An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model

The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The pre-existing vasculature is modeled as a one-dimensional inclusion and embedded into the three-dimensional tissue through a suitable coupling method, which allows for non-matching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology and flow patterns in the neovasculature which are challenging and computationally expensive to resolve with a discrete, one-dimensional angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, one-dimensional representation of the pre-existing vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the Thermodynamically Constrained Averaging Theory. The new model enables us to study mass transport from the pre-existing vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically.