Mechanobiological stability: a new paradigm to understand the enlargement of aneurysms?

Sustained Physiological Stretch Induces Abdominal Skin Growth in Pregnancy

Supraphysiological stretches are exploited in skin expanders to induce tissue growth for autologous implants. As pregnancy is associated with large levels of sustained stretch, we investigated whether skin growth occurs in pregnancy. Therefore, we combined a mechanical model of skin and the observations from suction experiments on several body locations of five pregnant women at different gestational ages. The measurements show a continuous increase in stiffness, with the largest change observed during the last trimester. A comparison with numerical simulations indicates that the measured increase in skin stiffness is far below the level expected for the corresponding deformation of abdominal skin. A new set of simulations accounting for growth could rationalize all observations. The predicted amount of tissue growth corresponds to approximately 40% area increase before delivery. The results of the simulations also offered the opportunity to investigate the biophysical cues present in abdominal skin along gestation and to compare them with those arising in skin expanders. Alterations of the skin mechanome were quantified, including tissue stiffness, hydrostatic and osmotic pressure of the interstitial fluid, its flow velocity and electrical potential. The comparison between pregnancy and skin expansion highlights similarities as well as differences possibly influencing growth and remodeling.

Growth and remodeling of the dissected membrane in an idealized dissected aorta model

While transitioning from the acute to chronic phase, the wall of a dissected aorta often expands in diameter and adaptations in thickness and microstructure take place in the dissected membrane. Including the mechanisms, leading to these changes, in a computational model is expected to improve the accuracy of predictions of the long-term complications and optimal treatment timing of dissection patients. An idealized dissected wall was modeled to represent the elastin and collagen production and/or degradation imposed by stress- and inflammation-mediated growth and remodeling, using the homogenized constrained mixture theory. As no optimal growth and remodeling parameters have been defined for aortic dissections, a Latin hypercube sampling with 1000 parameter combinations was assessed for four inflammation patterns, with a varying spatial extent (full/local) and temporal evolution (permanent/transient). The dissected membrane thickening and microstructure was considered together with the diameter expansion over a period of 90 days. The highest success rate was found for the transient inflammation patterns, with about 15% of the samples leading to converged solutions after 90 days. Clinically observed thickening rates were found for 2-4% of the transient inflammation samples, which represented median total diameter expansion rates of about 5 mm/year. The dissected membrane microstructure showed an elastin decrease and, in most cases, a collagen increase. In conclusion, the model with the transient inflammation pattern allowed the reproduction of clinically observed dissected membrane thickening rates, diameter expansion rates and adaptations in microstructure, thus providing guidance in reducing the parameter space in growth and remodeling models of aortic dissections.

Narrative Review of Risk Assessment of Abdominal Aortic Aneurysm Rupture Based on Biomechanics-Related Morphology

CLINICAL IMPACT

Studies have shown that the biomechanical indicators based on multi-scale models are more effective in accurately assessing the rupture risk of AAA. To meet the need for clinical monitoring and rapid decision making, the typical morphological parameters associated with AAA rupture and their relationships with the mechanical environment have been summarized, which provide a reference for clinical preoperative risk assessment of AAA.

A homogenized constrained mixture model of cardiac growth and remodeling: analyzing mechanobiological stability and reversal

Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extracellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.

Fabrication of deformable patient-specific AAA models by material casting techniques

Background

Abdominal Aortic Aneurysm (AAA) is a balloon-like dilatation that can be life-threatening if not treated. Fabricating patient-specific AAA models can be beneficial for in-vitro investigations of hemodynamics, as well as for pre-surgical planning and training, testing the effectiveness of different interventions, or developing new surgical procedures. The current direct additive manufacturing techniques cannot simultaneously ensure the flexibility and transparency of models required by some applications. Therefore, casting techniques are presented to overcome these limitations and make the manufactured models suitable for in-vitro hemodynamic investigations, such as particle image velocimetry (PIV) measurements or medical imaging.

Methods

Two complex patient-specific AAA geometries were considered, and the related 3D models were fabricated through material casting. In particular, two casting approaches, i.e. lost molds and lost core casting, were investigated and tested to manufacture the deformable AAA models. The manufactured models were acquired by magnetic resonance, computed tomography (CT), ultrasound imaging, and PIV. In particular, CT scans were segmented to generate a volumetric reconstruction for each manufactured model that was compared to a reference model to assess the accuracy of the manufacturing process.

