A Multiscale Computational Framework to Understand Vascular Adaptation

Fully coupled hybrid in-silico modeling of atherosclerosis: A multi-scale framework integrating CFD, transport phenomena and agent-based modeling

Introduction: Atherosclerosis is a complex disease influenced by biological and mechanical factors, leading to plaque formation within arterial walls. Understanding the interplay between hemodynamics, cellular interactions, and biochemical transport is crucial for predicting disease progression and evaluating therapeutic strategies. Methods: We developed a hybrid in-silico model integrating computational fluid dynamics (CFD), mass transport, and agent-based modeling to simulate plaque progression in coronary arteries. The model incorporates key factors such as wall shear stress (WSS), low-density lipoprotein (LDL) filtration, and the interaction between smooth muscle cells (SMCs), cytokines, and extracellular matrix (ECM). Results: Our simulations demonstrate that the integration of CFD, transport phenomena, and agent-based modeling provides a comprehensive framework for predicting atherosclerotic plaque growth. The model successfully captures the mechanobiological interactions driving plaque development and suggests potential mechanisms underlying lesion progression. Discussion: The proposed methodology establishes a foundation for developing computational platforms to test therapeutic interventions, such as anti-inflammatory drugs and lipid-lowering agents, under patient-specific conditions. These findings highlight the potential of hybrid multi-scale in-silico models to advance the understanding of atherosclerosis and support the development of personalized treatment strategies.

An agent-based model of cardiac allograft vasculopathy: toward a better understanding of chronic rejection dynamics

Cardiac allograft vasculopathy (CAV) is a coronary artery disease affecting 50% of heart transplant (HTx) recipients, and it is the major cause of graft loss. CAV is driven by the interplay of immunological and non-immunological factors, setting off a cascade of events promoting endothelial damage and vascular dysfunction. The etiology and evolution of tissue pathology are largely unknown, making disease management challenging. So far, in vivo models, mostly mouse-based, have been widely used to study CAV, but they are resource-consuming, pose many ethical issues, and allow limited investigation of time points and important biomechanical measurements. Recently, agent-based models (ABMs) proved to be valid computational tools for deciphering mechanobiological mechanisms driving vascular adaptation processes at the cell/tissue level, augmenting cost-effective in vivo lab-based experiments, at the same time guaranteeing richness in observation time points and low consumption of resources. We hypothesize that integrating ABMs with lab-based experiments can aid in vivo research by overcoming those limitations. Accordingly, this work proposes a bidimensional ABM of CAV in a mouse coronary artery cross-section, simulating the arterial wall response to two distinct stimuli: inflammation and hemodynamic disturbances, the latter considered in terms of low wall shear stress (WSS). These stimuli trigger i) inflammatory cell activation and ii) exacerbated vascular cell activities. Moreover, an extensive analysis was performed to investigate the ABM sensitivity to the driving parameters and inputs and gain insights into the ABM working mechanisms. The ABM was able to effectively replicate a 4-week CAV initiation and progression, characterized by lumen area decrease due to progressive intimal thickening in regions exposed to high inflammation and low WSS. Moreover, the parameter and input sensitivity analysis highlighted that the inflammatory-related events rather than the WSS predominantly drive CAV, corroborating the inflammatory nature of the vasculopathy. The proof-of-concept model proposed herein demonstrated its potential in deepening the pathology knowledge and supporting the in vivo analysis of CAV.

Mechanical characterization of human umbilical arteries by thick-walled models: Enhanced vascular compliance by removing an abluminal lining

The decellularized human umbilical artery (HUA) is considered as a promising option for small-diameter, tissue-engineered vascular grafts (TEVGs). Our previous study showed that the HUA bears a thin, watertight lining on its outermost abluminal surface. Removal of this abluminal lining layer improves efficacy of the perfusion-assisted decellularization of the HUA and increases its compliance. As stress across the wall is believed to affect growth and remodeling of the TEVG, it is imperative to mechanically characterize the HUA using thick-walled models. Combining inflation experiments and computational methods, we investigate the mechanical properties of the HUA before and after the abluminal lining removal to examine the HUA's wall mechanics. The inflation tests of five HUAs were performed to obtain the mechanical and geometrical response of the vessel wall before and after the lining layer removal. Using nonlinear hyperelastic models, the same responses are obtained computationally using the thick-walled models. The experimental data are incorporated into the computational models to estimate the mechanical and orientation parameters of the fibers and isotropic matrix of different layers in the HUAs. The parameter fitting of both thick-walled models (before and after the abluminal lining removal) results in most of the R-squared values for measuring the goodness of fitting to be over 0.90 for all samples. The compliance of the HUA increases from a mean value of 2.60% per 100 mmHg before the removal of the lining to a mean value of 4.21% per 100 mmHg after the removal. The results reveal that, although the abluminal lining is thin, it is stiff and capable of supporting majority of the high luminal pressure, and that the inner layer is far less stressed than the abluminal lining. Computational simulations also show that removal of the abluminal lining increases the circumferential wall stress by up to 280 kPa under the in vivo luminal pressure. The integrated computational and experimental approaches provide more accurate estimates of the material behaviors of HUAs employed in grafts and, in turn, the study enhances our understanding of interactions between the graft and the native vessel on vascular growth and remodeling.

