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

## TL;DR

This paper introduces and analyzes new multi-species phase-field models for tumor growth and ECM invasion, incorporating local and nonlocal effects, with proofs of solution existence and numerical experiments illustrating key biological processes.

## Contribution

The paper develops and rigorously analyzes novel multi-species phase-field models for tumor invasion, including proofs of solution existence and numerical simulations of biological effects.

## Key findings

- Cell mobility and proliferation significantly influence ECM degradation.
- Necrosis and hypoxia impact MDE production and tumor invasion.
- Numerical results highlight the roles of various biological effects in tumor progression.

## 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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Source: https://tomesphere.com/paper/1906.07788