Parameter Estimation And Optimal Control Algorithm For Intermittent Hormone Inhibitory Treatment Of Prostate Cancer Model

Prostate cancer is a serious cause of cancer-related death in men; for example, it is now the second leading cause in the United States.[1] Hormone therapy with androgen deprivation is a major treatment for advanced prostate cancer. However, continuous androgen suppression(CAS) may lead to recurrence. Clinic trials suggest that intermittent androgen suppression(IAS) with alternating on- and off-treatment periods is a good alternative strategy to delay the relapse. Hirata et.al. [2] proposed a piecewise linear ODE system to model IAS strategy. Due to they can not find a reliable algorithm to fit the model parameters only depending on clinical data of single patient, it is not easy to operate the personal treatment. We propose an algorithm based on cross-entropy to determine parameters of a piecewise linear model. By comparing with clinical data, the parameter estimation for the switched system shows good fitting accuracy. Moreover, the algorithm can be parallelized so that the efficiency will be improved. We further optimize switching time points for the piecewise linear model to obtain more feasible therapeutic schedule. The simulating results of therapeutic effect are superior to those of previous strategy. Finally, we proposed a new ODE model which parameter is time variable for different stages. Numerical experiments show better fitting results than those of the existing piecewise linear model.