Survival curves and dose fractionation: some general characteristics

The response of a cellular population to fractionated doses of radiation has been investigated analytically based on the general kinetic model of radiation response with the multitarget and multihit models included as special cases. The results of this analysis are: 1) Maximum recovery occurs for equal-dose fractions. This conclusion is valid for the recovery ratio at a given dose as well as for the dose difference at a given survival level. 2) For equal-dose fractions explicit, but rather complicated, formulas were obtained for the recovery characteristics as a function of the number of fractions. 3) Simple relations and scaling rules are valid in the region, i.e., if the survival is at high doses and each fractional dose is high enough for each fractional survival to be in the region. The exponential restriction is important and the simple results must be used with caution. The biological limitations of the treatment are pointed out.