A new mathematical pharmacodynamic model of clonogenic cancer cell death by doxorubicin

Previous models for predicting tumor cell growth are mostly based on measurements of total cell numbers. The purpose of this paper is to provide a new simple mathematical model for calculating tumor cell growth focusing on the fraction of cells that is clonogenic. The non-clonogenic cells are considered to be relatively harmless. We performed a number of different types of experiments: a long-term drug "treatment", several concentrations/fixed time experiments and time-series experiments, in which human MCF-7 breast cancer cells were exposed to doxorubicin and the total number of cells were counted. In the latter two types, at every measurement point a plating efficiency experiment was started. The final number of colonies formed is equal to the number of clonogenic cells at the onset of the experiment. Based on the intracellular drug concentration, our model predicts cell culture effects taking clonogenic ability and growth inhibition by neighboring cells into account. The model fitted well to the experimental data. The estimated damage parameter which represents the chance of an MCF-7 cell to become non-clonogenic per unit time and per unit intracellular doxorubicin concentration was found to be 0.0025 ± 0.0008 (mean ± SD) nM(-1) h(-1). The model could be used to calculate the effect of every doxorubicin concentration versus time (C-t) profile. Although in vivo parameters may well be different from those found in vitro, the model can be used to predict trends, e.g. by comparing effects of different in vivo C-t profiles.