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Computational and Mathematical Methods in Medicine
Volume 11 (2010), Issue 1, Pages 3-11
Original Article

A Modified Stochastic Gompertz Model for Tumour Cell Growth

Department of Physics, Institute of Theoretical Physics, The Chinese University of Hong Kong, Hong Kong

Received 4 June 2008; Accepted 9 September 2008

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.


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.