The role of initial tumor biomass size in a mathematical model of periodically pulsed chemotherapy

The dosage and frequency of a chemotherapy regimen are important determinants for its success. Many research studies have attempted to identify optimal treatment strategies for certain purposes such as minimizing the tumor burden, maximizing the normal cells as well as the dose, and minimizing cytotoxicity to normal cells. In this paper, a combination of mathematical and numerical analysis is applied to study the effect of initial tumor biomass using a competition model describing tumor–normal cell interaction with periodically pulsed chemotherapy. Some properties of the set of initial tumor and normal cell biomasses for successful treatment are derived. On the basis of these properties, a numerical method is constructed for locating the boundary of such a set. The boundary identifies the ability of a chemotherapeutic treatment to eliminate a tumor. The optimal dosage and frequency for a large tumor are discussed. The numerical results show that tumor–host interactions have a great effect on the outcome of the treatment. The effect of resistant tumor subpopulations is also discussed.