Stochastic versus deterministic kernel-based superposition approaches for dose calculation of intensity-modulated arcs

Dose calculations for radiation arc therapy are traditionally performed by approximating continuous delivery arcs with multiple static beams. For 3D conformal arc treatments, the shape and weight variation per degree is usually small enough to allow arcs to be approximated by static beams separated by 5 degrees -10 degrees . But with intensity-modulated arc therapy (IMAT), the variation in shape and dose per degree can be large enough to require a finer angular spacing. With the increase in the number of beams, a deterministic dose calculation method, such as collapsed-cone convolution/superposition, will require proportionally longer computational times, which may not be practical clinically. We propose to use a homegrown Monte Carlo kernel-superposition technique (MCKS) to compute doses for rotational delivery. The IMAT plans were generated with 36 static beams, which were subsequently interpolated into finer angular intervals for dose calculation to mimic the continuous arc delivery. Since MCKS uses random sampling of photons, the dose computation time only increased insignificantly for the interpolated-static-beam plans that may involve up to 720 beams. Ten past IMRT cases were selected for this study. Each case took approximately 15-30 min to compute on a single CPU running Mac OS X using the MCKS method. The need for a finer beam spacing is dictated by how fast the beam weights and aperture shapes change between the adjacent static planning beam angles. MCKS, however, obviates the concern by allowing hundreds of beams to be calculated in practically the same time as for a few beams. For more than 43 beams, MCKS usually takes less CPU time than the collapsed-cone algorithm used by the Pinnacle(3) planning system.