The linear-quadratic (LQ) dose-effect formalism is currently providing new perspectives into the ways in which alterations in the dose per fraction in conventional radiotherapy may be used to bring about improved results with respect to early or late normal tissue reactions. In this paper, using a model initially developed by Roesch, the LQ equations are explored further in terms of dose-rate rather than dose. By the incorporation of one other parameter, mu, which relates to the rate of repair of sub-lethal radiation damage, a more general formalism is obtained. In particular, equations are derived which can be used to examine the relative effectiveness of different treatment regimes, including those involving decaying sources. Such equations are of wider applicability than other LQ derivations which relate only to dose-response relationships. The extended equations, which are fully consistent with the existing LQ method, are also shown to lead directly to other independently established, relationships for protracted irradiation. The nature of the link between high and low dose-rate treatments is discussed, and some worked examples provide indications of how the new equations may be used to assess further the potential clinical benefits of low dose-rate treatments and permanent implants.

By combining existing linear-quadratic equations relating to decaying-source therapy with an assumed tumour repopulation factor, it has been possible to devise a method for the radiobiological assessment of permanent implants. For calculation purposes there is a time after which an implant can no longer be considered effective in sterilizing tumour cells. This "effective" treatment time for a permanent implant can be approximately defined in terms of the radionuclide decay constant, the potential doubling time, the initial dose-rate and the value of alpha in the tumour alpha/beta ratio. The analytical technique has been applied to a specific intercomparison of commonly encountered implants using 125I and 198Au, and suggests that, even in the most favourable cases, the former radionuclide offers few radiobiological advantages. Although not specifically discussed here, the method can also be applied to the assessment of various forms of biologically targeted radiotherapy.

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A technique for deriving the tissue-absorbed dose resulting from the use of a selection of nuclides commonly employed in brachytherapy is given. The various parameters required have been obtained from a Monte Carlo computer program which derives tissue attenuation data from the equations of White and Fitzgerald (1977a). Some inconsistencies in the data used to obtain the equations are noted and corrected. Useful results are presented and, in particular, possible dosimetric errors associated with the clinical use of 125I seeds are highlighted.