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

Three-dimensional anisotropic unified continuum model for simulating the healing of damaged soft biological tissues

The soft biological tissues have the ability to heal and self-repair after damage or injury. During the healing process, damaged tissues are replaced by newly produced undamaged tissue to restore homeostasis. Computational modeling serves as an effective tool for simulating the healing process and understanding the underlying mechanisms. In previous work, we developed the first unified continuum damage model for the healing of soft biological tissues. However, the initial theory lacked generalizability to more realistic scenarios and applicability to biomechanical problems due to the simplicity of the isotropic constitutive model and two-dimensional simulations. Therefore, we further improve our approach by developing a three-dimensional anisotropic unified healing model to address more realistic challenges. By using the Holzapfel-Gasser-Ogden model as the hyperelastic term, the influence of the collagen fibers is considered and the reorientation of fibers in healing is simulated. Three numerical examples related to hypertension, aneurysm, and restenosis of the atherosclerotic artery after balloon angioplasty are presented to demonstrate the effectiveness of the proposed model. By comparing numerical solutions and reference solutions, we demonstrate the ability of the proposed model in simulating long-term tissue healing process and analyze the impact of anisotropic terms.

FSGe: A fast and strongly-coupled 3D fluid-solid-growth interaction method

Equilibrated fluid-solid-growth (FSGe) is a fast, open source, three-dimensional (3D) computational platform for simulating interactions between instantaneous hemodynamics and long-term vessel wall adaptation through mechanobiologically equilibrated growth and remodeling (G&R). Such models can capture evolving geometry, composition, and material properties in health and disease and following clinical interventions. In traditional G&R models, this feedback is modeled through highly simplified fluid solutions, neglecting local variations in blood pressure and wall shear stress (WSS). FSGe overcomes these inherent limitations by strongly coupling the 3D Navier-Stokes equations for blood flow with a 3D equilibrated constrained mixture model (CMMe) for vascular tissue G&R. CMMe allows one to predict long-term evolved mechanobiological equilibria from an original homeostatic state at a computational cost equivalent to that of a standard hyperelastic material model. In illustrative computational examples, we focus on the development of a stable aortic aneurysm in a mouse model to highlight key differences in growth patterns between FSGe and solid-only G&R models. We show that FSGe is especially important in blood vessels with asymmetric stimuli. Simulation results reveal greater local variation in fluid-derived WSS than in intramural stress (IMS). Thus, differences between FSGe and G&R models became more pronounced with the growing influence of WSS relative to pressure. Future applications in highly localized disease processes, such as for lesion formation in atherosclerosis, can now include spatial and temporal variations of WSS.

A computationally efficient gradient-enhanced healing model for soft biological tissues

Soft biological tissues, such as arterial tissue, have the ability to grow and remodel in response to damage. Computational method plays a critical role in understanding the underlying mechanisms of tissue damage and healing. However, the existing healing model often requires huge computation time and it is inconvenient to implement finite element simulation. In this paper, we propose a computationally efficient gradient-enhanced healing model that combines the advantages of the gradient-enhanced damage model, the homeostatic-driven turnover remodeling model, and the damage-induced growth model. In the proposed model, the evolution of healing-related parameters can be solved explicitly. Additionally, an adaptive time increment method is used to further reduce computation time. The proposed model can be easily implemented in Abaqus, requiring only a user subroutine UMAT. The effectiveness of proposed model is verified through a semi-analytical example, and the influence of the variables in the proposed model is investigated using uniaxial tension and open-hole plate tests. Finally, the long-term development of aneurysms is simulated to demonstrate the potential applications of the proposed model in real biomechanical problems.

Short-Term Disruption of TGFβ Signaling in Adult Mice Renders the Aorta Vulnerable to Hypertension-Induced Dissection

Hypertension and transient increases in blood pressure from extreme exertion are risk factors for aortic dissection in patients with age-related vascular degeneration or inherited connective tissue disorders. Yet, the common experimental model of angiotensin II-induced aortopathy in mice appears independent of high blood pressure as lesions do not occur in response to an alternative vasoconstrictor, norepinephrine, and are not prevented by co-treatment with a vasodilator, hydralazine. We investigated vasoconstrictor administration to adult mice 1 week after disruption of TGFβ signaling in smooth muscle cells. Norepinephrine increased blood pressure and induced aortic dissection by 7 days and even within 30 minutes that was rescued by hydralazine; results were similar with angiotensin II. Changes in regulatory contractile molecule expression were not of pathological significance. Rather, reduced synthesis of extracellular matrix yielded a vulnerable aortic phenotype by decreasing medial collagen, most dynamically type XVIII, and impairing cell-matrix adhesion. We conclude that transient and sustained increases in blood pressure cause dissection in aortas rendered vulnerable by inhibition of TGFβ-driven extracellular matrix production by smooth muscle cells. A corollary is that medial fibrosis, a frequent feature of medial degeneration, may afford some protection against aortic dissection.