Results

Both lost molds and lost core casting techniques were successful in the manufacturing of the models. The lost molds casting allowed a high-level surface finish in the final 3D model. In this first case, the average signed distance between the manufactured model and the reference was (- 0.2 ± 0.2 ) mm. However, this approach was more expensive and time-consuming. On the other hand, the lost core casting was more affordable and allowed the reuse of the external molds to fabricate multiple copies of the same AAA model. In this second case, the average signed distance between the manufactured model and the reference was (0.1 ± 0.6 ) mm. However, the final model's surface finish quality was poorer compared to the model obtained by lost molds casting as the sealing of the outer molds was not as firm as the other casting technique.

Conclusions

Both lost molds and lost core casting techniques can be used for manufacturing patient-specific deformable AAA models suitable for hemodynamic investigations, including medical imaging and PIV.

Numerical and experimental investigation of multi-species bacterial co-aggregation

This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an arbitrary number of species is straightforward. In addition to two-species (multi-species growth) dynamics, the transport of a nutritional substance and the extent of co-aggregation are introduced into the model as the third and fourth primary variables. A phase-field modeling approach is employed to describe the co-aggregation between the two species. The mathematical model is three-dimensional and fully based on the continuum description of the problem without any need for discrete agents which are the key elements of the individual-based modeling approach. It is shown that the use of a phase-field-based model is equivalent to a particular form of classical diffusion-reaction systems. Unlike the so-called mixture models, the evolution of each component of the multi-species system is captured thanks to the inherent capability of phase-field modeling in treating systems consisting of distinct multi-phases. The details of numerical implementation in a FEM framework are also presented. Indeed, a new multi-field user element is developed and implemented in ANSYS for this multiphysics problem. Predictions of the model are compared with the experimental observations. By that, the versatility and applicability of the model and the numerical tool are well established.

About prestretch in homogenized constrained mixture models simulating growth and remodeling in patient-specific aortic geometries

Evolution of mechanical and structural properties in the Ascending Thoracic Aorta (ATA) is the results of complex mechanobiological processes. In this work, we address some numerical challenges in order to elaborate computational models of these processes. For that, we extend the state of the art of homogenized constrained mixture (hCM) models. In these models, prestretches are assigned to the mixed constituents in order to ensure local mechanical equilibrium macroscopically, and to maintain a homeostatic level of tension in collagen fibers microscopically. Although the initial prestretches were assumed as homogeneous in idealized straight tubes, more elaborate prestretch distributions need to be considered for curved geometrical models such as patient-specific ATA. Therefore, we introduce prestretches having a three-dimensional gradient across the ATA geometry in the homeostatic reference state. We test different schemes with the objective to ensure stable growth and remodeling (G&R) simulations on patient-specific curved vessels. In these simulations, aneurysm progression is triggered by tissue changes in the constituents such as mass degradation of intramural elastin. The results show that the initial prestretches are not only critical for the stability of numerical simulations, but they also affect the G&R response. Eventually, we submit that initial conditions required for G&R simulations need to be identified regionally for ensuring realistic patient-specific predictions of aneurysm progression.

Microenvironment-mediated cancer dormancy: Insights from metastability theory

Dormancy is an evolutionarily conserved protective mechanism widely observed in nature. A pathological example is found during cancer metastasis, where cancer cells disseminate from the primary tumor, home to secondary organs, and enter a growth-arrested state, which could last for decades. Recent studies have pointed toward the microenvironment being heavily involved in inducing, preserving, or ceasing this dormant state, with a strong focus on identifying specific molecular mechanisms and signaling pathways. Increasing evidence now suggests the existence of an interplay between intracellular as well as extracellular biochemical and mechanical cues in guiding such processes. Despite the inherent complexities associated with dormancy, proliferation, and growth of cancer cells and tumor tissues, viewing these phenomena from a physical perspective allows for a more global description, independent from many details of the systems. Building on the analogies between tissues and fluids and thermodynamic phase separation concepts, we classify a number of proposed mechanisms in terms of a thermodynamic metastability of the tumor with respect to growth. This can be governed by interaction with the microenvironment in the form of adherence (wetting) to a substrate or by mechanical confinement of the surrounding extracellular matrix. By drawing parallels with clinical and experimental data, we advance the notion that the local energy minima, or metastable states, emerging in the tissue droplet growth kinetics can be associated with a dormant state. Despite its simplicity, the provided framework captures several aspects associated with cancer dormancy and tumor growth.

