Mathematical Models for Treating Prostate Cancer(<Special Topics>Mathematical Model of Disease)

Abstract

In this paper, we review our recent developments of mathematical models for prostate cancer under intermittent androgen suppression. In the intermittent androgen suppression, androgen suppression, which is hormone therapy for prostate cancer, is intermittently stopped to delay the relapse of cancer. To optimize the protocol to each patient, we have proposed some mathematical models including ordinary differential equation models and partial differential equation models. Our most recent model is a three-dimensional piecewise linear model. One of the three variables of the model is for androgen dependent cancer cells and the other two variables are for androgen independent cancer cells. This piecewise linear model can not only fit clinical datasets of tumor marker called prostate specific antigen very well but also classify patients based on past time series of the tumor in a manner similar to medical doctors' classifications. We also discuss the future developments of mathematical methods for mathematical medicine including personalized treatment scheduling.