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  • 1.
    Bokrantz, Rasmus
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fredriksson, Albin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Controlling robustness and conservativeness in multicriteria intensity-modulated proton therapy optimization under uncertainty2013Report (Other academic)
  • 2.
    Bokrantz, Rasmus
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Laboratories, Sweden.
    Fredriksson, Albin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Laboratories, Sweden.
    Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization2017In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 262, no 2, p. 682-692Article in journal (Refereed)
    Abstract [en]

    We provide necessary and sufficient conditions for robust efficiency (in the sense of Ehrgott et al., 2014) to multiobjective optimization problems that depend on uncertain parameters. These conditions state that a solution is robust efficient (under minimization) if it is optimal to a strongly increasing scalarizing function, and only if it is optimal to a strictly increasing scalarizing function. By counterexample, we show that the necessary condition cannot be strengthened to convex scalarizing functions, even for convex problems. We therefore define and characterize a subset of the robust efficient solutions for which an analogous necessary condition holds with respect to convex scalarizing functions. This result parallels the deterministic case where optimality to a convex and strictly increasing scalarizing function constitutes a necessary condition for efficiency. By a numerical example from the field of radiation therapy treatment plan optimization, we illustrate that the curvature of the scalarizing function influences the conservatism of an optimized solution in the uncertain case.

  • 3.
    Fredriksson, Albin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A characterization of robust radiation therapy treatment planning methods-from expected value to worst case optimization2012In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 39, no 8, p. 5169-5181Article in journal (Refereed)
    Abstract [en]

    Purpose: To characterize a class of optimization formulations used to handle systematic and random errors in radiation therapy, and to study the differences between the methods within this class. Methods: The class of robust methods that can be formulated as minimax stochastic programs is studied. This class generalizes many previously used methods, ranging between optimization of the expected and the worst case objective value. The robust methods are used to plan intensity-modulated proton therapy (IMPT) treatments for a case subject to systematic setup and range errors, random setup errors with and without uncertain probability distribution, and combinations thereof. As reference, plans resulting from a conventional method that uses a margin to account for errors are shown. Results: For all types of errors, target coverage robustness increased with the conservativeness of the method. For systematic errors, best case organ at risk (OAR) doses increased and worst case doses decreased with the conservativeness. Accounting for random errors of fixed probability distribution resulted in heterogeneous dose. The heterogeneities were reduced when uncertainty in the probability distribution was accounted for. Doing so, the OAR doses decreased with the conservativeness. All robust methods studied resulted in more robust target coverage and lower OAR doses than the conventional method. Conclusions: Accounting for uncertainties is essential to ensure plan quality in complex radiation therapy such as IMPT. The utilization of more information than conventional in the optimization can lead to robust target coverage and low OAR doses. Increased target coverage robustness can be achieved by more conservative methods.

  • 4.
    Fredriksson, Albin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Automated improvement of radiation therapy treatment plans by optimization under reference dose constraints2012In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 57, no 23, p. 7799-7811Article in journal (Refereed)
    Abstract [en]

    A method is presented that automatically improves upon previous treatment plans by optimization under reference dose constraints. In such an optimization, a previous plan is taken as reference and a new optimization is performed toward some goal, such as minimization of the doses to healthy structures under the constraint that no structure can become worse off than in the reference plan. Two types of constraints that enforce this are discussed: either each voxel or each dose-volume histogram of the improved plan must be at least as good as in the reference plan. These constraints ensure that the quality of the dose distribution cannot deteriorate, something that constraints on conventional physical penalty functions do not. To avoid discontinuous gradients, which may restrain gradient-based optimization algorithms, the positive part operators that constitute the optimization functions are regularized. The method was applied to a previously optimized plan for a C-shaped phantom and the effects of the choice of regularization parameter were studied. The method resulted in reduced integral dose and reduced doses to the organ at risk while maintaining target homogeneity. It could be used to improve upon treatment plans directly or as a means of quality control of plans.

  • 5.
    Fredriksson, Albin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Robust optimization of radiation therapy accounting for geometric uncertainty2013Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Geometric errors may compromise the quality of radiation therapy treatments. Optimization methods that account for errors can reduce their effects.

    The first paper of this thesis introduces minimax optimization to account for systematic range and setup errors in intensity-modulated proton therapy. The minimax method optimizes the worst case outcome of the errors within a given set. It is applied to three patient cases and shown to yield improved target coverage robustness and healthy structure sparing compared to conventional methods using margins, uniform beam doses, and density override. Information about the uncertainties enables the optimization to counterbalance the effects of errors.

    In the second paper, random setup errors of uncertain distribution---in addition to the systematic range and setup errors---are considered in a framework that enables scaling between expected value and minimax optimization. Experiments on a phantom show that the best and mean case tradeoffs between target coverage and critical structure sparing are similar between the methods of the framework, but that the worst case tradeoff improves with conservativeness.

    Minimax optimization only considers the worst case errors. When the planning criteria cannot be fulfilled for all errors, this may have an adverse effect on the plan quality. The third paper introduces a method for such cases that modifies the set of considered errors to maximize the probability of satisfying the planning criteria. For two cases treated with intensity-modulated photon and proton therapy, the method increased the number of satisfied criteria substantially. Grasping for a little less sometimes yields better plans.

    In the fourth paper, the theory for multicriteria optimization is extended to incorporate minimax optimization. Minimax optimization is shown to better exploit spatial information than objective-wise worst case optimization, which has previously been used for robust multicriteria optimization.

