Use of the fast Hartley transform for three-dimensional dose calculation in radionuclide therapy

Effective radioimmunotherapy may depend on a priori knowledge of the radiation absorbed dose distribution obtained by trace imaging activities administered to a patient before treatment. A new, fast, and effective treatment planning approach is developed to deal with a heterogeneous activity distribution. Calculation of the three-dimensional absorbed dose distribution requires convolution of a cumulated activity distribution matrix with a point-source kernel; both are represented by large matrices (64x64x64). To reduce the computation time required for these calculations, an implementation of convolution using three-dimensional (3-D) fast Hartley transform (FHT) is realized. Using the 3-D FHT convolution, absorbed dose calculation time was reduced over 1000 times. With this system, fast and accurate absorbed dose calculations are possible in radioimmunotherapy. This approach was validated in simple geometries and then was used to calculate the absorbed dose distribution for a patient's tumor and a bone marrow sample.