Calculation of radiation doses for nonuniformity distributed beta and gamma radionuclides in soft tissue

In cancer radioimmunotherapy nonuniform distributions of radionuclides in geometrically irregular tumor volumes will be encountered. If the tumor is surrounded by a homogeneous layer of soft tissue, the radiation dose distribution in the tumor due to a beta-emitting nuclide can be calculated by convolution of the appropriate Loevinger's point source dose function, J, with the nuclide concentration distribution. Computer programs using fast Fourier transform techniques have been developed to evaluate the three-dimensional spatial convolution accurately and efficiently. Equivalent techniques have also been applied to gamma-emitting nuclides by replacing J in the convolution by the photon point isotropic specific absorbed fraction. Illustrative results are presented for the radiation dose distribution in a 1-ml target volume with activity distribution which is (i) uniform, (ii) limited by diffusion into the target volume, or (iii) limited by diffusion and shedding of radionuclide in the peripheral layers of the target volume. Calculations for the three cases are presented for 32P, 131I, and 15-, 30-, and 100-keV photon emitters.