    The fifth and sixth papers introduce methods for improving treatment plans: one for deliverable Pareto surface navigation, which improves upon the Pareto set representations of previous methods; and one that minimizes healthy structure doses while constraining the doses of all structures not to deteriorate compared to a reference plan, thereby improving upon plans that have been reached with too weak planning goals.

  • 6.
    Fredriksson, Albin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Bokrantz, Rasmus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Deliverable navigation for multicriteria IMRT treatment planning by combining shared and individual apertures2013In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 58, no 21, p. 7683-7697Article in journal (Refereed)
    Abstract [en]

    We consider the problem of deliverable Pareto surface navigation for step-and-shoot intensity-modulated radiation therapy. This problem amounts to calculation of a collection of treatment plans with the property that convex combinations of plans are directly deliverable. Previous methods for deliverable navigation impose restrictions on the number of apertures of the individual plans, or require that all treatment plans have identical apertures. We introduce simultaneous direct step-and-shoot optimization of multiple plans subject to constraints that some of the apertures must be identical across all plans. This method generalizes previous methods for deliverable navigation to allow for treatment plans with some apertures from a collective pool and some apertures that are individual. The method can also be used as a post-processing step to previous methods for deliverable navigation in order to improve upon their plans. By applying the method to subsets of plans in the collection representing the Pareto set, we show how it can enable convergence toward the unrestricted (non-navigable) Pareto set where all apertures are individual.

  • 7.
    Fredriksson, Albin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Bokrantz, Rasmus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Deliverable navigation for multicriteria intensity-modulated radiation therapy planning by combining shared and individual apertures2013Report (Other academic)
  • 8.
    Fredriksson, Albin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hardemark, Björn
    Minimax optimization for handling range and setup uncertainties in proton therapy2011In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 38, no 3, p. 1672-1684Article in journal (Refereed)
    Abstract [en]

    Purpose: Intensity modulated proton therapy (IMPT) is sensitive to errors, mainly due to high stopping power dependency and steep beam dose gradients. Conventional margins are often insufficient to ensure robustness of treatment plans. In this article, a method is developed that takes the uncertainties into account during the plan optimization. Methods: Dose contributions for a number of range and setup errors are calculated and a minimax optimization is performed. The minimax optimization aims at minimizing the penalty of the worst case scenario. Any optimization function from conventional treatment planning can be utilized by the method. By considering only scenarios that are physically realizable, the unnecessary conservativeness of other robust optimization methods is avoided. Minimax optimization is related to stochastic programming by the more general minimax stochastic programming formulation, which enables accounting for uncertainties in the probability distributions of the errors. Results: The minimax optimization method is applied to a lung case, a paraspinal case with titanium implants, and a prostate case. It is compared to conventional methods that use margins, single field uniform dose (SFUD), and material override (MO) to handle the uncertainties. For the lung case, the minimax method and the SFUD with MO method yield robust target coverage. The minimax method yields better sparing of the lung than the other methods. For the paraspinal case, the minimax method yields more robust target coverage and better sparing of the spinal cord than the other methods. For the prostate case, the minimax method and the SFUD method yield robust target coverage and the minimax method yields better sparing of the rectum than the other methods. Conclusions: Minimax optimization provides robust target coverage without sacrificing the sparing of healthy tissues, even in the presence of low density lung tissue and high density titanium implants. Conventional methods using margins, SFUD, and MO do not utilize the full potential of IMPT and deliver unnecessarily high doses to healthy tissues.

  • 9.
    Fredriksson, Albin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hårdemark, Björn
    Maximizing the probability of satisfying the planning criteria in radiation therapy under setup uncertainty2013Manuscript (preprint) (Other academic)
    Abstract [en]

    We consider intensity-modulated photon and proton therapy in the presence of setup uncertainty. The uncertainty is accounted for by worst case optimization, in which the planning criteria are constrained to be satisfied under all setup errors from a specified set. To handle that the set may contain errors under which the planning criteria cannot be satisfied, a method is introduced that includes the magnitudes of the setup errors within the set as variables in the optimization, which is aimed at making these magnitudes as large as possible (within specified bounds) while satisfying all planning criteria under the errors. This is equivalent to maximizing the probability of satisfying the planning criteria.

    The method is studied with respect to photon and proton therapy applied to a prostate case and a lung case, and compared to worst case optimization with respect to an a priori determined set of errors. For both modalities, slight reductions of the magnitudes of the considered setup errors resulted in plans that satisfied a substantially larger number of planning criteria under the retracted errors, and also a larger number of criteria under the a priori errors: for the prostate case, the plans accounting for retracted errors satisfied 1.5 (photons) and 1.2 (protons) times as many planning criteria as the method accounting for a priori errors, and for the lung case, the numbers were 2.7 (photons) and 1.6 (protons).

  • 10.
    Fredriksson, Albin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Labs, Stockholm, Sweden..
    Hårdemark, Björn
    RaySearch Labs, Stockholm, Sweden..
    ROBUST OPTIMIZATION ACCOUNTING FOR ORGAN MOTION, RANGE ERRORS, AND SETUP ERRORS IN IMPT2011In: Radiotherapy and Oncology, ISSN 0167-8140, E-ISSN 1879-0887, Vol. 99, p. S100-S100Article in journal (Other academic)
1 - 10 of 10
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