Importance of initial aortic properties on the evolving regional anisotropy, stiffness and wall thickness of human abdominal aortic aneurysms

3D growth and remodeling theory supports the hypothesis of staphyloma formation from local scleral weakening under normal intraocular pressure

The purpose of this study was to assess whether growth and remodeling (G&R) theory could explain staphyloma formation from a local scleral weakening-as could occur from age-related elastin degradation, myopia progression, or other factors. A finite element model of a healthy eye was reconstructed, including the lamina cribrosa, the peripapillary sclera, and the peripheral sclera. The homogenized constrained mixture model was employed to simulate the adaptation of the sclera to alterations in its biomechanical environment over a duration of 13.7 years. G&R processes were triggered by reducing the shear stiffness of the ground matrix in the peripapillary sclera and lamina cribrosa by 85%. Three distinct G&R scenarios were investigated: (1) low mass turnover rate in combination with transmural volumetric growth; (2) high mass turnover rate in combination with transmural volumetric growth; and (3) high mass turnover rate in combination with mass density growth. In scenario 1, we observed a significant outpouching of the posterior pole, closely resembling the shape of a Type-III staphyloma. Additionally, we found a notable change in scleral curvature and a thinning of the peripapillary sclera by 84%. In contrast, scenario 2 and 3 exhibited less drastic deformations, with stable posterior staphylomas after approximately 7 years. Our proposed framework suggests that local scleral weakening is sufficient to trigger staphyloma formation under a normal level of intraocular pressure. Our model also reproduced characteristics of Type-III staphylomas. With patient-specific scleral geometries (as could be obtained with wide-field optical coherence tomography), our framework could be clinically translated to help us identify those at risks of developing posterior staphylomas.

Cell signaling and tissue remodeling in the pulmonary autograft after the Ross procedure: A computational study

In the Ross procedure, a patient's pulmonary valve is transplanted in the aortic position. Despite advantages of this surgery, reoperation is still needed in many cases due to excessive dilatation of the pulmonary autograft. To further understand the failure mechanisms, we propose a multiscale model predicting adaptive processes in the autograft at the cell and tissue scale. The cell-scale model consists of a network model, that includes important signaling pathways and relations between relevant transcription factors and their target genes. The resulting gene activity leads to changes in the mechanical properties of the tissue, modeled as a constrained mixture of collagen, elastin and smooth muscle. The multiscale model is calibrated with findings from experiments in which seven sheep underwent the Ross procedure. The model is then validated against a different set of sheep experiments, for which a qualitative agreement between model and experiment is found. Model outcomes at the cell scale, including the activity of genes and transcription factors, also match experimentally obtained transcriptomics data.

Post-angioplasty remodeling of coronary arteries investigated via a chemo-mechano-biological in silico model

This work presents the application of a chemo-mechano-biological constitutive model of soft tissues for describing tissue inflammatory response to damage in collagen constituents. The material model is implemented into a nonlinear finite element formulation to follow up a coronary standard balloon angioplasty for one year. Numerical results, compared with available in vivo clinical data, show that the model reproduces the temporal dynamics of vessel remodeling associated with subintimal damage. Such dynamics are bimodular, being characterized by an early tissue resorption and lumen enlargement, followed by late tissue growth and vessel constriction. Applicability of the modeling framework in retrospective studies is demonstrated, and future extension towards prospective applications is discussed.

Computational approaches for mechanobiology in cardiovascular development and diseases

The cardiovascular development in vertebrates evolves in response to genetic and mechanical cues. The dynamic interplay among mechanics, cell biology, and anatomy continually shapes the hydraulic networks, characterized by complex, non-linear changes in anatomical structure and blood flow dynamics. To better understand this interplay, a diverse set of molecular and computational tools has been used to comprehensively study cardiovascular mechanobiology. With the continual advancement of computational capacity and numerical techniques, cardiovascular simulation is increasingly vital in both basic science research for understanding developmental mechanisms and disease etiologies, as well as in clinical studies aimed at enhancing treatment outcomes. This review provides an overview of computational cardiovascular modeling. Beginning with the fundamental concepts of computational cardiovascular modeling, it navigates through the applications of computational modeling in investigating mechanobiology during cardiac development. Second, the article illustrates the utility of computational hemodynamic modeling in the context of treatment planning for congenital heart diseases. It then delves into the predictive potential of computational models for elucidating tissue growth and remodeling processes. In closing, we outline prevailing challenges and future prospects, underscoring the transformative impact of computational cardiovascular modeling in reshaping cardiovascular science and clinical practice.

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.

