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The ability to locally degrade the extracellular matrix (ECM) and interactwith the tumour microenvironment is a key process distinguishing cancer fromnormal cells, and is a critical step in the metastatic spread of the tumour.The invasion of the surrounding tissue involves the coordinated action betweencancer cells, the ECM, the matrix degrading enzymes, and theepithelial-to-mesenchymal transition (EMT). This is a regulatory processthrough which epithelial cells (ECs) acquire mesenchymal characteristics andtransform to mesenchymal-like cells (MCs). In this paper, we present a newmathematical model which describes the transition from a collective invasionstrategy for the ECs to an individual invasion strategy for the MCs. We achievethis by formulating a coupled hybrid system consisting of partial andstochastic differential equations that describe the evolution of the ECs andthe MCs, respectively. This approach allows one to reproduce in a very naturalway fundamental qualitative features of the current biomedical understanding ofcancer invasion that are not easily captured by classical modelling approaches,for example, the invasion of the ECM by self-generated gradients and theappearance of EC invasion islands outside of the main body of the tumour.

A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix