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Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization

Michael Lahanas1, Eduard Schreibmann, Dimos Baltas

  • 1Department of Medical Physics & Engineering, Strahlenklinik, Klinikum Offenbach, 63069 Offenbach, Germany. mlahanas@gmx.de

Physics in Medicine and Biology
|October 1, 2003
PubMed
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Limited memory L-BFGS optimizes intensity modulated radiotherapy (IMRT) dose distribution by eliminating negative beam fluences. This approach ensures globally optimal solutions for multiobjective (MO) IMRT, providing valuable trade-off information for treatment planning.

Area of Science:

  • Medical Physics
  • Computational Optimization
  • Radiotherapy Technology

Background:

  • Intensity modulated radiotherapy (IMRT) requires complex dose optimization.
  • Multiobjective (MO) optimization in IMRT faces challenges with constraint handling and computational efficiency.
  • The limited memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm is a gradient-based method with potential for MO dose optimization.

Purpose of the Study:

  • To analyze the global convergence properties of the L-BFGS algorithm for MO IMRT dose optimization.
  • To investigate the effectiveness of a parameter transformation in eliminating positivity constraints for beam fluences.
  • To assess the global Pareto optimality of L-BFGS solutions using a fast simulated annealing (FSA) algorithm.

Main Methods:

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  • Utilized a parameter transformation to address the issue of negative beam fluences in L-BFGS optimization.
  • Analyzed global convergence by examining local minima and employing a fast simulated annealing (FSA) algorithm.
  • Tested the methodology on three distinct clinical cases: brain tumor, prostate tumor, and a C-shaped planning target volume (PTV).

    • Main Results:

    • A parameter transformation effectively eliminated the problem of negative beam fluences, a previously misunderstood aspect.
    • Global convergence was violated in only 1% of optimizations, with a simple mechanism mitigating this failure.
    • L-BFGS solutions were found to be globally Pareto optimal, with optimization times under 4 seconds for complex scenarios.
    • MO dose optimization generated a spectrum of solutions, revealing trade-offs between objectives and dose ranges.

    Conclusions:

    • Constraint-free gradient-based algorithms, like L-BFGS, are viable for MO IMRT dose optimization due to efficient handling of beam fluences and computational speed.
    • The developed method provides a representative set of Pareto optimal solutions, facilitating informed clinical decision-making.
    • This approach enhances the ability to explore the trade-offs inherent in MO IMRT planning, leading to potentially improved treatment outcomes.