Arterial tissues and their inflammatory response to collagen damage: A continuum in silico model coupling nonlinear mechanics, molecular pathways, and cell behavior

Damage in soft biological tissues causes an inflammatory reaction that initiates a chain of events to repair the tissue. This work presents a continuum model and its in silico implementation that describe the cascade of mechanisms leading to tissue healing, coupling mechanical as well as chemo-biological processes. The mechanics is described by means of a Lagrangian nonlinear continuum mechanics framework and follows the homogenized constrained mixtures theory. Plastic-like damage, growth and remodeling as well as homeostasis are taken into account. The chemo-biological pathways account for two molecular and four cellular species, and are activated by damage of collagen molecules in fibers. To consider proliferation, differentiation, diffusion and chemotaxis of species, diffusion-advection-reaction equations are employed. To the best of authors' knowledge, the proposed model combines for the first time such high number of chemo-mechano-biological mechanisms in a consistent continuum biomechanical framework. The resulting set of coupled differential equations describe balance of linear momentum, evolution of kinematic variables as well as mass balance equations. They are discretized in time according to a backward Euler finite difference scheme, and in space through a finite element Galerkin discretization. The features of the model are firstly demonstrated presenting the species dynamics and highlighting the influence of damage intensities on the growth outcome. In terms of a biaxial test, the chemo-mechano-biological coupling and the model's applicability to reproduce normal as well as pathological healing are shown. A last numerical example underlines the model's applicability to complex loading scenarios and inhomogeneous damage distributions. Concluding, the present work contributes towards comprehensive in silico models in biomechanics and mechanobiology.

Layer-specific fiber distribution in arterial tissue modeled as a constrained mixture

Collagen fibers and their orientation greatly influence an artery's mechanical characteristics, determining its transversely isotropic behavior. It is generally assumed that these fibers are deposited along a preferred direction to maximize the load bearing capacity of the vessel wall. This implies a large spatial variation in collagen orientation which can be reconstructed in numerical models using so-called reorientation algorithms. Until now, these algorithms have used the classical continuum mechanics modeling framework which requires knowledge of tissue-level parameters and the artery's stress-free reference state, which is inaccessible in a clinical context. We present an algorithm to compute the preferred fiber distribution compatible with the constrained mixture theory, which orients two collagen fiber families according to the loading experienced by the isotropic non-collagenous extracellular matrix, without requiring prior knowledge of the stress-free state. Because consensus is lacking whether stress or stretch is the determining factor behind the preferred fiber distribution, we implemented both approaches and compared the results with experimental microstructural data of an abdominal aorta. The stress-based algorithm was able to describe several experimentally observed transitions of the fiber distribution across the intima, media and adventitia.

A quarter of a century biomechanical rupture risk assessment of abdominal aortic aneurysms. Achievements, clinical relevance, and ongoing developments

Abdominal aortic aneurysm (AAA) disease, the local enlargement of the infrarenal aorta, is a serious condition that causes many deaths, especially in men exceeding 65 years of age. Over the past quarter of a century, computational biomechanical models have been developed towards the assessment of AAA risk of rupture, technology that is now on the verge of being integrated within the clinical decision-making process. The modeling of AAA requires a holistic understanding of the clinical problem, in order to set appropriate modeling assumptions and to draw sound conclusions from the simulation results. In this article we summarize and critically discuss the proposed modeling approaches and report the outcome of clinical validation studies for a number of biomechanics-based rupture risk indices. Whilst most of the aspects concerning computational mechanics have already been settled, it is the exploration of the failure properties of the AAA wall and the acquisition of robust input data for simulations that has the greatest potential for the further improvement of this technology.

Location specific multi-scale characterization and constitutive modeling of pig aorta

The mechanical and structural behavior of the aorta depend on physiological functions and vary from proximal to distal. Understanding the relation between regionally varying mechanical and multi-scale structural response of aorta can be helpful to assess the disease outcomes. Therefore, this study investigated the variation in mechanical and multi-scale structural properties among the major segments of aorta such as ascending aorta (AA), descending aorta (DA) and abdominal aorta (ABA), and established a relation between mechanical and multi-structural parameters. The obtained results showed significant increase in anisotropy and nonlinearity from proximal to distal aorta. The change in periphery length and radii between load and stress free configuration was also found increasing far from the heart. Opening angle was significantly large for ABA than AA and DA (AA/DA vs ABA; p = 0.001). Mean circumferential residual stretch (ratio of mean periphery length at load and stress free configurations) was found decreasing between AA and DA, and then increasing between DA to ABA and its value was significantly more for ABA (AA vs DA; p = 0.041, AA vs ABA; p = 0.001, DA vs ABA; p = 0.001). The waviness of collagen fibers, collagen fiber content, collagen fibril diameter and total protein content were found significantly increasing from proximal to distal. Pearson correlation test showed a significant linear correlation between variation in mechanical and multi-scale structural parameters over the aortic length. Residual stretch was found positively correlated with collagen fiber content (r = 0.82) whereas opening angel was found positively correlated with total protein content (TPC) (r = 0.76).

