A Stochastic and State Space Model for Tumour Growth and ApplicationsReport as inadecuate




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Computational and Mathematical Methods in Medicine - Volume 10 2009, Issue 2, Pages 117-138

Original Article

Department of Mathematical Sciences, The University of Memphis, Memphis, TN, USA

Department of Mathematics and Statistics, South Dakota State University, Brookings, SD, USA

Department of Mathematics, Vanderbilt University, Nashville, TN, USA

Received 18 June 2007; Accepted 1 May 2008

Copyright © 2009 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.

Abstract

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb 1991, and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables number of tumour cells. We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.





Author: Wai-Yuan Tan, Weiming Ke, and G. Webb

Source: https://www.hindawi.com/



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