Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer

We propose a mathematical model that quantitatively reproduces the dynamics of the serum prostate-specific antigen (PSA) level under intermittent androgen suppression (IAS) for prostate cancer. Taking into account the biological knowledge that there are reversible and irreversible changes in a malignant cell, we constructed a piecewise-linear dynamical model where the testosterone dynamics are modelled with rapid shifts between two levels, namely the normal and castrate concentrations of the male hormone. The validity of the model was supported by patient data obtained from a clinical trial of IAS. It accurately reproduced the kinetics of the therapeutic reduction of PSA and predicted the future nadir level correctly. The coexistence of reversible and irreversible changes within the malignant cell provided the best explanation of early progression to androgen independence. Finally, since the model identified patients for whom IAS was effective, it potentially offers a novel approach to individualized therapy requiring the input of time sequence values of PSA only.