Evaluation of the ray-casting analytical algorithm for pencil beam scanning proton therapy

For pencil beam scanned (PBS) proton therapy, analytical dose calculation engines are still typically used for the optimisation process, and often for the final evaluation of the plan. Recently however, the suitability of analytical calculations for planning PBS treatments has been questioned. Conceptually, the two main approaches for these analytical dose calculations are the ray-casting (RC) and the pencil-beam (PB) method. In this study, we compare dose distributions and dosimetric indices, calculated on both the clinical dose calculation grid and as a function of dose grid resolution, to Monte Carlo (MC) calculations. The analysis is done using a comprehensive set of clinical plans which represent a wide choice of treatment sites. When analysing dose difference histograms for relative treatment plans, pencil beam calculations with double grid resolution perform best, with on average 97.7%/91.9% (RC), 97.9%/92.7% (RC, double grid resolution), 97.6%/91.0% (PB) and 98.6%/94.0% (PB, double grid resolution) of voxels agreeing within  ±5%/±  3% between the analytical and the MC calculations. Even though these point-to-point dose comparison shows differences between analytical and MC calculations, for all algorithms, clinically relevant dosimetric indices agree within  ±4% for the PTV and within  ±5% for critical organs. While the clinical agreement depends on the treatment site, there is no substantial difference of indices between the different algorithms. The pencil-beam approach however comes at a higher computational cost than the ray-casting calculation. In conclusion, we would recommend using the ray-casting algorithm for fast dose optimization and subsequently combine it with one MC calculation to scale the absolute dose and assure the quality of the treatment plan.