The application of dose-rate volume histograms and survival fractions to multicellular dosimetry

The distribution of therapeutic radiopharmaceuticals in volumes smaller than those that can be fully resolved by the imaging system, such as by PET and SPECT scanners, is usually assumed to be homogeneous. The aim of this study was to investigate the implications of such an assumption at a scale that can be defined as multicellular for heterogeneous activity localizations of (32)P, (90)Y, and (131)I. Dose-rate distributions from heterogeneous radioactivity uptakes have been calculated in cubic volumes of 1, 3, and 4 mm using the in-house software package DOVE. These have been studied by the use of dose-rate volume histograms, and the influence of the heterogeneous dose distribution on the treatment outcome has been analyzed by the calculation of Integral Survival Fractions. The results showed that the effect of the heterogeneous localization of the compound can be overridden by the amount of radioactivity administered. However, significant variations in the survival probability distributions have been observed, depending on the amount of initial activity considered, the activity configuration, the radionuclide, and the time over which the energy was deposited. It has been shown, for example, that the ability of longer-range beta emitters, such as (32)P and (90)Y, to invalidate heterogeneous dose-rate distributions may be negated by the decay rate of the radioactivity.