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

Implantation of a capsular tension ring during cataract surgery attenuates predicted remodeling of the post-surgical lens capsule along the visual axis

Introduction: Cataract surgery permanently alters the mechanical environment of the lens capsule by placing a hole in the anterior portion and implanting an intraocular lens (IOL) that has a very different geometry from the native lens. We hypothesized that implant configuration and mechanical interactions with the post-surgical lens capsule play a key role in determining long-term fibrotic remodeling. Methods: We developed the first finite element-growth and remodeling (FE-G&R) model of the post-surgical lens capsule to evaluate how implantation of an IOL with and without a capsular tension ring (CTR) impacted evolving lens capsule mechanics and associated fibrosis over time after cataract surgery. Results: Our models predicted that implantation of a CTR with the IOL into the post-surgical lens capsule reduced the mechanical perturbation, thickening, and stiffening along the visual axis in both the remnant anterior and posterior portions compared to implantation of the IOL alone. Discussion: These findings align with patient studies and suggest that implantation of a CTR with the IOL during routine cataract surgery would attenuate the incidence of visually-debilitating capsule fibrosis. Our work demonstrates that use of such modeling techniques has substantial potential to aid in the design of better surgical strategies and implants.

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

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

How to implement constrained mixture growth and remodeling algorithms for soft biological tissues

Biological soft tissues are constantly adapting to their mechanical environment and remodel to restore certain mechanobiological homeostatic conditions. These effects can be modeled using the constrained mixture theory, that assumes degradation of material over time and the gradual replacement of extant material by newly deposited material. While this theory presents an elegant way to grasp phenomena of growth and remodeling in soft biological tissues, implementation difficulties may arise. Therefore, we give a detailed overview of the mathematical description of the constrained mixture theory and its homogenized equivalent, and present practical suggestions to numerically implement the theories. These implementations are thoroughly tested with multiple example growth and remodeling models. Results show a good correspondence between both theories, with the homogenized theory favored in terms of time efficiency. Results of a step time convergence study show the importance of choosing a small enough time step, especially when using the classical theory.

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.

The study on the impact of AAA wall motion on the hemodynamics based on 4D CT image data

Purpose: To analyze the effect of the physiological deformation of the vessel wall on the hemodynamics in the abdominal aortic aneurysm (AAA), this paper compared the hemodynamics in AAA based on the moving boundary (MB) simulation and the rigid wall (RW) simulation.

Method: Patient-specific models were reconstructed to generate mesh based on four-dimensional computed tomography angiography (4D CT) data. The dynamic mesh technique was used to achieve deformation of the vessel wall, surface mesh and volume mesh of the fluid domain were successively remeshed at each time step. Besides, another rigid wall simulation was performed. Hemodynamics obtained from these two simulations were compared.

Results: Flow field and wall shear stress (WSS) distribution are similar. When using the moving boundary method (MBM), mean time-averaged wall shear stress (TAWSS) is lower, mean oscillatory shear index (OSI) and mean relative residence time (RRT) are higher. When using the 10th and 20th percentile values for TAWSS and 80th and 90th percentile values for RRT, the ratios of areas with low TAWSS, high OSI and high RRT to the entire vessel wall are higher than those assuming the vessel as rigid. In addition, one overlapping region of low TAWSS, high OSI and high RRT by using the MBM is consistent with the location of thrombus obtained from the follow-up imaging data.

Conclusion: The hemodynamics results by using the MBM reflect a higher blood retention effect. This paper presents a potential tool to assess the risk of intraluminal thrombus (ILT) formation based on the MBM.

PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data

We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed with an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then split into growth and elastic contributions. The growth tensor captures addition of mass, i.e. growth, and evolves according to a constitutive equation which is usually a function of the elastic deformation. Stress is generated in the material due to the elastic component of the deformation alone. The result of the registration is obtained by minimizing a total energy functional which includes: a distance measure reflecting similarity between the shapes, and the total elastic energy accounting for the growth of the tissue. We apply the proposed shape registration framework to study zebrafish embryo epiboly process and tissue expansion during skin reconstruction surgery. We anticipate that our PDE-constrained shape registration method will improve our understanding of biological and medical problems in which tissues undergo extreme deformations over time.