The risk of rupture and abdominal aortic aneurysm morphology: A computational study

Prediction of rupture and optimal timing for abdominal aortic aneurysm (AAA) surgical intervention remain wanting even after decades of clinical, histological, and numerical research. Although studies estimating rupture from AAA geometrical features from CT imaging showed some promising results, they are still not being used in practice. Patient-specific numerical stress analysis introduced too many assumptions about wall structure for the related rupture potential index (RPI) to be considered reliable. Growth and remodeling (G&R) numerical models eliminate some of these assumptions and thus might have the most potential to calculate mural stresses and RPI and increase our understanding of rupture. To recognize numerical models as trustworthy, it is necessary to validate the computed results with results derived from imaging. Elastin degradation function is one of the main factors that determine idealized aneurysm sac shape. Using a hundred different combinations of variables defining AAA geometry or influences AAA stability (elastin degradation function parameters, collagen mechanics, and initial healthy aortic diameters), we investigated the relationship between AAA morphology and RPI and compared numerical results with clinical findings. Good agreement of numerical results with clinical expectations from the literature gives us confidence in the validity of the numerical model. We show that aneurysm morphology significantly influences the stability of aneurysms. Additionally, we propose new parameters, geometrical rupture potential index (GRPI) and normalized aneurysm length (NAL), that might predict rupture of aneurysms without thrombus better than currently used criteria (i.e., maximum diameter and growth rate). These parameters can be computed quickly, without the tedious processing of CT images.

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.

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.

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.

Machine learning approaches to surrogate multifidelity Growth and Remodeling models for efficient abdominal aortic aneurysmal applications

Computational Growth and Remodeling (G&R) models have been widely used to capture the pathological development of arterial diseases and have shown promise for aiding clinical diagnosis, prognosis prediction, and staging classification. However, due to the high complexity of the arterial adaptation mechanism, high-fidelity arterial G&R simulation usually takes hours or even days, which hinders its application in clinical practice. To remedy this problem, we develop a computationally efficient arterial G&R simulation framework that comprehensively combines the physics-based G&R simulations and data-driven machine learning approaches. The proposed framework greatly enhances the computational efficiency of arterial G&R simulations, thereby enabling more time-consuming arterial applications, including personalized parameter estimation and arterial disease progression prediction. In particular, we achieve significant computational cost reduction mainly through two methods: (1) constructing a Multifidelity Surrogate (MFS) to approximate multifidelity G&R simulations by using a cokriging approach and (2) developing a novel iterative optimization algorithm for personalized parameter estimation. The proposed framework is demonstrated by estimating G&R model parameters and predicting individual aneurysm growth using follow-up CT images of Abdominal Aortic Aneurysms (AAAs) from 21 patients. Results show that the personalized parameters are satisfactorily estimated and the growth of AAAs is predicted within the clinically relevant time frame, i.e., less than 2 h, without a loss of accuracy.

Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing

Healing in soft biological tissues is a chain of events on different time and length scales. This work presents a computational framework to capture and couple important mechanical, chemical and biological aspects of healing. A molecular-level damage in collagen, i.e., the interstrand delamination, is addressed as source of plastic deformation in tissues. This mechanism initiates a biochemical response and starts the chain of healing. In particular, damage is considered to be the stimulus for the production of matrix metalloproteinases and growth factors which in turn, respectively, degrade and produce collagen. Due to collagen turnover, the volume of the tissue changes, which can result either in normal or pathological healing. To capture the mechanisms on continuum scale, the deformation gradient is multiplicatively decomposed in inelastic and elastic deformation gradients. A recently proposed elasto-plastic formulation is, through a biochemical model, coupled with a growth and remodeling description based on homogenized constrained mixtures. After the discussion of the biological species response to the damage stimulus, the framework is implemented in a mixed nonlinear finite element formulation and a biaxial tension and an indentation tests are conducted on a prestretched flat tissue sample. The results illustrate that the model is able to describe the evolutions of growth factors and matrix metalloproteinases following damage and the subsequent growth and remodeling in the respect of equilibrium. The interplay between mechanical and chemo-biological events occurring during healing is captured, proving that the framework is a suitable basis for more detailed simulations of damage-induced tissue response.

