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On the interplay between robustness and dynamic planning for adaptive radiation therapy
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-8660-4734
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-6252-7815
2019 (English)In: BIOMEDICAL PHYSICS & ENGINEERING EXPRESS, Vol. 5, no 4Article in journal (Refereed) Published
Abstract [en]

Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during the course of treatment, the authors propose a dynamic framework for robust adaptive radiation therapy in which a variety of robust adaptive treatment strategies are introduced and evaluated. This variety is a result of optimization variables with various degrees of freedom within robust optimization models that vary in their grade of conservativeness. The different degrees of freedom in the optimization variables are expressed through either time-and-uncertainty-scenario-independence, time-dependence or time-and-uncertainty-scenario-dependence, while the robust models are either based on expected value-, worst-case- or conditional value-at-risk-optimization. The goal of this study is to understand which mathematical properties of the proposed robust adaptive strategies are relevant such that the accumulated dose can be steered as close as possible to the prescribed dose as the treatment progresses. We apply a result from convex analysis to show that the robust non-adaptive approach under conditions of convexity and permutation-invariance is at least as good as the time-dependent robust adaptive approach, which implies that the time-dependent problem can be solved by dynamically solving the corresponding time-independent problem. According to the computational study, non-adaptive robust strategies may provide sufficient target coverage comparable to robust adaptive strategies if the occurring uncertainties follow the same distribution as those included in the robust model. Moreover, the results indicate that time-and-uncertainty-scenario-dependent optimization variables are most compatible with worst-case-optimization, while time-and-uncertainty-scenario-independent find their best match with expected value optimization. In conclusion, the authors introduced a novel framework for robust adaptive radiation therapy and identified mathematical requirements to further develop robust adaptive strategies in order to improve treatment outcome in the presence of interfractional uncertainties.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2019. Vol. 5, no 4
Keywords [en]
optimization, adaptive radiation therapy, robust optimization, model predictive control
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-251454DOI: 10.1088/2057-1976/ab1bfcISI: 000468299400004OAI: oai:DiVA.org:kth-251454DiVA, id: diva2:1315701
Note

QC 20190625

Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-06-25Bibliographically approved
In thesis
1. Toward Robust Optimization of Adaptive Radiation Therapy
Open this publication in new window or tab >>Toward Robust Optimization of Adaptive Radiation Therapy
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Adaptive radiation therapy is an evolving cancer treatment approach which relies on adapting the treatment plan in response to patient-specific interfractional geometric variations occurring during the fractionated treatment. If those variations are not addressed through adaptive replanning, the resulting treatment quality may be compromised.

The purpose of this thesis is to introduce a conceptual framework that combines a variety of robust optimization approaches with the concept of adaptive radiation therapy. Robust optimization approaches are useful in radiation therapy, since interfractional geometric variations are accounted for while optimizing the treatment plan. Thus, combining these two concepts in a framework for robust adaptive radiation therapy gives the opportunity to optimize adapted robust plans which account for the actual interfractional variations in the individual case. In this thesis, a variety of frameworks with increasing complexity is introduced and their ability to handle interfractional variations is evaluated.

In the first paper, a framework based on the concept of combining stochastic minimax optimization with adaptive replanning is introduced. Within this framework, three adaptive strategies are evaluated based on their ability to mitigate the impact of interfractional variations on the accumulated dose. In these strategies, treatment plans are adapted in response to the measured variations by (i) modifying the probability distribution that governs the variations accounted for in the optimization, (ii) varying the level of conservativeness of the robust optimization approach, and (iii) modifying safety-margins around the tumor.

In the second paper, robust optimization approaches of varying levels of conservativeness are combined with optimization variables of varying degrees of freedom which account for fractionation and the interfractional geometric variations. The mathematical analysis shows that the solution of a time-independent problem is as good as the solution by the corresponding time-dependent problem, under the condition of convexity and independently and identically distributed interfractional geometric variations.

In the third paper, the framework from the second paper is extended to (i) handle unaccounted interfractional geometric variations with Bayesian inference, (ii) address adaptation cost through varying the adaptation frequency, and (iii) address computational tractability of robust optimization approaches with an approximation algorithm.

