An explanatory hypothesis for early- and late-effect parameter values in the LQ model.

The isoeffect equation derived from the linear-quadratic (LQ) model of cell survival contains linear and quadratic terms in dose. Experimental studies have shown that higher-order terms may also be present. These terms have been previously attributed to the fact that the LQ model may be the first two terms in a power series approximation to a more complex model. This study shows that higher-order terms are introduced as a result of heterogeneity in the response of the cell population being irradiated. This heterogeneity is modeled by assuming that the parameters alpha and beta in the LQ model are distributed according to a bivariate normal distribution. Using this distribution, the expected value of cell survival contains third- and fourth-order terms in dose. These terms result in the previously observed downward curvature of Fe plots. Furthermore, these higher-order terms introduce bias in the estimated values of alpha and beta, if only the linear and quadratic terms of the LQ model are used, and higher-order terms are ignored. The bias is such that the estimated value of alpha/beta is substantially increased. Thus the higher values of alpha/beta observed for early effects as compared to late effects may be due to greater heterogeneity of response in early-responding tissues than in later-responding tissues. This differential effect is maintained even if the two cell populations have the same average values of alpha and beta.