A quantitative approach to the design of antitumor drug dosage schedule via cell cycle kinetics and systems theory

Abstract

A discrete-time kinetic model for chemotherapy was developed to deal with the effects of antitumor drugs on the cell cycle and proliferation kinetics of experimental tumor cell populations in which cell kinetic responses of chemotherapy are represented in terms of perturbation of cell kinetic parameters—cell age, cell size and DNA content distributions. The time-course behavior of these cell kinetic parameters was predicted by solving the discrete-time state equations which characterize the dynamics of tumor-drug interactions. The amount of antitumor drug administered was expressed to be the control function of the state equations and the transition matrix representing two modes of drug action, namely, cell kill and progression delay or accumulation of cells due to drug, was derived. The performance of the model, assessed by examining the effects of cell cycle stage-specific agents such as cytosine arabinoside on spontaneous AKR leukemia, compared favorably with experimental data. Utilizing an optimization scheme in engineering systems studies, an analytical method is described for optimizing the regimen of drug administration so as to maximize the effectiveness of drug dosage schedules and minimize the use of toxic amounts of the drug. The superiority of the schedule designed by an optimization scheme was evident at the termination of therapy, although the schedule designed by experimental trials reduced the number of surviving tumor cells more effectively than the one designed by an optimization scheme during the earlier therapy period. In the model, the proposed schedule will function more effectively for the entire therapy period when additional parameters of drug characteristics, such as the toxicity to the host and drug resistance, are encompassed.