Directionality of Macrophages Movement in Tumour Invasion: A Multiscale Moving-Boundary Approach
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Directionality of Macrophages Movement in Tumour Invasion: A Multiscale Moving-Boundary Approach Szabolcs Suveges1 · Raluca Eftimie1 · Dumitru Trucu1 Received: 4 February 2020 / Accepted: 7 October 2020 / Published online: 19 November 2020 © The Author(s) 2020
Abstract Invasion of the surrounding tissue is one of the recognised hallmarks of cancer (Hanahan and Weinberg in Cell 100: 57–70, 2000. https://doi.org/10.1016/S00928674(00)81683-9), which is accomplished through a complex heterotypic multiscale dynamics involving tissue-scale random and directed movement of the population of both cancer cells and other accompanying cells (including here, the family of tumour-associated macrophages) as well as the emerging cell-scale activity of both the matrix-degrading enzymes and the rearrangement of the cell-scale constituents of the extracellular matrix (ECM) fibres. The involved processes include not only the presence of cell proliferation and cell adhesion (to other cells and to the extracellular matrix), but also the secretion of matrix-degrading enzymes. This is as a result of cancer cells as well as macrophages, which are one of the most abundant types of immune cells in the tumour micro-environment. In large tumours, these tumourassociated macrophages (TAMs) have a tumour-promoting phenotype, contributing to tumour proliferation and spread. In this paper, we extend a previous multiscale moving-boundary mathematical model for cancer invasion, by considering also the multiscale effects of TAMs, with special focus on the influence that their directional movement exerts on the overall tumour progression. Numerical investigation of this new model shows the importance of the interactions between pro-tumour TAMs and the fibrous ECM, highlighting the impact of the fibres on the spatial structure of solid tumour. Keywords Cancer invasion · Macrophages · Multiscale modelling · Computational modelling · Cell adhesion · Flux limiter · Convolution
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Dumitru Trucu [email protected] Szabolcs Suveges [email protected] Raluca Eftimie [email protected]
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Division of Mathematics, University of Dundee, Dundee DD1 4HN, UK
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1 Introduction One of the key factors that distinguish cancer cells from normal cells is the ability of cancer cells to alter their local and non-local interactions to neighbouring cells (that are either cancerous or of different types) and to the extracellular matrix (ECM), which leads eventually to invasion and metastasis (Hanahan and Weinberg 2000, 2011). The ECM consists of a network of macromolecules (i.e. fibrous proteins, water, minerals, proteoglycans), which is present in all tissues and regulates cell behaviour and tissue homeostasis (Filipe et al. 2018). While the structure of the matrix undergoes constant remodelling (via synthesis and degradation), the ECM loses its integrity during cancer progression. There are many enzymes inside the solid tumours that can degrade the ECM, such as matrix metalloproteinases (MMPs) or urokinase plasminog
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