Modeling blood vessel growth and leukocyte extravasation in ischemic injury: an integrated agent-based and finite element analysis approach

Abstract

Background: Recovery from an ischemic insult is a major component of many acute diseases including stroke and myocardial infarctions. Here, we apply 2 computational techniques— agent-based modeling (ABM) and finite element analysis (FEA)— to study the interactions between circulating inflammatory cells and changing blood flow profiles, both key components of ischemic injury. Agent-based modeling defines tissues as a collection of agents representing individual cells. Finite element analysis is a numerical-methods approach that approximates solutions to continuum problems definable by partial differential equations and provides the solutions at discretized nodes and elements. It is ideally suited for calculation of mechanical forces and flow profiles within a vascular network. Objectives: We sought to develop a computational model that will increase our understanding of inflammatory cell trafficking (circulation, margination, adhesion, arrest, and cross-endothelium extravasation) in response to ischemic injury. To accurately capture this physiological process with computational modeling, it is necessary to include both cellular processes, which are included within the ABM framework, and fluid mechanical forces (eg, shear stress, pressure, blood flow), which are modeled by the FEA simulation. This model will enable the generation and testing of multiple hypotheses, which will better direct basic science research. Methods: We developed a computational framework, termed FEABM , that integrates NetLogo, a freely available ABM platform, with a MatLab implementation of the FEA. Microvascular network architectures and their anatomical parameters (vessel diameter and length) were obtained from intravital microscopy images of thin in vivo rat and mice tissues, such as the spinotrapezius muscle. These measurements were input directly into the FEABM computational framework. Simulated vessels in the ABM component of the framework infer their hemodynamic properties (blood flow rates and hydrostatic blood pressure) from the FEA, which is based on the method of Pries and Secomb to calculate flow velocity, shear stress, and pressure throughout the network while taking into account the Fahraeus-Lindquist effect (changes in apparent blood viscosity with vessel diameter). The results from this automated process then direct blood flow through the simulated microvascular network, as well as govern the behaviors of circulating cells and surface adhesion molecule expression. To this framework, we added an initial literature-based rule set to govern circulating cell interactions with the endothelium and extravasated cell interactions with the tissue environment. This rule set includes protein expression levels, ligand/receptor affinity, mechanical force sensitivity, and cellular migration rates. The spatial and temporal profile of inflammatory cell behavior, including circulation through the microvasculature, adhesion to the endothelium, arrest and transmigration through the vessel, and migration in the interstitial tissue space, is predicted for monocytes/ macrophages in the ischemic tissue. Results: We successfully developed an agent-based NetLogo model coupled with a finite element–based MatLab model to aid in the study of inflammatory cell trafficking after ischemic injury. With the addition of a literature-based rule set, we are able to capture and quantify tissue level properties involved in inflammation, including leukocyte capture, adhesion, and extravasation. Conclusions: This fully integrated NetLogo (Northwestern University, eel.northwestern.edu/netlogo/) ABM, which is capable of continuous updates from an FEA implemented in MatLab (The Math Works, Natick, MA), will allow the evaluation of hypotheses relating to the participation of circulating inflammatory cells during ischemic injury.