Simulation of vessel morphogenesis using cellular automata

A Cellular Automaton Model of Early Tumor Growth and Invasion: The Effects of Native Tissue Vascularity and Increased Anaerobic Tumor Metabolism

“…Chaplain & Anderson (1996) and Anderson & Chaplain (1998) have used cellular automata to solve the discrete version of a system of nonlinear partial di!erential equations which describe the response in space and time of endothelial cells to tumor angiogenesis factor and "bronectin, including migration, proliferation, anastomosis and branching. The broader topic of vessel morphogenesis has been investigated by Markus et al (1999) using cellular automata to model the development of leaf veins, insect trachea and tumor neovascularization.…”

Network Systems Modelled by Complex Cellular Automata Paradigm

“…• biological processes: tissue growth Wang et al (2008), angiogenesis Markus et al (1999), cancer development Reis et al (2009) etc.…”

Harnessing Systems Biology Approaches to Engineer Functional Microvascular Networks

“…A decade ago, Markus et al developed a CA model of vessel morphogenesis that describes leaf vein patterning based on rules for branching, chemotaxis, anastomosis, and tip death. 25 By adding an angiogenic gradient to their basic model, the authors showed a proof of concept that the CA could be applied to blood vessel growth; however, model revision and validation were not completed. Peirce et al developed one of the first biological agent-based models to predict microvascular network patterning from a rule set based on epigenetic stimuli, molecular signals (PDGF-BB VEGF, TGF-b), and cellular behaviors (proliferation, migration, and differentiation).…”