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Stockholm, Sweden

RaySearch Laboratories

Stockholm, Sweden
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Bokrantz R.,RaySearch Laboratories | Fredriksson A.,RaySearch Laboratories
Physics in Medicine and Biology | Year: 2017

This work extends and validates the scenario-based generalization of margins presented in Fredriksson and Bokrantz (2016 Phys. Med. Biol. 61 2067-82). Scenario-based margins are, in their original form, a method for robust planning under setup uncertainty where the sum of a plan evaluation criterion over a set of scenarios is optimized. The voxelwise penalties in the summands are weighted by a distribution of coefficients defined such that the method is mathematically equivalent to the use of conventional geometric margins if the scenario doses are calculated using the static dose cloud approximation. The purpose of this work is to extend scenario-based margins to general types of geometric uncertainty and to validate their use on clinical cases. Specifically, we outline how to incorporate density heterogeneity in the calculation of coefficients and demonstrate the extended method's ability to safeguard against setup errors, organ motion, and range shifts (and combinations thereof). For a water phantom with a high-density slab partly covering the target, the extended form of scenario-based margins method led to improved target coverage robustness compared to the original method. At most minor differences in robustness were, however, observed between the extended and original method for a prostate and two lung patients, all treated with intensity-modulated proton therapy, yielding evidence that the calculation of weighting coefficients is generally insensitive to tissue heterogeneities. The scenario-based margins were, furthermore, verified to provide a comparable level of robustness to expected value and worst case optimization while circumventing some known shortcomings of these methods. © 2017 Institute of Physics and Engineering in Medicine.

Fredriksson A.,KTH Royal Institute of Technology | Fredriksson A.,RaySearch Laboratories | Forsgren A.,KTH Royal Institute of Technology | Hardemark B.,RaySearch Laboratories
Medical Physics | Year: 2011

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. © 2011 American Association of Physicists in Medicine.

Bokrantz R.,KTH Royal Institute of Technology | Bokrantz R.,RaySearch Laboratories | Forsgren A.,KTH Royal Institute of Technology
INFORMS Journal on Computing | Year: 2013

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. © 2013 INFORMS.

Fredriksson A.,KTH Royal Institute of Technology | Fredriksson A.,RaySearch Laboratories | Bokrantz R.,KTH Royal Institute of Technology | Bokrantz R.,RaySearch Laboratories
Physics in Medicine and Biology | Year: 2013

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. © 2013 Institute of Physics and Engineering in Medicine.

Bokrantz R.,KTH Royal Institute of Technology | Bokrantz R.,RaySearch Laboratories
Physics in Medicine and Biology | Year: 2013

We consider multicriteria radiation therapy treatment planning by navigation over the Pareto surface, implemented by interpolation between discrete treatment plans. Current state of the art for calculation of a discrete representation of the Pareto surface is to sandwich this set between inner and outer approximations that are updated one point at a time. In this paper, we generalize this sequential method to an algorithm that permits parallelization. The principle of the generalization is to apply the sequential method to an approximation of an inexpensive model of the Pareto surface. The information gathered from the model is sub-sequently used for the calculation of points from the exact Pareto surface, which are processed in parallel. The model is constructed according to the current inner and outer approximations, and given a shape that is difficult to approximate, in order to avoid that parts of the Pareto surface are incorrectly disregarded. Approximations of comparable quality to those generated by the sequential method are demonstrated when the degree of parallelization 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. © 2013 Institute of Physics and Engineering in Medicine.

Fredriksson A.,KTH Royal Institute of Technology | Fredriksson A.,RaySearch Laboratories
Physics in Medicine and Biology | Year: 2012

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. © 2012 IOP Publishing Ltd.

Wedenberg M.,Karolinska Institutet | Wedenberg M.,RaySearch Laboratories | Toma-Dasu I.,Karolinska Institutet
Medical Physics | Year: 2014

Purpose: Currently in proton radiation therapy, a constant relative biological effectiveness (RBE) equal to 1.1 is assumed. The purpose of this study is to evaluate the impact of disregarding variations in RBE on the comparison of proton and photon treatment plans. Methods: Intensity modulated treatment plans using photons and protons were created for three brain tumor cases with the target situated close to organs at risk. The proton plans were optimized assuming a standard RBE equal to 1.1, and the resulting linear energy transfer (LET) distribution for the plans was calculated. In the plan evaluation, the effect of a variable RBE was studied. The RBE model used considers the RBE variation with dose, LET, and the tissue specific parameter α /β of photons. The plan comparison was based on dose distributions, DVHs and normal tissue complication probabilities (NTCPs). Results: Under the assumption of RBE = 1.1, higher doses to the tumor and lower doses to the normal tissues were obtained for the proton plans compared to the photon plans. In contrast, when accounting for RBE variations, the comparison showed lower doses to the tumor and hot spots in organs at risk in the proton plans. These hot spots resulted in higher estimated NTCPs in the proton plans compared to the photon plans. Conclusions: Disregarding RBE variations might lead to suboptimal proton plans giving lower effect in the tumor and higher effect in normal tissues than expected. For cases where the target is situated close to structures sensitive to hot spot doses, this trend may lead to bias in favor of proton plans in treatment plan comparisons. © 2014 American Association of Physicists in Medicine.

