Cell cycle kinetic analysis in vitro has conventionally been accomplished by labeling S-phase cells using two DNA specific labels given sequentially and separated from each other by a certain time interval. By counting the cells labeled by both versus those labeled by either one of the two labels, and using the formulas described by Wimber and Quastler, approximate values for durations of S-phase (Ts) and the total cell cycle (Tc) can be determined. More recently, instead of radioisotope labeled thymidine, two thymidine analogues have been used to label Sphase cells in vivo in a variety of human tumors based on the same principles. In the present report, new formulas are proposed for the calculation of Ts and Tc which are simpler to apply since only one type of labeled cells (those exiting Sphase as identified by containing only the first label) need to be differentiated from the remaining population for Tc calculations.Key terms: Thymidine analogues, cell cycle formulas, set theoryTo determine the rate of proliferation of cells by labeling S-phase cells sequentially with two varieties of radio-labeled thymidine, Wimber and Quastler (12) introduced their now classic equation, which has been extensively applied in cell cycle kinetic studies for approximately 30 years (5,11,14). We have also exploited this approach in studying large number of patients with acute myelocytic leukemia (AML). Our strategy required infusion of the first DNA-specific label bromodeoxyuridine (BrdUrd), in vivo and the second, tritiated thymidine label in vitro. By counting the number of leukemia cells which were singly labeled by either of the labels or doubly labeled, and employing the formulae described by Wimber and Quastler, we have been able to estimate the labeling index (LI), the duration of S-phase (Ts) and the total cell cycle time (Tc) of myeloblasts (8). Furthermore, we have determined the clinical relevance of these measurements by demonstrating a direct relationship between cell cycle times and duration of complete remission (7,9). With the rapid evolution of new techniques, better and more reliable probes are now available for detailed investigation of cell cycle kinetics. For example, instead of using the thymidine analogue bromodeoxyuridine in vivo and tritiated thymidine in vitro, we now routinely use iodo-deoxyuridine (IdUrd) and BrdUrd, both of which can be given in vivo. The actual counting of cells labeled by either one or both labels is an extremely tedious job, and because of the immunohistochemical techniques employed, it is not always possible to distinguish between a cell which contains BrdUrd alone or both BrdUrd and IdUrd. This problem is irrelevant in terms of results obtained since only IdUrd labeled cells need to be distinguished from all other labeled cells for the appropriate Ts calculations. However, attempts to improve upon the formula which would simplify the counting process lead us to the development of a reliable new mathematical equation which is being presented in this paper. This new equation can...