Cell loss and the concept of potential doubling time

The in vivo infusion of Bromodeoxyuridine (BrdUrd), followed by delayed biopsy and bivariate DNA-BrdUrd flow cytometry, allows the potential doubling time (Tpot) of human tumors to be estimated. According to Steel, the mathematical definition of Tpot is Tpot = ln 2/Kp, where Kp is the rate constant of cell production. All the operative formulas which allow the estimation of Tpot from flow cytometric data derive from this definition. Most authors, however, identify the potential doubling time as the doubling time that the same cell population would exhibit if cell loss were removed. We denote here as T(d)noloss this quantity. Although these two definitions are equivalent in the case of uniform random cell loss, we show, in the framework of Steel's theory of growing cell populations, that Tpot and T(d)noloss become distinct kinetic quantities when cell loss is not uniform, i.e., when loss differently affects the quiescent and the proliferative compartment. We discuss the validity of the two formulas currently used for the calculation of Tpot, one based on LI and the other on the v-function, in conditions of non-uniform cell loss. Moreover, we propose two formulas for the estimation of the cycle time T(C), which require, in addition to T(S) and LI, that a measure of the growth fraction be available.