  In this work, we present and analyze a mathematical model for tumor growth
incorporating ECM erosion, interstitial flow, and the effect of vascular flow
and nutrient transport. The model is of phase-field or diffused-interface type
in which multiple phases of cell species and other constituents are separated
by smooth evolving interfaces. The model involves a mesoscale version of
Darcy's law to capture the flow mechanism in the tissue matrix. Modeling flow
and transport processes in the vasculature supplying the healthy and cancerous
tissue, one-dimensional (1D) equations are considered. Since the models
governing the transport and flow processes are defined together with cell
species models on a three-dimensional (3D) domain, we obtain a 3D-1D coupled
model. We show some mathematical results on the existence of weak solutions.
Furthermore, simulation results are presented illustrating the evolution of
tumors and the effects of ECM erosion.
