Computational modeling of flow-mediated angiogenesis: Stokes–Darcy flow on a growing vessel network

Tumor angiogenesis, the growth of new blood vessels towards a tumor, plays a critical role in cancer progression. Tumors release tumor angiogenic factors (TAF) that trigger angiogenesis upon reaching a pre-existing capillary. Although not frequently studied, the convective transport of TAF plays a key role in determining the resulting shape of the vasculature. In this work, we propose a computational method that couples an angiogenesis model with Stokes–Darcy flow to simulate the impact of flow on angiogenesis. We use the phase-field method to implicitly describe the vasculature and capture the temporally evolving interface between the intra- and extravascular flow. The implicit description of the interface eliminates the need to re-mesh the vasculature which would otherwise be required due to the movement of the interface. We propose a finite-element discretization to solve the coupled problem and illustrate the accuracy of the algorithm by comparing a numerical solution with a manufactured test case in a simplified scenario. The numerical simulations demonstrate the impact of the convective transport of TAF on the shape of the vasculature. It predicts that the vasculature network grows prominently against the flow direction and that the growth of vasculature is enhanced with increasing interstitial flow magnitude.