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Modelling Aspects of Cancer Growth: Insight from Mathematical and Numerical Analysis and Computational Simulation

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Multiscale Problems in the Life Sciences

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1940))

In this chapter we present a variety of reaction-diffusion-taxis (i.e. macroscopic) models of several key stages of solid tumour growth – avascular growth, the immune response to solid tumours and invasive growth. The basis for all of the models is deriving the continuum PDE using a conservation of mass argument. In the model for avascular growth we examine the potential role prepattern theory (diffusion-driven instability à la Turing) may play in the generation of spatio-temporal heterogeneity of mitotic activity on the surface of multicell spheroids. In the model for the immune response to cancer, working from an initial “microscale” cell interaction scheme, we derive a system of PDEs which are used to predict the capacity of the immune system to eradicate cancer (or not). In the final model of cancer invasion, once again we initially focus on “microscale” activity of matrix degrading enzymes and their binding to cell-surface receptors to derive a PDE model of the process of cancer invasion of the local tissue. For each system, we carry out mathematical and numerical analyses of the model and perform computational simulations and attempt to draw relevant biological conclusions and make experimentally-testable predictions from the results.

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  1. Division of Mathematics, University of Dundee, DD1 4HN, Dundee, Scotland

    Mark A. J. Chaplain

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  1. Department of Mathematics & ADAMSS (Centre for Advanced Applied Mathematical and Statistical Sciences), University of Milan, Via Saldini 50, 20133, Milano, Italy

    Vincenzo Capasso

  2. Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha, 2, 02-097, Warsaw, Poland

    Mirosław Lachowicz

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Chaplain, M.A.J. (2008). Modelling Aspects of Cancer Growth: Insight from Mathematical and Numerical Analysis and Computational Simulation. In: Capasso, V., Lachowicz, M. (eds) Multiscale Problems in the Life Sciences. Lecture Notes in Mathematics, vol 1940. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78362-6_3

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