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Multiscale Computational Modelling and Analysis of Cancer Invasion

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Mathematical Models and Methods for Living Systems

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2167))

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.

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Author information

Authors and Affiliations

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

    Dumitru Trucu

  2. Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, Darmstadt, 64293, Germany

    Pia Domschke & Alf Gerisch

  3. School of Mathematics and Statistics, Mathematical Institute (MI), University of St Andrews, St Andrews, KY16 9SS, UK

    Mark A. J. Chaplain

Authors
  1. Dumitru Trucu
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  2. Pia Domschke
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  3. Alf Gerisch
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  4. Mark A. J. Chaplain
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Correspondence to Dumitru Trucu .

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Editors and Affiliations

  1. Mathematical Sciences, Politecnico di Torino, Torino, Italy

    Luigi Preziosi

  2. School of Mathematics and Statistics, University of St. Andrews, St. Andrews, United Kingdom

    Mark Chaplain

  3. Department of Mathematics, Università di Trento, Povo, Italy

    Andrea Pugliese

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Trucu, D., Domschke, P., Gerisch, A., Chaplain, M.A.J. (2016). Multiscale Computational Modelling and Analysis of Cancer Invasion. In: Preziosi, L., Chaplain, M., Pugliese, A. (eds) Mathematical Models and Methods for Living Systems. Lecture Notes in Mathematics(), vol 2167. Springer, Cham. https://doi.org/10.1007/978-3-319-42679-2_5

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