A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix

TL;DR

This paper models the transition between differentiated cancer cells and cancer stem cells via EMT, and studies how this transition influences tumor invasion into the extracellular matrix through mathematical and numerical methods.

Contribution

It introduces a novel mathematical model combining algebraic-elliptic and Keller-Segel type systems to analyze EMT-driven cancer cell transition and invasion.

Findings

Model captures EMT transition dynamics

Numerical simulations illustrate invasion patterns

Provides insights into cancer progression mechanisms

Abstract

Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are termed Cancer Stem Cells (CSCs}, and as opposed to the more usual Differentiated Cancer Cells (DCCs), they exhibit higher motility, they are more resilient to therapy, and are able to metastasize to secondary locations within the organism and produce new tumours. The origin of the CSCs is not completely clear; they seem to stem from the DCCs via a transition process related to the Epithelial-Mesenchymal Transition (EMT) that can also be found in normal tissue. In the current work we model and numerically study the transition between these two types of cancer cells, and the resulting "ensemble" invasion of the extracellular matrix. This leads to the derivation and numerical simulation of two systems: an algebraic-elliptic system for the transition and an advection-reaction-diffusion system of Keller-Segel taxis type for the invasion.