Cellular Automata Model of Microvascular Remodeling

Microvascular growth and remodeling in the adult animal involves angiogenesis, arteriogenesis, and regression. Many cellular behaviors, such as proliferation, differentiation, migration, and apoptosis contribute to these processes, and coordination of these events is achieved via combinations of biochemical and biomechanical signals. This study examines patterning changes in subcutaneous microvascular networks induced by focal applications of exogenous vascular endothelial growth factor (VEGF) and models the spatial and temporal growth response using a novel cellular automata (CA) computer simulation. The CA model predicts experimentally-verified changes in spatial vascularity and vessel maturation, or perivascular cell recruitment, in response to the growth factor stimulus. The model also parametrically analyzes how growth factor sequestration by the extracellular matrix (ECM), a phenomenon hypothesized to regulate diffusible growth factor levels, affects network remodeling. PREVIOUS COMPUTATIONAL MODELS VS. THE CELLULAR AUTOMATA APPROACH The development and use of mathematical and computer models for the study of pattern formation in biology has a history over twenty years long [1, 2], and computational models based on a system of field equations have been used to study biological patterning phenomenon ranging from pigmentation patterns in the shells of mollusks [3] to neuronal connections in the developing brain [4]. Recently, computational models of whole cells, such as ECELL [5], have been developed to understand complex metabolic signaling pathways in individual cells. In the field of microvascular remodeling, computational models have been developed and employed to study network pattern changes, and in general, these models consist of systems of equations that describe functional characteristics of the system, such as pressure distributions across a network or growth factor concentrations within an extracellular matrix environment, which are then solved in space and time using analytical and numerical techniques [6-8]. Arterial tree formation has also been modeled using constrained constructive optimization (CCO), in which new terminal segments are successively added at randomly selected locations in the tree while the geometric location of each connection is optimized with respect to intravascular volume [9]. In contrast to probabilistic models, fractal analysis [10] has given rise to diffusion limited aggregation (DLA) models of vascular growth. Here we report on a novel computational model based on cellular automata (CA), an approach which allows pattern evolution through the independent behavior of discrete cells and growth factors. Global boundary conditions and parameters obtained from the literature are applied to the complex system, and the ensuing pattern is a result of individual cell behaviors. We demonstrate the utility of this approach in studying microvascular remodeling, a complex biological patterning phenomenon generated by autonomous cells responding to a statealtering stimulus of exogenous growth factor. By comparing measurements of angiogenesis and vessel maturation obtained experimentally with those predicted by the CA model, we report graphical and numerical agreement between in vivo and in silico remodeling events. We also analyze the role of extracellular matrix material in concentrating growth factor in focal tissue regions and the resultant effect on vascular patterning. METHODS Twelve 250 gram Fischer 344 male rats were implanted with dorsal skin window chambers. Five days later, two 150 μm-diameter alginate microbeads containing VEGF164 (10 μg/ml) and two containing vehicle (PBS) were implanted, one per quadrant, into opposing quadrants of subcutaneous tissue. Light microscope images of stimulated tissue quadrants were acquired prior to bead implantation and 4 and 14 days later. Images were used to obtain functional length measurements of microvascular networks, reflecting the amount of angiogenesis in response to the state-altering stimulus. At each analysis time-point, three animals were sacrificed and their window chamber tissues were harvested, fixed in 4% paraformaldehyde, and immunostained with 1A4-Cy3 smooth muscle α-actin mouse monoclonal antibody. Total lengths of vessels containing perivascular 2003 Summer Bioengineering Conference, June 25-29, Sonesta Beach Resort in Key Biscayne, Florida Starting page #: 0225 cells expressing smooth muscle α-actin were measured to deter the amount of vessel maturation in response to the exogenous stimuli. Using JAVA-based modeling software Netlogo version 1. graphically mapped three digitized in vivo networks onto the in tissue space. Over 1,000 cells were arranged into vessels according to the network maps and assigned the appropriate cell types, smooth muscle α-actin-expressing perivascular cells and endothelial cells. Interstitial precursor cells were also randomly placed i tissue space. Relative cell sizes were scaled to the dimensions of silico tissue space according to published values. Exogenous sources of VEGF were input into the simulated tissues in locations * * mine