Calculation of generic dose kernels for cubic and non-cubic voxels of arbitrary dimension to be used in dose calculations in radionuclide therapy

Objectives In radionuclide therapy personalized, voxel-based dose assessment gains more and more importance and can be performed by convolving the cumulated activity distribution with a dose kernel. Due to differently reconstructed voxel sizes in molecular imaging dose kernels for arbitrary dimensions are necessary. So far these are only available for cubic voxels which is why this work focuses on the calculation of generic dose kernels for cubic as well as non-cubic voxels.

Methods Based on validated dose kernels for integer millimeter steps different interpolation approaches for the calculation of non-integer dose kernels were tested, using the two nearest integer kernels. Interpolation values for ten different, non-integer voxel sizes, non-cubic as well as cubic, were computed for three radionuclides representing short, middle and long csda range, i.e. P-32, P-33 as well as Y-90 and subsequently compared to MCNP simulations. A Python script for an automated calculation of dose kernels was developed. Additionally, the accuracy of the interpolation and its effect on the calculated dose was analyzed. For this reason the convolution between the interpolation results as well as the MCNP results and a tumor model with different cumulated activity distributions was computed and the obtained voxel doses were compared. sizes, non-cubic as well as cubic, were computed for three radionuclides representing short, middle and long csda range, i.e. P-32, P-33 as well as Y-90 and subsequently compared to MCNP simulations. A Python script for an automated calculation of dose kernels was developed. Additionally, the accuracy of the interpolation and its effect on the calculated dose was analyzed. For this reason the convolution between the interpolation results as well as the MCNP results and a tumor model with different cumulated activity distributions was computed and the obtained voxel doses were compared.

Results A mono-exponential interpolation of the dose values as a function of the natural logarithm of the volume yields the best approach to the simulation results. The developed Python script enables the calculation of dose kernels for non-cubic voxel sizes whose values are in a very good agreement with the Monte Carlo simulations. For 17 out of 30 calculated dose kernels the relative deviation to MCNP is smaller than 10% for each matrix element. Considering only the Moore-neighbourhood of the source voxel, i.e. the voxels which deliver the highest dose values, the mean error is 2.67%. Furthermore the deviations of the interpolated kernel never amount to more than 5.3% of the corresponding central source voxel. On this account also the convolution results show negligible small differences (< 1%) in the calculation of the tumor dose.

Conclusions Summing up, the chosen interpolation method provides a good approximation for non-cubic dose kernels of non-integer millimeter dimensions. Larger deviations at the edge of the kernel hardly affect the calculated dose due to their small, absolute values. The present work therefore enables the calculation of generic dose kernel for cubic and non-cubic voxels of arbitrary dimension to be used for voxel-based dose assessment in radionuclide therapy.