Mathematical Modelings for Angiogenesis - A Cellular Automaton Model and its Continuous Model
Cellular Automata and Lattice Gases
2015-07-22 v2 Cell Behavior
Abstract
Based on recent experiments with time-lapse fluorescent imaging, we propose a cellular automaton model for the dynamics of vascular endothelial cells (ECs) in angiogenic morphogenesis. The model successfully reproduces cell mixing behavior, elongation and bifurcation of blood vessels. The results suggest that the two-body interaction between ECs, which is repulsive in short distance and become attractive in moderately long distance, is essential to the dynamics of ECs, in particular, to the cell mixing behavior. The corresponding analytically solvable differential equation model is also proposed.
Cite
@article{arxiv.1501.05406,
title = {Mathematical Modelings for Angiogenesis - A Cellular Automaton Model and its Continuous Model},
author = {Keisuke Matsuya and Hiroki Kurihara and Tetsuji Tokihiro},
journal= {arXiv preprint arXiv:1501.05406},
year = {2015}
}
Comments
This paper has been withdrawn by the authors, since they intend to refine this paper and to add other contents