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.

Simulation model of doxorubicin activity in islets of human breast cancer cells.

During cytotoxic chemotherapy, cancer cells are exposed to a dynamic concentration-versus-time curve. Besides the area under this curve, the shape of this curve may determine the cytotoxic effect. This report describes the concept that cell damage is determined by the molar drug accumulation history inside the tumor cells. Cell numbers of large populations of human MCF-7 cells exposed to three different doxorubicin concentration-versus-time profiles were recorded for 31 days. The drug accumulation history in the cells was calculated using cellular drug transport parameters derived from doxorubicin uptake and efflux measurements on MCF-7 cells attached to culture dishes. Recovery of the proliferation rate of a cell population after drug exposure was described using a mathematical model of cell damage. The model fitted well to the proliferation assays. It allowed for comparison of the effects of changes in doxorubicin concentration-versus-time profiles in vitro. The model was then used to predict the effect of the changes in the doxorubicin concentration profile in vivo, in tumor islets, after a bolus injection of doxorubicin. In the model doxorubicin exposure resulted in less cell damage inside the tumor islets than at the rim.