Tumour induced angiogenesis as a reinforced random walk: Modelling capillary network formation without endothelial cell proliferation

Tumour angiogenesis is the process whereby a capillary network is formed from a preexisting vasculature in response to tumour secreted growth factors (TAFs). The capillary network is largely composed of migrating endothelial cells (EC) which organise themselves into dendritic structures. In this paper, we model angiogenesis via the theory of reinforced random walks, whereby the chemotactic response of the endothelial cells to TAF and their haptotactic response to the matrix macromolecule fibronectin is accomplished through transition probability rate functions. These functions essentially assign directional probabilities for the movement of endothelial cells. Under a pseudosteady state hypothesis, whereby the TAF and fibronectin gradients are specified a priori, simulations in one, two, and three space dimensions are performed. tic elementary capillary networks are obtained and analysed. In addition, even without EC proliferation, the formation of microloops or anastomoses is observed. The model provides a “bridge” linking microcellular and macrocellular events. As such, it indicates a new step towards understanding tumour angiogenesis and possible mechanisms for its control.