Multiscale Modeling of Vascular Remodeling Induced by Wall Shear Stress

Objective

Hemodynamics-induced low wall shear stress (WSS) is one of the critical reasons leading to vascular remodeling. However, the coupling effects of WSS and cellular kinetics have not been clearly modeled. The aim of this study was to establish a multiscale modeling approach to reveal the vascular remodeling behavior under the interaction between the macroscale of WSS loading and the microscale of cell evolution.

Methods

Computational fluid dynamics (CFD) method and agent-based model (ABM), which have significantly different characteristics in temporal and spatial scales, were adopted to establish the multiscale model. The CFD method is for the second/organ scale, and the ABM is for the month/cell scale. The CFD method was used to simulate blood flow in a vessel and obtain the WSS in a vessel cross-section. The simulations of the smooth muscle cell (SMC) proliferation/apoptosis and extracellular matrix (ECM) generation/degradation in a vessel cross-section were performed by using ABM. During the simulation of the vascular remodeling procedure, the damage index of the SMC and ECM was defined as deviation from the obtained WSS. The damage index decreased gradually to mimic the recovery of WSS-induced vessel damage.

Results

(1) The significant wall thickening region was consistent with the low WSS region. (2) There was no evident change of wall thickness in the normal WSS region. (3) When the damage index approached to 0, the amount and distribution of SMCs and ECM achieved a stable state, and the vessel reached vascular homeostasis.

Conclusion

The established multiscale model can be used to simulate the vascular remodeling behavior over time under various WSS conditions.

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

The widespread incidence of cardiovascular diseases and associated mortality and morbidity, along with the advent of powerful computational resources, have fostered an extensive research in computational modeling of vascular pathophysiology field and promoted in-silico models as a support for biomedical research. Given the multiscale nature of biological systems, the integration of phenomena at different spatial and temporal scales has emerged to be essential in capturing mechanobiological mechanisms underlying vascular adaptation processes. In this regard, agent-based models have demonstrated to successfully embed the systems biology principles and capture the emergent behavior of cellular systems under different pathophysiological conditions. Furthermore, through their modular structure, agent-based models are suitable to be integrated with continuum-based models within a multiscale framework that can link the molecular pathways to the cell and tissue levels. This can allow improving existing therapies and/or developing new therapeutic strategies. The present review examines the multiscale computational frameworks of vascular adaptation with an emphasis on the integration of agent-based approaches with continuum models to describe vascular pathophysiology in a systems biology perspective. The state-of-the-art highlights the current gaps and limitations in the field, thus shedding light on new areas to be explored that may become the future research focus. The inclusion of molecular intracellular pathways (e.g., genomics or proteomics) within the multiscale agent-based modeling frameworks will certainly provide a great contribution to the promising personalized medicine. Efforts will be also needed to address the challenges encountered for the verification, uncertainty quantification, calibration and validation of these multiscale frameworks.

Computational modeling for cardiovascular tissue engineering: the importance of including cell behavior in growth and remodeling algorithms

Understanding cardiovascular growth and remodeling (G&R) is fundamental for designing robust cardiovascular tissue engineering strategies, which enable synthetic or biological scaffolds to transform into healthy living tissues after implantation. Computational modeling, particularly when integrated with experimental research, is key for advancing our understanding, predicting the in vivo evolution of engineered tissues, and efficiently optimizing scaffold designs. As cells are ultimately the drivers of G&R and known to change their behavior in response to mechanical cues, increasing efforts are currently undertaken to capture (mechano-mediated) cell behavior in computational models. In this selective review, we highlight some recent examples that are relevant in the context of cardiovascular tissue engineering and discuss the current and future biological and computational challenges for modeling cell-mediated G&R.

