# American Institute of Mathematical Sciences

February  2004, 4(1): 187-201. doi: 10.3934/dcdsb.2004.4.187

## A mathematical model of prostate tumor growth and androgen-independent relapse

 1 Department of Mathematics, University of Michigan, Ann Arbor, Michigan

Received  December 2002 Revised  April 2003 Published  November 2003

A mathematical model is developed that investigates polyclonality and decreased apoptosis as mechanisms for the androgen-independent relapse of human prostate cancer. The tumor is treated as a continuum of two types of cells (androgen-dependent and androgen- independent) whose proliferation and apoptotic death rates differ in response to androgen rich and androgen poor conditions. Insight into the tumor's response to therapies which both partially and completely block androgen production is gained by applying a combination of analytical and numerical techniques to the model equations. The analysis predicts that androgen deprivation therapy can only be successful for a small range of the biological parameters no matter how completely androgen production is blocked. Numerical simulations show that the model captures all three experimentally observed phases of human prostate cancer progression including exponential growth prior to treatment, androgen sensitivity immediately following therapy, and the eventual androgen-independent relapse of the tumor. Simulations also agree with experimental evidence that androgen-independent relapse is associated with a decrease in apoptosis without an increase in proliferation.
Citation: T.L. Jackson. A mathematical model of prostate tumor growth and androgen-independent relapse. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 187-201. doi: 10.3934/dcdsb.2004.4.187
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