  In this work, we present a coupled 3D-1D model of solid tumor growth within a
dynamically changing vascular network to facilitate realistic simulations of
angiogenesis. Additionally, the model includes erosion of the extracellular
matrix, interstitial flow, and coupled flow in blood 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 factors (TAFs);
blood vessels grow towards the increasing TAFs concentrations. This process is
not deterministic, allowing random growth of blood vessels and, therefore, due
to the coupling of nutrients in tissue and vessels, makes the growth of tumors
stochastic. 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.
