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

Qingkun Fan; Xiaoyuan Zhang; Riao Dao; Yujia Qian; Lewei Zhao; Xiaoqiang Li; Xuanfeng Ding; Gang Liu; Shuyang Dai

doi:10.3389/fonc.2024.1328147

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

Front Oncol. 2024 Feb 28:14:1328147. doi: 10.3389/fonc.2024.1328147. eCollection 2024.

Authors

Qingkun Fan¹, Xiaoyuan Zhang¹, Riao Dao², Yujia Qian², Lewei Zhao³, Xiaoqiang Li³, Xuanfeng Ding³, Gang Liu^{4

5}, Shuyang Dai^{1

5}

Affiliations

¹ School of Mathematics and Statistics, Wuhan University, Wuhan, China.
² School of Physics and Technology, Wuhan University, Wuhan, China.
³ Department of Radiation Oncology, Corewell Health William Beaumont University Hospital, Royal Oak, MI, United States.
⁴ Cancer Center, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.
⁵ Hubei Key Laboratory of Precision Radiation Oncology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.

Abstract

Purpose: This 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 methods: The 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.

Results: The 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).

Conclusion: This 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.

Keywords: alternating direction method of multipliers (ADMM); intensity-modulated proton therapy (IMPT); linear energy transfer (LET); relative biological effectiveness (RBE); treatment planning.

Grants and funding

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This study is supported by the National Natural Science Foundation of China (No. 12005072), the Open Research Funding of Hubei Key Laboratory of Precision Radiation Oncology (No. jzfs003, No. jzfs014).