Purpose: Empirical relative biological effectiveness (RBE) models and dose averaged LET surrogates have been separately used to estimate the biological dose in proton therapy. Neither method adequately captures the factors influencing RBE values for treatment planning. Here we incorporate McNamara RBE (RBE(M)) and LET in a beam orientation (BOO) and fluence map optimization (FMO) framework with alternating objective functions.
Methods: Based on our previously developed robust sensitivity-regularized and heterogeneity weighted BOO (SHBOO) framework, we formulated the optimization problem using two different methods. The first method optimized RBE(M)-weighted dose, updating RBE(M) values with each round of optimization until they converged (RBEwFMO). The second alternated between RBE(M)-weighted and LET-weighted doses, until the RBE values converged (RBELETwFMO). We compare their performance with a physical dose optimizer assuming RBE(1.1) (PHYSFMO). Three head and neck patients were planned with the three techniques and compared on dosimetry and robustness.
Results: Compared to PHYSFMO, CTV homogeneity and Dmax were improved by an average of 0.02 and 1.4 GyRBE for RBELETwFMO, and 0.03 and 2.3 GyRBE for RBEwFMO. D98% was improved by RBEwFMO by 0.6 GyRBE. Slight decrease in mean and maximum RBE dose was seen in the larynx, esophagus, and constrictors with RBEwFMO and RBELETwFMO. Regarding robustness, worst [Dmax, V95%, D95%, D98%] for CTVs improved by [4.2%, 31.9%, 5.5%, 4.7%] with RBEwFMO and [2.4%, 33.2%, 6.7%, 5.4%] with RBELETwFMO under range and setup uncertainties. For OARs, the worst [Dmax, Dmean] improved by an average of [3.1, 0.8] GyRBE for RBEwFMO and [5.3, 2.0] GyRBE for RBELETwFMO under setup uncertainties.
Conclusion: The three optimization techniques deliver comparable physical doses for the head and neck cases. Beside modest OAR RBE dose sparing improvement, CTV coverage and overall robustness were substantially improved with RBEwFMO and RBELETwFMO, showing potential benefit for directly incorporating McNamara RBE in proton treatment planning.