The Hug-Kellerer equation as the universal cell survival curve.

The Hug-Kellerer (H-K) equation is one of the earliest proposed radiation cell survival curves. We examine this equation in view of the recent perceived need for a universal cell survival curve which would be applicable to single radiation fractions at high doses. We derive relationships between the three parameters of the H-K equation and the parameters alpha and beta of the linear-quadratic equation. Using these relationships we show how the H-K equation can be used to determine single-fraction doses which are equivalent in theory to the dose in a conventional multi-fraction course of radiation therapy.