A convergent explicit finite difference scheme for a mechanical model for tumor growth

TL;DR

This paper introduces a convergent explicit finite difference scheme for a multi-phase flow mechanical model of tumor growth, enabling accurate numerical simulations of tumor dynamics based on imaging data.

Contribution

It presents a novel finite difference scheme that guarantees convergence to weak solutions for a complex tumor growth model involving transport and flow equations.

Findings

The scheme converges to a weak solution.

The method is computationally efficient.

It provides a reliable tool for tumor growth simulation.

Abstract

Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of a mechanical model for tumor growth and the analysis of its dynamics. The system under investigation is given by a multi-phase flow model: The densities of the different cells are governed by a transport equation for the evolution of tumor cells, whereas the velocity field is given by a Brinkman regularization of the classical Darcy's law. An efficient finite difference scheme is proposed and shown to converge to a weak solution of the system. Our approach relies on convergence and compactness arguments in the spirit of Lions (Mathematical Topics in Fluid Dynamics, 1998).