Averaging of absorbed doses: How matter matters
Authors: Gustafsson Johan , Ljungberg Michael , Alm Carlsson Gudrun , Larsson Erik , Warfvinge Carl Fredrik , Asp Pernilla , Sjögreen Gleisner Katarina 
Published: June 2023

Background

Dosimetry in radionuclide therapy often requires the calculation of average absorbed doses within and between spatial regions, for example, for voxel‐based dosimetry methods, for paired organs, or across multiple tumors. Formation of such averages can be made in different ways, starting from different definitions.

Purpose

The aim of this study is to formally specify different averaging strategies for absorbed doses, and to compare their results when applied to absorbed dose distributions that are non‐uniform within and between regions.

Methods

For averaging within regions, two definitions of the average absorbed dose are considered: the simple average over the region (the region average) and the average when weighting by the mass density (density‐weighted region average). The latter is shown to follow from the definition of mean absorbed dose according to the ICRU, and to be consistent with the MIRD formalism. For averaging between different spatial regions, three definitions follow: the volume‐weighted, the mass‐weighted, and the unweighted average. With respect to characterizing non‐uniformity, the different average definitions lead to the use of dose‐volume histograms (DVHs) (region average), dose‐mass histograms (DMHs) (density‐weighted region average), and unweighted histograms (unweighted average). Average absorbed doses are calculated for three worked examples, starting from the different definitions. The first, schematic, example concerns the calculation of the average absorbed dose between two regions with different volumes or mass densities. The second, stylized, example concerns voxel‐based dosimetry, for which the average absorbed‐dose rate within a region is calculated. The geometries studied include three 177Lu‐filled voxelized spheres, where the sphere masses are held constant while the material compositions, densities, and volumes are varied. For comparison, the mean absorbed‐dose rates obtained using unit‐density sphere S‐values are also included. The third example concerns SPECT/CT‐based tumor dosimetry for five patients undergoing therapy with 177Lu‐PSMA and six patients undergoing therapy with 177Lu‐DOTA‐TATE, for which the average absorbed‐dose rates across multiple tumors are calculated. For the second and third examples, analyses also include representations by histograms.

Results

Example 1 shows that the average absorbed doses, calculated using different definitions, can differ considerably if the masses and absorbed doses for two regions are markedly different. From example 2 it is seen that the density‐weighted region average is stable under different activity and density distributions and is also in line with results using S‐values. In contrast, the region average varies as function of the activity distribution. In example 3, the absorbed dose rates for individual tumors differ by (1.1 ± 4.3)% and (−0.1 ± 0.4)% with maximum deviations of +34.4% and −1.4% for 177Lu‐PSMA and 177Lu‐DOTA‐TATE, respectively, when calculated as region averages or density‐weighted region averages, with largest deviations obtained when the density is non‐uniform. The average absorbed doses calculated across all tumors are similar when comparing mass‐weighted and volume‐weighted averages but these differ substantially from unweighted averages.

Conclusion

Different strategies for averaging of absorbed doses within and between regions can lead to substantially different absorbed‐dose estimates. At reporting of radionuclide therapy dosimetry, it is important to specify the averaging strategy applied.