Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning

Hojin Kim, Stephen Becker, Rena Lee, Soonhyouk Lee, Sukyoung Shin, Emmanuel Candès, Lei Xing, Ruijiang Li

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Purpose: This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality. Methods: First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of the objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency. Results: The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery. Conclusions: The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.

Original languageEnglish
Article number071719
JournalMedical Physics
Issue number7
StatePublished - Jul 2013

Bibliographical note

Funding Information:
This work is partially supported by National Institutes of Health (NIH) Grant Nos. 1K99 CA166186 and 1R01 CA133474 and the Industrial Strategic technology development program (10035527) funded by the Ministry of Knowledge Economy (MKE, Korea) and a grant of the Korea Healthcare technology R&D Project, Ministry of Health & Welfare, Republic of Korea (A111098). The authors report no conflicts of interest in conducting the research.


  • IMRT
  • delivery efficiency
  • fluence-map complexity
  • reweighted L1-minimization
  • total-variation


Dive into the research topics of 'Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning'. Together they form a unique fingerprint.

Cite this