Modelling of vascular growth processes: A stochastic biophysical approach to embryonic angiogenesis

Abstract

In a computer simulation, growth of a capillary network is driven by a stochastic process on a planar hexagonal grid. Starting at a point source, the probabilities for the formation of new capillary elements depend on local biophysical knowledge. This knowledge is mainly derived from the flow theorem of Hagen–Poiseuille and the diameter exponent Δ. The hexagonal grid is visualized as being supported by a cylinder or a sphere. An arterial tree results from the adaptive diameter augmentation, and is considered to have limited fractal properties. The dimension of its border, and the time course of growth and of blood pressure are compared with biological data from the chorioallantoic membrane (CAM) of incubated chicken eggs. The model is discussed in view of mechanosensitivity and cell–matrix interactions of endothelial cells, and CAM haemodynamics.