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Multicriteria optimization for managing tradeoffs in radiation therapy treatment planning
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-6642-3282
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Treatment planning for radiation therapy inherently involves tradeoffs, such as between tumor control and normal tissue sparing, between time-efficiency and dose quality, and between nominal plan quality and robustness. The purpose of this thesis is to develop methods that can facilitate decision making related to such tradeoffs. The main focus of the thesis is on multicriteria optimization methods where a representative set of treatment plans are first calculated and the most appropriate plan contained in this representation then selected by the treatment planner through continuous interpolation between the precalculated alternatives. These alternatives constitute a subset of the set of Pareto optimal plans, meaning plans such that no criterion can be improved without a sacrifice in another.

Approximation of Pareto optimal sets is first studied with respect to fluence map optimization for intensity-modulated radiation therapy. The approximation error of a discrete representation is minimized by calculation of points one at the time at the location where the distance between an inner and outer approximation of the Pareto set currently attains its maximum. A technique for calculating this distance that is orders of magnitude more efficient than the best previous method is presented. A generalization to distributed computational environments is also proposed.

Approximation of Pareto optimal sets is also considered with respect to direct machine parameter optimization. Optimization of this form is used to calculate representations where any interpolated treatment plan is directly deliverable. The fact that finite representations of Pareto optimal sets have approximation errors with respect to Pareto optimality is addressed by a technique that removes these errors by a projection onto the exact Pareto set. Projections are also studied subject to constraints that prevent the dose-volume histogram from deteriorating.

Multicriteria optimization is extended to treatment planning for volumetric-modulated arc therapy and intensity-modulated proton therapy. Proton therapy plans that are robust against geometric errors are calculated by optimization of the worst case outcome. The theory for multicriteria optimization is extended to accommodate this formulation. Worst case optimization is shown to be preferable to a previous more conservative method that also protects against uncertainties which cannot be realized in practice.

Abstract [sv]

En viktig aspekt av planering av strålterapibehandlingar är avvägningar mellan behandlingsmål vilka står i konflikt med varandra. Exempel på sådana avvägningar är mellan tumörkontroll och dos till omkringliggande frisk vävnad, mellan behandlingstid och doskvalitet, och mellan nominell plankvalitet och robusthet med avseende på geometriska fel. Denna avhandling syftar till att utveckla metoder som kan underlätta beslutsfattande kring motstridiga behandlingsmål. Primärt studeras en metod för flermålsoptimering där behandlingsplanen väljs genom kontinuerlig interpolation över ett representativt urval av förberäknade alternativ. De förberäknade behandlingsplanerna utgör en delmängd av de Paretooptimala planerna, det vill säga de planer sådana att en förbättring enligt ett kriterium inte kan ske annat än genom en försämring enligt ett annat.

Beräkning av en approximativ representation av mängden av Paretooptimala planer studeras först med avseende på fluensoptimering för intensitetsmodulerad strålterapi. Felet för den approximativa representationen minimeras genom att innesluta mängden av Paretooptimala planer mellan inre och yttre approximationer. Dessa approximationer förfinas iterativt genom att varje ny plan genereras där avståndet mellan approximationerna för tillfället är som störst. En teknik för att beräkna det maximala avståndet mellan approximationerna föreslås vilken är flera storleksordningar snabbare än den bästa tidigare kända metoden. En generalisering till distribuerade beräkningsmiljöer föreslås även.

Approximation av mängden av Paretooptimala planer studeras även för direkt maskinparameteroptimering, som används för att beräkna representationer där varje interpolerad behandlingsplan är direkt levererbar. Det faktum att en ändlig representation av mängden av Paretooptimala lösningar har ett approximationsfel till Paretooptimalitet hanteras via en metod där en interpolerad behandlingsplan projiceras på Paretomängden. Projektioner studeras även under bivillkor som förhindrar att den interpolerade planens dos-volym histogram kan försämras.

Flermålsoptimering utökas till planering av rotationsterapi och intensitetsmodulerad protonterapi. Protonplaner som är robusta mot geometriska fel beräknas genom optimering med avseende på det värsta möjliga utfallet av de föreliggande osäkerheterna. Flermålsoptimering utökas även teoretiskt till att innefatta denna formulering. Nyttan av värsta fallet-optimering jämfört med tidigare mer konservativa metoder som även skyddar mot osäkerheter som inte kan realiseras i praktiken demonstreras experimentellt.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , xvi, 54 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 13:07
Keyword [en]
Optimization, multicriteria optimization, robust optimization, Pareto optimality, Pareto surface approximation, Pareto surface navigation, intensity-modulated radiation therapy, volumetric-modulated arc therapy, intensity-modulated proton therapy
Keyword [sv]
Optimering, flermålsoptimering, robust optimering, Paretooptimalitet, Paretofrontsapproximation, Paretofrontsnavigering, intensitetsmodulerad strålterapi, rotationsterapi, intensitetsmodulerad protonterapi
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-122663ISBN: 978-91-7501-790-7 (print)OAI: oai:DiVA.org:kth-122663DiVA: diva2:623179
Public defence
2013-06-14, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20130527

