Multiscale Computational Modelling and Analysis of Cancer Invasion

Recognised as a key stage in cancer growth and spread in the human body, the cancer cell invasion process is crucial for metastatic spread and the subsequent development of secondary cancers. Tissue scale proliferation and migration in conjunction with a

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Multiscale Computational Modelling and Analysis of Cancer Invasion Dumitru Trucu, Pia Domschke, Alf Gerisch, and Mark A.J. Chaplain

Abstract Recognised as a key stage in cancer growth and spread in the human body, the cancer cell invasion process is crucial for metastatic spread and the subsequent development of secondary cancers. Tissue scale proliferation and migration in conjunction with a pallet of arising cell-scale dynamics including altered adhesion and secretion of matrix degrading enzymes enable the cancer cells to actively spread locally into the surrounding tissue. This biological multiscale character that cancer invasion exhibits therefore explores the natural two-way link between the molecular processes occurring at the level of individual cells (micro-scale) and the processes occurring at the level of cell population (macro-scale). This chapter will address these multiscale biological processes from a mathematical modelling and analysis perspective, gradually paving the way towards an integrated multiscale framework that explores the tight connection between the tissues scale changes in tumour morphology and the cell-scale dynamics of proteolytic enzymes in the neighbourhood of the tumour interface.

5.1 Introduction Known as one of the hallmarks of cancer [22], cancer invasion is a complex, multiscale phenomenon involving many inter-related genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Its complicated spatiotemporal multiscale dynamics enables a localised solid tumour to transform into a

D. Trucu () Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK e-mail: [email protected] P. Domschke • A. Gerisch Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, 64293 Darmstadt, Germany e-mail: [email protected]; [email protected] M.A.J. Chaplain School of Mathematics and Statistics, Mathematical Institute (MI), University of St Andrews, St Andrews KY16 9SS, UK e-mail: [email protected] © Springer International Publishing Switzerland 2016 L. Preziosi et al. (eds.), Mathematical Models and Methods for Living Systems, Lecture Notes in Mathematics 2167, DOI 10.1007/978-3-319-42679-2_5

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systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that the solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Combining abnormal proliferation and migration, which is enabled and enhanced by altered cell-cell and cell-matrix adhesion and the secretion of various proteolitic enzymes, the cancer cells population affects the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. During the growth and spread of malignant tumours, several classes of matrixdegrading enzymes (MDEs) [17, 55] such as matrix metalloproteinases (

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