Computational and Mathematical Methods in Medicine

Computational and Mathematical Methods in Medicine / 2010 / Article

Original Article | Open Access

Volume 11 |Article ID 765839 | 9 pages | https://doi.org/10.1080/17486700802545543

A Modified Stochastic Gompertz Model for Tumour Cell Growth

Received04 Jun 2008
Accepted09 Sep 2008

Abstract

Based upon the deterministic Gompertz law of cell growth, we have proposed a stochastic model of tumour cell growth, in which the size of the tumour cells is bounded. The model takes account of both cell fission (which is an ‘action at a distance’ effect) and mortality too. Accordingly, the density function of the size of the tumour cells obeys a functional Fokker–Planck Equation (FPE) associated with the bounded stochastic process. We apply the Lie-algebraic method to derive the exact analytical solution via an iterative approach. It is found that the density function exhibits an interesting kink-like structure generated by cell fission as time evolves.

Copyright © 2010 Hindawi Publishing Corporation. 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.

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