Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

TL;DR

This paper introduces a coupled 3D-1D mathematical model for tumor growth that integrates phase-field methods, ECM erosion, interstitial and vascular flow, and nutrient transport, providing insights into tumor evolution.

Contribution

The work develops a novel 3D-1D coupled model combining phase-field tumor modeling with vascular flow and nutrient transport, along with mathematical analysis of solution existence.

Findings

Simulation shows tumor evolution and ECM erosion effects.

Model captures complex flow and transport in tumor microenvironment.

Mathematical proof of weak solution existence.

Abstract

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy's law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D-1D coupled model. We show some mathematical results on the existence of weak solutions. Furthermore, simulation results are presented illustrating the evolution of tumors and the effects of ECM erosion.