| 1. |
- Smolders, A., et al.
(författare)
-
Robust optimization strategies for contour uncertainties in online adaptive radiation therapy
- 2024
-
Ingår i: Physics in Medicine and Biology. - : IOP Publishing. - 0031-9155 .- 1361-6560. ; 69:16
-
Tidskriftsartikel (refereegranskat)abstract
- Objective. Online adaptive radiation therapy requires fast and automated contouring of daily scans for treatment plan re-optimization. However, automated contouring is imperfect and introduces contour uncertainties. This work aims at developing and comparing robust optimization strategies accounting for such uncertainties. Approach. A deep-learning method was used to predict the uncertainty of deformable image registration, and to generate a finite set of daily contour samples. Ten optimization strategies were compared: two baseline methods, five methods that convert contour samples into voxel-wise probabilities, and three methods accounting explicitly for contour samples as scenarios in robust optimization. Target coverage and organ-at-risk (OAR) sparing were evaluated robustly for simplified proton therapy plans for five head-and-neck cancer patients. Results. We found that explicitly including target contour uncertainty in robust optimization provides robust target coverage with better OAR sparing than the baseline methods, without increasing the optimization time. Although OAR doses first increased when increasing target robustness, this effect could be prevented by additionally including robustness to OAR contour uncertainty. Compared to the probability-based methods, the scenario-based methods spared the OARs more, but increased integral dose and required more computation time. Significance. This work proposed efficient and beneficial strategies to mitigate contour uncertainty in treatment plan optimization. This facilitates the adoption of automatic contouring in online adaptive radiation therapy and, more generally, enables mitigation also of other sources of contour uncertainty in treatment planning.
|
|
| 2. |
- Bengtsson, Ivar, et al.
(författare)
-
Implications of using the clinical target distribution as voxel-weights in radiation therapy optimization
- 2023
-
Ingår i: Physics in Medicine and Biology. - : IOP Publishing. - 0031-9155 .- 1361-6560. ; 68:9
-
Tidskriftsartikel (refereegranskat)abstract
- Objective. Delineating and planning with respect to regions suspected to contain microscopic tumor cells is an inherently uncertain task in radiotherapy. The recently proposed clinical target distribution (CTD) is an alternative to the conventional clinical target volume (CTV), with initial promise. Previously, using theCTDin planning has primarily been evaluated in comparison to a conventionally defined CTV. Wepropose to compare theCTDapproach against CTVmargins of various sizes, dependent on the threshold at which the tumor infiltration probability is considered relevant. Approach. First, a theoretical framework is presented, concerned with optimizing the trade-off between the probability of sufficient target coverage and the penalties associated with high dose. From this framework we derive conventional CTV-based planning and contrast it with theCTDapproach. The approaches are contextualized further by comparison with established methods for managing geometric uncertainties. Second, for both one- and three-dimensional phantoms, we compare a set of CTDplans created by varying the target objective function weight against a set of plans created by varying both the target weight and the CTVmargin size. Main results. The results show that CTD-based planning gives slightly inefficient trade-offs between the evaluation criteria for a case in which near-minimum target dose is the highest priority. However, in a case when sparing a proximal organ at risk is critical, theCTDis better at maintaining sufficiently high dose toward the center of the target. Significance. Weconclude that CTD-based planning is a computationally efficient method for planning with respect to delineation uncertainties, but that the inevitable effects on the dose distribution should not be disregarded.
|
|
| 3. |
- Ek, David, 1988-, et al.
(författare)
-
A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming
- 2023
-
Ingår i: Computational optimization and applications. - : Springer Nature. - 0926-6003 .- 1573-2894. ; 86:1, s. 1-48
-
Tidskriftsartikel (refereegranskat)abstract
- The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high quality solutions, but we are interested in modified Newton systems that are computationally less expensive at the expense of lower quality solutions. We propose a structured modified Newton approach where each modified Jacobian is composed of a previous Jacobian, plus one low-rank update matrix per succeeding iteration. Each update matrix is, for a given rank, chosen such that the distance to the Jacobian at the current iterate is minimized, in both 2-norm and Frobenius norm. The approach is structured in the sense that it preserves the nonzero pattern of the Jacobian. The choice of update matrix is supported by results in an ideal theoretical setting. We also produce numerical results with a basic interior-point implementation to investigate the practical performance within and beyond the theoretical framework. In order to improve performance beyond the theoretical framework, we also motivate and construct two heuristics to be added to the method.
|
|
| 4. |
|
|
| 5. |
- Ek, David, 1988-, et al.
(författare)
-
Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization
- 2021
-
Ingår i: Computational optimization and applications. - : Springer Nature. - 0926-6003 .- 1573-2894. ; 79:1, s. 155-191
-
Tidskriftsartikel (refereegranskat)abstract
- The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.
|
|
| 6. |
- Ek, David, 1988-, et al.
