Modelling Tumor-induced Angiogenesis: Combination of Stochastic Sprout Spacing and Sprout Progression

Background: Angiogenesis initiated by cancerous cells is the process by which new blood vessels are formed to enhance oxygenation and growth of tumor. Objective: In this paper, we present a new multiscale mathematical model for the formation of a vascular network in tumor angiogenesis process. Methods: Our model couples an improved sprout spacing model as a stochastic mathematical model of sprouting along an existing parent blood vessel, with a mathematical model of sprout progression in the extracellular matrix (ECM) in response to some tumor angiogenic factors (TAFs). We perform simulations of the siting of capillary sprouts on an existing blood vessel using finite difference approximation of the dynamic equations of some angiogenesis activators and inhibitors. Angiogenesis activators are chemicals secreted by hypoxic tumor cells for initiating angiogenesis, and inhibitors of the angiogenesis are chemicals that are produced around every new sprout during tumor angiogenesis to inhibit the formation of further sprouts as a feedback of sprouting in angiogenesis. Moreover, for modelling sprout progression in ECM, we use three equations for the motility of endothelial cells at the tip of the activated sprouts, the consumption of TAF and the production and uptake of Fibronectin by endothelial cells. Results: Coupling these two basic models not only does provide a better time estimation of angiogenesis process, but also it is more compatible with reality. Conclusion: This model can be used to provide basic information for angiogenesis in the related studies. Related simulations can estimate the position and number of sprouts along parent blood vessel during the initial steps of angiogenesis and models the process of sprout progression in ECM until they vascularize a tumor.