Multiscale Computational Analysis of Right Ventricular Mechanoenergetics

Right ventricular (RV) failure, which occurs in the setting of pressure overload, is characterized by abnormalities in mechanical and energetic function. The effects of these cell- and tissue-level changes on organ-level RV function are unknown. The primary aim of this study was to investigate the effects of myofiber mechanics and mitochondrial energetics on organ-level RV function in the context of pressure overload using a multiscale model of the cardiovascular system. The model integrates the mitochondria-generated metabolite concentrations that drive intracellular actin-myosin cross-bridging and extracellular myocardial tissue mechanics in a biventricular heart model coupled with simple lumped parameter circulations. Three types of pressure overload were simulated and compared to experimental results. The computational model was able to capture a wide range of cardiovascular physiology and pathophysiology from mild RV dysfunction to RV failure. Our results confirm that, in response to pressure overload alone, the RV is able to maintain cardiac output (CO) and predict that alterations in either RV active myofiber mechanics or RV metabolite concentrations are necessary to decrease CO.

Multiscale computing for science and engineering in the era of exascale performance

In this position paper, we discuss two relevant topics: (i) generic multiscale computing on emerging exascale high-performing computing environments, and (ii) the scaling of such applications towards the exascale. We will introduce the different phases when developing a multiscale model and simulating it on available computing infrastructure, and argue that we could rely on it both on the conceptual modelling level and also when actually executing the multiscale simulation, and maybe should further develop generic frameworks and software tools to facilitate multiscale computing. Next, we focus on simulating multiscale models on high-end computing resources in the face of emerging exascale performance levels. We will argue that although applications could scale to exascale performance relying on weak scaling and maybe even on strong scaling, there are also clear arguments that such scaling may no longer apply for many applications on these emerging exascale machines and that we need to resort to what we would call multi-scaling. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

A versatile hybrid agent-based, particle and partial differential equations method to analyze vascular adaptation

Peripheral arterial occlusive disease is a chronic pathology affecting at least 8–12 million people in the USA, typically treated with a vein graft bypass or through the deployment of a stent in order to restore the physiological circulation. Failure of peripheral endovascular interventions occurs at the intersection of vascular biology, biomechanics, and clinical decision making. It is our hypothesis that the majority of endovascular treatment approaches share the same driving mechanisms and that a deep understanding of the adaptation process is pivotal in order to improve the current outcome of the procedure. The postsurgical adaptation of vein graft bypasses offers the perfect example of how the balance between intimal hyperplasia and wall remodeling determines the failure or the success of the intervention. Accordingly, this work presents a versatile computational model able to capture the feedback loop that describes the interaction between events at cellular/tissue level and mechano-environmental conditions. The work here presented is a generalization and an improvement of a previous work by our group of investigators, where an agent-based model uses a cellular automata principle on a fixed hexagonal grid to reproduce the leading events of the graft’s restenosis. The new hybrid model here presented allows a more realistic simulation both of the biological laws that drive the cellular behavior and of the active role of the membranes that separate the various layers of the vein. The novel feature is to use an immersed boundary implementation of a highly viscous flow to represent SMC motility and matrix reorganization in response to graft adaptation. Our implementation is modular, and this makes us able to choose the right compromise between closeness to the physiological reality and complexity of the model. The focus of this paper is to offer a new modular implementation that combines the best features of an agent-based model, continuum mechanics, and particle-tracking methods to cope with the multiscale nature of the adaptation phenomena. This hybrid method allows us to quickly test various hypotheses with a particular attention to cellular motility, a process that we demonstrated should be driven by mechanical homeostasis in order to maintain the right balance between cells and extracellular matrix in order to reproduce a distribution similar to histological experimental data from vein grafts.

Impaired Myofilament Contraction Drives Right Ventricular Failure Secondary to Pressure Overload: Model Simulations, Experimental Validation, and Treatment Predictions

