Simulation of tumor induced angiogenesis using an analytical adaptive modeling including dynamic sprouting and blood flow modeling

•An adaptive model of tumor induced angiogenesis process considering dynamic sprouting and blood flow is developed.•An adaptive sprout spacing model (ASS) determines position, time and number of sprouts activated from the parent vessel.•The developed vascular network is modified by a novel sprout branching prediction algorithm.•The model considers time delays between sprout progressions and the number of sprouts activated at different time.•The model provides information about micro-vessel density in the network and could be useful in drug delivery and treatment.

In this paper, an adaptive model for tumor induced angiogenesis is developed that integrates generation and diffusion of a growth factor originated from hypoxic cells, adaptive sprouting from a parent vessel, blood flow and structural adaptation. The proposed adaptive sprout spacing model (ASS) determines position, time and number of sprouts which are activated from a parent vessel and also the developed vascular network is modified by a novel sprout branching prediction algorithm. This algorithm couples local vascular endothelial growth factor (VEGF) concentrations, stresses due to the blood flow and stochastic branching to the structural reactions of each vessel segment in response to mechanical and biochemical stimuli. The results provide predictions for the time-dependent development of the network structure, including the position and diameters of each segment and the resulting distributions of blood flow and VEGF. Considering time delays between sprout progressions and number of sprouts activated at different time durations provides information about micro-vessel density in the network. Resulting insights could be useful for motivating experimental investigations of vascular pattern in tumor induced angiogenesis and development of therapies targeting angiogenesis.