@article{fritz2020analysis,
title = {Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network},
journal = {Nonlinear Analysis: Real World Applications},
volume = {61},
pages = {103331},
year = {2021},
issn = {1468-1218},
doi = {10.1016/j.nonrwa.2021.103331},
url = {https://www.sciencedirect.com/science/article/pii/S1468121821000432},
author = {Marvin Fritz and Prashant K. Jha and Tobias Köppl and J. Tinsley Oden and Barbara Wohlmuth},
keywords = {Tumor growth, 3D–1D coupled blood flow models, ECM degradation, Existence of weak solutions, Energy inequality, Galerkin method},
abstract = {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.}
}