Theoretical simulation of angiogenesis and structural adaptation in microvascular networks

Abstract

A theoretical model is presented for simulating growth, structural adaptation and pruning of microvascular networks. The network is described as a set of interconnected segments. Blood flow is simulated using a hemodynamic model. Diffusion of oxygen and a growth factor in the extravascular space is simulated. Vessels are assumed to undergo structural diameter change, including pruning, in response to hemodynamic and metabolic signals, and angiogenesis is governed by growth factor levels. The model shows that over‐abundant stochastic angiogenesis occurring in parallel with refinement of the network by structural adaptation and pruning can generate networks that provide efficient convective transport over large distances, together with dense space‐filling meshes for short diffusion distances to every point in the tissue. Angiogenesis in response to a growth factor produced in hypoxic regions, and structural adaptation in response to both local and upstream propagated signals, are essential components of the model. This approach gives a framework for understanding vascular network formation in normal and pathological conditions and for predicting effects of therapies targeting angiogenesis. Supported by NIH grants HL034555 and CA40355.