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Iterative regularization in intensity-modulated radiation therapy optimization
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-6252-7815
2006 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 33, no 1, 225-234 p.Article in journal (Refereed) Published
Abstract [en]

A common way to solve intensity-modulated radiation therapy (IMRT) optimization problems is to use a beamlet-based approach. The approach is usually employed in a three-step manner: first a beamlet-weight optimization problem is solved, then the fluence profiles are converted into stepand-shoot segments, and finally postoptimization of the segment weights is performed. A drawback of beamlet-based approaches is that beamlet-weight optimization problems are ill-conditioned and have to be regularized in order to produce smooth fluence profiles that are suitable for conversion. The purpose of this paper is twofold: first, to explain the suitability of solving beamlet-based IMRT problems by a BFGS quasi-Newton sequential quadratic programming method with diagonal initial Hessian estimate, and second, to empirically show that beamlet-weight optimization problems should be solved in relatively few iterations when using this optimization method. The explanation of the suitability is based on viewing the optimization method as an iterative regularization method. In iterative regularization, the optimization problem is solved approximately by iterating long enough to obtain a solution close to the optimal one, but terminating before too much noise occurs. Iterative regularization requires an optimization method that initially proceeds in smooth directions and makes rapid initial progress. Solving ten beamlet-based IMRT problems with dose-volume objectives and bounds on the beamlet-weights, we find that the considered optimization method fulfills the requirements for performing iterative regularization. After segment-weight optimization, the treatments obtained using 35 beamlet-weight iterations outperform the treatments obtained using 100 beamlet-weight iterations, both in terms of objective value and of target uniformity. We conclude that iterating too long may in fact deteriorate the quality of the deliverable plan.

Place, publisher, year, edition, pages
2006. Vol. 33, no 1, 225-234 p.
Keyword [en]
intensity-modulated radiation therapy; quasi-Newton method; conjugate gradient method; regularization; iterative regularization; IMAGE-RECONSTRUCTION; IMRT OPTIMIZATION; PHOTON BEAMS; RADIOTHERAPY; DELIVERY; CONSTRAINTS; DEGENERACY; ALGORITHMS; EFFICIENCY; PATTERNS
National Category
Computational Mathematics Radiology, Nuclear Medicine and Medical Imaging
URN: urn:nbn:se:kth:diva-8184DOI: 10.1118/1.2148918ISI: 000234772100028ScopusID: 2-s2.0-31044450092OAI: diva2:13438
QC 20100709Available from: 2008-04-03 Created: 2008-04-03 Last updated: 2010-07-09Bibliographically approved
In thesis
1. Utilizing Problem Structure in Optimization of Radiation Therapy
Open this publication in new window or tab >>Utilizing Problem Structure in Optimization of Radiation Therapy
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis, optimization approaches for intensity-modulated radiation therapy are developed and evaluated with focus on numerical efficiency and treatment delivery aspects. The first two papers deal with strategies for solving fluence map optimization problems efficiently while avoiding solutions with jagged fluence profiles. The last two papers concern optimization of step-and-shoot parameters with emphasis on generating treatment plans that can be delivered efficiently and accurately. In the first paper, the problem dimension of a fluence map optimization problem is reduced through a spectral decomposition of the Hessian of the objective function. The weights of the eigenvectors corresponding to the p largest eigenvalues are introduced as optimization variables, and the impact on the solution of varying p is studied. Including only a few eigenvector weights results in faster initial decrease of the objective value, but with an inferior solution, compared to optimization of the bixel weights. An approach combining eigenvector weights and bixel weights produces improved solutions, but at the expense of the pre-computational time for the spectral decomposition. So-called iterative regularization is performed on fluence map optimization problems in the second paper. The idea is to find regular solutions by utilizing an optimization method that is able to find near-optimal solutions with non-jagged fluence profiles in few iterations. The suitability of a quasi-Newton sequential quadratic programming method is demonstrated by comparing the treatment quality of deliverable step-and-shoot plans, generated through leaf sequencing with a fixed number of segments, for different number of bixel-weight iterations. A conclusion is that over-optimization of the fluence map optimization problem prior to leaf sequencing should be avoided. An approach for dynamically generating multileaf collimator segments using a column generation approach combined with optimization of segment shapes and weights is presented in the third paper. Numerical results demonstrate that the adjustment of leaf positions improves the plan quality and that satisfactory treatment plans are found with few segments. The method provides a tool for exploring the trade-off between plan quality and treatment complexity by generating a sequence of deliverable plans of increasing quality. The final paper is devoted to understanding the ability of the column generation approach in the third paper to find near-optimal solutions with very few columns compared to the problem dimension. The impact of different restrictions on the generated columns is studied, both in terms of numerical behaviour and convergence properties. A bound on the two-norm of the columns results in the conjugate-gradient method. Numerical results indicate that the appealing properties of the conjugate-gradient method on ill-conditioned problems are inherited in the column generation approach of the third paper.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. xi, 32 p.
Trita-MAT. OS, ISSN 1401-2294 ; 08/OS/03
Optimization, intensity-modulated radiation therapy, conjugate-gradient method, step-and-shoot delivery, column generation, quasi-Newton method, regularization, sequential quadratic programming
National Category
Computational Mathematics
urn:nbn:se:kth:diva-4689 (URN)978-91-7178-920-4 (ISBN)
Public defence
2008-04-25, F3, Lindstedtsvägen 26, Stockholm, 10:00
QC 20100709Available from: 2008-04-03 Created: 2008-04-03 Last updated: 2010-07-09Bibliographically approved

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