodeling.

Quantitative assessment of collagen fibre orientations from two-dimensional images of soft biological tissues

In this work, we outline an automated method for the extraction and quantification of material parameters characterizing collagen fibre orientations from two-dimensional images. Morphological collagen data among different length scales were obtained by combining the established methods of Fourier power spectrum analysis, wedge filtering and progressive regions of interest splitting. Our proposed method yields data from which we can determine parameters for computational modelling of soft biological tissues using fibre-reinforced constitutive models and gauge the length scales most appropriate for obtaining a physically meaningful measure of fibre orientations, which is representative of the true tissue morphology of the two-dimensional image. Specifically, we focus on three parameters quantifying different aspects of the collagen morphology: first, using maximum-likelihood estimation, we extract location parameters that accurately determine the angle of the principal directions of the fibre reinforcement (i.e. the preferred fibre directions); second, using a dispersion model, we obtain dispersion parameters quantifying the collagen fibre dispersion about these principal directions; third, we calculate the weighted error entropy as a measure of changes in the entire fibre distributions at different length scales, as opposed to their average behaviour. With fully automated imaging techniques (such as multiphoton microscopy) becoming increasingly popular (which often yield large numbers of images to analyse), our method provides an ideal tool for quickly extracting mechanically relevant tissue parameters which have implications for computational modelling (e.g. on the mesh density) and can also be used for the inhomogeneous modelling of tissues.

Perspectives on biomechanical growth and remodeling mechanisms in glaucoma()

Glaucoma is a blinding diseases in which damage to the axons results in loss of retinal ganglion cells. Experimental evidence indicates that chronic intraocular pressure elevation initiates axonal insult at the level of the lamina cribrosa. The lamina cribrosa is a porous collagen structure through which the axons pass on their path from the retina to the brain. Recent experimental studies revealed the extensive structural changes of the lamina cribrosa and its surrounding tissues during the development and progression of glaucoma. In this perspective paper we review the experimental evidence for growth and remodeling mechanisms in glaucoma including adaptation of tissue anisotropy, tissue thickening/thinning, tissue elongation/shortening and tissue migration. We discuss the existing predictive computational approaches that try to elucidate the potential biomechanical basis of theses growth and remodeling mechanisms and highlight open questions, challenges, and avenues for further development.

Constrained Mixture Models as Tools for Testing Competing Hypotheses in Arterial Biomechanics: A Brief Survey

Hypothesis testing via numerical models has emerged as a powerful tool which permits the verification of theoretical frameworks against canonical experimental and clinical observations. Cleverly designed computational experiments also inspire new methodologies by elucidating important biological processes and restricting parametric spaces. Constrained mixture models of arterial growth and remodeling (G&R) can facilitate the design of computational experiments which can bypass technical limitations in the laboratory, by considering illustrative special cases. The resulting data may then inform the design of focused experimental techniques and the development of improved theories. This work is a survey of computational hypothesis-testing studies, which exploit the unique abilities offered by the constrained mixture theory of arterial G&R. Specifically, we explore the core hypotheses integrated in these models, review their basic mathematical conceptualizations, and recapitulate their most salient and illuminating findings. We then assess how a decade's worth of constrained mixture models have contributed to a lucid, emerging picture of G&R mechanisms.

Computational hemodynamic optimization predicts dominant aortic arch selection is driven by embryonic outflow tract orientation in the chick embryo

In the early embryo, a series of symmetric, paired vessels, the aortic arches, surround the foregut and distribute cardiac output to the growing embryo and fetus. During embryonic development, the arch vessels undergo large-scale asymmetric morphogenesis to form species-specific adult great vessel patterns. These transformations occur within a dynamic biomechanical environment, which can play an important role in the development of normal arch configurations or the aberrant arch morphologies associated with congenital cardiac defects. Arrested migration and rotation of the embryonic outflow tract during late stages of cardiac looping has been shown to produce both outflow tract and several arch abnormalities. Here, we investigate how changes in flow distribution due to a perturbation in the angular orientation of the embryonic outflow tract impact the morphogenesis and growth of the aortic arches. Using a combination of in vivo arch morphometry with fluorescent dye injection and hemodynamics-driven bioengineering optimization-based vascular growth modeling, we demonstrate that outflow tract orientation significantly changes during development and that the associated changes in hemodynamic load can dramatically influence downstream aortic arch patterning. Optimization reveals that balancing energy expenditure with diffusive capacity leads to multiple arch vessel patterns as seen in the embryo, while minimizing energy alone led to the single arch configuration seen in the mature arch of aorta. Our model further shows the critical importance of the orientation of the outflow tract in dictating morphogenesis to the adult single arch and accurately predicts arch IV as the dominant mature arch of aorta. These results support the hypothesis that abnormal positioning of the outflow tract during early cardiac morphogenesis may lead to congenital defects of the great vessels due to altered hemodynamic loading.

Determination of the layer-specific distributed collagen fibre orientations in human thoracic and abdominal aortas and common iliac arteries

The established method of polarized microscopy in combination with a universal stage is used to determine the layer-specific distributed collagen fibre orientations in 11 human non-atherosclerotic thoracic and abdominal aortas and common iliac arteries (63 ± 15.3 years, mean ± s.d.). A dispersion model is used to quantify over 37 000 recorded fibre angles from tissue samples. The study resulted in distinct fibre families, fibre directions, dispersion and thickness data for each layer and all vessels investigated. Two fibre families were present for the intima, media and adventitia in the aortas, with often a third and sometimes a fourth family in the intima in the respective axial and circumferential directions. In all aortas, the two families were almost symmetrically arranged with respect to the cylinder axis, closer to the axial direction in the adventitia, closer to the circumferential direction in the media and in between in the intima. The same trend was found for the intima and adventitia of the common iliac arteries; however, there was only one preferred fibre alignment present in the media. In all locations and layers, the observed fibre orientations were always in the tangential plane of the walls, with no radial components and very small dispersion through the wall thickness. A wider range of in-plane fibre orientations was present in the intima than in the media and adventitia. The mean total wall thickness for the aortas and the common iliac artery was 1.39 and 1.05 mm, respectively. For the aortas, a slight thickening of the intima and a thinning of the media in increasingly distal regions were observed. A clear intimal thickening was present distal to the branching of the celiac arteries. All data, except for the media of the common iliac arteries, showed two prominent collagen fibre families for all layers so that two-fibre family models seem most appropriate.