A unified path seeking algorithm for IMRT and IMPT beam orientation optimization

Objective. Fully automated beam orientation optimization (BOO) for intensity-modulated radiotherapy and intensity modulated proton therapy (IMPT) is gaining interest, since achieving optimal plan quality for an unknown number of fixed beam arrangements is tedious. Fast group sparsity-based optimization methods have been proposed to find the optimal orientation, but manual tuning is required to eliminate the exact number of beams from a large candidate set. Here, we introduce a fast, automated gradient descent-based path-seeking algorithm (PathGD), which performs fluence map optimization for sequentially added beams, to visualize the dosimetric benefit of one added field at a time. Approach. Several configurations of 2-4 proton and 5-15 photon beams were selected for three head-and-neck patients using PathGD, which was compared to group sparsity-regularized BOO solved with the fast iterative shrinkage-thresholding algorithm (GS-FISTA), and manually selected IMPT beams or one coplanar photon VMAT arc (MAN). Once beams were chosen, all plans were compared on computational efficiency, dosimetry, and for proton plans, robustness. Main results. With each added proton beam, Clinical Target Volume (CTV) and organs at risk (OAR) dosimetric cost improved on average across plans by [1.1%, 13.6%], and for photons, [0.6%, 2.0%]. Comparing algorithms, beam selection for PathGD was faster than GS-FISTA on average by 35%, and PathGD matched the CTV coverage of GS-FISTA plans while reducing OAR mean and maximum dose in all structures by an average of 13.6%. PathGD was able to improve CTV [Dmax, D95%] by [2.6%, 5.2%] and reduced worst-case [max, mean] dose in OARs by [11.1%, 13.1%]. Significance. The benefit of a path-seeking algorithm is the beam-by-beam analysis of dosimetric cost. PathGD was shown to be most efficient and dosimetrically desirable amongst group sparsity and manual BOO methods, and highlights the sensitivity of beam addition for IMPT in particular.