  In this work, we present a coupled 3D-1D model of tumor growth within a
dynamically changing vascular network to facilitate realistic simulations of
angiogenesis. Additionally, the model includes ECM erosion, interstitial flow,
and coupled flow in vessels and tissue. We employ continuum mixture theory with
stochastic Cahn--Hilliard type phase-field models of tumor growth. The
interstitial flow is governed by a mesoscale version of Darcy's law. The flow
in the blood vessels is controlled by Poiseuille flow, and Starling's law is
applied to model the mass transfer in and out of blood vessels. The evolution
of the network of blood vessels is orchestrated by the concentration of the
tumor angiogenesis factor (TAF) by growing towards increasing TAF
concentration. The process is not deterministic, allowing random growth of
blood vessels and, therefore, due to the coupling of nutrients in tissue and
vessels, stochastic tumor growth. We demonstrate the performance of the model
by applying it to a variety of scenarios. Numerical experiments illustrate the
flexibility of the model and its ability to generate satellite tumors.
Simulations of the effects of angiogenesis on tumor growth are presented as
well as sample-independent features of cancer.
