A mathematical model for cisplatin cellular pharmacodynamics

Abstract

A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls) on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (approximately 100 hours). The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.

Figure 1

Schematic representation of proposed model. Concentrations of platinum are: c_e, extracellular; c_i, intracellular non-DNA bound; c_k, intracellular DNA-bound; $c_{\text{i}}^{\prime }$, released from DNA as a result of DNA repair. Arrows indicate transport or reaction processes. The concentration c_i is much larger than c_k and $c_{\text{i}}^{\prime }$.

Figure 2

Fits of cellular pharmacokinetic model to data on the uptake of platinum by human cancer cells in vitro. Curves show model predictions. (A) Data of Andrews et al. [26] for ovarian carcinoma cells. Extracellular concentration: 0.195 µg/ml Pt. (B) Data of Troger et al. [2] for head and neck cancer cells. Extracellular concentrations: (●) 0.65 µg/ml Pt; (■) 1.62 µg/ml Pt; (▲) 3.2 µg/ml Pt; and (▼) 6.5 µg/ml Pt.

Figure 3

Best fits of six cytotoxicity models to the data of Troger et al. [2] for human head and neck cancer cells. Exposure times: (●) 1 hour; (■) 2 hours; (▲) 11 hours; and (▼) 121 hours. Curves: model predictions. Res: root mean square residual deviation between experimental data and model.

Figure 4

Best fits of six cytotoxicity models to the data of Levasseur et al. [11] for a human ovarian cancer cell line. Exposure times: (●) 1 hour; (■) 2 hours; (▲) 3 hours; (▼) 4 hours; (○) 6 hours; (□) 9 hours; (△) 12 hours; and (▽) 24 hours. Curves: model predictions. Res: root mean square residual deviation between experimental data and model.

Figure 5

Best fits of six cytotoxicity models to the data of Kurihara et al. [3] for a human gastric cancer cell line. Exposure times: (●) 1 hour; (■) 5 hours; (▲) 10 hours; and (▼) 25 hours. Curves: model predictions. Res: root mean square residual deviation between experimental data and model.

Figure 6

Survival relative to controls as predicted by the peak-bound intracellular model for a wide range of exposure times, showing a threshold concentration below which no substantial cell kill can be achieved, regardless of exposure time. Parameter values are those for the Levasseur et al. [11] data set.