To emphasize the mathematical properties of the introduced frameworks, their performance is evaluated on an idealized one-dimensional phantom geometry subjected to a series of rigid translations. In this idealized phantom geometry, the relation between a modified optimization parameter and a feature in the resulting dose profile can be identified in a straightforward manner. This contributes to a better understanding of the underlying mechanisms between robustness, the adaptive strategies and the optimized dose profiles. The findings of this thesis are intended to provide a mathematical foundation for further development of the framework for, and research on, robust optimization of adaptive radiation therapy toward a clinical setting.

Abstract [sv]

Adaptiv strålterapi är en modern cancerbehandlingsmetod som tillåter adaption av behandlingsplaner för att hantera individuella geometriska förändringar mellan behandlingstillfällen. Om dessa interfraktionella geometriska förändringar inte hanteras genom adaptiv omplanering, uppstår risken att behandlingskvaliteten försämras.

Denna avhandling introducerar ett konceptuellt ramverk som baseras på en kombination av olika metoder inom robust optimering och adaptiv strålterapi. Robusta optimeringsmetoder är fördelaktiga inom dosplaneringen eftersom interfraktionella geometriska förändringar beaktas under optimeringen av behandlingsplanen. Kombinationen av robust optimering och adaptiv strålterapi ger möjlighet att optimera adaptiva robusta behandlingsplaner som tar hänsyn till faktiskt förekommande förändringar i det individuella fallet. I denna avhandling introduceras ett antal ramverk med ökande komplexitet och deras förmåga att hantera interfraktionella geometriska förändringar utvärderas.

I den första artikeln presenteras ett ramverk som kombinerar stokastisk minimaxoptimering med adaptiv strålterapi. Inom ramverket utvärderas förmågan hos tre olika adaptiva strategier att bibehålla planerad dos vid interfraktionella geometriska förändringar. I dessa strategier adapteras behandlingsplanerna baserat på uppmätta förändringar genom att (i) modifiera sannolikhetsfördelningen i optimeringsproblemet som beskriver de förändringar som hanteras, (ii) variera graden av försiktighet i den robusta modellen, och (iii) variera säkerhetsmarginalerna kring tumören.

I den andra arikeln presenteras robusta optimeringsstrategier med olika grader av försiktighet i kombination med optimeringsvariabler av varierande frihetsgrad. Dessa optimeringsvariabler introduceras för att ta hänsyn till fraktionering och olika utfall av interfraktionella geometriska förändringar. Den matematiska studien visar att lösningen till det tidsoberoende problemet är lika bra som lösningen till det motsvarande tidsberoende problemet, givet att problemen är konvexa och att de interfraktionella variationerna är oberoende och likafördelade.

I den tredje artikeln utökas ramverket i den andra artikeln till att (i) hantera okända interfraktionella geometriska förändringar med hjälp av bayesiansk inferens, (ii) inkludera kostnad för adaptiv omplanering genom att variera adaptionsfrekvensen, och (iii) hantera beräkningskomplexiteten av de robusta optimeringsproblemen med hjälp av en approximationsalgoritm.

För att understryka de matematiska egenskaperna hos de presenterade ramverken, utvärderas deras prestanda på ett endimensionellt fantom som utsätts för en serie av rigida helkroppsförflyttningar. Detta underlättar ett rättframt undersökande av kopplingen mellan en modifierad optimeringsparameter och en egenskap i den resulterande dosprofilen. Dessutom bidrar dessa studier till en djupare förståelse för underliggande samband mellan robusthet, adaptiva strategier och optimerade dosprofiler. Resultaten i denna avhandling är avsedda att ge ett underliggande matematiskt ramverk för vidareutveckling av, och forskning inom, robust optimering av adaptiv strålterapi inriktad mot klinisk användning.

Place, publisher, year, edition, pages
Stockholm, Sweden: KTH Royal Institute of Technology, 2019. p. 109
Series
TRITA-SCI-FOU ; 2019:23
Keywords
optimization, adaptive radiation therapy, radiation therapy treatment planning, uncertainty, robust optimization, stochastic programming
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-251390 (URN)978-91-7873-188-6 (ISBN)
Public defence
2019-06-14, F3, Lindstedtsvägen 26, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC20190514

Available from: 2019-05-14 Created: 2019-05-13 Last updated: 2019-05-23Bibliographically approved

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