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A Mechanistic, Predictive Model of Dose-Response Curves for Cell Cycle Phase-specific and -nonspecific Drugs¹

National Environment Research Council Centre for Population Biology, Imperial College at Silwood Park, Ascot, Berkshire SL5 7PY, United Kingdom

In vitro dose-response curves for anticancer agents are useful for predicting the clinical response to chemotherapy, and models to capture the time-dependency of dose-response curves are necessary for potential clinical extrapolation. Usually, the modified Hill model is used (see Levasseur et al., Cancer Res., 58: 5749–5761, 1998), although this model is neither mechanistic nor predictive for understanding how drug and tumor cell characteristics affect the shape of the dose-response curve. A new exponential kill (EK) model is proposed to predict the shape of dose-response curves based on the cell cycle phase specificity of a drug, the cell cycle time, the duration and concentration of drug exposure at the site of action, and a scaling factor for the level of drug resistance. Explicit analytical equations are presented for predicting the IC_x (the concentration required to reduce cell growth by x%), the maximum cell kill achievable at high doses after a given duration of drug exposure, and the slope of the survival fraction versus log (concentration) plot at the IC_x. Numerical solutions illustrate that there may be an optimal, finite duration of drug exposure that maximizes cell kill for a given area under the concentration versus time curve, and an analytical equation is given to calculate when such an optimal, finite duration exists.

The EK model generates sigmoidal dose-response curves, like those seen empirically and previously described by the Hill model, which eventually plateau with increasing drug concentration at levels that depend on the cell cycle specificity of the drug, the cell cycle time, and the duration of exposure to the drug. This study includes no original data. Instead, empirical results in the literature are used to test the model. Because data by Levasseur et al. (1998) was fit to the Hill model assuming the plateau in the effect versus concentration curve to be independent of exposure duration, a full test of the model is not possible using their published data. Some tests of the EK model were possible, however, showing that EK model predictions yield good fits to in vitro data published in that and in another study. In addition, combining the EK model with a pharmacokinetic model resulted in predictions that were consistent with results of clinical studies comparing etoposide given in different schedules. Further tests of the model are necessary.

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