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 computational growth and remodeling framework for adaptive and maladaptive pulmonary arterial hemodynamics

Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step toward predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.

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

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

Effects of Age, Sex, and Extracellular Matrix Integrity on Aortic Dilatation and Rupture in a Mouse Model of Marfan Syndrome

BACKGROUND

Transmural failure of the aorta is responsible for substantial morbidity and mortality; it occurs when mechanical stress exceeds strength. The aortic root and ascending aorta are susceptible to dissection and rupture in Marfan syndrome, a connective tissue disorder characterized by a progressive reduction in elastic fiber integrity. Whereas competent elastic fibers endow the aorta with compliance and resilience, cross-linked collagen fibers confer stiffness and strength. We hypothesized that postnatal reductions in matrix cross-linking increase aortopathy when turnover rates are high.

METHODS

We combined ex vivo biaxial mechanical testing with multimodality histological examinations to quantify expected age- and sex-dependent structural vulnerability of the ascending aorta in Fbn1C1041G/+ Marfan versus wild-type mice without and with 4-week exposures to β-aminopropionitrile, an inhibitor of lysyl oxidase-mediated cross-linking of newly synthesized elastic and collagen fibers.

RESULTS

We found a strong β-aminopropionitrile-associated sexual dimorphism in aortic dilatation in Marfan mice and aortic rupture in wild-type mice, with dilatation correlating with compromised elastic fiber integrity and rupture correlating with compromised collagen fibril organization. A lower incidence of rupture of β-aminopropionitrile-exposed Marfan aortas associated with increased lysyl oxidase, suggesting a compensatory remodeling of collagen that slows disease progression in the otherwise compromised Fbn1C1041G/+ aorta.

CONCLUSIONS

Collagen fiber structure and function in the Marfan aorta are augmented, in part, by increased lysyl oxidase in female and especially male mice, which improves structural integrity, particularly via fibrils in the adventitia. Preserving or promoting collagen cross-linking may represent a therapeutic target for an otherwise vulnerable aorta.

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.

Computational analysis of the role of mechanosensitive Notch signaling in arterial adaptation to hypertension

Arteries grow and remodel in response to mechanical stimuli. Hypertension, for example, results in arterial wall thickening. Cell-cell Notch signaling between vascular smooth muscle cells (VSMCs) is known to be involved in this process, but the underlying mechanisms are still unclear. Here, we investigated whether Notch mechanosensitivity to strain may regulate arterial thickening in hypertension. We developed a multiscale computational framework by coupling a finite element model of arterial mechanics, including residual stress, to an agent-based model of mechanosensitive Notch signaling, to predict VSMC phenotypes as an indicator of growth and remodeling. Our simulations revealed that the sensitivity of Notch to strain at mean blood pressure may be a key mediator of arterial thickening in hypertensive arteries. Further simulations showed that loss of residual stress can have synergistic effects with hypertension, and that changes in the expression of Notch receptors, but not Jagged ligands, may be used to control arterial growth and remodeling and to intensify or counteract hypertensive thickening. Overall, we identify Notch mechanosensitivity as a potential mediator of vascular adaptation, and we present a computational framework that can facilitate the testing of new therapeutic and regenerative strategies.

Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms

Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta that can lead to life-threatening dissection or rupture. In vivo assessments of TAA progression are largely limited to measurements of aneurysm size and growth rate. There is promise, however, that computational modelling of the evolving biomechanics of the aorta could predict future geometry and properties from initiating mechanobiological insults. We present an integrated framework to train a deep operator network (DeepONet)-based surrogate model to identify TAA contributing factors using synthetic finite-element-based datasets. For training, we employ a constrained mixture model of aortic growth and remodelling to generate maps of local aortic dilatation and distensibility for multiple TAA risk factors. We evaluate the performance of the surrogate model for insult distributions varying from fusiform (analytically defined) to complex (randomly generated). We propose two frameworks, one trained on sparse information and one on full-field greyscale images, to gain insight into a preferred neural operator-based approach. We show that this continuous learning approach can predict the patient-specific insult profile associated with any given dilatation and distensibility map with high accuracy, particularly when based on full-field images. Our findings demonstrate the feasibility of applying DeepONet to support transfer learning of patient-specific inputs to predict TAA progression.

