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A tumour shrinkage factor is incorporated into previously derived linear-quadratic (LQ) formulae which allowed radiobiological assessment of the efficacy of permanently implanted radionuclides. The new formulations relate the biologically effective dose (BED) to radionuclide half-life, recovery half-life, tumour radiosensitivity, potential doubling time and linear shrinkage rate. Specific attention has been given to the following radionuclides: gold-198 (half-life, 2.7 days), palladium-103 (half-life, 17 days), ytterbium-169 (half-life, 32 days) and iodine-125 (half-life, 60 days). For each nuclide the log cell kill resulting from typically prescribed doses was calculated for a range of tumour clonogen doubling times at various radiosensitivities and linear shrinkage rates. It is shown that even relatively modest shrinkage rates are capable of enhancing the clinical potential of the longer-lived nuclides. However, even though the effect of tumour shrinkage is minimal in the case of gold-198, for fast growing and/or insensitive tumours there are fewer radiobiological uncertainties associated with the use of this nuclide. The revised equations may also have applications in certain types of biologically targeted radiotherapy.

Original publication




Journal article


British Journal of Radiology

Publication Date





639 - 645