TU‐G‐BRB‐09: A Bregman Iteration Method for IMRT Optimization with Dose‐Volume Histogram Constraints

X. Jia, A. Uribe‐sanchez, S. Jiang

Research output: Contribution to journalArticlepeer-review


Purpose: Dose‐volume histogram (DVH) is a clinically relevant criterion to evaluate treatment plan quality. It is hence desirable to incorporate the associated DVH constraints in treatment plan optimization. Yet, these constraints usually lead to difficulties due to their non‐convex nature. This project develops an algorithm to solve the intensity modulated radiation therapy (IMRT) optimization problem with DVH constraints considered via a Bregman iteration. Methods: We consider an objective function of a quadratic form with different overdose and underdose penalties, subject to DVH constraints. The constrained optimization problem is converted into a sequence of unconstrained problems via Bregman iteration approach, which are then solved sequentially using gradient‐descent algorithm with inexact line search. The objective functions in those unconstrained optimization problems contains terms that requires the computation of DVH values. In practice, this is achieved by approximating the Heaviside step‐functions in the expression of a DVH curve by a smoothed arctangent function. This approach also allows for the computation of gradient of the objective functions during optimization process. Results: We have tested our algorithm in the context of 7‐field IMRT treatment planning for prostate cancer in 4 patient cases. Clinically relevant DVH constraints are considered for PTV, rectum, and bladder. In all the cases, the algorithm is able to find the solutions that satisfy all the DVH constraints, while as DVH constraints may be violated when the Bregman algorithm is not applied. The local‐minima problem caused by the non‐convex constraints is not observed, which may be ascribed to the good quality of the initial dose distribution obtained after a standard IMRT optimization problem without DVH constraints. Conclusions: We have developed an algorithm to solve the IMRT optimization problem with DVH constraints using Bregman iteration approach. Tests conducted in prostate cancer cases have demonstrated the validity of our algorithm and its effectiveness.

Original languageEnglish (US)
Pages (from-to)3921
Number of pages1
JournalMedical Physics
Issue number6
StatePublished - 2012

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging


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