Including robustness in multi-criteria optimization for intensity-modulated proton therapy (original) (raw)
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We review the field of multi-criteria optimization for radiation therapy treatment planning. Special attention is given to the technique known as Pareto surface navigation, which allows physicians and treatment planners to interactively navigate through treatment planning options to get an understanding of the tradeoffs (dose to the target versus over-dosing of important nearby organs) involved in each patient's plan. We also describe goal programming and prioritized optimization, two other methods designed to handle multiple conflicting objectives. Issues related to nonconvexities, both in terms of dosimetric goals and the fact that the mapping from controllable hardware parameters to patient doses is usually nonconvex, are discussed at length since nonconvexities have a large impact on practical solution techniques for Pareto surface construction and navigation. A general planning strategy is recommended which handles the issue of nonconvexity by first finding an ideal Pareto surface with radiation delivered from many preset angles. This can be cast as a convex optimization problem. Once a high quality solution is selected from the Pareto surface, a sparse version (which can mean fewer beams, fewer segments, less leaf travel for arc therapy techniques, etc.) is obtained using an appropriate sparsification heuristic. We end by discussing issues of efficiency regarding the planning and the delivery of radiation therapy.
A fast optimization algorithm for multicriteria intensity modulated proton therapy planning
Medical Physics, 2010
Purpose: To describe a fast projection algorithm for optimizing intensity modulated proton therapy ͑IMPT͒ plans and to describe and demonstrate the use of this algorithm in multicriteria IMPT planning. Methods: The authors develop a projection-based solver for a class of convex optimization problems and apply it to IMPT treatment planning. The speed of the solver permits its use in multicriteria optimization, where several optimizations are performed which span the space of possible treatment plans. The authors describe a plan database generation procedure which is customized to the requirements of the solver. The optimality precision of the solver can be specified by the user. Results: The authors apply the algorithm to three clinical cases: A pancreas case, an esophagus case, and a tumor along the rib cage case. Detailed analysis of the pancreas case shows that the algorithm is orders of magnitude faster than industry-standard general purpose algorithms ͑MOSEK's interior point optimizer, primal simplex optimizer, and dual simplex optimizer͒. Additionally, the projection solver has almost no memory overhead. Conclusions: The speed and guaranteed accuracy of the algorithm make it suitable for use in multicriteria treatment planning, which requires the computation of several diverse treatment plans. Additionally, given the low memory overhead of the algorithm, the method can be extended to include multiple geometric instances and proton range possibilities, for robust optimization.
Intensity-modulated radiotherapy - a large scale multi-criteria programming problem
OR Spectrum, 2003
Radiation therapy planning is often a tight rope walk between dangerous insufficient dose in the target volume and life threatening overdosing of organs at risk. Finding ideal balances between these inherently contradictory goals challenges dosimetrists and physicians in their daily practice. Todays inverse planning systems calculate treatment plans based on a single evaluation function that measures the quality of a radiation treatment plan. Unfortunately, such a one dimensional approach cannot satisfactorily map the different backgrounds of physicians and the patient dependent necessities. So, too often a time consuming iterative optimization process between evaluation of the dose distribution and redefinition of the evaluation func-1 tion is needed. In this paper we propose a generic multi-criteria approach based on Pareto's solution concept. For each entity of interest -target volume or organ at risk -a structure dependent evaluation function is defined measuring deviations from ideal doses that are calculated from statistical functions. A reasonable bunch of clinically meaningful Pareto optimal solutions are stored in a data base, which can be interactively searched by physicians. The system guarantees dynamic planning as well as the discussion of tradeoffs between different entities. Mathematically, we model the inverse problem as a multi-criteria linear programming problem. Because of the large scale nature of the problem it is not possible to solve the problem in a 3D-setting without adaptive reduction by appropriate approximation schemes. Our approach is twofold: First, the discretization of the continuous problem is based on an adaptive hierarchical clustering process which is used for a local refinement of constraints during the optimization procedure. Second, the set of Pareto optimal solutions is approximated by an adaptive grid of representatives that are found by a hybrid process of calculating extreme compromises and interpolation methods.
Multicriteria optimization in intensity modulated radiotherapy planning
PM Pardalos, HE Romeijn: Handbook of Optimization in Medicine, 2009
The inverse treatment planning problem of IMRT is formulated as a multicriteria optimization problem. The problem is embedded in the more general family of design problems. The concept of Reverse Engineering, when interpreted as an optimization paradigm for design problems, reveals favourable structural properties. The numerical complexity of large-scale instances can then be significantly reduced by an appropriate exploitation of a structural property called asymmetry.