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.

Vascular Mechanobiology: Homeostasis, Adaptation, and Disease

Cells of the vascular wall are exquisitely sensitive to changes in their mechanical environment. In healthy vessels, mechanical forces regulate signaling and gene expression to direct the remodeling needed for the vessel wall to maintain optimal function. Major diseases of arteries involve maladaptive remodeling with compromised or lost homeostatic mechanisms. Whereas homeostasis invokes negative feedback loops at multiple scales to mediate mechanobiological stability, disease progression often occurs via positive feedback that generates mechanobiological instabilities. In this review, we focus on the cell biology, wall mechanics, and regulatory pathways associated with arterial health and how changes in these processes lead to disease. We discuss how positive feedback loops arise via biomechanical and biochemical means. We conclude that inflammation plays a central role in overriding homeostatic pathways and suggest future directions for addressing therapeutic needs.

Mapping pre-dissection aortic wall abnormalities: a multiparametric assessment

OBJECTIVES

Maximal aortic diameter is commonly used to assess aortic risk but poorly predicts the timing and location of dissection events in patients with connective tissue disease who undergo regular imaging surveillance. Hence, we aimed to use available surveillance computed tomography angiography (CTA) scans to investigate the correlation between 3-dimensional (3D) growth and cyclic transmural wall stress with the location of intimal tear formation.

METHODS

Three type B aortic dissection patients with 2 available electrocardiogram (ECG)-gated pre-dissection CTA scans and without surgical repair during the pre-dissection interval were retrospectively identified at our institution. Vascular deformation mapping was used to measure 3D aortic growth between 2 pre-dissection clinical CTA studies. In addition, we performed a computational analysis to estimate cyclic transmural wall stress in patient-specific baseline CTA geometries.

RESULTS

In all 3 connective tissue disease patients, the site of type B aortic intimal tear co-localized with areas of peak 3D aortic wall growth. Aortic growth was detected by clinical radiological assessment in only 1 case. Co-localization of peak transmural stress and the site of intimal tear formation were found in all cases.

CONCLUSIONS

Focal areas of growth and transmural wall stress co-localized with the site of intimal tear formation. These hypothesis-generating results suggest a possible new analytic pathway for a more sophisticated assessment of the factors leading to the initiation of dissection in patients with connective tissue disease. These methods could improve on current risk-stratification techniques.

Spontaneous reversal of stenosis in tissue-engineered vascular grafts

We developed a tissue-engineered vascular graft (TEVG) for use in children and present results of a U.S. Food and Drug Administration (FDA)-approved clinical trial evaluating this graft in patients with single-ventricle cardiac anomalies. The TEVG was used as a Fontan conduit to connect the inferior vena cava and pulmonary artery, but a high incidence of graft narrowing manifested within the first 6 months, which was treated successfully with angioplasty. To elucidate mechanisms underlying this early stenosis, we used a data-informed, computational model to perform in silico parametric studies of TEVG development. The simulations predicted early stenosis as observed in our clinical trial but suggested further that such narrowing could reverse spontaneously through an inflammation-driven, mechano-mediated mechanism. We tested this unexpected, model-generated hypothesis by implanting TEVGs in an ovine inferior vena cava interposition graft model, which confirmed the prediction that TEVG stenosis resolved spontaneously and was typically well tolerated. These findings have important implications for our translational research because they suggest that angioplasty may be safely avoided in patients with asymptomatic early stenosis, although there will remain a need for appropriate medical monitoring. The simulations further predicted that the degree of reversible narrowing can be mitigated by altering the scaffold design to attenuate early inflammation and increase mechano-sensing by the synthetic cells, thus suggesting a new paradigm for optimizing next-generation TEVGs. We submit that there is considerable translational advantage to combined computational-experimental studies when designing cutting-edge technologies and their clinical management.

