This report describes a mathematical model of cell proliferation for simulation of bivariate DNAhromodeoxyuridine (BrdUrd) distributions. The model formulates the change with time in the frequency of cells with any DNA content and in the amount of incorporated BrdUrd, according to given cytokinetic parameters, i.e., durations and dispersions of cell cycle phases and DNA synthesis rate during S-phase. We have applied this model to sequential DNA/BrdUrd distributions measured for Chinese hamster ovary cells asynchronously grown in vitro, 1) for 30 min in 10 pM BrdUrd followed by growth in BrdUrdfree medium for 0 to 24 h, or 2) during continuous incubation in 3 pM BrdUrd plus 30 pM thymidine for 2 to 24 h. The matches between the experimental and simulated distributions give the G1, S, G2M, and total cell cycle durations (and coefficients of variation) of 5.6 h (0.081, 7.0 h (0.03, 1.4 h (0.161, and 14.0 h (0.05), respectively. The model is shown to be useful for quantitative interpretation of the bivariate distributions.Key terms: Mathematical model, cell proliferation, cell cycle, DNAhromodeoxyuridine, flow cytometry Quantitative analysis of the cytokinetic properties of normal and neoplastic cell populations is important for determination of the basic growth characteristics of these tissues, for analysis of the cell cycle phase-specific effects of perturbing agents such as anticancer drugs, and to provide a rational basis for cancer therapeutic strategies-especially for the optimal scheduling of chemotherapy and radiation therapy (8). Estimation of cell cycle phase durations, dispersions, growth fraction, etc., for populations under various experimental and therapeutic conditions is usually accomplished by mathematical modeling of experimental data. In this approach, a mathematical model of cell cycle traverse is used to simulate experimental data such as for DNA distribution sequences, fraction of labeled mitosis curves, or bivariate DNA/bromodeoxyuridine (BrdUrd) distribution sequences. The model parameters such as the G1-, S-, and G2M-phase durations, growth fraction, etc., are varied until the simulations match the experimental data as closely as possible. These parameters are then taken as an accurate description of the cytokinetic properties of the cell population under analysis. So far, numerous mathematical models of cell cycle traverse have been proposed (16) and used for simulation of a variety of experimental data (1,7,8,12,17). The validity of these mathematical analyses, of course, depends on the appropriateness of the mathematical model and on the accuracy and information content of the experimental data.The recently developed flow cytometric technique for the simultaneous quantification of total cellular DNA content and incorporated BrdUrd has significantly increased the information available in experimental measurements (3-6). The technique facilitates a rapid, statistically accurate measurement of the distribution (not merely the average) of the amount of BrdUrd incorporated into DNA as a functi...