[Foundation of the Ellis-formula (author's transl)]

Abstract

The Ellis-formula is used in radiation therapy to derive the nominal dose. This nominal dose is an index of effectiveness applicable to different fraction schemes. Its critical value, the standard nominal dose, corresponds to the tolerance of normal tissue. The Ellis-formula is first compared to the earlier equation of Strandqvist. The Strandqvist equation accounts only for the total duration of the irradiation series. In contrast, the dominant factor in the Ellis-formula is the dose per fraction; the total duration is of secondary importance. It is then explained how the so-called TDF-factor is applied to derive the nominal dose for the combination of two partial fractionation series. The usual way to account for an extended interruption in a fractionation schedule is also considered. The common generalozation of the Ellis-formula rests on approximations; it is also restricted to the combination of two partial series. In order to overcome the limitation a new numerical method is presented which provides nominal doses for irregular fractionation schedules. The procedure follows without additional postulates from the basic assumptions underlying the Ellis-formula. It does not apply to continuous irradiation.