Mechanical homeostasis in tissue equivalents: a review

There is substantial evidence that growth and remodeling of load bearing soft biological tissues is to a large extent controlled by mechanical factors. Mechanical homeostasis, which describes the natural tendency of such tissues to establish, maintain, or restore a preferred mechanical state, is thought to be one mechanism by which such control is achieved across multiple scales. Yet, many questions remain regarding what promotes or prevents homeostasis. Tissue equivalents, such as collagen gels seeded with living cells, have become an important tool to address these open questions under well-defined, though limited, conditions. This article briefly reviews the current state of research in this area. It summarizes, categorizes, and compares experimental observations from the literature that focus on the development of tension in tissue equivalents. It focuses primarily on uniaxial and biaxial experimental studies, which are well-suited for quantifying interactions between mechanics and biology. The article concludes with a brief discussion of key questions for future research in this field.

[Review of studies on the biomechanical modelling of the coupling effect between stent degradation and blood vessel remodeling]

The dynamic coupling of stent degradation and vessel remodeling can influence not only the structural morphology and material property of stent and vessel, but also the development of in-stent restenosis. The research achievements of biomechanical modelling and analysis of stent degradation and vessel remodeling were reviewed; several noteworthy research perspectives were addressed, a stent-vessel coupling model was developed based on stent damage function and vessel growth function, and then concepts of matching ratio and risk factor were established so as to evaluate the treatment effect of stent intervention, which may lay the scientific foundation for the structure design, mechanical analysis and clinical application of biodegradable stent.

Fast, Rate-Independent, Finite Element Implementation of a 3D Constrained Mixture Model of Soft Tissue Growth and Remodeling

Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.

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.

On Rate Boundary Conditions for Soft Tissue Bifurcation Analysis

Mechanical instability of soft tissues can either risk their normal function or alternatively trigger patterning mechanisms during growth and morphogenesis processes. Unlike standard stability analysis of linear elastic bodies, for soft tissues undergoing large deformations it is imperative to account for the nonlinearities induced by the coupling between load and surface changes at onset of instability. The related issue of boundary conditions, in context of soft tissues, has hardly been addressed in the literature, with most of available research employing dead-load conditions. This paper is concerned with the influence of imposed homogeneous rate (incremental) surface data on critical loads and associated modes in soft tissues, within the context of linear bifurcation analysis. Material behavior is modeled by compressible isotropic hyperelastic strain energy functions (SEFs), with experimentally validated material parameters for the Fung-Demiray SEF, over a range of constitutive response (including brain and liver tissues). For simplicity, we examine benchmark problems of basic spherical patterns: full sphere, spherical cavity, and thick spherical shell. Limiting the analysis to primary hydrostatic states we arrive at universal closed-form solutions, thus providing insight on the role of imposed boundary data. Influence of selected rate boundary conditions (RBCs) like dead-load and fluid-pressure (FP), coupled with constitutive parameters, on the existence and levels of bifurcation loads is compared and discussed. It is argued that the selection of the appropriate type of homogeneous RBC can have a critical effect on the level of bifurcation loads and even exclude the emergence of bifurcation instabilities.

Mechanotransmission of haemodynamic forces by the endothelial glycocalyx in a full-scale arterial model

The glycocalyx has been identified as a key mechano-sensor of the shear forces exerted by streaming blood onto the vascular endothelial lining. Although the biochemical reaction to the blood flow has been extensively studied, the mechanism of transmission of the haemodynamic shear forces to the endothelial transmembrane anchoring structures and, consequently, to the subcellular elements in the cytoskeleton, is still not fully understood. Here we apply a multiscale approach to elucidate how haemodynamic shear forces are transmitted to the transmembrane anchors of endothelial cells. Wall shear stress time histories, as obtained from image-based computational haemodynamics models of a carotid bifurcation, are used as a load and a continuum model is applied to obtain the mechanical response of the glycocalyx all along the cardiac cycle. The main findings of this in silico study are that: (1) the forces transmitted to the transmembrane anchors are in the range of 1-10 pN, which is in the order of magnitude reported for the different conformational states of transmembrane mechanotranductors; (2) locally, the forces transmitted to the anchors of the glycocalyx structure can be markedly different from the near-wall haemodynamic shear forces both in amplitude and frequency content. The findings of this in silico approach warrant future studies focusing on the actual forces transmitted to the transmembrane mechanotransductors, which might outperform haemodynamic descriptors of disturbed shear as localizing factors of vascular disease.

