A fast analytic dose calculation method for arc treatments for kilovoltage small animal irradiators

Arc treatments require calculation of dose for collections of discrete gantry angles. The sampling of angles must balance between short computation time of small angle sets and the better calculation reliability of large sets. In this paper, an analytical formula is presented that allows calculation of dose delivered during continuous rotation of the gantry. The formula holds valid for continuous short arcs of up to about 30° and is derived by integrating a dose formula over gantry angles within a small angle approximation. Doses for longer arcs may be obtained in terms of doses for shorter arcs. The formula is derived with an empirical beam model in water and extended to inhomogeneous media. It is validated with experimental data obtained by applying arc treatment using kV small animal irradiator to a phantom of solid water and lung-equivalent material. The results are a promising step towards efficient 3D dose calculation and inverse planning purposes. In principle, this method also applies to VMAT dose calculation and optimization but requires extensions.