A spherical dose model for radiosurgery plan optimization

Conventional 3D dose calculations for stereotactic radiosurgery involve integration of individual static beams comprising a set of arcs. For iterative optimization of multiple isocentre treatment, which requires repetitive dose calculations at a large number of sample points, the conventional method is too slow. To overcome this problem spherically symmetric dose distributions are assumed. The authors describe a spherical dose model derived from a parametrized convolution of the collimator width and a dose spread kernel. The method is fast and easy to implement requiring just a single empirically derived value. Furthermore, the model is differentiable with respect to the parameters to be optimized. This property is useful when the optimization strategies rely on gradient information.