Introduction: Pulmonary hypertension (PH) causes pressure overload leading to right ventricular failure (RVF). Myocardial structure and myocyte mechanics are altered in RVF but the direct impact of these cellular level factors on organ level function remain unclear. A computational model of the cardiovascular system that integrates cellular function into whole organ function has recently been developed. This model is a useful tool for investigating how changes in myocyte structure and mechanics contribute to organ function. We use this model to determine how measured changes in myocyte and myocardial mechanics contribute to RVF at the organ level and predict the impact of myocyte-targeted therapy. Methods: A multiscale computational framework was tuned to model PH due to bleomycin exposure in mice. Pressure overload was modeled by increasing the pulmonary vascular resistance (PVR) and decreasing pulmonary artery compliance (CPA). Myocardial fibrosis and the impairment of myocyte maximum force generation (Fmax) were simulated by increasing the collagen content (↑PVR + ↓CPA + fibrosis) and decreasing Fmax (↑PVR + ↓CPA + fibrosis + ↓Fmax). A61603 (A6), a selective α1A-subtype adrenergic receptor agonist, shown to improve Fmax was simulated to explore targeting myocyte generated Fmax in PH. Results: Increased afterload (RV systolic pressure and arterial elastance) in simulations matched experimental results for bleomycin exposure. Pressure overload alone (↑PVR + ↓CPA) caused decreased RV ejection fraction (EF) similar to experimental findings but preservation of cardiac output (CO). Myocardial fibrosis in the setting of pressure overload (↑PVR + ↓PAC + fibrosis) had minimal impact compared to pressure overload alone. Including impaired myocyte function (↑PVR + ↓PAC + fibrosis + ↓Fmax) reduced CO, similar to experiment, and impaired EF. Simulations predicted that A6 treatment preserves EF and CO despite maintained RV pressure overload. Conclusion: Multiscale computational modeling enabled prediction of the contribution of cellular level changes to whole organ function. Impaired Fmax is a key feature that directly contributes to RVF. Simulations further demonstrate the therapeutic benefit of targeting Fmax, which warrants additional study. Future work should incorporate growth and remodeling into the computational model to enable prediction of the multiscale drivers of the transition from dysfunction to failure.

Vascular Adaptation: Pattern Formation and Cross Validation between an Agent Based Model and a Dynamical System

Myocardial infarction is the global leading cause of mortality (Go et al., 2014). Coronary artery occlusion is its main etiology and it is commonly treated by Coronary Artery Bypass Graft (CABG) surgery (Wilson et al, 2007). The long-term outcome remains unsatisfactory (Benedetto, 2016) as the graft faces the phenomenon of restenosis during the post-surgery, which consists of re-occlusion of the lumen and usually requires secondary intervention even within one year after the initial surgery (Harskamp, 2013). In this work, we propose an extensive study of the restenosis phenomenon by implementing two mathematical models previously developed by our group: a heuristic Dynamical System (DS) (Garbey and Berceli, 2013), and a stochastic Agent Based Model (ABM) (Garbey et al., 2015). With an extensive use of the ABM, we retrieved the pattern formations of the cellular events that mainly lead the restenosis, especially focusing on mitosis in intima, caused by alteration in shear stress, and mitosis in media, fostered by alteration in wall tension. A deep understanding of the elements at the base of the restenosis is indeed crucial in order to improve the final outcome of vein graft bypass. We also turned the ABM closer to the physiological reality by abating its original assumption of circumferential symmetry. This allowed us to finely replicate the trigger event of the restenosis, i.e. the loss of the endothelium in the early stage of the post-surgical follow up (Roubos et al., 1995) and to simulate the encroachment of the lumen in a fashion aligned with histological evidences (Owens et al., 2015). Finally, we cross-validated the two models by creating an accurate matching procedure. In this way we added the degree of accuracy given by the ABM to a simplified model (DS) that can serve as powerful predictive tool for the clinic.

Mechanobiological model of arterial growth and remodeling

A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).

Patient-Specific, Multi-Scale Modeling of Neointimal Hyperplasia in Vein Grafts

Neointimal hyperplasia is amongst the major causes of failure of bypass grafts. The disease progression varies from patient to patient due to a range of different factors. In this paper, a mathematical model will be used to understand neointimal hyperplasia in individual patients, combining information from biological experiments and patient-specific data to analyze some aspects of the disease, particularly with regard to mechanical stimuli due to shear stresses on the vessel wall. By combining a biochemical model of cell growth and a patient-specific computational fluid dynamics analysis of blood flow in the lumen, remodeling of the blood vessel is studied by means of a novel computational framework. The framework was used to analyze two vein graft bypasses from one patient: a femoro-popliteal and a femoro-distal bypass. The remodeling of the vessel wall and analysis of the flow for each case was then compared to clinical data and discussed as a potential tool for a better understanding of the disease. Simulation results from this first computational approach showed an overall agreement on the locations of hyperplasia in these patients and demonstrated the potential of using new integrative modeling tools to understand disease progression.

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.