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

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.

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.

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

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

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.

A multiphase model of growth factor-regulated atherosclerotic cap formation

Atherosclerosis is characterised by the growth of fatty plaques in the inner artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from adjacent tissue to deposit a collagenous cap over the fatty plaque core. This cap isolates the thrombogenic plaque content from the bloodstream and prevents the clotting cascade that leads to myocardial infarction or stroke. Despite the protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why some caps become stable, while others become vulnerable to rupture. We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to diffusible growth factor signals from the endothelium. Platelet-derived growth factor stimulates SMC migration, proliferation and collagen degradation, while transforming growth factor (TGF)-[Formula: see text] stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using in vivo and in vitro experimental data, reproduces several observations from plaque growth in mice. Numerical and analytical results demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGF-[Formula: see text] in effective cap formation. These findings provide unique insight into the mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque model.

An agent-based model of prostate Cancer bone metastasis progression and response to Radium223

BACKGROUND

Bone metastasis is the most frequent complication in prostate cancer patients and associated outcome remains fatal. Radium223 (Rad223), a bone targeting radioisotope improves overall survival in patients (3.6 months vs. placebo). However, clinical response is often followed by relapse and disease progression, and associated mechanisms of efficacy and resistance are poorly understood. Research efforts to overcome this gap require a substantial investment of time and resources. Computational models, integrated with experimental data, can overcome this limitation and drive research in a more effective fashion.

METHODS

Accordingly, we developed a predictive agent-based model of prostate cancer bone metastasis progression and response to Rad223 as an agile platform to maximize its efficacy. The driving coefficients were calibrated on ad hoc experimental observations retrieved from intravital microscopy and the outcome further validated, in vivo.

RESULTS

In this work we offered a detailed description of our data-integrated computational infrastructure, tested its accuracy and robustness, quantified the uncertainty of its driving coefficients, and showed the role of tumor size and distance from bone on Rad223 efficacy. In silico tumor growth, which is strongly driven by its mitotic character as identified by sensitivity analysis, matched in vivo trend with 98.3% confidence. Tumor size determined efficacy of Rad223, with larger lesions insensitive to therapy, while medium- and micro-sized tumors displayed up to 5.02 and 152.28-fold size decrease compared to control-treated tumors, respectively. Eradication events occurred in 65 ± 2% of cases in micro-tumors only. In addition, Rad223 lost any therapeutic effect, also on micro-tumors, for distances bigger than 400 μm from the bone interface.

CONCLUSIONS

This model has the potential to be further developed to test additional bone targeting agents such as other radiopharmaceuticals or bisphosphonates.

A fully coupled framework for in silico investigation of in-stent restenosis

Finite element analysis (FEA) can be implemented along with Agent-based model (ABM) to investigate the biomechanical and mechanobiological mechanisms of pathophysiological processes. However, traditional ABM-FEA approaches are often partially coupled and lack the feedback responses from biological analysis. To overcome this problem, a fully coupled ABM-FEA framework is developed in this paper by linking the macro-scale and cell-scale modules bi-directionally. Numerical studies of the in-stent restenosis process are conducted using the proposed approach and comparisons are made between the two types of frameworks. A reduction in lumen loss rate, which is possibly caused by the time-varying stresses, is observed in the fully coupled simulations. The re-endothelialisation process is also simulated under different frameworks and the simulation results show strong inhibition of endothelial cells to vascular restenosis. The proposed method is proved to be effective to explain the biomechanical-mechanobiological coupling characteristics of the restenosis problem and can be utilized for stent design and optimization.

A Twofold Usage of an Agent-Based Model of Vascular Adaptation to Design Clinical Experiments

Several computational models of Vein Graft Bypass (VGB) adaptation have been developed in order to improve the surgical outcome and they all share a common property: their accuracy relies on a winning choice of their driving coefficients which are best to be retrieved from experimental data. Since experiments are time-consuming and resources-demanding, the golden standard is to know in advance which measures need to be retrieved on the experimental table and out of how many samples. Accordingly, our goal is to build a computational framework able to pre-design an effective experimental structure to optimize the computational models setup. Our hypothesis is that an Agent-Based Model (ABM) developed by our group is comparable enough to a true set of experiments to be used to generate reliable virtual experimental data. Thanks to a twofold usage of our ABM, we created a filter to be posed before the real experiment in order to drive its optimal design. This work is the natural continuation of a previous study from our group [1], where the attention was posed on simple single-cellular events models. With this new version we focused on more complex models with the purpose of verifying that the complexity of the experimental setup grows proportionally with the accuracy of the model itself.

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.

A Computational Model-Based Framework to Plan Clinical Experiments - an Application to Vascular Adaptation Biology

Several computational models have been developed in order to improve the outcome of Vein Graft Bypasses in response to arterial occlusions and they all share a common property: their accuracy relies on a winning choice of the coefficients' value related to biological functions that drive them. Our goal is to optimize the retrieval of these unknown coefficients on the base of experimental data and accordingly, as biological experiments are noisy in terms of statistical analysis and the models are typically stochastic and complex, this work wants first to elucidate which experimental measurements might be sufficient to retrieve the targeted coefficients and second how many specimens would constitute a good dataset to guarantee a sufficient level of accuracy. Since experiments are often costly and time consuming, the planning stage is critical to the success of the operation and, on the base of this consideration, the present work shows how, thanks to an ad hoc use of a computational model of vascular adaptation, it is possible to estimate in advance the entity and the quantity of resources needed in order to efficiently reproduce the experimental reality.