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, 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 . To 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 multigrid, hybrid, individual-based approach. This framework accounts for the spatiotemporal evolution of mesenchymal- and epithelial-like cancer cells, membrane-type-1 matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase-2 (MMP-2), and for their interactions with the extracellular matrix. Using 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 such as MMP-2.

Discrete and continuum phenotype-structured models for the evolution of cancer cell populations under chemotherapy

“…An additional development of this study would be to include a spatial structure, for instance by embedding the cancer cells in the geometry of a solid tumour, and to take explicitly into account the effect of spatial interactions between cancer cells, therapeutic agents and other abiotic factors, such as oxygen and glucose [54,55]. In this case, the resulting individual-based model would be integrated with a system of PDEs modelling the dynamics of the abiotic factors, thus leading to a hybrid model [4,9,10,15,16,31,34,40,48,75,76]. These are all lines of research that we will be pursuing in the near future.…”

The role of mechanical interactions in EMT

“…In contrast, for wound healing we may prefer cell-detachment driven by EMT and more proliferation to encourage the wound to heal faster. It will be useful to explore these ideas by extending this model to track individual cells or clusters of cells [19] that detach from the tissue in a two-regime model [45] or multi-organ model [46,47], and incorporating mesenchymal-epithelial transitions (MET) [48,49,50].…”

Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue: The effects of fibre and vascular structure

“…Due to the realistic simulations they offer, IB models are now used widely within mathematical oncology and in many other areas of biomedical systems research. Here we focus particularly on a model of solid tumour growth but other researchers have used and are using IB models to look at tumour-immune interactions (e.g., [35,28,29,30]), invasion (e.g., [1,46,39]) and metastatic spread (e.g., [2,19]). Our model is a force-based (centre-based) lattice-free model, and much pioneering work in this area has been carried out by Drasdo and colleagues (see, e.g., [13,21,14,38]).…”