A general formula for equating protracted and acute regimes of radiation

Abstract

Suppose that a continuous low dose-rate radium treatment lasting t hours is replaced by a high dose-rate after-loading treatment employing N fractions. Theory, based on the recovery of intracellular sub-lethal damage, suggests that the total fractionated dose necessary to produce an equivalent effect on each irradiated tissue will be the same as the protracted dose, provided N and t are related by a formula which, for values of t>12 hours, approximates to N=t/4. If, in order to give Nfractions without spacing them too close together, the overall treatment time is increased to (N—1) days, the total fractionated dose should, however, be increased by C rads for each day by which the overall time is increased. It is suggested that for skin C is approximately equal to 25 rads per day. The formula is shown to be valid for skin reactions in patients and for LD50(3O) in mice. Theory suggests that the formula is likely to be approximately true for most mammalian tissues irradiated at normal body temperature, irrespective of their recovery regression coefficients. Thus, changing to a high dose-rate regime should produce no deterioration in the therapeutic ratio provided the treatment is fractionated in accordance with the proposed formula. If the number of fractions is reduced from N to some lower number, the corresponding reduction in required dose may be found using the formula of Ellis (1967) or the nomogram of Shuttleworth and Fowler (1966). Such a change may, however, be accompanied by a change in therapeutic ratio.