RESEARCH ARTICLE


On Some Probabilistic Aspects of Diffusion Models for Tissue Growth



Jozef Kiseľák1, Kamal Raj Pardasani2, Neeru Adlakha2, Milan Stehlík1, *, Mamta Agrawal2
1 Department of Applied Statistics, Johannes Kepler University in Linz, Altenberger Straße 69, A-4040 Linz a. D., Austria.
2 Maulana Azad National Institute of Technology, Bhopal, India


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© 2013 Agrawal et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Applied Statistics, Johannes Kepler University in Linz, Altenberger Straße 69, A-4040 Linz a. D., Austria. Tel: +43 732 2468 6806, Fax: +43 732 2468 9846; E-mail: Milan.Stehlik@jku.at,


Abstract

Understanding of tissue growth is in its nature multidisciplinary, since it varies from cancer diagnostics, image processing, fractal analysis to regular and non-regular heat flows. By medical sciences it was requested to better understood the tissue grow relation to mathematical modelling (stochastic geometry, fractal growth, diffusions). It is clear, that deterministic fractal is not an appropriate model for cancer growth. Stochastic fractal is more appropriate, however, a validation measure should be developed for better comparability with advanced stochastic geometry model, e.g. Quermass- interaction process. Moreover, relation temperature-geometry of the tissue is studied. We have partial results, where it is observed, that benign alterations and malignant tumors originating from glandular tissues (e.g.mammary, prostatic, pancreatic) are naturally modelled by non-standard diffusions. For standard diffusions, fair approximation is provided by analytical models based on convective heat transfer in infinite tissues volume (e.g. model given by Perl 1962, later extended by [1]).

Keywords: Cancer, diffusion, temperature.