Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network. (October 2021)

• Record Type: Journal Article
• Authors: Fritz, Marvin; Jha, Prashant K.; Köppl, Tobias; Oden, J. Tinsley; Wohlmuth, Barbara
• Is Part Of: Nonlinear analysis. Volume 61(2021)
• Publication Date: 2021-10
• Subjects: Tumor growth -- 3D–1D coupled blood flow models -- ECM degradation -- Existence of weak solutions -- Energy inequality -- Galerkin method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103331
• Languages: English
• ISSNs: 1468-1218

Abstract

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.