Numerical knockouts-In silico assessment of factors predisposing to thoracic aortic aneurysms

Myriad risk factors–including uncontrolled hypertension, aging, and diverse genetic mutations–contribute to the development and enlargement of thoracic aortic aneurysms. Detailed analyses of clinical data and longitudinal studies of murine models continue to provide insight into the natural history of these potentially lethal conditions. Yet, because of the co-existence of multiple risk factors in most cases, it has been difficult to isolate individual effects of the many different factors or to understand how they act in combination. In this paper, we use a data-informed computational model of the initiation and progression of thoracic aortic aneurysms to contrast key predisposing risk factors both in isolation and in combination; these factors include localized losses of elastic fiber integrity, aberrant collagen remodeling, reduced smooth muscle contractility, and dysfunctional mechanosensing or mechanoregulation of extracellular matrix along with superimposed hypertension and aortic aging. In most cases, mild-to-severe localized losses in cellular function or matrix integrity give rise to varying degrees of local dilatations of the thoracic aorta, with enlargement typically exacerbated in cases wherein predisposing risk factors co-exist. The simulations suggest, for the first time, that effects of compromised smooth muscle contractility are more important in terms of dysfunctional mechanosensing and mechanoregulation of matrix than in vessel-level control of diameter and, furthermore, that dysfunctional mechanobiological control can yield lesions comparable to those in cases of compromised elastic fiber integrity. Particularly concerning, therefore, is that loss of constituents such as fibrillin-1, as in Marfan syndrome, can compromise both elastic fiber integrity and mechanosensing.

Aneurysms are local dilatations of the arterial wall that are responsible for significant disability and death. Detailed analyses of clinical data continue to provide insight into the natural history of these potentially lethal conditions, with myriad risk factors–including uncontrolled hypertension, aging, and diverse genetic mutations–contributing to their development and enlargement. Yet, because of the co-existence of these risk factors in most cases, it has been difficult to isolate individual effects or to understand how they act in combination. In this paper, we use a computational model of the initiation and progression of thoracic aortic aneurysms to contrast key predisposing factors both in isolation and in combination as well as with superimposed hypertension and aging. The present study recovers many findings from mouse models but with new and important observations that promise to guide in vivo and ex vivo studies as we seek to understand and eventually better treat these complex, multi-factorial lesions, with data-informed patient-specific computations eventually the way forward.

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.

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.

Shear stress rosettes capture the complex flow physics in diseased arteries

Wall shear stress (WSS) is an important parameter in arterial mechanobiology. Various flow metrics, such as time averaged WSS (TAWSS), oscillatory shear index (OSI), and transWSS, have been used to characterize and relate possible WSS variations in arterial diseases like aneurysms and atherosclerosis. We use a graphical representation of WSS using shear rosettes to map temporal changes in the flow dynamics during a cardiac cycle at any spatial location on the vessel surface. The presence of secondary flows and flow reversals can be interpreted directly from the shape of the shear rosette. The mean WSS is given by the rosette centroid, the OSI by the splay around the rosette origin, and the transWSS by its width. We define a new metric, anisotropy ratio (AR), based on the ratio of the length to width of the shear rosette, to capture flow bi-directionality. We characterized the flow physics in controls and patient specific geometries of the ascending aorta (AA) and internal carotid artery (ICA) that have fundamentally different flow dynamics due to differences in the Reynolds and Womersley numbers. The differences in the flow dynamics are well reflected in the shapes of the WSS rosettes and the corresponding flow metrics.

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.

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.

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).

Absence of LTBP-3 attenuates the aneurysmal phenotype but not spinal effects on the aorta in Marfan syndrome

Fibrillin-1 is an elastin-associated glycoprotein that contributes to the long-term fatigue resistance of elastic fibers as well as to the bioavailability of transforming growth factor-beta (TGFβ) in arteries. Altered TGFβ bioavailability and/or signaling have been implicated in aneurysm development in Marfan syndrome (MFS), a multi-system condition resulting from mutations to the gene that encodes fibrillin-1. We recently showed that the absence of the latent transforming growth factor-beta binding protein-3 (LTBP-3) in fibrillin-1-deficient mice attenuates the fragmentation of elastic fibers and focal dilatations that are characteristic of aortic root aneurysms in MFS mice, at least to 12 weeks of age. Here, we show further that the absence of LTBP-3 in this MFS mouse model improves the circumferential mechanical properties of the thoracic aorta, which appears to be fundamental in preventing or significantly delaying aneurysm development. Yet, a spinal deformity either remains or is exacerbated in the absence of LTBP-3 and seems to adversely affect the axial mechanical properties of the thoracic aorta, thus decreasing overall vascular function despite the absence of aneurysmal dilatation. Importantly, because of the smaller size of mice lacking LTBP-3, allometric scaling facilitates proper interpretation of aortic dimensions and thus the clinical phenotype. While this study demonstrates that LTBP-3/TGFβ directly affects the biomechanical function of the thoracic aorta, it highlights that spinal deformities in MFS might indirectly and adversely affect the overall aortic phenotype. There is a need, therefore, to consider together the vascular and skeletal effects in this syndromic disease.