Evolving Mural Defects, Dilatation, and Biomechanical Dysfunction in Angiotensin II-Induced Thoracic Aortopathies

BACKGROUND

Thoracic aortopathy associates with extracellular matrix remodeling and altered biomechanical properties. We sought to quantify the natural history of thoracic aortopathy in a common mouse model and to correlate measures of wall remodeling such as aortic dilatation or localized mural defects with evolving microstructural composition and biomechanical properties of the wall.

METHODS

We combined a high-resolution multimodality imaging approach (panoramic digital image correlation and optical coherence tomography) with histopathologic examinations and biaxial mechanical testing to correlate spatially, for the first time, macroscopic mural defects and medial degeneration within the ascending aorta with local changes in aortic wall composition and mechanical properties.

RESULTS

Findings revealed strong correlations between local decreases in elastic energy storage and increases in circumferential material stiffness with increasing proximal aortic diameter and especially mural defect size. Mural defects tended to exhibit a pronounced biomechanical dysfunction that is driven by an altered organization of collagen and elastic fibers.

CONCLUSIONS

While aneurysmal dilatation is often observed within particular segments of the aorta, dissection and rupture initiate as highly localized mechanical failures. We show that wall composition and material properties are compromised in regions of local mural defects, which further increases the dilatation and overall structural vulnerability of the wall. Identification of therapies focused on promoting robust collagen accumulation may protect the wall from these vulnerabilities and limit the incidence of dissection and rupture.

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.

Bayesian calibration of a computational model of tissue expansion based on a porcine animal model

Tissue expansion is a technique used clinically to grow skin in situ to correct large defects. Despite its enormous potential, lack of fundamental knowledge of skin adaptation to mechanical cues, and lack of predictive computational models limit the broader adoption and efficacy of tissue expansion. In our previous work, we introduced a finite element model of tissue expansion that predicted key patterns of strain and growth which were then confirmed by our porcine animal model. Here we use the data from a new set of experiments to calibrate the computational model within a Bayesian framework. Four 10×10cm2 patches were tattooed in the dorsal skin of four 12 weeks-old minipigs and a total of six patches underwent successful tissue expander placement and inflation to 60cc for expansion times ranging from 1 h to 7 days. Six patches that did not have expanders implanted served as controls for the analysis. We find that growth can be explained based on the elastic deformation. The predicted area growth rate is k∈[0.02,0.08] [h-1]. Growth is anisotropic and reflects the anisotropic mechanical behavior of porcine dorsal skin. The rostral-caudal axis shows greater deformation than the transverse axis, and the time scale of growth in the rostral-caudal direction is given by rate parameters k1∈[0.04,0.1] [h-1] compared to k2∈[0.01,0.05] [h-1] in the transverse direction. Moreover, the calibration results underscore the high variability in biological systems, and the need to create probabilistic computational models to predict tissue adaptation in realistic settings. STATEMENT OF SIGNIFICANCE: Tissue expansion is a widely used technique in reconstructive surgery because it triggers growth of skin for the correction of large skin lesions and for breast reconstruction after mastectomy. Despite of its potential, complications and undesired outcomes persist due to our incomplete understanding of skin mechanobiology. Here we quantify the deformation and growth fields induced by an expander over 7 days in a porcine animal model and use these data to calibrate a computational model of skin growth using finite element simulations and a Bayesian framework. The calibrated model is a leap forward in our understanding skin growth, we now have quantitative understanding of this process: area growth is anisotropic and it is proportional to stretch with a characteristic rate constant of k∈[0.02,0.08] [h-1].

Roles of mTOR in thoracic aortopathy understood by complex intracellular signaling interactions

Thoracic aortopathy–aneurysm, dissection, and rupture–is increasingly responsible for significant morbidity and mortality. Advances in medical genetics and imaging have improved diagnosis and thus enabled earlier prophylactic surgical intervention in many cases. There remains a pressing need, however, to understand better the underlying molecular and cellular mechanisms with the hope of finding robust pharmacotherapies. Diverse studies in patients and mouse models of aortopathy have revealed critical changes in multiple smooth muscle cell signaling pathways that associate with disease, yet integrating information across studies and models has remained challenging. We present a new quantitative network model that includes many of the key smooth muscle cell signaling pathways and validate the model using a detailed data set that focuses on hyperactivation of the mechanistic target of rapamycin (mTOR) pathway and its inhibition using rapamycin. We show that the model can be parameterized to capture the primary experimental findings both qualitatively and quantitatively. We further show that simulating a population of cells by varying receptor reaction weights leads to distinct proteomic clusters within the population, and that these clusters emerge due to a bistable switch driven by positive feedback in the PI3K/AKT/mTOR signaling pathway.

