Reformulated McNamara RBE-weighted beam orientation optimization for intensity modulated proton therapy

Empirical relative biological effectiveness (RBE) models have been used to estimate the biological dose in proton therapy but do not adequately capture the factors influencing RBE values for treatment planning. We reformulate the McNamara RBE model such that it can be added as a linear biological dose fidelity term within our previously developed sensitivity-regularized and heterogeneity-weighted beam orientation optimization (SHBOO) framework.

Based on our SHBOO framework, we formulated the biological optimization problem to minimize total McNamara RBE dose to OARs. We solve this problem using two optimization algorithms: FISTA (McNam-FISTA) and Chambolle-Pock (McNam-CP). We compare their performances with a physical dose optimizer assuming RBE = 1.1 in all structures (PHYS-FISTA) and an LET-weighted dose model (LET-FISTA). Three head and neck patients were planned with the four techniques and compared on dosimetry and robustness.

Compared to Phys-FISTA, McNam-CP was able to match CTV [HI, Dmax, D95%, D98%] by [0.00, 0.05%, 1.4%, 0.8%]. McNam-FISTA and McNam-CP were able to significantly improve overall OAR [Dmean, Dmax] by an average of [36.1%,26.4%] and [29.6%, 20.3%], respectively. Regarding CTV robustness, worst [Dmax, V95%, D95%, D98%] improvement of [-6.6%, 6.2%, 6.0%, 4.8%] was reported for McNam-FISTA and [2.7%, 2.7%, 5.3%, -4.3%] for McNam-CP under combinations of range and setup uncertainties. For OARs, worst [Dmax, Dmean] were improved by McNam-FISTA and McNam-CP by an average of [25.0%, 19.2%] and [29.5%, 36.5%], respectively. McNam-FISTA considerably improved dosimetry and CTV robustness compared to LET-FISTA, which achieved better worst-case OAR doses.

The four optimization techniques deliver comparable biological doses for the head and neck cases. Besides modest CTV coverage and robustness improvement, OAR biological dose and robustness were substantially improved with both McNam-FISTA and McNam-CP, showing potential benefit for directly incorporating McNamara RBE in proton treatment planning.