Use of the fast Hartley transform for efficient 3D convolution in calculation of radiation dose

In radionuclide therapy, absorbed dose is calculated by convolution of a three-dimensional activity matrix with a three-dimensional dose point kernel. A technique employing the fast Hartley Transform (FHT) has been developed to perform this calculation. An important part of that development was the indexing scheme for 3D data. The results of this new FHT convolution technique were compared to direct convolution. A cube was convolved with itself by these two techniques. The results differed by less than 2 percent. In an effort to show the practical applicability of 3D convolution, a three-dimensional activity matrix from a I-131-labeled 16.88 monoclonal antibody patient was convolved with beta and photon dose point kernels using direct convolution. Isodose contours were then generated from the calculated absorbed dose matrix and overlaid on a CT image of the patient.<>