A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix

TL;DR

This paper introduces a coupled hybrid mathematical model combining partial and stochastic differential equations to simulate cancer invasion, capturing key biological features like ECM degradation, cell transition, and invasion patterns.

Contribution

It presents a novel hybrid multiscale model that integrates collective and individual invasion strategies of cancer cells, enhancing understanding of tumor microenvironment interactions.

Findings

Reproduces ECM invasion by self-generated gradients

Models transition from epithelial to mesenchymal cells

Captures invasion islands outside main tumor mass

Abstract

The ability to locally degrade the extracellular matrix (ECM) and interact with the tumour microenvironment is a key process distinguishing cancer from normal cells, and is a critical step in the metastatic spread of the tumour. The invasion of the surrounding tissue involves the coordinated action between cancer cells, the ECM, the matrix degrading enzymes, and the epithelial-to-mesenchymal transition (EMT). This is a regulatory process through which epithelial cells (ECs) acquire mesenchymal characteristics and transform to mesenchymal-like cells (MCs). In this paper, we present a new mathematical model which describes the transition from a collective invasion strategy for the ECs to an individual invasion strategy for the MCs. We achieve this by formulating a coupled hybrid system consisting of partial and stochastic differential equations that describe the evolution of the ECs and the MCs, respectively. This approach allows one to reproduce in a very natural way fundamental qualitative features of the current biomedical understanding of cancer invasion that are not easily captured by classical modelling approaches, for example, the invasion of the ECM by self-generated gradients and the appearance of EC invasion islands outside of the main body of the tumour.