Multiscale Computational Modeling in Vascular Biology: From Molecular Mechanisms to Tissue-Level Structure and Function - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 216

insignificant and significant constituents (the former via classical reaction-diffu-
sion type relations) and stored-energy functions for the structurally significant
constituents. Each of these relations must be formulated based on appropriate
experimental data. For example, data reveal that NO not only causes vasodilatation
(thus affecting the stress-strain behavior), it also affects the synthesis of collagen
(production relation) and inhibits inflammation (which influences the removal
relation).
3.2 Agent Based Modeling and Illustrative
Vascular-Specific Models
Multi-cell biological phenomena, such as the assembly of cells into tissues in
response to environmental cues, can be modeled using either continuum or discrete
approaches. A primary focus of multi-cell modeling has been to quantify how
patterns emerge in tissues and whether they arise from diffusible biochemical
factors, mechanical forces, cell-cell interactions, cell-matrix interactions, or any
combinations thereof. While most continuum-based models approximate indi-
vidual cells as a series of similar units, discrete multi-cell models explicitly rep-
resent individual cells as distinct entities capable of exhibiting individual
behaviors, which provides increased generality. Amongst the different approaches
to discrete cell modeling, the most common are Agent-Based Models (ABMs),
Cellular Potts Models (CPMs) [ 25 ], and statistical models. CPMs generalize an
approach from statistical mechanics called the Ising model, and simulate biolog-
ical cells by mapping them to domains on a lattice. Cell behaviors are described by
effective energies and elastic constraints, and cellular dynamics, such as migration
and cell shape changes, are guided by principles of energy minimization [ 16 , 17 ,
34 , 40 , 70 ]. Statistical approaches, such as Monte Carlo simulations, model bio-
logical cells as discrete objects, and their behaviors are dictated by purely prob-
abilistic rules [ 21 ].
3.2.1 Agent Based Modeling
ABMs represent a computational approach that has been used extensively in the
social sciences and ecology [ 27 ], but only recently has it been employed in bio-
medical research to study multi-cell phenomena such as tumorigenesis [ 71 ],
angiogenesis [ 44 ], inflammation [ 7 ], and arterial wall remodeling in hypertension
[ 58 ]. This technique rests on the idea that local interactions between members of a
population can result in complex higher-level emergent phenomena. The key
components of an ABM include the agents themselves, their behaviors within their
environment (i.e., simulation space), the rules that govern their behaviors, and the
simulation inputs and outputs.