(författare)
-
Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function
- 2021
-
Ingår i: Computational optimization and applications. - : Springer Nature. - 0926-6003 .- 1573-2894. ; 79:3, s. 789-816
-
Tidskriftsartikel (refereegranskat)abstract
- The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel to those of the BFGS method, or equivalently, to those of the method of preconditioned conjugate gradients. In the setting of reduced Hessians, the class provides a dynamical framework for the construction of limited-memory quasi-Newton methods. These methods attain finite termination on quadratic optimization problems in exact arithmetic. We show performance of the methods within this framework in finite precision arithmetic by numerical simulations on sequences of related systems of linear equations, which originate from the CUTEst test collection. In addition, we give a compact representation of the Hessian approximations in the full Broyden class for the general unconstrained optimization problem. This representation consists of explicit matrices and gradients only as vector components.
|
|
| 7. |
- Ek, David, 1988-
(författare)
-
Approaches to accelerate methods for solving systems of equations arising in nonlinear optimization
- 2020
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Methods for solving nonlinear optimization problems typically involve solving systems of equations. This thesis concerns approaches for accelerating some of those methods. In our setting, accelerating involves finding a trade-off between the computational cost of an iteration and the quality of the computed search direction. We design approaches for which theoretical results in ideal settings are derived. We also investigate the practical performance of the approaches within and beyond the boundaries of the theoretical frameworks with numerical simulations.Paper A concerns methods for solving strictly convex unconstrained quadratic optimization problems. This is equivalent to solving systems of linear equations where the matrices are symmetric positive definite. The main focus is exact linesearch limited-memory quasi-Newton methods which generate search directions parallel to those of the method of preconditioned conjugate gradients. We give a class of limited-memory quasi-Newton methods. In addition, we provide a dynamic framework for the construction of these methods. The methods are meant to be particularly useful for solving sequences of related systems of linear equations. Such sequences typically arise as methods for solving systems of nonlinear equations converge.Paper B deals with solving systems of nonlinear equations that arise in interior-point methods for bound-constrained nonlinear programming. Application of Newton's method gives sequences of systems of linear equations. We propose partial and full approximate solutions to the Newton systems. The partial approximate solutions are computationally inexpensive, whereas each full approximate solution typically requires a reduced Newton system to be solved. In addition, we suggest two Newton-like approaches, which are based upon the proposed partial approximate solutions, for solving the systems of nonlinear equations.Paper C is focused on interior-point methods for quadratic programming. We propose a structured modified Newton approach to solve the systems of nonlinear equations that arise. The modified Jacobians are composed of a previous Jacobian, plus one low-rank update matrix per succeeding iteration. For a given rank restriction, we construct a low-rank update matrix such that the modified Jacobian becomes closest to the current Jacobian, in both 2-norm and Frobenious norm. The approach is structured in the sense that it preserves the nonzero pattern of the Jacobian.The approaches suggested in Paper B and Paper C are motivated by asymptotic results in ideal theoretical frameworks. In particular, it is shown that the approaches become increasingly accurate as primal-dual interior-point methods converge. A demonstration of the practical performance is given by numerical results. The results indicate the performance and limitations of the approaches suggested.We envisage that the approaches of Paper A, Paper B and Paper C can be useful in parallel, or in combination, with existing solvers in order to accelerate methods.Paper D is more pedagogical in nature. We give a derivation of the method of conjugate gradients in an optimization framework. The result itself is well known but the derivation has, to the best of our knowledge, not been presented before.
|
|
| 8. |
- Forsgren, Anders, et al.
(författare)
-
On the existence of a short pivoting sequence for a linear program
- 2020
-
Ingår i: Operations Research Letters. - : Elsevier B.V.. - 0167-6377 .- 1872-7468. ; 48:6, s. 697-702
-
Tidskriftsartikel (refereegranskat)abstract
- We show that given a feasible primal–dual pair of linear programs in canonical form, there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, leading from the origin to the optimum. The sequence of pivots give a sequence of square and nonsingular submatrices of the constraint matrix. Solving two linear equations involving such a submatrix give primal–dual optimal solutions to the corresponding linear program in canonical form.
|
|
| 9. |
- Böck, Michelle, et al.
(författare)
-
On the interplay between robustness and dynamic planning for adaptive radiation therapy
- 2019
-
Ingår i: BIOMEDICAL PHYSICS & ENGINEERING EXPRESS. - : Institute of Physics (IOP). - 2057-1976. ; 5:4
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 10. |
- Böck, Michelle
(författare)
-
Toward Robust Optimization of Adaptive Radiation Therapy
- 2019
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
