Global convergence analysis of fast multiobjective gradient-based dose optimization algorithms for high-dose-rate brachytherapy.
We consider the problem of the global convergence of gradient-based optimization algorithms for interstitial high-dose-rate (HDR) brachytherapy dose optimization using variance-based objectives. Possible local minima could lead to only sub-optimal solutions. We perform a configuration space analysis using a representative set of the entire non-dominated solution space. A set of three prostate implants is used in this study. We compare the results obtained by conjugate gradient algorithms, two variable metric algorithms and fast-simulated annealing. For the variable metric algorithm BFGS from numerical recipes, large fluctuations are observed. The limited memory L-BFGS algorithm and the conjugate gradient algorithm FRPR are globally convergent. Local minima or degenerate states are not observed. We study the possibility of obtaining a representative set of non-dominated solutions using optimal solution rearrangement and a warm start mechanism. For the surface and volume dose variance and their derivatives, a method is proposed which significantly reduces the number of required operations. The optimization time, ignoring a preprocessing step, is independent of the number of sampling points in the planning target volume. Multiobjective dose optimization in HDR brachytherapy using L-BFGS and a new modified computation method for the objectives and derivatives has been accelerated, depending on the number of sampling points, by a factor in the range 10-100.
Lahanas
M
M
Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach, 63069 Offenbach, Germany. mlahanas@gmx.de
Baltas
D
D
Giannouli
S
S
D000465:Algorithms; D001918:Brachytherapy / Q000379:methods*; D006801:Humans; D008297:Male; D011471:Prostatic Neoplasms / Q000532:radiotherapy*; D011786:Quality Control; D011874:Radiometry / Q000379:methods*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity