An analytic model to calculate voxel s-values for¹⁷⁷Lu

Objective.¹⁷⁷Lu is one of the most employed isotopes in targeted radionuclide therapies and theranostics, and 3D internal dosimetry for such procedures has great importance. Voxel S-Values (VSVs) approach is widely used for this purpose, but VSVs are available for a limited number of voxel dimensions. The aim of this work is to develop an analytic model for the calculation of¹⁷⁷Lu-VSVs in any cubic voxelized geometry of practical interest.Approach. Monte Carlo (MC) simulations were implemented with the toolkit GAMOS to evaluate VSVs in voxelized geometries of soft tissue from a source of¹⁷⁷Lu homogeneously distributed in the central voxel. Nine geometric setups, containing 15 × 15 × 15 cubic voxels of sideslranging from 2 mm to 6 mm, in steps of 0.5 mm, were considered. For eachl, the VSVs computed as a function of the 'normalized radius',R= R/l(withR = distance from the center of the source voxel), were fitted with a parametric function. The dependencies of the parameters as a function oflwere then fitted with appropriate functions, in order to implement the model for deducing¹⁷⁷Lu-VSVs for anylwithin the aforementioned range.Main results. The MC-derived VSVs were satisfactorily compared with literature data for validation, and the VSVs computed with the analytic model agree with the MC ones within 2% forR≤ 2 and within 6% forR> 2.Significance. The proposed model enables the easy and fast calculation, with a simple spreadsheet, of¹⁷⁷Lu-VSVs in any cubic voxelized geometry of practical interest, avoiding the necessity of implementingad-hocMC simulations to estimate VSVs for specific voxel dimensions not available in literature data.