Wedenberg M.,Karolinska Institutet | Wedenberg M.,RaySearch Laboratories | Lind B.K.,Karolinska Institutet | Hardemark B.,RaySearch Laboratories
Acta Oncologica | Year: 2013

Background. The biological effects of particles are often expressed in relation to that of photons through the concept of relative biological effectiveness, RBE. In proton radiotherapy, a constant RBE of 1.1 is usually assumed. However, there is experimental evidence that RBE depends on various factors. The aim of this study is to develop a model to predict the RBE based on linear energy transfer (LET), dose, and the tissue specific parameter α/β of the linear-quadratic model for the reference radiation. Moreover, the model should capture the basic features of the RBE using a minimum of assumptions, each supported by experimental data. Material and methods. The α and β parameters for protons were studied with respect to their dependence on LET. An RBE model was proposed where the dependence of LET is affected by the (α/β)phot ratio of photons. Published cell survival data with a range of well-defined LETs and cell types were selected for model evaluation rendering a total of 10 cell lines and 24 RBE values. Results and Conclusion. A statistically significant relation was found between α for protons and LET. Moreover, the strength of that relation varied significantly with (α/β)phot. In contrast, no significant relation between β and LET was found. On the whole, the resulting RBE model provided a significantly improved fit (p-value <0.01) to the experimental data compared to the standard constant RBE. By accounting for the α/β ratio of photons, clearer trends between RBE and LET of protons were found, and our results suggest that late responding tissues are more sensitive to LET changes than early responding tissues and most tumors. An advantage with the proposed RBE model in optimization and evaluation of treatment plans is that it only requires dose, LET, and (α/β)phot as input parameters. Hence, no proton specific biological parameters are needed. © 2013 Informa Healthcare.

Wedenberg M.,Karolinska Institutet | Wedenberg M.,RaySearch Laboratories
International Journal of Radiation Oncology Biology Physics | Year: 2013

Purpose: To apply a statistical bootstrap analysis to assess the uncertainty in the dose-response relation for the endpoints pneumonitis and myelopathy reported in the QUANTEC review. Methods and Materials: The bootstrap method assesses the uncertainty of the estimated population-based dose-response relation due to sample variability, which reflects the uncertainty due to limited numbers of patients in the studies. A large number of bootstrap replicates of the original incidence data were produced by random sampling with replacement. The analysis requires only the dose, the number of patients, and the number of occurrences of the studied endpoint, for each study. Two dose-response models, a Poisson-based model and the Lyman model, were fitted to each bootstrap replicate using maximum likelihood. Results: The bootstrap analysis generates a family of curves representing the range of plausible dose-response relations, and the 95% bootstrap confidence intervals give an estimated upper and lower toxicity risk. The curve families for the 2 dose-response models overlap for doses included in the studies at hand but diverge beyond that, with the Lyman model suggesting a steeper slope. The resulting distributions of the model parameters indicate correlation and non-Gaussian distribution. For both data sets, the likelihood of the observed data was higher for the Lyman model in >90% of the bootstrap replicates. Conclusions: The bootstrap method provides a statistical analysis of the uncertainty in the estimated dose-response relation for myelopathy and pneumonitis. It suggests likely values of model parameter values, their confidence intervals, and how they interrelate for each model. Finally, it can be used to evaluate to what extent data supports one model over another. For both data sets considered here, the Lyman model was preferred over the Poisson-based model. © 2013 Elsevier Inc.

Fredriksson A.,RaySearch Laboratories | Bokrantz R.,RaySearch Laboratories
Medical Physics | Year: 2014

Purpose: To critically evaluate and compare three worst case optimization methods that have been previously employed to generate intensity-modulated proton therapy treatment plans that are robust against systematic errors. The goal of the evaluation is to identify circumstances when the methods behave differently and to describe the mechanism behind the differences when they occur. Methods: The worst case methods optimize plans to perform as well as possible under the worst case scenario that can physically occur (composite worst case), the combination of the worst case scenarios for each objective constituent considered independently (objectivewise worst case), and the combination of the worst case scenarios for each voxel considered independently (voxelwise worst case). These three methods were assessed with respect to treatment planning for prostate under systematic setup uncertainty. An equivalence with probabilistic optimization was used to identify the scenarios that determine the outcome of the optimization. Results: If the conflict between target coverage and normal tissue sparing is small and no dose-volume histogram (DVH) constraints are present, then all three methods yield robust plans. Otherwise, they all have their shortcomings: Composite worst case led to unnecessarily low plan quality in boundary scenarios that were less difficult than the worst case ones. Objectivewise worst case generally led to nonrobust plans. Voxelwise worst case led to overly conservative plans with respect to DVH constraints, which resulted in excessive dose to normal tissue, and less sharp dose fall-off than the other two methods. Conclusions: The three worst case methods have clearly different behaviors. These behaviors can be understood from which scenarios that are active in the optimization. No particular method is superior to the others under all circumstances: composite worst case is suitable if the conflicts are not very severe or there are DVH constraints whereas voxelwise worst case is advantageous if there are severe conflicts but no DVH constraints. The advantages of composite and voxelwise worst case outweigh those of objectivewise worst case. © 2014 American Association of Physicists in Medicine.

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