Browsing by Author "Zubik-Kowal B."

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Correlation between animal and mathematical models for prostate cancer progression
    (2009-01-01) Jackiewicz Z.; Jorcyk C.L.; Kolev M.; Zubik-Kowal B.
    This work demonstrates that prostate tumour progression in vivo can be analysed by using solutions of a mathematical model supplemented by initial conditions chosen according to growth rates of cell lines in vitro. The mathematical model is investigated and solved numerically. Its numerical solutions are compared with experimental data from animal models. The numerical results confirm the experimental results with the growth rates in vivo. © 2009 Taylor & Francis.
  • No Thumbnail Available
    Item
    Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells
    (2011-01-01) Zubik-Kowal B.; Kolev M.
    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. Copyright © 2011 M. Kolev and B. Zubik-Kowal.