2018/05/26 by Nikolaos Sfakianakis, Anotida Madzvamuse, Sfakianakis, Nikolaos +3 · 1 citation
Mathematics · Medicine · Biochemistry, Genetics and Molecular Biology · #Mathematical Biology Tumor Growth #Cancer Cells and Metastasis #Cellular Mechanics and Interactions
paper · pdf · doi:10.48550/arxiv.1805.10541
The ability to locally degrade the extracellular matrix (ECM) and interact\nwith the tumour microenvironment is a key process distinguishing cancer from\nnormal cells, and is a critical step in the metastatic spread of the tumour.\nThe invasion of the surrounding tissue involves the coordinated action between\ncancer cells, the ECM, the matrix degrading enzymes, and the\nepithelial-to-mesenchymal transition (EMT). This is a regulatory process\nthrough which epithelial cells (ECs) acquire mesenchymal characteristics and\ntransform to mesenchymal-like cells (MCs). In this paper, we present a new\nmathematical model which describes the transition from a collective invasion\nstrategy for the ECs to an individual invasion strategy for the MCs. We achieve\nthis by formulating a coupled hybrid system consisting of partial and\nstochastic differential equations that describe the evolution of the ECs and\nthe MCs, respectively. This approach allows one to reproduce in a very natural\nway fundamental qualitative features of the current biomedical understanding of\ncancer invasion that are not easily captured by classical modelling approaches,\nfor example, the invasion of the ECM by self-generated gradients and the\nappearance of EC invasion islands outside of the main body of the tumour.\n