Tumor dependence of observed thymidine index as a function of emulsion exposure

The graphs of observed pulse thymidine index against duration of emulsion exposure for seven experimental tumor systems have been observed to exhibit significant differences; either they were parallel and displaced, or they were nonparallel. The immediate practical consequence of this phenomenon is that identical emulsion exposure times, other experimental conditions being equal, may not be sufficient to provide valid comparison of thymidine indices among tumors. A mathematical model is described which relates observed autoradiographic labeling index to the distribution of radioactive atoms among individual cells that initially incorporate labeled material. Two distributions for uptake are considered, and the results are compared. One model assumes uniform uptake, and the other assumes that the number of radioactive atoms among cells acquiring label follows a gamma distribution. The gamma-distributed uptake model fits the observed thymidine index data for the seven tumors and may be expressed as Lj(t) = a[1 - Qj(1 + bt) -u] where Lj(t) is the labeling index for emulsion exposure duration of t, Qj is a polynomial, and a, b, and u are adjustable parameters. The counting threshold for scoring a cell as labeled is j and for j = 1, Q1 = 1. The model indicates that the labeling index should increase with the duration of emulsion exposure and that this increase is related to the proportion of "lightly" labeled cells. The parameter a is the maximum expected labeling index, and an estimate of this parameter should theoretically be independent of emulsion exposure time.