Relationships between cell survival and specific energy spectra for therapeutic alpha-particle emitters

Cell survival studies are a means of quantifying the biological effects of radiation. However, for alpha-particle sources, the dose-response relationship is complicated by the dominance of microdosimetric effects. In this work, we relate observed cell survival to the microdosimetric energy deposition spectra. The chord length distributions through spherical cell nuclei for sources distributed inside of, on the surface of and outside of the critical target are used as approximate analytical representations of the single-event specific energy spectra. Mathematical relationships are derived which relate cell survival to the Laplace transform of the single-event specific energy spectrum. The result is an analytical relationship between D0 (the observed slope of the cell survival curve) and Z0 (the specific energy required to reduce the survival probability of a single cell to 1/e). These studies indicate that for small energy deposition events, Z0 is approximately equal to D0. However, as the maximum energy deposited by a single event is increased, there are marked deviations between Z0 and D0. These differences between Z0 and D0 are also related to the shape of the single-event spectrum. This technique provides a powerful tool for relating observed cell survival to microdosimetric quantities for therapeutic alpha-particle emitters.