title: Optimization of activity distribution in brachytherapy.
abstract: We investigated the problem of how to minimize the dose rate outside a spherical target volume for a given minimal dose rate inside the sphere for 1/r2 photon emitters. An integral equation for an activity distribution is derived from the demand that the dose rate is constant inside the sphere. The solution of this equation is given and it is proven that the resulting activity distribution gives the smallest dose rate at every point outside the target volume. Some other activity distributions are discussed; they are assessed by the required integral activity, which is proportional to the dose rate at some distance from the target volume. Compared with a single point source at the center of the sphere, one can save 50% of the total activity when using the optimal activity distribution. The benefit reduces to about 30% for the other continuous activity distributions and to a few % for symmetrical arrangements of a few point sources.
mesh_terms: D001918:Brachytherapy / Q000379:methods*; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical