Optimizing Drug Regimens in Cancer Chemotherapy

Abstract

Cancer chemotherapy triggers toxic effects due to the interaction of the drug with normal cells, which prevents sufficient doses from being administered to obtain a complete cure. Thus it becomes important to design treatment strategies for ensuring a desired rate of tumor cell kill without overdosing the host. To design optimal chemotherapy strategies, mathematical models describing the mechanisms of cytotoxic drug availability and action on tumour cell populations, and expressing drug use constraints may be used. However, the main difficulty is to correctly formulate and use the constraint related to drug-induced toxicity. Constraints are formulated to specify the maximum allowed drug amounts, the circulating concentrations, and the haematologic prerequisites associated to the time-courses of absolute neutrophil and platelet counts: 1) control neutrophil and platelet counts at levels higher than a fixed down level, WA; 2) prevent neutrophil and platelet counts from staying too long below a fixed upper level, WR; and 3) ensure a minimum recovery of neutrophil and platelet counts at the end of the current cycle, WC. This study concerns the administration of two drugs and the optimization of regimens along several cycles of chemotherapy. After specifying the pharmacokinetic model, and the pharmacodynamic, efficacy and toxicity models, and given a schedule of drug administrations, we optimized the drug doses that could minimize the tumour burden while limiting the toxicity expressed by the above constraints (Iliadis & Barbolosi 2000). We applied this methodology to etoposide-cisplatin chemotherapy data (Ihde et al. 1994). For a 14 day interval, fig. 1 shows the optimized drug rates along 3 cycles, and the dynamics of tumour size and of the neutrophil and platelet counts. The form of optimized administrations turns out to be a combination per cycle of high doses at the start of cycle up to saturation of constraints attached to normal cell toxicity and then moderate drug administration to manage active constraints. The problem is fully constrained and the form of the optimal inputs is completely dictated by the extent of constraints associated to the pharmacodynamic-toxicity model. Simulation of the optimized protocol over 3 cycles of chemotherapy (time in days). • Up left: Optimized infusion rates (in g/days) for etoposide (VP16) and cisplatin (CDDP). • Up right: Reduction of tumour size as % of the initial burden. t*: the time of minimum size. • Down left: Neutrophil count (in Mcells/ml) kinetics. • Down right: Platelet count (in Mcells/ml) kinetics. • WA: lower allowed levels of neutrophils (WA1) and platelets (WA2). • WR: upper level below of which the neutriphil (WR1) and platelet (WR2) cell counts could remain but no longer than a fixed time. • WC: recovery levels for neutrophils (WC1) and platelets (WC2). Although many anticancer drugs have been in clinical use for over 20 years, their optimum schedule of administration is still not clear. Mathematical models need to be developed to better understand how to implement this work and perhaps to elaborate new optimal treatment strategies.