Multiphase modeling and qualitative analysis of the growth of tumor cords

TL;DR

This paper develops a macroscopic multiphase model for tumor cord growth using deformable porous media theory, analyzing tumor and host tissue interactions and providing numerical simulations and qualitative insights.

Contribution

It introduces a novel two-phase PDE model for tumor growth considering nutrient dynamics and tissue interactions, with qualitative analysis and simulations.

Findings

Model captures tumor growth dynamics near blood vessels

Nutrient levels influence proliferation and death of tumor cells

Qualitative analysis provides insights into tumor development mechanisms

Abstract

In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular matrix, that occupies a spatial region close to a blood vessel whence cells get the nutrient needed for their vital functions. Growth of tumor cells takes place within a healthy host tissue, which is in turn modeled as a saturated mixture of non-proliferating cells. Interactions between these two regions are accounted for as an essential mechanism for the growth of the tumor mass. By weakening the role of the extracellular matrix, which is regarded as a rigid non-remodeling scaffold, a system of two partial differential equations is derived, describing the evolution of the cell volume ratio coupled to the dynamics of the nutrient, whose higher and lower concentration levels determine proliferation or death of tumor cells, respectively. Numerical simulations of a reference two-dimensional problem are shown and commented, and a qualitative mathematical analysis of some of its key issues is proposed.