Optimizing linear energy transfer distribution in intensity-modulated proton therapy using the alternating direction method of multipliers

Abstract

PurposeThis study develop a novel linear energy transfer (LET) optimization method for intensity-modulated proton therapy (IMPT) with minimum monitor unit (MMU) constraint using the alternating direction method of multipliers (ADMM).Material and methodsThe novel LET optimization method (ADMM-LET) was proposed with (1) the dose objective and the LET objective as the optimization objective and (2) the non-convex MMU threshold as a constraint condition. ADMM was used to solve the optimization problem. 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. Three representative cases, including brain, liver, and prostate cancer, were utilized to evaluate the performance of the proposed method. The dose and LET distributions from ADMM-LET were compared to those obtained using the published iterative convex relaxation (ICR-LET) method.ResultsThe results demonstrate the superiority of ADMM-LET over ICR-LET in terms of LET distribution while achieving a comparable dose distribution. More specifically, for the brain case, the maximum LET (unit: keV/µm) at the optic nerve decreased from 5.45 (ICR-LET) to 1.97 (ADMM-LET). For the liver case, the mean LET (unit: keV/µm) at the clinical target volume increased from 4.98 (ICR-LET) to 5.50 (ADMM-LET). For the prostate case, the mean LET (unit: keV/µm) at the rectum decreased from 2.65 (ICR-LET) to 2.14 (ADMM-LET).ConclusionThis study establishes ADMM-LET as a new approach for LET optimization with the MMU constraint in IMPT, offering potential improvements in treatment outcomes and biological effects.