A model of heat-induced clonogenic cell death.

When cells are exposed to elevated temperatures, clonogenicity decreases in a temperature-dependent manner displaying non-linear kinetics. In this report we show that the survival of synchronized cell populations after heat exposure can be characterized by a parameter epsilon, which is normally-distributed throughout the population. Cells whose corresponding epsilon-value lies below an arbitrary threshold value epsilon min are unable to form a colony. Upon transfer of a cell culture to an elevated temperature, the mean value of the epsilon distribution decreases exponentially over time with a rate dependent upon the difference between the current and final mean value, until reaching a final value epsilon f dependent on the particular temperature used, thus representing a larger proportion of cells with epsilon less than epsilon min which are non-clonogenic. The analyses evaluate a temperature-independent parameter k which is presumed to be dependent upon the growth conditions of the cell population, and a temperature-dependent parameter epsilon f, which is characteristic of the new temperature-perturbed steady state. Comparison of the results of analysis of synchronized G1 cell survival data to that for S phase cells obtained over a range of temperatures shows that it is sufficient to ascribe the increased thermal sensitivity of S phase cells to a different k value, the temperature-dependence of epsilon f being identical in the two cases. Linear regression analysis of the temperature-dependence of epsilon f, when expressed as 1n (-epsilon f) = a0 + a1/T demonstrated strong linearity (r2 = 0.99) for either the individual (G1 or S) or combined data sets. This description of heat-induced cytotoxicity may be of use as the basis for a dose concept for the clinical administration of hyperthermia.