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Proceedings of the British Institute of Radiology

In radiotherapy, the total dose delivered has to be increased with increase in the number of "daily" fractions. Strandqvist has expressed the relationship between the total dose and the number of fractions by an empirical formula. We have shown that when the effectiveness of a single dose is considered to be proportional to the sum of two terms, the first varying with the dose and the second varying with the square of the dose, the Strandqvist formula may be replaced by one based on these concepts, which have a biological instead of an empirical basis. The resulting expression

(where a dose d repeated for n fractions is equivalent to a single dose D₀) fits collected radiotherapy data at least as well as the Strandqvist formula. It is assumed that recovery does not vary greatly between the first fraction and the last. It follows that for systems where the biological effect is proportional to the number of cells damaged:

(i) Doses of the order of those used in radiotherapy are equivalent to a single dose in which the square dose term is three times as important as the linear dose term.

(ii) The effectiveness of different single doses may be compared and increases more rapidly than the magnitude of the dose.

(iii) Small doses (less than a few tens of rads) are additive, regardless of fractionation.