Quantitative comparison between carotid plaque hardness and histopathological findings: an observational study

Background

Plaque hardness in carotid artery stenosis correlates with cerebral infarction. This study aimed to quantitatively compare plaque hardness with histopathological findings and identify the pathological factors involved in plaque hardness.

Methods

This study included 84 patients (89 lesions) undergoing carotid endarterectomy (CEA) at our institution. Plaque hardness was quantitatively measured immediately after excision using a hardness meter. Collagen and calcification were evaluated as the pathological factors. Collagen was stained with Elastica van Gieson stain, converted to a gray-scale image, and displayed in a 256-step histogram. The median gray-scale median (GSM) was used as the collagen content. The degree of calcification was defined by the hematoxylin–eosin stain as follows: "0:" no calcification, "1:" scattered microcalcification, or "2:" calcification greater than 1 mm or more than 2% of the total calcification. Carotid echocardiographic findings, specifically echoluminance or the brightness of the narrowest lesion of the plaque, classified as hypo-, iso-, or hyper-echoic by comparison with the intima-media complex surrounding the plaque, and clinical data were reviewed.

Results

Plaque hardness was significantly negatively correlated with GSM [Spearman's correlation coefficient: -0.7137 (p < 0.0001)]: the harder the plaque, the higher the collagen content. There were significant differences between plaque hardness and degree of calcification between "0" and "2" (p = 0.0206). For plaque hardness and echoluminance (hypo-iso-hyper), significant differences were found between hypo-iso (p = 0.0220), hypo-hyper (p = 0.0006), and iso-hyper (p = 0.0015): the harder the plaque, the higher the luminance. In single regression analysis, GSM, sex, and diabetes mellitus were significant variables, and in multiple regression analysis, only GSM was extracted as a significant variable.

Conclusions

Plaque hardness was associated with a higher amount of collagen, which is the main component of the fibrous cap. Greater plaque hardness was associated with increased plaque stability. The degree of calcification may also be associated with plaque hardness.

Blood-Artery Interaction in Calcified Aortas and Abdominal Aortic Aneurysms

A stabilized FSI method is presented for coupling shear-rate dependent model of blood with finitely deforming anisotropic hyperelastic model of arteries. The blood-artery coupling conditions are weakly enforced to accommodate non-matching blood-artery meshes which provides great flexibility in independent discretization of fluid and solid subdomains in the patient-specific geometric models. The variationally derived interface coupling terms play an important role in the concurrent solution of the nonlinear mixed-field problem across non-matching discretizations. Two test cases are presented that investigate the effect of growth of aortic aneurysm on local changes in blood flow and stress concentrations in calcified arteries under pulsating flows to highlight the clinical relevance of the proposed method for cardiovascular applications.

In vivo development of tissue engineered vascular grafts: a fluid-solid-growth model

Methods of tissue engineering continue to advance, and multiple clinical trials are underway evaluating tissue engineered vascular grafts (TEVGs). Whereas initial concerns focused on suture retention and burst pressure, there is now a pressing need to design grafts to have optimal performance, including an ability to grow and remodel in response to changing hemodynamic loads. Toward this end, there is similarly a need for computational methods that can describe and predict the evolution of TEVG geometry, composition, and material properties while accounting for changes in hemodynamics. Although the ultimate goal is a fluid-solid-growth (FSG) model incorporating fully 3D growth and remodeling and 3D hemodynamics, lower fidelity models having high computational efficiency promise to play important roles, especially in the design of candidate grafts. We introduce here an efficient FSG model of in vivo development of a TEVG based on two simplifying concepts: mechanobiologically equilibrated growth and remodeling of the graft and an embedded control volume analysis of the hemodynamics. Illustrative simulations for a model Fontan conduit reveal the utility of this approach, which promises to be particularly useful in initial design considerations involving formal methods of optimization which otherwise add considerably to the computational expense.

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.

Growth and remodeling in the pulmonary autograft: Computational evaluation using kinematic growth models and constrained mixture theory

Computational investigations of how soft tissues grow and remodel are gaining more and more interest and several growth and remodeling theories have been developed. Roughly, two main groups of theories for soft tissues can be distinguished: kinematic-based growth theory and theories based on constrained mixture theory. Our goal was to apply these two theories on the same experimental data. Within the experiment, a pulmonary artery was exposed to systemic conditions. The change in diameter was followed-up over time. A mechanical and microstructural analysis of native pulmonary artery and pulmonary autograft was conducted. Whereas the kinematic-based growth theory is able to accurately capture the growth of the tissue, it does not account for the mechanobiological processes causing this growth. The constrained mixture theory takes into account the mechanobiological processes including removal, deposition and adaptation of all structural constituents, allowing us to simulate a changing microstructure and mechanical behavior.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

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.

