Differences in Survival Curve Shapes for Formal Multi-target and Multi-hit Models

Abstract

Shapes of survival curves calculated from the two basic types of target model are examined. The multi-target, one-hit-on-each-target model is well known and gives rise to survival curves having an exponential form at high doses, and an extrapolation number equal to the assumed number of targets. The other type of model, requiring multiple hits on a single target, has been seldom discussed, and the properties of the resulting survival curves are explored. There are no finite extrapolation numbers, since the curves continue to bend over with increasing dose so that the tangent to the survival curve intercepts the ordinate axis at values which increase progressively with dose. These ` extrapolation numbers ' are much higher than the number of hits required to inactivate the target. In a combined model, where m targets, each requiring several hits, must be inactivated, the high ` extrapolation numbers ' will become still greater by the factor m. The case where large numbers of targets are present, only a few of which need be inactivated, is also discussed, and this model would also give increased extrapolation numbers. A one-target, multi-hit model with a broad distribution of hit humbers n is sufficient to explain any shape of mammalian cell survival curve so far observed. The multi-hit aspect is important, and may be considered to arise from the wide range of energies dissipated per particle track in different microscopic volumes in an irradiated population.