Mechanobiological Stability of Biological Soft Tissues

Like all other materials, biological soft tissues are subject to general laws of physics, including those governing mechanical equilibrium and stability. In addition, however, these tissues are able to respond actively to changes in their mechanical and chemical environment. There is, therefore, a pressing need to understand such processes theoretically. In this paper, we present a new rate-based constrained mixture formulation suitable for studying mechanobiological equilibrium and stability of soft tissues exposed to transient or sustained changes in material composition or applied loading. These concepts are illustrated for canonical problems in arterial mechanics, which distinguish possible stable versus unstable mechanobiological responses. Such analyses promise to yield insight into biological processes that govern both health and disease progression.

Patient-Specific Prediction of Abdominal Aortic Aneurysm Expansion Using Bayesian Calibration

Translating recent advances in abdominal aortic aneurysm (AAA) growth and remodeling (G&R) knowledge into a predictive, patient-specific clinical treatment tool requires a major paradigm shift in computational modeling. The objectives of this study are to develop a prediction framework that first calibrates the physical AAA G&R model using patient-specific serial computed tomography (CT) scan images, predicts the expansion of an AAA in the future, and quantifies the associated uncertainty in the prediction. We adopt a Bayesian calibration method to calibrate parameters in the G&R computational model and predict the magnitude of AAA expansion. The proposed Bayesian approach can take different sources of uncertainty; therefore, it is well suited to achieve our aims in predicting the AAA expansion process as well as in computing the propagated uncertainty. We demonstrate how to achieve the proposed aims by solving the formulated Bayesian calibration problems for cases with the synthetic G&R model output data and real medical patient-specific CT data. We compare and discuss the performance of predictions and computation time under different sampling cases of the model output data and patient data, both of which are simulated by the G&R computation. Furthermore, we apply our Bayesian calibration to real patient-specific serial CT data and validate our prediction. The accuracy and efficiency of the proposed method is promising, which appeals to computational and medical communities.

Central artery stiffness and thoracic aortopathy

Thoracic aortopathy, especially aneurysm, dissection, and rupture, is responsible for significant morbidity and mortality. Uncontrolled hypertension and aging are primary risk factors for such conditions, and they contribute to an increase in the mechanical stress on the wall and an increase in its structural vulnerability, respectively. Select genetic mutations also predispose to these lethal conditions, and the collection of known mutations suggests that dysfunctional mechanosensing and mechanoregulation of the extracellular matrix may contribute to pathogenesis and disease progression. In the absence of a well-accepted pharmacotherapy, nonsurgical treatments tend to focus on reducing the mechanical loading on the aorta, particularly via the use of antihypertensive medications and recommendations to avoid strenuous exercises such as weight lifting. In this brief review, we discuss the important effects of central artery stiffening on global hemodynamics and, in particular, on the increase in pulse pressure that acts on the proximal thoracic aorta. We consider Marfan syndrome as an illustrative aortopathy but discuss other conditions leading to thoracic aortic aneurysm and dissection. We highlight the importance of phenotyping the aorta biomechanically, not just clinically, and emphasize the utility of mouse models in elucidating molecular and mechanical mechanisms of disease. Notwithstanding the widely recognized role of central artery stiffening in driving end-organ disease, we suggest that there is similarly a need to consider its key role in thoracic aortopathy.

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.

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).

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.

Vascular Mechanobiology: Towards Control of In Situ Regeneration

The paradigm of regenerative medicine has recently shifted from in vitro to in situ tissue engineering: implanting a cell-free, biodegradable, off-the-shelf available scaffold and inducing the development of functional tissue by utilizing the regenerative potential of the body itself. This approach offers a prospect of not only alleviating the clinical demand for autologous vessels but also circumventing the current challenges with synthetic grafts. In order to move towards a hypothesis-driven engineering approach, we review three crucial aspects that need to be taken into account when regenerating vessels: (1) the structure-function relation for attaining mechanical homeostasis of vascular tissues, (2) the environmental cues governing cell function, and (3) the available experimental platforms to test instructive scaffolds for in situ tissue engineering. The understanding of cellular responses to environmental cues leads to the development of computational models to predict tissue formation and maturation, which are validated using experimental platforms recapitulating the (patho)physiological micro-environment. With the current advances, a progressive shift is anticipated towards a rational and effective approach of building instructive scaffolds for in situ vascular tissue regeneration.

Growth and Remodeling of Load-Bearing Biological Soft Tissues

The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues - tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.

