A mathematical framework for modelling the metastatic spread of cancer

Abstract

Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network (tumour-induced angiogenesis), they can spread to distant secondary sites in the body. This process, known as metastatic spread, is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer.\n\nTo shed light on the metastatic process, we present a mathematical modelling framework that captures for the first time the interconnected processes of invasion and metastatic spread of individual cancer cells in a spatially explicit manner -- a multi-grid, hybrid, individual-based approach. This framework accounts for the spatio-temporal evolution of mesenchymal- and epithelial-like cancer cells, as well as MT1-MMP and MMP-2 dynamics, and interactions with the extracellular matrix.\n\nUsing computational simulations, we demonstrate that our model captures all the key steps of the invasion-metastasis cascade, i.e. invasion by both heterogeneous cancer cell clusters and by single mesenchymal-like cancer cells; intravasation of these clusters and single cells both via active mechanisms mediated by matrix degrading enzymes (MDEs) and via passive shedding; circulation of cancer cell clusters and single cancer cells in the vasculature with the associated risk of cell death and disaggregation of clusters; extravasation of clusters and single cells; and metastatic growth at distant secondary sites in the body. By faithfully reproducing experimental results, our simulations support the evidence-based hypothesis that the membrane-bound MT1-MMP is the main driver of invasive spread rather than diffusible MDEs like MMP-2.