Optimizing an analytical dose calculation algorithm for fast 2D calculations

Previously, an analytical dose calculation algorithm for MLC-based radiotherapy was developed and commissioned, which includes a detailed model of various MLC effects as a unique feature [1]. The algorithm was originally developed as an independent verification of the treatment planning system's dose calculation and it explicitly modeled spatial and depth dependent MLC effects such as interleaf transmission, the tongue-and-groove effect, rounded leaf ends, MLC scatter, beam hardening, and divergence of the beam, which in turn resulted in a gradual MLC transmission frill-off with increasing off-axis distance. Originally the algorithm was implemented in Mathematica (TM) (Wolfram). To speed up the calculation time and to be able to calculate high resolution 2D dose distributions within a reasonable time frame (<2 s) the algorithm needs to be optimized and to be embedded in a user friendly environment. To achieve this goal, the dose calculation model is implemented in VisualBasic 6.0, which decreases the calculation time moderately. More importantly, the numerical algorithm for dose calculation is changed at two levels: the dose contributions are split into their x- and y-contributions and the calculation is aperture- rather than as originally point-based. Implementing these three major changes, the calculation time is reduced considerably without loosing accuracy. The time for a typical IMRT field with about 2500 calculation points decreased from 2387 seconds to 0.624 seconds (a factor of about 3800). The mean agreement of the optimized and the not optimized calculation algorithm at the isocenter fir a fairly complex IMRT plan with 23 fields is better than 1% relative to the local dose at the measuring point.