An in silico Framework of Cartilage Degeneration That Integrates Fibril Reorientation and Degradation Along With Altered Hydration and Fixed Charge Density Loss

Injurious mechanical loading of articular cartilage and associated lesions compromise the mechanical and structural integrity of joints and contribute to the onset and progression of cartilage degeneration leading to osteoarthritis (OA). Despite extensive in vitro and in vivo research, it remains unclear how the changes in cartilage composition and structure that occur during cartilage degeneration after injury, interact. Recently, in silico techniques provide a unique integrated platform to investigate the causal mechanisms by which the local mechanical environment of injured cartilage drives cartilage degeneration. Here, we introduce a novel integrated Cartilage Adaptive REorientation Degeneration (CARED) algorithm to predict the interaction between degenerative variations in main cartilage constituents, namely collagen fibril disorganization and degradation, proteoglycan (PG) loss, and change in water content. The algorithm iteratively interacts with a finite element (FE) model of a cartilage explant, with and without variable depth to full-thickness defects. In these FE models, intact and injured explants were subjected to normal (2 MPa unconfined compression in 0.1 s) and injurious mechanical loading (4 MPa unconfined compression in 0.1 s). Depending on the mechanical response of the FE model, the collagen fibril orientation and density, PG and water content were iteratively updated. In the CARED model, fixed charge density (FCD) loss and increased water content were related to decrease in PG content. Our model predictions were consistent with earlier experimental studies. In the intact explant model, minimal degenerative changes were observed under normal loading, while the injurious loading caused a reorientation of collagen fibrils toward the direction perpendicular to the surface, intense collagen degradation at the surface, and intense PG loss in the superficial and middle zones. In the injured explant models, normal loading induced intense collagen degradation, collagen reorientation, and PG depletion both on the surface and around the lesion. Our results confirm that the cartilage lesion depth is a crucial parameter affecting tissue degeneration, even under physiological loading conditions. The results suggest that potential fibril reorientation might prevent or slow down fibril degradation under conditions in which the tissue mechanical homeostasis is perturbed like the presence of defects or injurious loading.

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.

A distributed lumped parameter model of blood flow with fluid-structure interaction

A distributed lumped parameter (DLP) model of blood flow was recently developed that can be simulated in minutes while still incorporating complex sources of energy dissipation in blood vessels. The aim of this work was to extend the previous DLP modeling framework to include fluid-structure interactions (DLP-FSI). This was done by using a simple compliance term to calculate pressure that does not increase the simulation complexity of the original DLP models. Verification and validation studies found DLP-FSI simulations had good agreement compared to analytical solutions of the wave equations, experimental measurements of pulsatile flow in elastic tubes, and in vivo MRI measurements of thoracic aortic flow. This new development of DLP-FSI allows for significantly improved computational efficiency of FSI simulations compared to FSI approaches that solve the full 3D conservation of mass and momentum equations while also including the complex sources of energy dissipation occurring in cardiovascular flows that other simplified models neglect.

The Contribution of Glycosaminoglycans/Proteoglycans to Aortic Mechanics in Health and Disease: A Critical Review

While elastin and collagen have received a lot of attention as major contributors to aortic biomechanics, glycosaminoglycans (GAGs) and proteoglycans (PGs) recently emerged as additional key players whose roles must be better elucidated if one hopes to predict aortic ruptures caused by aneurysms and dissections more reliably. GAGs are highly negatively charged polysaccharide molecules that exist in the extracellular matrix (ECM) of the arterial wall. In this critical review, we summarize the current understanding of the contributions of GAGs/PGs to the biomechanics of the normal aortic wall, as well as in the case of aortic diseases such as aneurysms and dissections. Specifically, we describe the fundamental swelling behavior of GAGs/PGs and discuss their contributions to residual stresses and aortic stiffness, thereby highlighting the importance of taking these polyanionic molecules into account in mathematical and numerical models of the aorta. We suggest specific lines of investigation to further the acquisition of experimental data to complement simulations and solidify our current understanding. We underscore different potential roles of GAGs/PGs in thoracic aortic aneurysm (TAAD) and abdominal aortic aneurysm (AAA). Namely, we report findings according to which the accumulation of GAGs/PGs in TAAD causes stress concentrations which may be sufficient to initiate and propagate delamination. On the other hand, there seems to be no clear indication of a relationship between the marked reduction in GAG/PG content and the stiffening and weakening of the aortic wall in AAA.

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury

Vascular clamping often causes injury to arterial tissue, leading to a cascade of cellular and extracellular events. A reliable in silico prediction of these processes following vascular injury could help us to increase our understanding thereof, and eventually optimize surgical techniques or drug delivery to minimize the amount of long-term damage. However, the complexity and interdependency of these events make translation into constitutive laws and their numerical implementation particularly challenging. We introduce a finite element simulation of arterial clamping taking into account acute endothelial denudation, damage to extracellular matrix, and smooth muscle cell loss. The model captures how this causes tissue inflammation and deviation from mechanical homeostasis, both triggering vascular remodeling. A number of cellular processes are modeled, aiming at restoring this homeostasis, i.e., smooth muscle cell phenotype switching, proliferation, migration, and the production of extracellular matrix. We calibrated these damage and remodeling laws by comparing our numerical results to in vivo experimental data of clamping and healing experiments. In these same experiments, the functional integrity of the tissue was assessed through myograph tests, which were also reproduced in the present study through a novel model for vasodilator and -constrictor dependent smooth muscle contraction. The simulation results show a good agreement with the in vivo experiments. The computational model was then also used to simulate healing beyond the duration of the experiments in order to exploit the benefits of computational model predictions. These results showed a significant sensitivity to model parameters related to smooth muscle cell phenotypes, highlighting the pressing need to further elucidate the biological processes of smooth muscle cell phenotypic switching in the future.

Computational models of cardiac hypertrophy

Cardiac hypertrophy, defined as an increase in mass of the heart, is a complex process driven by simultaneous changes in hemodynamics, mechanical stimuli, and hormonal inputs. It occurs not only during pre- and post-natal development but also in adults in response to exercise, pregnancy, and a range of cardiovascular diseases. One of the most exciting recent developments in the field of cardiac biomechanics is the advent of computational models that are able to accurately predict patterns of heart growth in many of these settings, particularly in cases where changes in mechanical loading of the heart play an import role. These emerging models may soon be capable of making patient-specific growth predictions that can be used to guide clinical interventions. Here, we review the history and current state of cardiac growth models and highlight three main limitations of current approaches with regard to future clinical application: their inability to predict the regression of heart growth after removal of a mechanical overload, inability to account for evolving hemodynamics, and inability to incorporate known growth effects of drugs and hormones on heart growth. Next, we outline growth mechanics approaches used in other fields of biomechanics and highlight some potential lessons for cardiac growth modeling. Finally, we propose a multiscale modeling approach for future studies that blends tissue-level growth models with cell-level signaling models to incorporate the effects of hormones in the context of pregnancy-induced heart growth.

Computational Study of Growth and Remodeling in Ascending Thoracic Aortic Aneurysms Considering Variations of Smooth Muscle Cell Basal Tone

In this paper, we investigate the progression of Ascending Thoracic Aortic Aneurysms (ATAA) using a computational model of Growth and Remodeling (G&R) taking into account the composite (elastin, four collagen fiber families and Smooth Muscle Cells—SMCs) and multi-layered (media and adventitia) nature of the aorta. The G&R model, which is based on the homogenized Constrained Mixture theory, is implemented as a UMAT in the Abaqus finite-element package. Each component of the mixture is assigned a strain energy density function: nearly-incompressible neo-Hookean for elastin and Fung-type for collagen and SMCs. Active SMCs tension is additionally considered, through a length-tension relationship having a classic inverted parabola shape, in order to investigate its effects on the progression of ATAA in a patient-specific model. A sensitivity analysis is performed to evaluate the potential impact of variations in the parameters of the length-tension relationships. These variations reflect in variations of SMCs normal tone during ATAA progression, with active stress contributions ranging between 30% (best case scenario) and 0% (worst case scenario) of the total wall circumferential stress. Low SMCs active stress in the worst case scenarios, in fact, affect the rates of collagen deposition by which the elastin loss is gradually compensated by collagen deposition in the simulated ATAA progression, resulting eventually in larger aneurysm diameters. The types of length-tension relationships leading to a drop of SMCs active stress in our simulations reveal a critical condition which could also result in SMCs apoptosis.

Reconstructing vascular homeostasis by growth-based prestretch and optimal fiber deposition

Computational modeling of cardiovascular biomechanics should generally start from a homeostatic state. This is particularly relevant for image-based modeling, where the reference configuration is the loaded in vivo state obtained from imaging. This state includes residual stress of the vascular constituents, as well as anisotropy from the spatially varying orientation of collagen and smooth muscle fibers. Estimation of the residual stress and fiber orientation fields is a formidable challenge in realistic applications. To help address this challenge, we herein develop a growth based Algorithm to recover a residual stress distribution in vascular domains such that the stress state in the loaded configuration is equal to a prescribed homeostatic stress distribution at physiologic pressure. A stress-driven fiber deposition process is included in the framework, which defines the distribution of the fiber alignments in the vascular homeostatic state based on a minimization procedure. Numerical simulations are conducted to test this two-stage homeostasis generation algorithm in both idealized and non-idealized geometries, yielding results that agree favorably with prior numerical and experimental data.

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.

Mitigating the Consequences of Subconcussive Head Injuries

Subconcussive head injury represents a pathophysiology that spans the expertise of both clinical neurology and biomechanical engineering. From both viewpoints, the terms injury and damage, presented without qualifiers, are synonymously taken to mean a tissue alteration that may be recoverable. For clinicians, concussion is evolving from a purely clinical diagnosis to one that requires objective measurement, to be achieved by biomedical engineers. Subconcussive injury is defined as subclinical pathophysiology in which underlying cellular- or tissue-level damage (here, to the brain) is not severe enough to present readily observable symptoms. Our concern is not whether an individual has a (clinically diagnosed) concussion, but rather, how much accumulative damage an individual can tolerate before they will experience long-term deficit(s) in neurological health. This concern leads us to look for the history of damage-inducing events, while evaluating multiple approaches for avoiding injury through reduction or prevention of the associated mechanically induced damage.

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

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

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

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

Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics

Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel-Gasser-Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results.

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.

A relaxed growth modeling framework for controlling growth-induced residual stresses

BACKGROUND

Constitutive models of the mechanical response of soft tissues have been established and are widely accepted, but models of soft tissues remodeling are more controversial. Specifically for growth, one important question arises pertaining to residual stresses: existing growth models inevitably introduce residual stresses, but it is not entirely clear if this is physiological or merely an artifact of the modeling framework. As a consequence, in simulating growth, some authors have chosen to keep growth-induced residual stresses, and others have chosen to remove them.

METHODS

In this paper, we introduce a novel "relaxed growth" framework allowing for a fine control of the amount of residual stresses generated during tissue growth. It is a direct extension of the classical framework of the multiplicative decomposition of the transformation gradient, to which an additional sub-transformation is introduced in order to let the original unloaded configuration evolve, hence relieving some residual stresses. We provide multiple illustrations of the framework mechanical response, on time-driven constrained growth as well as the strain-driven growth problem of the artery under internal pressure, including the opening angle experiment.

FINDINGS

The novel relaxed growth modeling framework introduced in this paper allows for a better control of growth-induced residual stresses compared to standard growth models based on the multiplicative decomposition of the transformation gradient.

INTERPRETATION

Growth-induced residual stresses should be better handled in soft tissues biomechanical models, especially in patient-specific models of diseased organs that are aimed at augmented diagnosis and treatment optimization.

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

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

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

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

Gradient-enhanced continuum models of healing in damaged soft tissues

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

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.

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 theoretical model of inflammation- and mechanotransduction-driven asthmatic airway remodelling

Inflammation, airway hyper-responsiveness and airway remodelling are well-established hallmarks of asthma, but their inter-relationships remain elusive. In order to obtain a better understanding of their inter-dependence, we develop a mechanochemical morphoelastic model of the airway wall accounting for local volume changes in airway smooth muscle (ASM) and extracellular matrix in response to transient inflammatory or contractile agonist challenges. We use constrained mixture theory, together with a multiplicative decomposition of growth from the elastic deformation, to model the airway wall as a nonlinear fibre-reinforced elastic cylinder. Local contractile agonist drives ASM cell contraction, generating mechanical stresses in the tissue that drive further release of mitogenic mediators and contractile agonists via underlying mechanotransductive signalling pathways. Our model predictions are consistent with previously described inflammation-induced remodelling within an axisymmetric airway geometry. Additionally, our simulations reveal novel mechanotransductive feedback by which hyper-responsive airways exhibit increased remodelling, for example, via stress-induced release of pro-mitogenic and pro-contractile cytokines. Simulation results also reveal emergence of a persistent contractile tone observed in asthmatics, via either a pathological mechanotransductive feedback loop, a failure to clear agonists from the tissue, or a combination of both. Furthermore, we identify various parameter combinations that may contribute to the existence of different asthma phenotypes, and we illustrate a combination of factors which may predispose severe asthmatics to fatal bronchospasms.

Application of Patient-Specific Computational Fluid Dynamics in Coronary and Intra-Cardiac Flow Simulations: Challenges and Opportunities

The emergence of new cardiac diagnostics and therapeutics of the heart has given rise to the challenging field of virtual design and testing of technologies in a patient-specific environment. Given the recent advances in medical imaging, computational power and mathematical algorithms, patient-specific cardiac models can be produced from cardiac images faster, and more efficiently than ever before. The emergence of patient-specific computational fluid dynamics (CFD) has paved the way for the new field of computer-aided diagnostics. This article provides a review of CFD methods, challenges and opportunities in coronary and intra-cardiac flow simulations. It includes a review of market products and clinical trials. Key components of patient-specific CFD are covered briefly which include image segmentation, geometry reconstruction, mesh generation, fluid-structure interaction, and solver techniques.

Computational predictions of damage propagation preceding dissection of ascending thoracic aortic aneurysms

Dissections of ascending thoracic aortic aneurysms (ATAAs) cause significant morbidity and mortality worldwide. They occur when a tear in the intima-media of the aorta permits the penetration of the blood and the subsequent delamination and separation of the wall in 2 layers, forming a false channel. To predict computationally the risk of tear formation, stress analyses should be performed layer-specifically and they should consider internal or residual stresses that exist in the tissue. In the present paper, we propose a novel layer-specific damage model based on the constrained mixture theory, which intrinsically takes into account these internal stresses and can predict appropriately the tear formation. The model is implemented in finite-element commercial software Abaqus coupled with user material subroutine. Its capability is tested by applying it to the simulation of different exemplary situations, going from in vitro bulge inflation experiments on aortic samples to in vivo overpressurizing of patient-specific ATAAs. The simulations reveal that damage correctly starts from the intimal layer (luminal side) and propagates across the media as a tear but never hits the adventitia. This scenario is typically the first stage of development of an acute dissection, which is predicted for pressures of about 2.5 times the diastolic pressure by the model after calibrating the parameters against experimental data performed on collected ATAA samples. Further validations on a larger cohort of patients should hopefully confirm the potential of the model in predicting patient-specific damage evolution and possible risk of dissection during aneurysm growth for clinical applications.

Degradation and erosion mechanisms of bioresorbable porous acellular vascular grafts: an in vitro investigation

A fundamental mechanism of in situ tissue regeneration from biodegradable synthetic acellular vascular grafts is the effective interplay between graft degradation, erosion and the production of extracellular matrix. In order to understand this crucial process of graft erosion and degradation, we conducted an in vitro investigation of grafts (n = 4 at days 1, 4, 7, 10 each) exposed to enzymatic degradation. Herein, we provide constitutive relationships for mass loss and mechanical properties based on much-needed experimental data. Furthermore, we formulate a mathematical model to provide a physics-based framework for understanding graft erosion. A novel finding is that despite their porous nature, grafts lost mass exponentially via surface erosion demonstrating a 20% reduction in outer diameter and no significant change in apparent density. A diffusion based, concentration gradient-driven mechanistic model of mass loss through surface erosion was introduced which can be extended to an in vivo setting through the use of two degradation parameters. Furthermore, notably, mechanical properties of degrading grafts did not scale with mass loss. Thus, we introduced a damage function scaling a neo-Hookean model to describe mechanical properties of the degrading graft; a refinement to existing mass-dependent growth and remodelling (G&R) models. This framework can be used to improve accuracy of well-established G&R theories in biomechanics; tools that predict evolving structure-function relationships of neotissues and guide graft design.

