Pharmacodynamic modeling of chemotherapeutic effects: Application of a transit compartment model to characterize methotrexate effects in vitro

The time course of chemotherapeutic effect is often delayed relative to the time course of chemotherapeutic exposure. In many cases, this delay is difficult to characterize mathematically through the use of standard pharmacodynamic models. In the present work, we investigated the relationship between methotrexate (MTX) exposure and the time course of MTX effects on tumor cell growth in culture. Two cancer cell lines, Ehrlich ascites cells and sarcoma 180 cells, were exposed for 24 hours to MTX concentrations that varied more than 700-fold (0.19–140 μg/mL). Viable cells were counted on days 1, 3, 5, 7, 9, 11, 13, 15, 17, 20, 22, and 24 for Ehrlich ascites cells and on days 1, 2, 3, 5, 7, 9, 11, 13, 14, 15, 17, 19, and 21 for sarcoma 180 cells, through the use of a tetrazolium assay. Although MTX was removed 24 hours after application, cell numbers reached nadir values more than 100 hours after MTX exposure. Data from each cell line were fitted to 3 pharmacodynamic models of chemotherapeutic cell killing: a cell cycle phase-specific model, a phase-nonspecific model, and a transit compartment model (based on the general model recently reported by Mager and Jusko, Clin Pharmacol Ther. 70:210–216, 2001). The transit compartment model captured the data much more accurately than the standard pharmacodynamic models, with correlation coefficients ranging from 0.86 to 0.999. This report shows the successful application of a transit compartment model for characterization of the complex time course of chemotherapeutic effects; such models may be very useful in the development of optimization strategies for cancer chemotherapy.