MATHEMATICAL MODELING OF PROSTATE TUMOR GROWTH UNDER INTERMITTENT ANDROGEN SUPPRESSION WITH PARTIAL DIFFERENTIAL EQUATIONS

摘要

Since most prostate tumors are initially hormone-sensitive, hormonal therapy with androgen suppression is a major treatment for them. In this hormonal therapy, however, a tumor relapse is a crucial problem. Androgen-independent tumor cells are considered to be responsible for such a relapse. These cells are not sensitive to androgen suppression but rather apt to proliferate even in an androgen-poor environment. Bruchovsky et al. proposed intermittent androgen suppression (IAS), which may prolong the relapse time when compared with continuous androgen suppression (CAS). IAS therapy is based on switching of medication through monitoring of the serum prostate-specific antigen (PSA). Namely, the medication is suspended when the PSA concentration falls below the lower threshold during on-treatment periods and it is reinstituted when the concentration exceeds the upper threshold during off-treatment periods. In this paper, we propose a model of partial differential equations (PDE) for IAS therapy, on the basis of our previous model of ordinary differential equations, under the assumption that the prostate tumor is a mixed assembly of androgen-dependent (AD) and androgen-independent (AI) cells. Numerical analysis compares the effect of the IAS therapy with that of the CAS therapy for different growth rates of the AI cells, which suggests an optimal protocol of the IAS therapy.