Medical Physics, 2018
PurposeIntensity‐modulated proton therapy (IMPT) is known to be sensitive to patient setup and range uncertainty issues. Multiple robust optimization methods have been developed to mitigate the impact of these uncertainties. Here, we propose a new robust optimization method, which provides an alternative way of robust optimization in IMPT, and is clinically practical, which will enable users to control the balance between nominal plan quality and plan robustness in a user‐defined fashion.MethodWe calculated nine individual dose distributions which corresponded to one nominal and eight extreme scenarios caused by patient setup and proton beam's range uncertainties. For each voxel, the normalized dose interval (NDI) is defined as the full dose range variation divided by the maximum dose in all uncertainty scenarios (NDI = [max – min dose]/max dose), which was then used to calculate the normalized dose interval volume histogram (NDIVH) curves. The areas under the NDIVH curves were ...
Medical physics, 2016
Intensity-modulated proton therapy (IMPT) is highly sensitive to range uncertainties and uncertainties caused by setup variation. The conventional inverse treatment planning of IMPT based on the planning target volume (PTV) is not often sufficient to ensure robustness of treatment plans. We applied a probabilistic framework (chance-constrained optimization) in IMPT planning to hedge against the influence of uncertainties. We retrospectively selected one patient with lung cancer, one patient with head and neck (H&N) cancer, and one with prostate cancer for this analysis. Using their original images and prescriptions, we created new IMPT plans using two methods: (1) a robust chance-constrained treatment planning method with the clinical target volume (CTV) as the target; (2) the margin-based method with PTV as the target, which was solved by commercial software, CPLEX, using linear programming. For the first method, we reformulated the model into a tractable mixed-integer programming ...
Radiotherapy and Oncology, 2007
Background and purpose: Currently, inverse planning for intensity-modulated radiotherapy (IMRT) can be a timeconsuming trial and error process. This is because many planning objectives are inherently contradictory and cannot reach their individual optimum all at the same time. Therefore in clinical practice the potential of IMRT cannot be fully exploited for all patients. Multicriteria (multiobjective) optimization combined with interactive plan navigation is a promising approach to overcome these problems.
Application of constrained optimization to radiotherapy planning
Medical Physics, 1999
Essential for the calculation of photon fluence distributions for intensity modulated radiotherapy ͑IMRT͒ is the use of a suitable objective function. The objective function should reflect the clinical aims of tumor control and low side effect probability. Individual radiobiological parameters for patient organs are not yet available with sufficient accuracy. Some of the major drawbacks of some current optimization methods include an inability to converge to a solution for arbitrary input parameters, and/or a need for intensive user input in order to guide the optimization. In this work, a constrained optimization method was implemented and tested. It is closely related to the demanded clinical aims, avoiding the drawbacks mentioned above. In a prototype treatment planning system for IMRT, tumor control was guaranteed by setting a lower boundary for target dose. The aim of low complication is fulfilled by minimizing the dose to organs at risk. If only one type of tissue is involved, there is no absolute need for radiobiological parameters. For different organs, threshold dose, relative seriality of the organs or an upper dose limit could be set. All parameters, however, were optional, and could be omitted. Dose-volume constraints were not used, avoiding the possibility of local minima in the objective function. The approach was benchmarked through the simulation of both a head and neck and a lung case. A cylinder phantom with precalculated dose distributions of individual pencil beams was used. The dose to regions at risk could be significantly reduced using at least seven ports of beam incidence. Increasing the number of ports beyond seven produced only minor further gain. The relative seriality of organs was modeled through the use of an added exponent to the dose. This approach however increased calculation time significantly. The alternative of setting an upper limit is much faster and allows direct control of the maximum dose. Constrained optimization guarantees high tumor control probability, it is computationally more efficient than adding penalty terms to the objective function, and the input parameters are dose limits known in clinical practice.
Robust optimization for intensity modulated radiation therapy treatment planning under uncertainty
Physics in Medicine and Biology, 2005
The recent development of Intensity Modulated Radiation Therapy (IMRT) allows the dose distribution to be tailored to match the tumour's shape and position, avoiding damage to healthy tissue to a greater extent than previously possible. Traditional treatment plans assume the target structure remains in a fixed location throughout treatment. However, many studies have shown that because of organ motion, inconsistencies in patient positioning over the weeks of treatment, etc., the tumour location is not stationary. We present a probabilistic model for the IMRT inverse problem and show that it is identical to using robust optimization techniques, under certain assumptions. For a sample prostate case, our computational results show that this method is computationally feasible and promising -compared to traditional methods, our model has the potential to find treatment plans that are more adept at sparing healthy tissue while maintaining the prescribed dose to the target.