Cell signaling drives changes across scales, from altered transcription at the single-cell level to tissue-level growth and remodeling. Studying complex interactions within cell signaling pathways can lead to a better understanding of the progression of disease. In particular, we are interested in how vascular cells can change their phenotype in a way that exacerbates aortopathy, namely, the development of aneurysms, dissections, and rupture. In this study we built a novel cell signaling network model of a vascular smooth muscle cell using archival data and used it to capture the effects of a genetic knock-out and subsequent pharmacologic rescue. We then used the model to simulate populations of smooth muscle cells and found that small perturbations to the strength of signaling can lead to distinct clusters of cells. With further analysis of the network substructures, we found that a positive feedback loop within the network was responsible for the distinct phenotypes we saw in our clusters of simulated cells. We believe that this work not only helps us to understand changes in smooth muscle cell phenotype but also opens the possibility to study other signaling perturbations associated with aortopathy.

Biomechanical consequences of compromised elastic fiber integrity and matrix cross-linking on abdominal aortic aneurysmal enlargement

Abdominal aortic aneurysms (AAAs) are characterized histopathologically by compromised elastic fiber integrity, lost smooth muscle cells or their function, and remodeled collagen. We used a recently introduced mouse model of AAAs that combines enzymatic degradation of elastic fibers and blocking of lysyl oxidase, and thus matrix cross-linking, to study progressive dilatation of the infrarenal abdominal aorta, including development of intraluminal thrombus. We quantified changes in biomaterial properties and biomechanical functionality within the aneurysmal segment as a function of time of enlargement and degree of thrombosis. Towards this end, we combined multi-modality imaging with state-of-the art biomechanical testing and histology to quantify regional heterogeneities for the first time and we used a computational model of arterial growth and remodeling to test multiple hypotheses, suggested by the data, regarding the degree of lost elastin, accumulation of glycosaminoglycans, and rates of collagen turnover. We found that standard histopathological findings can be misleading, while combining advanced experimental and computational methods revealed that glycosaminoglycan accumulation is pathologic, not adaptive, and that heightened collagen deposition is ineffective if not cross-linked. In conclusion, loss of elastic fiber integrity can be a strong initiator of aortic aneurysms, but it is the rate and effectiveness of fibrillar collagen remodeling that dictates enlargement. STATEMENT OF SIGNIFICANCE: Precise mechanisms by which abdominal aortic aneurysms enlarge remain unclear, but a recent elastase plus β-aminopropionitrile mouse model provides new insight into disease progression. As in the human condition, the aortic degeneration and adverse remodeling are highly heterogeneous in this model. Our multi-modality experiments quantify and contrast the heterogeneities in geometry and biomaterial properties, and our computational modeling shows that standard histopathology can be misleading. Neither accumulating glycosaminoglycans nor frustrated collagen synthesis slow disease progression, thus highlighting the importance of stimulating adaptive collagen remodeling to limit lesion enlargement.

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.

Developmental origins of mechanical homeostasis in the aorta

BACKGROUND

Mechanical homeostasis promotes proper aortic structure and function. Pathological conditions may arise, in part, from compromised or lost homeostasis. There is thus a need to quantify the homeostatic state and when it emerges. Here we quantify changes in mechanical loading, geometry, structure, and function of the murine aorta from the late prenatal period into maturity.

RESULTS

Our data suggest that a homeostatic set-point is established by postnatal day P2 for the flow-induced shear stress experienced by endothelial cells; this value deviates from its set-point from P10 to P21 due to asynchronous changes in mechanical loading (flow, pressure) and geometry (radius, wall thickness), but is restored thereafter consistent with homeostasis. Smooth muscle contractility also decreases during this period of heightened matrix deposition but is also restored in maturity. The pressure-induced mechanical stress experienced by intramural cells initially remains low despite increasing blood pressure, and then increases while extracellular matrix accumulates.

CONCLUSIONS

These findings suggest that cell-level mechanical homeostasis emerges soon after birth to allow mechanosensitive cells to guide aortic development, with deposition of matrix after P2 increasingly stress shielding intramural cells. The associated tissue-level set-points that emerge for intramural stress can be used to assess and model the aorta that matures biomechanically by P56.

Aortic aneurysms and dissections: Unmet needs from physicians and engineers perspectives

The treatment of aortic disease is complex, requiring cardiothoracic and vascular surgeons to make pre-, post- and intraoperative decisions directly influencing patient survival and well-being. Despite tremendous advancement in vascular surgery and endovascular techniques in the last two decades, along with the abundance of research in the field, many unmet needs and unanswered questions remain. Tight collaboration between engineers and physicians is a keystone in translating new tools, techniques, and devices into practice. Here, we have gathered our perspective, as physicians and engineers, in several pressing issues associated with the diagnosis and treatment of aortic aneurysms and dissection, referring to the current knowledge and practice, signifying unmet needs as well as future directions.