An analytic model to calculate voxel s-values for¹⁷⁷Lu.

<i>Objective</i>.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.<i>Approach</i>. 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 sides<i>l</i>ranging from 2 mm to 6 mm, in steps of 0.5 mm, were considered. For each<i>l</i>, the VSVs computed as a function of the 'normalized radius',<i>R</i>_<i>n</i>= <i>R/l</i>(with<i>R</i> = distance from the center of the source voxel), were fitted with a parametric function. The dependencies of the parameters as a function of<i>l</i>were then fitted with appropriate functions, in order to implement the model for deducing¹⁷⁷Lu-VSVs for any<i>l</i>within the aforementioned range.<i>Main results</i>. 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% for<i>R</i>_<i>n</i>≤ 2 and within 6% for<i>R</i>_<i>n</i>&gt; 2.<i>Significance</i>. 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 implementing<i>ad-hoc</i>MC simulations to estimate VSVs for specific voxel dimensions not available in literature data.