Proton Arc Therapy Linear Energy Transfer Optimization for Stereotactic Radiosurgery of Multiple Small-Volume Brain Metastases Using the Alternating Direction Method of Multipliers

Abstract

Purpose: This study investigates the feasibility and potential clinical benefits of a novel linear energy transfer (LET) optimization method for proton arc therapy (PAT) in stereotactic radiosurgery (SRS) for small-volume brain metastases. The method incorporates a minimum monitor unit constraint and employs the alternating direction method of multipliers (ADMM) for optimization.Methods: PAT plans were developed for small-volume brain metastases (lesion diameter ≤3 cm, volume ≤6 cm³) using a MATLAB-based ADMM framework for plan optimization. PAT plan is created by a 360 degree full arc with 15 degree and 30 degree beam angle field frequency. The approach integrates LET optimization into PAT optimization. In the ADMM-LET framework, the optimization process entails iteratively solving the dose sub-problem and the LET sub-problem, simultaneously ensuring compliance with the MMU constraint. The weight of the dose objective and LET objectives are tuned. Two dual target small-volume and a ten target small-volume brain metastases clinical case was selected to demonstrate the feasibility of the method. Multiple beam configurations were evaluated to assess the advantages of LET-optimized PAT over multi-beam intensity-modulated proton therapy (IMPT) on both tumor coverage and organ-at-risk (OAR) sparing. Results: LET-optimized PAT plans were compared with non-LET-optimized plans across three patients with varying numbers of target lesions, and the results consistently demonstrated significant improvements in LET distribution following optimization. For the first two-target case (24-beam PAT), GTV1 showed increases in maximum, minimum, and mean LET by 4.92, 2.22, and 3.62 keV/μm, respectively, while GTV2 showed corresponding increases of 4.24, 1.35, and 3.03 keV/μm; concurrently, high-LET exposure to adjacent OARs was substantially reduced, with the left inner ear exhibiting reductions in maximum, minimum, and mean LET by 1.96, 0.24, and 0.97 keV/μm, and the brainstem showing reductions in maximum LET by 0.90 keV/μm and mean LET by 0.06 keV/μm. The second two-target case (24-beam PAT) yielded consistent results, with mean LET increases of 3.13 keV/μm for both GTVs and corresponding OAR LET reductions of 1.03 keV/μm in the brainstem and 0.33 keV/μm in the inner ear. Notably, the ten-target case (12-beam PAT) demonstrated the generalizability of the approach, with mean LET increase for individual GTVs reaching 2.41 keV/μm, while the left inner ear showed maximum LET reduction of 1.3 keV/μm (from 6.9 to 5.6 keV/μm) and mean LET reduction of 1.2 keV/μm (from 3.5 to 2.2 keV/μm), and the left optic nerve exhibited maximum LET reduction of 2.2 keV/μm (from 6.5 to 4.7 keV/μm) and mean LET reduction of 1.2 keV/μm (from 3.5 to 2.2 keV/μm), with the volume of high-LET regions (threshold 4 keV/μm) decreasing by 65% in the brainstem and 60% in the inner ear. In the 14 tumor targets, the BED distribution in PAT plans was more concentrated and uniform. Across all patients, as the number of beam fields increased, OAR LET exposure decreased substantially in LET-optimized plans without compromising tumor dose, and the PAT LET-optimized plans consistently showed more favorable uniformity of LET distribution within the target volume and greater reduction in high-LET regions within OARs compared to 3-field, 4-field, and 5-field IMPT plans, while minimum LET reduction remained relatively unchanged. Conclusion: This work demonstrates the feasibility and significant potential of LET-optimized PAT using ADMM for SRS. The method enables localized LET escalation within the tumor target while effectively reducing high-LET exposure to adjacent OARs. These findings support the application of LET-based biological optimization to improve therapeutic ratio for brain metastasis SRS.