Abstract
Agent-based models (ABMs) represent a novel approach to study and simulate complex mechano chemo-biological responses at the cellular level. Such models have been used to simulate a variety of emergent responses in the vasculature, including angiogenesis and vasculogenesis. Although not used previously to study large vessel adaptations, we submit that ABMs will prove equally useful in such studies when combined with well-established continuum models to form multi-scale models of tissue-level phenomena. In order to couple agent-based and continuum models, however, there is a need to ensure that each model faithfully represents the best data available at the relevant scale and that there is consistency between models under baseline conditions. Toward this end, we describe the development and verification of an ABM of endothelial and smooth muscle cell responses to mechanical stimuli in a large artery. A refined rule-set is proposed based on a broad literature search, a new scoring system for assigning confidence in the rules, and a parameter sensitivity study. To illustrate the utility of these new methods for rule selection, as well as the consistency achieved with continuum-level models, we simulate the behavior of a mouse aorta during homeostasis and in response to both transient and sustained increases in pressure. The simulated responses depend on the altered cellular production of seven key mitogenic, synthetic, and proteolytic biomolecules, which in turn control the turnover of intramural cells and extracellular matrix. These events are responsible for gross changes in vessel wall morphology. This new ABM is shown to be appropriately stable under homeostatic conditions, insensitive to transient elevations in blood pressure, and responsive to increased intramural wall stress in hypertension.
Highlights
Vascular development, homeostasis, adaptation, disease progression, and responses to injury or surgical intervention are governed, in large part, by underlying mechanobiological processes
Continuum mechanical analyses are essential for relating global loads to local metrics such as stress and strain; constrained mixture models (CMMs) of growth and remodeling allow one to prescribe lumped-parameter models of local cell-mediated production and turnover based on altered stresses and strains; agent-based models (ABMs) address discrete cell level activity and production of diverse molecules; molecular level models of both the mechanics and the reaction kinetics permit mechanistic considerations
Some of these models have accounted for mechanical stimuli of cellular protein expression (Peirce et al, 2004; Bailey et al, 2007, 2009) and/or the effects of growth factors on angiogenesis (Peirce et al, 2004), but no ABM had yet coupled mechanosensation with growth factor and protease production to describe structural remodeling of the vascular wall, and no ABM has been combined with mechanical models at higher levels of scale (Peirce et al, 2006; Robertson et al, 2007)
Summary
Homeostasis, adaptation, disease progression, and responses to injury or surgical intervention are governed, in large part, by underlying mechanobiological processes. As more and more is learned about the complex mechanisms at molecular and cellular levels and their manifestations at the tissue level, it is becoming increasingly evident that computational modeling will need to play a greater role in integrating these vast knowledge bases, thereby deepening our understanding of both the vascular biology and the pathophysiology. Toward this end, multi-scale models hold great promise, as they allow details at different spatial and temporal scales to be modeled in the most natural way and to be linked together in computationally efficient ways. Models at each scale should be developed in ways that are most natural, we must begin to anticipate how such models will need to be linked in multi-scale computations to ensure consistency and communication across scales
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