Stability analysis of a continuum-based constrained mixture model for vascular growth and remodeling

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed differential equations can be reduced to a nonlinear ODE system. We demonstrate the degeneracy of the linearized system about the homeostatic state, which is a fundamental cause of the neutral stability observations reported in prior studies. Due to this degeneracy, stability conclusions for the original nonlinear system cannot be directly inferred. To resolve this problem, a sub-system is constructed by recognizing a linear relation between two states. Subsequently, Lyapunov's indirect method is used to connect stability properties between the linearized system and the original nonlinear system, to rigorously establish the neutral stability properties of the original system. In particular, this analysis leads to a stability criterion for vascular expansion in terms of growth and remodeling kinetic parameters, geometric quantities and material properties. Numerical simulations were conducted to evaluate the theoretical stability criterion under broader conditions, as well as study the influence of key parameters and physical factors on growth properties. The theoretical results are also compared with prior numerical and experimental findings in the literature.

A Geodesics-Based Surface Parameterization to Assess Aneurysm Progression

Abdominal aortic aneurysm (AAA) intervention and surveillance is currently based on maximum transverse diameter, even though it is recognized that this might not be the best strategy. About 10% of patients with small AAA transverse diameters, for whom intervention is not considered, still rupture; while patients with large AAA transverse diameters, for whom intervention would have been recommended, have stable aneurysms that do not rupture. While maximum transverse diameter is easy to measure and track in clinical practice, one of its main drawbacks is that it does not represent the whole AAA and rupture seldom occurs in the region of maximum transverse diameter. By following maximum transverse diameter alone clinicians are missing information on the shape change dynamics of the AAA, and clues that could lead to better patient care. We propose here a method to register AAA surfaces that were obtained from the same patient at different time points. Our registration method could be used to track the local changes of the patient-specific AAA. To achieve registration, our procedure uses a consistent parameterization of the AAA surfaces followed by strain relaxation. The main assumption of our procedure is that growth of the AAA occurs in such a way that surface strains are smoothly distributed, while regions of small and large surface growth can be differentiated. The proposed methodology has the potential to unravel different patterns of AAA growth that could be used to stratify patient risks.

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

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

Vascular homeostasis and the concept of mechanobiological stability

Vascular mechanics has been studied in depth since the early 1970s mainly following classical concepts from continuum mechanics. Yet, an important distinction of blood vessels, in contrast to typical engineering materials, is the continuous degradation and deposition of material in these living tissues. In this paper we examine mechanical consequences of such mass turnover. Motivated by Lyapunov's stability theory, we introduce the new concepts of mechanobiological equilibrium and stability and demonstrate that blood vessels can maintain their structure and function under physiological conditions only if new material is deposited at a certain prestress and the vessels are both mechanically and mechanobiologically stable. Moreover, we introduce the concept of mechanobiological adaptivity as a third corner stone to understand vascular behavior on a continuum level. We demonstrate that adaptivity represents a key difference between the stability of mechanobiological and typical human-made systems. Based on these ideas, we suggest a change of paradigm that can be illustrated by considering a common arterial pathology. We suggest that aneurysms can be interpreted as mechanobiological instabilities and that predictions of their rupture risk should not only consider the maximal diameter or wall stress, but also the mechanobiological stability. A mathematical analysis of the impact of the different model parameters on the so-called mechanobiological stability margin, a single scalar used to characterize mechanobiological stability, reveals that this stability increases with the characteristic time constant of mass turnover, material stiffness, and capacity for stress-dependent changes in mass production. As each of these parameters may be modified by appropriate drugs, the theory developed in this paper may guide both prognosis and the development of new therapies for arterial pathologies such as aneurysms.

Mechanotransduction and extracellular matrix homeostasis

Soft connective tissues at steady state are dynamic; resident cells continually read environmental cues and respond to them to promote homeostasis, including maintenance of the mechanical properties of the extracellular matrix (ECM) that are fundamental to cellular and tissue health. The mechanosensing process involves assessment of the mechanics of the ECM by the cells through integrins and the actomyosin cytoskeleton, and is followed by a mechanoregulation process, which includes the deposition, rearrangement or removal of the ECM to maintain overall form and function. Progress towards understanding the molecular, cellular and tissue-level effects that promote mechanical homeostasis has helped to identify key questions for future research.