Modeling mechano-driven and immuno-mediated aortic maladaptation in hypertension

Uncontrolled hypertension is a primary risk factor for diverse cardiovascular diseases and thus remains responsible for significant morbidity and mortality. Hypertension leads to marked changes in the composition, structure, properties, and function of central arteries; hence, there has long been interest in quantifying the associated wall mechanics. Indeed, over the past 20 years there has been increasing interest in formulating mathematical models of the evolving geometry and biomechanical behavior of central arteries that occur during hypertension. In this paper, we introduce a new mathematical model of growth (changes in mass) and remodeling (changes in microstructure) of the aortic wall for an animal model of induced hypertension that exhibits both mechano-driven and immuno-mediated matrix turnover. In particular, we present a bilayered model of the aortic wall to account for differences in medial versus adventitial growth and remodeling and we include mechanical stress and inflammatory cell density as determinants of matrix turnover. Using this approach, we can capture results from a recent report of adventitial fibrosis that resulted in marked aortic maladaptation in hypertension. We submit that this model can also be used to identify novel hypotheses to guide future experimentation.

In vivo quantification of regional circumferential Green strain in the thoracic and abdominal aorta by 2D spiral cine DENSE MRI

INTRODUCTION

Regional tissue mechanics play a fundamental role in patient-specific cardiovascular function. Nevertheless, regional assessments of aortic kinematics remain lacking due to the challenge of imaging the thin aortic wall. Herein, we present a novel application of DENSE (Displacement Encoding with Stimulated Echoes) MRI to quantify the circumferential Green strain of the thoracic and abdominal aorta.

METHODS

2D spiral cine DENSE and steady-state free procession (SSFP) cine images were acquired at 3T at the infrarenal aorta (IAA), descending thoracic aorta (DTA), or distal aortic arch (DAA) in a pilot study of 6 healthy volunteers. DENSE data was processed with multiple custom noise-reduction techniques to calculate circumferential Green strain across 16 equispaced sectors around the aorta. Each volunteer was scanned twice to evaluate interstudy repeatability.

RESULTS

Circumferential strain was heterogeneously distributed in all volunteers and locations. Spatial heterogeneity index by location was 0.37 (IAA), 0.28 (DTA), and 0.59 (DAA). Mean peak strain by DENSE for each cross-section was consistent with the homogenized linearized strain estimated from SSFP cine. The mean difference in peak strain across all sectors following repeat imaging was -0.1±2.2%, with a mean absolute difference of 1.7%.

CONCLUSIONS

Aortic cine DENSE MRI is a viable non-invasive technique for quantifying heterogeneous regional aortic wall strain and has significant potential to improve patient-specific clinical assessments of numerous aortopathies, as well as to provide the lacking spatiotemporal data required to refine computational models of aortic growth and remodeling.

Immuno-driven and Mechano-mediated Neotissue Formation in Tissue Engineered Vascular Grafts

In vivo development of a neovessel from an implanted biodegradable polymeric scaffold depends on a delicate balance between polymer degradation and native matrix deposition. Studies in mice suggest that this balance is dictated by immuno-driven and mechanotransduction-mediated processes, with neotissue increasingly balancing the hemodynamically induced loads as the polymer degrades. Computational models of neovessel development can help delineate relative time-dependent contributions of the immunobiological and mechanobiological processes that determine graft success or failure. In this paper, we compare computational results informed by long-term studies of neovessel development in immuno-compromised and immuno-competent mice. Simulations suggest that an early exuberant inflammatory response can limit subsequent mechano-sensing by synthetic intramural cells and thereby attenuate the desired long-term mechano-mediated production of matrix. Simulations also highlight key inflammatory differences in the two mouse models, which allow grafts in the immuno-compromised mouse to better match the biomechanical properties of the native vessel. Finally, the predicted inflammatory time courses revealed critical periods of graft remodeling. We submit that computational modeling can help uncover mechanisms of observed neovessel development and improve the design of the scaffold or its clinical use.

Prediction of Abdominal Aortic Aneurysm Growth Using Dynamical Gaussian Process Implicit Surface

OBJECTIVE

We propose a novel approach to predict the Abdominal Aortic Aneurysm (AAA) growth in future time, using longitudinal computer tomography (CT) scans of AAAs that are captured at different times in a patient-specific way.

