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Computational and Mathematical Methods in Medicine
Volume 2011, Article ID 452320, 16 pages
Research Article

Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells

1Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolnierska 14, 10-561, Olsztyn, Poland
2Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725, USA

Received 15 January 2010; Accepted 18 July 2010

Copyright © 2011 M. Kolev and B. Zubik-Kowal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.