On a nonlinear model for tumor growth with drug application

TL;DR

This paper develops a comprehensive nonlinear model for tumor growth incorporating multiple cell states, nutrient and drug diffusion, and domain evolution, providing global solutions without symmetry constraints.

Contribution

It introduces a multi-phase flow model for tumor growth with drug application, establishing global weak solutions for general initial data and domain evolution.

Findings

Existence of global-in-time weak solutions

Model captures complex tumor dynamics with multiple cell types

No symmetry assumptions required

Abstract

We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The system is given by a multi-phase flow model: the densities of the different cells are governed by a set of transport equations, the density of the nutrient and the density of the drug are governed by rather general diffusion equations, while the velocity of the tumor is given by Brinkman's equation. The domain occupied by the tumor in this setting is a growing continuum $\Omega$ with boundary $\partial \Omega$ both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation. Both the solutions and the domain are rather general, no symmetry assumption is required and the result holds for large initial data. This article is part of a research program whose aim is the investigation of the effect of drug application in tumor growth.