A Modified Stochastic Gompertz Model for Tumour Cell Growth. Issue 1 (2010)

• Record Type: Journal Article
• Authors: Lo, C. F.
• Is Part Of: Computational and mathematical methods in medicine. Volume 11:Issue 1(2010)
• Page Start: 3
• Page End: 11
• Publication Date: 2010
• Subjects: bounded random process -- Fokker–Planck equation -- Lie-algebraic method; Medicine -- Computer simulation -- Periodicals; Medicine -- Mathematical models -- Periodicals; 610.11
• DOI: 10.1080/17486700802545543
• Languages: English
• ISSNs: 1748-670X

Abstract

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.