A dose kernel based analytical algorithm for voxel dose calculation in nuclear medicine

Introduction Dose calculation in Nuclear Medicine is performed using the MIRD formalism, which calculates the average dose in each organ, rather than in each voxel. This precludes the development of dose-volume organ constraints, as is done in Radiation Therapy. Purpose To develop a voxel-based analytical dose calculation algorithm that relies on individual radionuclide dose kernels. Methods First, using ray-tracing techniques, the algorithm calculates the path, in 3D, from the source voxel to the target voxel. Then, in each voxel traversed, the fractional energy absorbed and the fractional energy transmitted are calculated using the radionuclide dose kernels. The dose kernels, i.e. the dose as a function of distance, have been previously calculated in spherical geometry for various radionuclides and homogeneous media using the GATE Monte Carlo toolkit. At each step, the dose kernel curve is read beginning at the fractional energy already deposited as a correction to account for photon spectral changes. Results The algorithm was compared with GATE for various geometric setups containing different materials, as well as the XCAT computational anthropomorphic model, using 99m Tc. Agreement is to within a few percent for relatively homogenous regions, worse at interfaces or in highly inhomogeneous regions. Conclusion A 3D voxel-based analytical dose calculation algorithm that relies on pre-calculated dose kernels has been developed. Discrepancies between the algorithm and Monte Carlo simulations can be attributed to the fact that the dose kernels have been calculated in homogeneous media and, therefore, do not sufficiently predict interface effects and scatter dose between different materials.