An analytical method for computing voxel S values for electrons and photons

Purpose: The use of voxel S values (VSVs) is perhaps the most common approach to radiation dosimetry for nonuniform distributions of activity within organs or tumors. However, VSVs are cur- rently available only for a limited number of voxel sizes and radionuclides. The objective of this study was to develop a general method to evaluate them for any spectrum of electrons and photons in any cubic voxel dimension of practical interest for clinical dosimetry in targeted radionuclide therapy. Methods: The authors developed a Monte Carlo simulation in Geant4 in order to evaluate the energy deposited per disintegration (Edep ) in a voxelized region of soft tissue from monoenergetic electrons (10–2000 keV) or photons (10–1000 keV) homogeneously distributed in the central voxel, consid- ering voxel dimensions ranging from 3 mm to 10 mm. Edep was represented as a function of a di- mensionless quantity termed the “normalized radius,” Rn = R/l, where l is the voxel size and R is the distance from the origin. The authors introduced two parametric functions in order to fit the electron and photon results, and they interpolated the parameters to derive VSVs for any energy and voxel side within the ranges mentioned above. In order to validate the results, the authors determined VSV for two radionuclides (131 I and 89 Sr) and two voxel dimensions and they compared them with ref- erence data. A validation study in a simple sphere model, accounting for tissue inhomogeneities, is presented. Results: The Edep (Rn ) for both monoenergetic electrons and photons exhibit a smooth variation with energy and voxel size, implying that VSVs for monoenergetic electrons or photons may be derived by interpolation over the range of energies and dimensions considered. By integration, S values for continuous emission spectra from β − decay may be derived as well. Conclusions: The approach allows the determination of VSVs for monoenergetic (Auger or con- version) electrons and (x-ray or gamma-ray) photons by means of two functions whose parame- ters can be interpolated from tabular data provided. Through integration, it is possible to general- ize the method to any continuous (beta) spectrum, allowing to calculate VSVs for any electron and photon emitter in a voxelized structure.