Mathematical solutions of the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus sources, and applications for quality assurance

Analytic solutions for the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus shapes containing uniform distributions of air-kerma are derived. These geometry functions describe how dose distributions vary strictly due to source geometry and not including attenuation or scatter effects. This work extends the use of geometry functions for individual sources to applicators containing multiple sources. Such geometry functions may be used to verify dose distributions computed using advanced techniques, including QA of model-based dose calculation algorithms. The impact of source curvature on linear and planar implants is considered along with the specific clinical case of brachytherapy eye plaques. For eye plaques, the geometry function for a domed distribution is used with published Monte Carlo dose distributions to determine a radial dose function and anisotropy function which includes all the scatter and attenuation effects due to the phantom, eye plaque and sources. This TG-43 model of brachytherapy eye plaques exactly reproduces azimuthally averaged Monte Carlo calculations, both inside and outside the eye.