Available from: 2013-05-27 Created: 2013-05-24 Last updated: 2013-05-28Bibliographically approved
List of papers
1. An algorithm for approximating convex Pareto surfaces based on dual techniques
Open this publication in new window or tab >>An algorithm for approximating convex Pareto surfaces based on dual techniques
2013 (English)In: INFORMS journal on computing, ISSN 1091-9856, E-ISSN 1526-5528, Vol. 25, no 2, 377-393 p.Article in journal (Refereed) Published
Abstract [en]

We consider the problem of approximating Pareto surfaces of convex multicriteria optimization problems by a discrete set of points and their convex combinations. Finding the scalarization parameters that optimally limit the approximation error when generating a single Pareto optimal solution is a nonconvex optimization problem. This problem can be solved by enumerative techniques but at a cost that increases exponentially with the number of objectives. We present an algorithm for solving the Pareto surface approximation problem that is practical with 10 or less conflicting objectives, motivated by an application to radiation therapy optimization. Our enumerative scheme is, in a sense, dual to a family of previous algorithms. The proposed technique retains the quality of the best previous algorithm in this class while solving fewer subproblems. A further improvement is provided by a procedure for discarding subproblems based on reusing information from previous solves. The combined effect of the enhancements is empirically demonstrated to reduce the computational expense of solving the Pareto surface approximation problem by orders of magnitude. For problems where the objectives have positive curvature, an improved bound on the approximation error is demonstrated using transformations of the initial objectives with strictly increasing and concave functions.

Keyword
multicriteria optimization, Pareto optimality, sandwich algorithms, radiation therapy, Hausdorff distance
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-122665 (URN)10.1287/ijoc.1120.0508 (DOI)000317966700014 ()2-s2.0-84877962755 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20130527

Available from: 2013-05-24 Created: 2013-05-24 Last updated: 2017-12-06Bibliographically approved
2. Multicriteria optimization for volumetric-modulated arc therapy by decomposition into a fluence-based relaxation and a segment weight-based restriction
Open this publication in new window or tab >>Multicriteria optimization for volumetric-modulated arc therapy by decomposition into a fluence-based relaxation and a segment weight-based restriction
2012 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 39, no 11, 6712-6725 p.Article in journal (Refereed) Published
Abstract [en]

Purpose: To develop a method for inverse volumetric-modulated arc therapy (VMAT) planning that combines multicriteria optimization (MCO) with direct machine parameter optimization. The ultimate goal is to provide an efficient and intuitive method for generating high quality VMAT plans. Methods: Multicriteria radiation therapy treatment planning amounts to approximating the relevant treatment options by a discrete set of plans, and selecting the combination thereof that strikes the best possible balance between conflicting objectives. This approach is applied to two decompositions of the inverse VMAT planning problem: a fluence-based relaxation considered at a coarsened gantry angle spacing and under a regularizing penalty on fluence modulation, and a segment weight-based restriction in a neighborhood of the solution to the relaxed problem. The two considered variable domains are interconnected by direct machine parameter optimization toward reproducing the dose-volume histogram of the fluence-based solution. Results: The dose distribution quality of plans generated by the proposed MCO method was assessed by direct comparison with benchmark plans generated by a conventional VMAT planning method. The results for four patient cases (prostate, pancreas, lung, and head and neck) are highly comparable between the MCO plans and the benchmark plans: Discrepancies between studied dose-volume statistics for organs at risk were-with the exception of the kidneys of the pancreas case-within 1 Gy or 1 percentage point. Target coverage of the MCO plans was comparable with that of the benchmark plans, but with a small tendency toward a shift from conformity to homogeneity. Conclusions: MCO allows tradeoffs between conflicting objectives encountered in VMAT planning to be explored in an interactive manner through search over a continuous representation of the relevant treatment options. Treatment plans selected from such a representation are of comparable dose distribution quality to conventionally optimized VMAT plans.

Keyword
direct aperture optimization, direct machine parameter optimization, multicriteria optimization, Pareto optimality, total variation regularization, treatment planning, volumetric-modulated arc therapy
National Category
Medical and Health Sciences Mathematics
Identifiers
urn:nbn:se:kth:diva-107254 (URN)10.1118/1.4754652 (DOI)000310726300019 ()2-s2.0-84868561824 (Scopus ID)
Note

QC 20121214

Available from: 2012-12-13 Created: 2012-12-10 Last updated: 2017-12-07Bibliographically approved
3. Improved plan quality in multicriteria radiation therapy optimization by projections onto the Pareto surface
Open this publication in new window or tab >>Improved plan quality in multicriteria radiation therapy optimization by projections onto the Pareto surface
2012 (English)Report (Other academic)
Abstract [en]

We consider an approach to multicriteria radiation therapy optimization where the clinical treatment plan is selected from a representationof the set of Pareto optimal treatment plans in the form of a discrete setof plans and their combinations. The approximate nature of this representation implies that a selected plan in general has an approximationerror with respect to Pareto optimality. To assess and, if necessary, improve the quality of such plans, a technique is suggested that eliminatesthe approximation error of a given treatment plan by a projection ontothe Pareto surface. A more elaborate form of projection is also suggested that requires the projected solution to be not only as good asthe input plan in terms of objective function values, but also equallygood or better with respect to the three-dimensional dose distribution.The versatility of the suggested technique is demonstrated by application to planning for step-and-shoot and sliding window delivery ofintensity-modulated radiation therapy, and planning for spot-scanneddelivery of intensity-modulated proton therapy. Our numerical resultsshow that the proposed projections generally lead to improved sparingof organs at risk and a higher degree of dose conformity compared towhen projections are not performed.

Place, publisher, year, edition, pages
Stockhholm: KTH Royal Institute of Technology, 2012
Series
Trita-MAT. OS, ISSN 1401-2294 ; 12:04
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-122664 (URN)
Note

QC 20130527

Available from: 2013-05-24 Created: 2013-05-24 Last updated: 2013-05-27Bibliographically approved
4. Distributed approximation of Pareto surfaces in multicriteria radiation therapy treatment planning
Open this publication in new window or tab >>Distributed approximation of Pareto surfaces in multicriteria radiation therapy treatment planning
2013 (English)In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 58, no 11, 3501-3516 p.Article in journal (Refereed) Published
Abstract [en]

We consider multicriteria radiation therapy treatment planning by navigationover the Pareto surface, implemented by interpolation between discretetreatment plans. Current state of the art for calculation of a discreterepresentation of the Pareto surface is to sandwich this set between inner andouter approximations that are updated one point at a time. In this paper, wegeneralize this sequential method to an algorithm that permits parallelization.The principle of the generalization is to apply the sequential method to anapproximation of an inexpensive model of the Pareto surface. The informationgathered from the model is sub-sequently used for the calculation of pointsfrom the exact Pareto surface, which are processed in parallel. The model isconstructed according to the current inner and outer approximations, and givena shape that is difficult to approximate, in order to avoid that parts of the Paretosurface are incorrectly disregarded. Approximations of comparable quality tothose generated by the sequential method are demonstrated when the degree ofparallelization is up to twice the number of dimensions of the objective space.For practical applications, the number of dimensions is typically at least five,so that a speed-up of one order of magnitude is obtained.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-122666 (URN)10.1088/0031-9155/58/11/3501 (DOI)000318966200004 ()2-s2.0-84878249203 (Scopus ID)
Note

QC 20130527

Available from: 2013-05-24 Created: 2013-05-24 Last updated: 2017-12-06Bibliographically approved
5. Deliverable navigation for multicriteria intensity-modulated radiation therapy planning by combining shared and individual apertures
Open this publication in new window or tab >>Deliverable navigation for multicriteria intensity-modulated radiation therapy planning by combining shared and individual apertures
2013 (English)Report (Other academic)
Series
Trita-MAT. OS, ISSN 1401-2294 ; 2013:04
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-122198 (URN)
Note

QC 20130516

Available from: 2013-05-14 Created: 2013-05-14 Last updated: 2013-05-27Bibliographically approved
6. Controlling robustness and conservativeness in multicriteria intensity-modulated proton therapy optimization under uncertainty
Open this publication in new window or tab >>Controlling robustness and conservativeness in multicriteria intensity-modulated proton therapy optimization under uncertainty
2013 (English)Report (Other academic)
Series
Trita-MAT. OS, ISSN 1401-2294 ; 2013:05
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-122197 (URN)
Note

QC 20130516

Available from: 2013-05-14 Created: 2013-05-14 Last updated: 2013-05-27Bibliographically approved

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