Linear energy transfer weighted beam orientation optimization for intensity-modulated proton therapy

Abstract

Purpose: In intensity-modulated proton therapy (IMPT), unaccounted-for variation in biological effectiveness contributes to the discrepancy between the constant relative biological effectiveness (RBE) model prediction and experimental observation. It is desirable to incorporate biological doses in treatment planning to improve modeling accuracy and consequently achieve a higher therapeutic ratio. This study addresses this demand by developing a method to incorporate linear energy transfer (LET) into beam orientation optimization (BOO).

Methods: Instead of RBE-weighted dose, this LET weighted BOO (LETwBOO) framework uses the dose and LET product (LET $\times$ D) as the biological surrogate. The problem is formulated with a physical dose fidelity term, a LET $\times$ D constraint term, and a group sparsity term. The LET $\times$ D of organs at risks is penalized for minimizing the biological effect while maintaining the physical dose objectives. Group sparsity is used to reduce the number of active beams from 600-800 non-coplanar candidate beams to between 2 and 4. This LETwBOO method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The LETwBOO plans were compared with IMPT plans using manually selected beams with only physical dose constraint (MAN) and the initial MAN plan reoptimized with additional LET $\times$ D constraint (LETwMAN).

Results: The LETwBOO plans show superior physical dose and LET $\times$ D sparing. On average, the [mean, maximal] doses of organs at risks (OARs) in LETwBOO are reduced by [2.85, 4.6] GyRBE from the MAN plans in the SBT cases and reduced by [0.9, 2.5] GyRBE in the H&N cases, while LETwMAN is comparable to MAN. cLET × Ds of PTVs are comparable in LETwBOO and LETwMAN, where c is a scaling factor of 0.04 μm/keV. On average, in the SBT cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [1.1, 2.9] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.7, 1.7] Gy. In the H&N cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [0.8, 2.6] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.3, 1.2] Gy.

Conclusion: We developed a novel LET weighted BOO method for IMPT to generate plans with improved physical and biological OAR sparing compared with the plans unaccounted for biological effects from BOO.

Keywords: RBE; intensity modulation; linear energy transfer; optimization; proton therapy; spot scanning.