Robust beam orientation optimization for intensity-modulated proton therapy

Dose conformality and robustness are equally important in intensity modulated proton therapy (IMPT). Despite the obvious implication of beam orientation on both dosimetry and robustness, an automated, robust beam orientation optimization algorithm has not been incorporated due to the problem complexity and paramount computational challenge. In this study, we developed a novel IMPT framework that integrates robust beam orientation optimization (BOO) and robust fluence map optimization (FMO) in a unified framework.

The unified framework is formulated to include a dose fidelity term, a heterogeneity-weighted group sparsity term, and a sensitivity regularization term. The L2, 1/2-norm group sparsity is used to reduce the number of active beams from the initial 1162 evenly distributed noncoplanar candidate beams, to between two and four. A heterogeneity index, which evaluates the lateral tissue heterogeneity of a beam, is used to weigh the group sparsity term. With this index, beams more resilient to setup uncertainties are encouraged. There is a symbiotic relationship between the heterogeneity index and the sensitivity regularization; the integrated optimization framework further improves beam robustness against both range and setup uncertainties. This Sensitivity regularization and Heterogeneity weighting based BOO and FMO framework (SHBOO-FMO) was tested on two skull-base tumor (SBT) patients and two bilateral head-and-neck (H&N) patients. The conventional CTV-based optimized plans (Conv) with SHBOO-FMO beams (SHBOO-Conv) and manual beams (MAN-Conv) were compared to investigate the beam robustness of the proposed method. The dosimetry and robustness of SHBOO-FMO plan were compared against the manual beam plan with CTV-based voxel-wise worst-case scenario approach (MAN-WC).

With SHBOO-FMO method, the beams with superior range robustness over manual beams were selected while the setup robustness was maintained or improved. On average, the lowest [D95%, V95%, V100%] of CTV were increased from [93.85%, 91.06%, 70.64%] in MAN-Conv plans, to [98.62%, 98.61%, 96.17%] in SHBOO-Conv plans with range uncertainties. With setup uncertainties, the average lowest [D98%, D95%, V95%, V100%] of CTV were increased from [92.06%, 94.83%, 94.31%, 78.93%] in MAN-Conv plans, to [93.54%, 96.61%, 97.01%, 91.98%] in SHBOO-Conv plans. Compared with the MAN-WC plans, the final SHBOO-FMO plans achieved comparable plan robustness and better OAR sparing, with an average reduction of [Dmean, Dmax] of [6.31, 6.55] GyRBE for the SBT cases and [1.89, 5.08] GyRBE for the H&N cases from the MAN-WC plans.

We developed a novel method to integrate robust BOO and robust FMO into IMPT optimization for a unified solution of both BOO and FMO, generating plans with superior dosimetry and good robustness.