Purpose: Convolution-based radionuclide dose calculations require energy deposition kernels of appropriate size and resolution. The purpose of this work was to demonstrate a method for efficient and accurate resampling of publicly available energy deposition kernels from the pre-tabulated radial coordinates to the Cartesian image domain.
Methods: Kernels from a previously described library (Graves et al., AAPM, 2018) were sampled onto a Cartesian matrix, consisting of voxels sized smaller than the image data by an integer multiplier (resample factor â€“ rf). The energy contained within the center voxel in this high-resolution matrix was calculated by integrating the radial dose point kernel to a volume equal to the volume of the center voxel. To enforce the requirement that activity is uniformly distributed within a voxel in the image domain, this high-resolution kernel was convolved with a rectangular function equal to the size of an image voxel. The result of this convolution was down-sampled to the target image resolution, and scaled to conserve energy.
Results: Kernel generation (25x25x25 voxels; rf=8) was complete within ~3.2 seconds on a workstation grade CPU in MatLab. With a peak memory allocation of <200 MB, this process appears feasible on standard clinical workstations. Computation time did not depend significantly on voxel-size, and diminishing returns on spatial accuracy were observed for rf > 8. The resulting kernels compared favorably against literature kernels that were generated natively in a Cartesian geometry. For accurate incorporation of photon dose it was found desirable to generate a larger low-resolution photon-only kernel. This two-kernel approach accelerates the subsequent dose calculation, potentially increasing collapsed cone-type calculation speed.
Conclusion: It is feasible to rapidly and accurately compute a custom radionuclide dose kernel from publicly available radial energy deposition kernels. These methods expand calculation flexibility in voxelwise targeted radiopharmaceutical dosimetry.