125I liquid in an intracranial balloon: TG-43 formalism for an extended source

Purpose To present a calculation formalism for spherical homogeneous liquid brachytherapy sources and to analyze the difficulties encountered in numerical integration over non-spherical source volumes. Methods and Materials TG-43 formalism provides a general definition of the geometric factor for distributed source distributions. Here the geometric factor and dose for a spherical source are computed for an 125I balloon. The errors in numerical summation of dose from point sources are assessed by computing ratios of the geometric factors of point-source and extended-source voxel volumes. Results This sphere calculation agrees well with measured dose values, showing maximum and average differences of 4.8% and 0.5% at the balloon surface. Numerical integration gives errors greater than 1% within five voxel radii of a voxel source. Conclusions A new spherical dose calculation technique is proposed for brachytherapy treatment planning systems. Numerical integration over point source voxels is not accurate near the balloon surface.