METHODS

We adopt a formulation that considers a surface of the AAA as a manifold embedded in a scalar field over the three dimensional (3D) space. For this formulation, we develop our Dynamical Gaussian Process Implicit Surface (DGPIS) model based on observed surfaces of 3D AAAs as visible variables while the scalar fields are hidden. In particular, we use Gaussian process regression to construct the field as an observation model from CT training image data. We then learn a dynamic model to represent the evolution of the field. Finally, we derive the predicted AAA surface from the predicted field along with uncertainty quantified in future time.

RESULTS

A dataset of 7 subjects (4-7 scans) was collected and used to evaluate the proposed method by comparing its prediction Hausdorff distance errors against those of simple extrapolation. In addition, we evaluate the prediction results with respect to a conventional shape analysis technique such as Principal Component Analysis (PCA). All comparative results show the superior prediction performance of the proposed approach.

CONCLUSION

We introduce a novel approach to predict the AAA growth and its predicted uncertainty in future time, using longitudinal CT scans in a patient-specific fashion.

SIGNIFICANCE

The capability to predict the AAA shape and its confidence region by our approach establish the potential for guiding clinicians with informed decision in conducting medical treatment and monitoring of AAAs.

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.

Toward modeling the effects of regional material properties on the wall stress distribution of abdominal aortic aneurysms

The overall geometry and different biomechanical parameters of an abdominal aortic aneurysm (AAA), contribute to its severity and risk of rupture, therefore they could be used to track its progression. Previous and ongoing research efforts have resorted to using uniform material properties to model the behavior of AAA. However, it has been recently illustrated that different regions of the AAA wall exhibit different behavior due to the effect of the biological activities in the metalloproteinase matrix that makes up the wall at the aneurysm site. In this work, we introduce a non-invasive patient-specific regional material property model to help us better understand and investigate the AAA wall stress distribution, peak wall stress (PWS) severity, and potential rupture risk. Our results indicate that the PWS and the overall wall stress distribution predicted using the proposed regional material property model, are higher than those predicted using the traditional homogeneous, hyper-elastic model (p <1.43E-07). Our results also show that to investigate AAA, the overall geometry, presence of intra-luminal thrombus (ILT), and loading condition in a patient specific manner may be critical for capturing the biomechanical complexity of AAAs.

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.

Should We Ignore What We Cannot Measure? How Non-Uniform Stretch, Non-Uniform Wall Thickness and Minor Side Branches Affect Computational Aortic Biomechanics in Mice

In order to advance the state-of-the-art in computational aortic biomechanics, we investigated the influence of (i) a non-uniform wall thickness, (ii) minor aortic side branches and (iii) a non-uniform axial stretch distribution on the location of predicted hotspots of principal strain in a mouse model for dissecting aneurysms. After 3 days of angiotensin II infusion, a murine abdominal aorta was scanned in vivo with contrast-enhanced micro-CT. The animal was subsequently sacrificed and its aorta was scanned ex vivo with phase-contrast X-ray tomographic microscopy (PCXTM). An automatic morphing framework was developed to map the non-pressurized, non-stretched PCXTM geometry onto the pressurized, stretched micro-CT geometry. The output of the morphing model was a structural FEM simulation where the output strain distribution represents an estimation of the wall deformation, not only due to the pressurization, but also due to the local axial stretch field. The morphing model also included minor branches and a mouse-specific wall thickness. A sensitivity study was then performed to assess the influence of each of these novel features on the outcome of the simulations. The results were supported by comparing the computed hotspots of principal strain to hotspots of early vascular damage as detected on PCXTM. Non-uniform axial stretch, non-uniform wall thickness and minor subcostal arteries significantly alter the locations of calculated hotspots of maximal principal strain. Even if experimental data on these features are often not available in clinical practice, one should be aware of the important implications that simplifications in the model might have on the final simulated result.

Hemodynamics-driven deposition of intraluminal thrombus in abdominal aortic aneurysms

Accumulating evidence suggests that intraluminal thrombus plays many roles in the natural history of abdominal aortic aneurysms. There is, therefore, a pressing need for computational models that can describe and predict the initiation and progression of thrombus in aneurysms. In this paper, we introduce a phenomenological metric for thrombus deposition potential and use hemodynamic simulations based on medical images from 6 patients to identify best-fit values of the 2 key model parameters. We then introduce a shape optimization method to predict the associated radial growth of the thrombus into the lumen based on the expectation that thrombus initiation will create a thrombogenic surface, which in turn will promote growth until increasing hemodynamically induced frictional forces prevent any further cell or protein deposition. Comparisons between predicted and actual intraluminal thrombus in the 6 patient-specific aneurysms suggest that this phenomenological description provides a good first estimate of thrombus deposition. We submit further that, because the biologically active region of the thrombus appears to be confined to a thin luminal layer, predictions of morphology alone may be sufficient to inform fluid-solid-growth models of aneurysmal growth and remodeling.

Correlation of Wall Microstructure and Heterogeneous Distributions of Strain in Evolving Murine Abdominal Aortic Aneurysms

A primary deficiency in predicting the progression and rupture-risk of abdominal aortic aneurysms (AAAs) is an inability to assign patient-specific, heterogeneous biomechanical properties to the remodelling aortic wall. Toward this end, we investigated possible correlations between three quantities having the potential for non-invasive measurement (diameter, wall thickness, and strain) and local wall microstructure within evolving experimental AAAs. AAAs were initiated in male C57BL/6J mice via in situ adventitial application of elastase and allowed to progress for 1-4 weeks. Regional in vitro Green strain was assessed using custom panoramic digital image correlation and compared to local geometry and histology. Diameter correlated mildly with elastin grade and collagen, when considering all circumferential locations and remodeling times. Normalized wall thickness correlated strongly with normalized collagen area fraction, though with outliers in highly cellular regions. Circumferential Green strain correlated strongly with elastin grade when measured over the range of 20-140 mmHg, though the correlation weakened across a physiologic range of 80-120 mmHg. Axial strain correlated strongly between in vitro and physiologic ranges of pressures. Circumferential heterogeneities render diameter a poor predictor of underlying regional microstructure. Thickness may indicate collagen content, though corrections are needed in regions of increased cellularity. In vitro circumferential strain predicts local functional elastin over large ranges of pressure, but there is a need to extend this correlation to clinically relevant pressures. Axial strain in the aneurysmal shoulder region may reflect the elastic integrity within the apical region of the lesion and should be explored as an indicator of disease severity.

Racial and social predictors of longitudinal cervical measures: the Cervical Ultrasound Study

OBJECTIVE

To evaluate whether the racial and socioeconomic disparities are present in adverse cervical parameters, and, if so, when such disparities develop.

STUDY DESIGN

A prospective cohort study was conducted. 175 women with a prior preterm birth had up to four endovaginal ultrasounds between gestational weeks 16 and 24 (Cervical Ultrasound Trial of the MFMU). Each sociodemographic factor (race/ethnicity, marital status, insurance funding and education) was examined as a predictor of short cervix or U/funnel shape, using multiple logistic and linear regression. Changes in the cervical length and shape across pregnancy and after pressure were also examined.

RESULTS

The strongest associations were seen between race and government-funded insurance and short cervix and U shape per funneling (race and length <25 mm per funnel: adjusted odds ratio (OR) 5.52, 2.24 to 13.63; government-funded insurance and length <30 mm per funnel: adjusted OR 3.10, 1.34 to 7.15). Changes in cervical length were not associated with sociodemographics.

CONCLUSION

African-American race and, to a lesser extent, insurance funder, are associated with cervical length and shapes that have been associated with preterm birth, and those properties are present largely early in pregnancy.

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.

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.

Prior Distributions of Material Parameters for Bayesian Calibration of Growth and Remodeling Computational Model of Abdominal Aortic Wall

For the accurate prediction of the vascular disease progression, there is a crucial need for developing a systematic tool aimed toward patient-specific modeling. Considering the interpatient variations, a prior distribution of model parameters has a strong influence on computational results for arterial mechanics. One crucial step toward patient-specific computational modeling is to identify parameters of prior distributions that reflect existing knowledge. In this paper, we present a new systematic method to estimate the prior distribution for the parameters of a constrained mixture model using previous biaxial tests of healthy abdominal aortas (AAs). We investigate the correlation between the estimated parameters for each constituent and the patient's age and gender; however, the results indicate that the parameters are correlated with age only. The parameters are classified into two groups: Group-I in which the parameters ce, ck1, ck2, cm2,Ghc, and ϕe are correlated with age, and Group-II in which the parameters cm1, Ghm, G1e, G2e, and α are not correlated with age. For the parameters in Group-I, we used regression associated with age via linear or inverse relations, in which their prior distributions provide conditional distributions with confidence intervals. For Group-II, the parameter estimated values were subjected to multiple transformations and chosen if the transformed data had a better fit to the normal distribution than the original. This information improves the prior distribution of a subject-specific model by specifying parameters that are correlated with age and their transformed distributions. Therefore, this study is a necessary first step in our group's approach toward a Bayesian calibration of an aortic model. The results from this study will be used as the prior information necessary for the initialization of Bayesian calibration of a computational model for future applications.