Growth Description for Vessel Wall Adaptation: A Thick-Walled Mixture Model of Abdominal Aortic Aneurysm Evolution

(1) Background: Vascular tissue seems to adapt towards stable homeostatic mechanical conditions, however, failure of reaching homeostasis may result in pathologies. Current vascular tissue adaptation models use many ad hoc assumptions, the implications of which are far from being fully understood; (2) Methods: The present study investigates the plausibility of different growth kinematics in modeling Abdominal Aortic Aneurysm (AAA) evolution in time. A structurally motivated constitutive description for the vessel wall is coupled to multi-constituent tissue growth descriptions; Constituent deposition preserved either the constituent’s density or its volume, and Isotropic Volume Growth (IVG), in-Plane Volume Growth (PVG), in-Thickness Volume Growth (TVG) and No Volume Growth (NVG) describe the kinematics of the growing vessel wall. The sensitivity of key modeling parameters is explored, and predictions are assessed for their plausibility; (3) Results: AAA development based on TVG and NVG kinematics provided not only quantitatively, but also qualitatively different results compared to IVG and PVG kinematics. Specifically, for IVG and PVG kinematics, increasing collagen mass production accelerated AAA expansion which seems counterintuitive. In addition, TVG and NVG kinematics showed less sensitivity to the initial constituent volume fractions, than predictions based on IVG and PVG; (4) Conclusions: The choice of tissue growth kinematics is of crucial importance when modeling AAA growth. Much more interdisciplinary experimental work is required to develop and validate vascular tissue adaption models, before such models can be of any practical use.

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.

A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues

Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data.

Influence of shear stress magnitude and direction on atherosclerotic plaque composition

The precise flow characteristics that promote different atherosclerotic plaque types remain unclear. We previously developed a blood flow-modifying cuff for ApoE^-/- mice that induces the development of advanced plaques with vulnerable and stable features upstream and downstream of the cuff, respectively. Herein, we sought to test the hypothesis that changes in flow magnitude promote formation of the upstream (vulnerable) plaque, whereas altered flow direction is important for development of the downstream (stable) plaque. We instrumented ApoE^-/- mice (n = 7) with a cuff around the left carotid artery and imaged them with micro-CT (39.6 µm resolution) eight to nine weeks after cuff placement. Computational fluid dynamics was then performed to compute six metrics that describe different aspects of atherogenic flow in terms of wall shear stress magnitude and/or direction. In a subset of four imaged animals, we performed histology to confirm the presence of advanced plaques and measure plaque length in each segment. Relative to the control artery, the region upstream of the cuff exhibited changes in shear stress magnitude only (p < 0.05), whereas the region downstream of the cuff exhibited changes in shear stress magnitude and direction (p < 0.05). These data suggest that shear stress magnitude contributes to the formation of advanced plaques with a vulnerable phenotype, whereas variations in both magnitude and direction promote the formation of plaques with stable features.

Quantification of plaque stiffness by Brillouin microscopy in experimental thin cap fibroatheroma

Plaques vulnerable to rupture are characterized by a thin and stiff fibrous cap overlaying a soft lipid-rich necrotic core. The ability to measure local plaque stiffness directly to quantify plaque stress and predict rupture potential would be very attractive, but no current technology does so. This study seeks to validate the use of Brillouin microscopy to measure the Brillouin frequency shift, which is related to stiffness, within vulnerable plaques. The left carotid artery of an ApoE(-/-)mouse was instrumented with a cuff that induced vulnerable plaque development in nine weeks. Adjacent histological sections from the instrumented and control arteries were stained for either lipids or collagen content, or imaged with confocal Brillouin microscopy. Mean Brillouin frequency shift was 15.79 ± 0.09 GHz in the plaque compared with 16.24 ± 0.15 (p < 0.002) and 17.16 ± 0.56 GHz (p < 0.002) in the media of the diseased and control vessel sections, respectively. In addition, frequency shift exhibited a strong inverse correlation with lipid area of -0.67 ± 0.06 (p < 0.01) and strong direct correlation with collagen area of 0.71 ± 0.15 (p < 0.05). This is the first study, to the best of our knowledge, to apply Brillouin spectroscopy to quantify atherosclerotic plaque stiffness, which motivates combining this technology with intravascular imaging to improve detection of vulnerable plaques in patients.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Theory and application of arterial tissue in-host remodelling

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