Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation

Abstract

We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and hypoxic cells), necrotic cells, and the evolution of MDE and ECM, together with chemotaxis, haptotaxis, apoptosis, nutrient distribution, and cell-to-matrix adhesion. We provide a rigorous proof of the existence of solutions of the coupled system with gradient-based and adhesion-based haptotaxis effects. In addition, we discuss finite element discretizations of the model, and we present the results of numerical experiments designed to show the relative importance and roles of various effects, including cell mobility, proliferation, necrosis, hypoxia, and nutrient concentration on the generation of MDEs and the degradation of the ECM.

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• On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport
• Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis
• Nonlocal Cahn-Hilliard-Hele-Shaw systems with singular potential and degenerate mobility
• Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis
• Well-posedness analysis of the Cahn-Hilliard-Biot model
• Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility
• Analysis and structure-preserving approximation of a Cahn-Hilliard-Forchheimer system with solution-dependent mass and volume source