A novel chemo-mechano-biological model of arterial tissue growth and remodelling

Arterial growth and remodelling (G&R) is mediated by vascular cells in response to their chemical and mechanical environment. To date, mechanical and biochemical stimuli tend to be modelled separately, however this ignores their complex interplay. Here, we present a novel mathematical model of arterial chemo-mechano-biology. We illustrate its application to the development of an inflammatory aneurysm in the descending human aorta. The arterial wall is modelled as a bilayer cylindrical non-linear elastic membrane, which is internally pressurised and axially stretched. The medial degradation that accompanies aneurysm development is driven by an inflammatory response. Collagen remodelling is simulated by adaption of the natural reference configuration of constituents; growth is simulated by changes in normalised mass-densities. We account for the distribution of attachment stretches that collagen fibres are configured to the matrix and, innovatively, allow this distribution to remodel. This enables the changing functional role of the adventitia to be simulated. Fibroblast-mediated collagen growth is represented using a biochemical pathway model: a system of coupled non-linear ODEs governs the evolution of fibroblast properties and levels of key biomolecules under the regulation of Transforming Growth Factor (TGF)-β, a key promoter of matrix deposition. Given physiologically realistic targets, different modes of aneurysm development can be captured, while the predicted evolution of biochemical variables is qualitatively consistent with trends observed experimentally. Interestingly, we observe that increasing the levels of collagen-promoting TGF-β results in arrest of aneurysm growth, which seems to be consistent with experimental evidence. We conclude that this novel Chemo-Mechano-Biological (CMB) mathematical model has the potential to provide new mechanobiological insight into vascular disease progression and therapy.

Loss of Elastic Fiber Integrity Compromises Common Carotid Artery Function: Implications for Vascular Aging

Competent elastic fibers endow central arteries with the compliance and resilience that are fundamental to their primary mechanical function in vertebrates. That is, by enabling elastic energy to be stored in the arterial wall during systole and then to be used to work on the blood during diastole, elastic fibers decrease ventricular workload and augment blood flow in pulsatile systems. Indeed, because elastic fibers are formed during development and stretched during somatic growth, their continual tendency to recoil contributes to the undulation of the stiffer collagen fibers, which facilitates further the overall compliance of the wall under physiologic pressures while allowing the collagen to limit over-distension during acute increases in blood pressure. In this paper, we use consistent methods of measurement and quantification to compare the biaxial material stiffness, structural stiffness, and energy storage capacity of murine common carotid arteries having graded degrees of elastic fiber integrity - normal, elastin-deficient, fibrillin-1 deficient, fibulin-5 null, and elastase-treated. The finding that the intrinsic material stiffness tends to be maintained nearly constant suggests that intramural cells seek to maintain a favorable micromechanical environment in which to function. Nevertheless, a loss of elastic energy storage capability due to the loss of elastic fiber integrity severely compromises the primary function of these central arteries.

Coupled Simulation of Hemodynamics and Vascular Growth and Remodeling in a Subject-Specific Geometry

A computational framework to couple vascular growth and remodeling (G&R) with blood flow simulation in a 3D patient-specific geometry is presented. Hyperelastic and anisotropic properties are considered for the vessel wall material and a constrained mixture model is used to represent multiple constituents in the vessel wall, which was modeled as a membrane. The coupled simulation is divided into two time scales-a longer time scale for G&R and a shorter time scale for fluid dynamics simulation. G&R is simulated to evolve the boundary of the fluid domain, and fluid simulation is in turn used to generate wall shear stress and transmural pressure data that regulates G&R. To minimize required computation cost, the fluid dynamics are only simulated when G&R causes significant vascular geometric change. For demonstration, this coupled model was used to study the influence of stress-mediated growth parameters, and blood flow mechanics, on the behavior of the vascular tissue growth in a model of the infrarenal aorta derived from medical image data.

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

Static and dynamic mechanical instabilities were previously suggested, and then rejected, as mediators of aneurysmal development, which leaves open the question of the underlying mechanism. In this paper, we suggest as a new paradigm the interpretation of aneurysms as mechanobiological instabilities. For illustrative purposes, we compare analytical calculations with computational simulations of the growth and remodelling of idealized fusiform abdominal aortic aneurysms and experimental and clinical findings. We show that the concept of mechanobiological stability is consistent with the impact of risk factors such as age, smoking or diabetes on the initiation and enlargement of these lesions as well as adaptive processes in the healthy abdominal aorta such as dilatation during ageing or in hypertension. In general, high stiffness, an increased capacity for stress-mediated matrix production, and slow matrix turnover all improve the mechanobiological stability of blood vessels. This theoretical understanding may help guide prognosis and the development of future therapies for aneurysms as it enables systematic ways to attenuate enlargement.

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.