Mathematic models for cancer chemotherapy: pharmacokinetic and cell kinetic considerations

This paper presents a theoretic study of pharmacokinetic and cell kinetic models for cancer chemotherapeutic systems. The mathematic analysis is based on a modified procedure deduced from DeVita's scheme of the relationship between the cellular kinetics of normal and tumor tissues and the pharmacokinetics of antitumor agents for designing an optimal dose and schedule for cancer treatment. In this scheme pharmacokinetic models and cell-drug interactions at the tumor site are incorporated into the cell cycle kinetic models to form the cancer chemotherapeutic model systems. Three cell cycle kinetic models are presented under alternative hypotheses concerning the mechanism of the resting cells, while each tumor mass is comprised of cells in proliferating (consisting of the four cycle phases G1, S, G2, and M), resting (Go), and non dividing (D, dead) states. An algorithm and a computer program for simulating the tumor populations during scheduled treatments have been prepared. By a suitable selection of expressions for cell-drug interactions, the program is able to simulate tumor behavior during scheduled treatments with different classes of anticancer agent such as cell cycle phase-specific, cell cycle-specific, or cell cycle-specific, or cell cycle-nonspecific drugs. A preliminary study of the L1210-ara-C therapeutic system is included to demonstrate the computer simulation procedures.