Dose and dose rate objectives in Bragg peak and shoot-through beam orientation optimization for FLASH proton therapy

Abstract

Purpose: The combined use of Bragg peak (BP) and shoot-through (ST) beams has previously been shown to increase the normal tissue volume receiving FLASH dose rates while maintaining dose conformality compared to conventional intensity-modulated proton therapy (IMPT) methods. However, the fixed beam optimization method has not considered the effects of beam orientation on the dose and dose rates. To maximize the proton FLASH effect, here, we incorporate dose rate objectives into our beam orientation optimization framework.

Methods: From our previously developed group-sparsity dose objectives, we add upper and lower dose rate terms using a surrogate dose-averaged dose rate definition and solve using the fast-iterative shrinking threshold algorithm. We compare the dosimetry for three head-and-neck cases between four techniques: (1) spread-out BP IMPT (BP), (2) dose rate optimization using BP beams only (BP-DR), (3) dose rate optimization using ST beams only (ST-DR), and (4) dose rate optimization using combined BP and ST (BPST-DR), with the goal of sparing organs at risk without loss of tumor coverage and maintaining high dose rate within a 10 mm region of interest (ROI) surrounding the clinical target volume (CTV).

Results: For BP, BP-DR, ST-DR, and BPST-DR, CTV homogeneity index and Dmax were found to be on average 0.886, 0.867, 0.687, and 0.936 and 107%, 109%, 135%, and 101% of prescription, respectively. Although ST-DR plans were not able to meet dosimetric standards, BPST-DR was able to match or improve either maximum or mean dose in the right submandibular gland, left and right parotids, constrictors, larynx, and spinal cord compared to BP plans. Volume of ROIs receiving greater than 40 Gy/s ( $V_{\gamma 0})$ was 51.0%, 91.4%, 95.5%, and 92.1% on average.

Conclusions: The dose rate techniques, particularly BPST-DR, were able to significantly increase dose rate without compromising physical dose compared with BP. Our algorithm efficiently selects beams that are optimal for both dose and dose rate.

Keywords: FLASH; dose optimization; proton.