Mathematical Modelling of Natural Phenomena

Research Article

Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models

A. R.A. Andersona1, K. A. Rejniaka1, P. Gerleea1 and V. Quarantaa2

a1 Division of Mathematics, University of Dundee, Dundee, Scotland, UK

a2 Department of Cancer Biology, Vanderbilt University School of Medicine, Nashville, TN, USA


Since cancer is a complex phenomenon that incorporates events occurring on different length and time scales, therefore multiscale models are needed if we hope to adequately address cancer specific questions. In this paper we present three different multiscale individual-cell-based models, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular, cellular or subcellular, but also incorporating relevant information from other levels. We apply these hybrid models to investigate the influence of the microenvironement on tumour invasion, cell-cell collaboration and competition leading to the initiation and growth of epithelial tumours, and to evolution of cell phenotypes/genotypes arising in tumours growing in different oxygen concentrations. We also discuss how these models relate to one another and can be used to bridge biological scales relevant to cancer.

(Online publication June 15 2008)

Key Words:

  • tumour growth;
  • tumour evolution;
  • tumour invasion;
  • single-cell-based models;
  • hybrid models;
  • multiscale

Mathematics Subject Classification:

  • 82B24;
  • 92C15;
  • 92C17;
  • 92B20;
  • 92D15;
  • 76D05;
  • 76Z99;
  • 92C37;
  • 92C50