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Global convergence analysis of fast multiobjective gradient-based dose optimization algorithms for high-dose-rate

M Lahanas1, D Baltas, S Giannouli

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

Physics in Medicine and Biology
|April 17, 2003
PubMed
Summary

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Gradient-based optimization for high-dose-rate (HDR) brachytherapy is improved. The L-BFGS algorithm ensures global convergence, avoiding suboptimal solutions and accelerating treatment planning.

Area of Science:

  • Medical Physics
  • Computational Optimization
  • Radiation Oncology

Background:

  • Interstitial high-dose-rate (HDR) brachytherapy dose optimization faces challenges with local minima, potentially leading to suboptimal treatment plans.
  • Variance-based objectives are crucial for achieving optimal dose distributions in HDR brachytherapy.
  • Evaluating the global convergence of various optimization algorithms is essential for reliable treatment planning.

Purpose of the Study:

  • To assess the global convergence of gradient-based optimization algorithms for HDR brachytherapy dose optimization.
  • To compare the performance of different algorithms, including conjugate gradient, variable metric (BFGS, L-BFGS), and fast-simulated annealing.
  • To develop and evaluate a novel method for accelerating multiobjective dose optimization and obtaining representative non-dominated solutions.

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Main Methods:

  • Configuration space analysis using a representative set of non-dominated solutions from three prostate implant cases.
  • Comparison of conjugate gradient (FRPR), variable metric (BFGS, L-BFGS), and fast-simulated annealing algorithms.
  • Development of a modified computation method for surface and volume dose variance derivatives to reduce operational complexity.

Main Results:

  • The limited memory BFGS (L-BFGS) and conjugate gradient FRPR algorithms demonstrated global convergence, avoiding local minima and degenerate states.
  • The BFGS algorithm exhibited significant fluctuations, indicating potential instability.
  • A new method for calculating dose variance derivatives accelerated multiobjective dose optimization by a factor of 10-100, independent of planning target volume sampling points.

Conclusions:

  • L-BFGS and FRPR are suitable for globally convergent HDR brachytherapy dose optimization.
  • The proposed modified computation method significantly enhances the efficiency of multiobjective dose optimization in HDR brachytherapy.
  • This research contributes to faster and more reliable treatment planning in radiation oncology.