Analysis of a tumor model as a multicomponent deformable porous medium

TL;DR

This paper introduces a diffuse interface model for tumors as multicomponent deformable porous media, integrating mechanical effects with coupled PDEs for tumor growth, nutrient dynamics, and tissue mechanics, and proves the existence of solutions.

Contribution

It develops a novel coupled PDE framework for tumor modeling that includes mechanical effects and proves the well-posedness of the initial-boundary value problem.

Findings

Model captures tumor and healthy tissue interactions with mechanics.

Mathematically proves existence of solutions for the complex PDE system.

Provides a foundation for further numerical and analytical studies.

Abstract

We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a mechanical equilibrium equation with phase-dependent elasticity coefficients. The resulting PDE system couples two Cahn--Hilliard type equations for the tumor phase and the healthy phase with a PDE linking the evolution of the interstitial fluid to the pressure of the system, a reaction-diffusion type equation for the nutrient proportion, and a quasistatic momentum balance. We prove here that the corresponding initial-boundary value problem has a solution in appropriate function spaces.