Binary Level-Set Shape Optimization Model and Algorithm for Volumetric Modulated Arc Therapy in Radiotherapy Treatment

Cheng, Li Tien; Dong, Bin; Men, Chunhua; Jia, Xun; Jiang, Steve B

doi:10.1137/120890430

Cited by 8 publications

(15 citation statements)

References 62 publications

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“…The collimator angles are set manually. The following optimization problem is an adaptation of the binary level set optimization model, where the MLC init set and the corresponding weights are cast into a master problem consisting of two recurring optimization subroutines, in which the weights of each aperture are optimized, followed by optimization of the iteratively updated

MLC

set …”

Section: Methodsmentioning

confidence: 99%

“…The following optimization problem is an adaptation of the binary level set optimization model, where the MLC init set and the corresponding weights are cast into a master problem consisting of two recurring optimization subroutines, in which the weights of each aperture are optimized, followed by optimization of the iteratively updated MLC set. 18 First, beam weights x corresponding to beams extracted from K final are optimized using a GPU-based bounded Broyden-Fletcher-Goldfarb-Shanno (BFGS-B) optimization engine implemented in CUDA 19,20 . In order to extract x, a BFGS-B based optimization subroutine P 3 is defined, which is derived from G, such that…”

Section: Cmentioning

confidence: 99%

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A continuous arc delivery optimization algorithm for CyberKnife m6

et al. 2018

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MLC

set …”

Section: Methodsmentioning

confidence: 99%

Section: Cmentioning

confidence: 99%

A continuous arc delivery optimization algorithm for CyberKnife m6

et al. 2018

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“…Cheng et al introduced a binary level-set shape optimization model for VMAT, illustrating the efficacy of level-set methods for radiotherapy. 19 While efficient, the disadvantage to using a binary level-set lies in that fact the level-set function is discontinuous. Derivatives of the level-set at the boundary do not exist and this can lead to poor accuracy in the variational approach.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive formulation for volumetric modulated arc therapy planning

et al. 2016

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Purpose: Volumetric modulated arc therapy (VMAT) is a widely employed radiation therapy technique, showing comparable dosimetry to static beam intensity modulated radiation therapy (IMRT) with reduced monitor units and treatment time. However, the current VMAT optimization has various greedy heuristics employed for an empirical solution, which jeopardizes plan consistency and quality. The authors introduce a novel direct aperture optimization method for VMAT to overcome these limitations. Methods: The comprehensive VMAT (comVMAT) planning was formulated as an optimization problem with an L2-norm fidelity term to penalize the difference between the optimized dose and the prescribed dose, as well as an anisotropic total variation term to promote piecewise continuity in the fluence maps, preparing it for direct aperture optimization. A level set function was used to describe the aperture shapes and the difference between aperture shapes at adjacent angles was penalized to control MLC motion range. A proximal-class optimization solver was adopted to solve the large scale optimization problem, and an alternating optimization strategy was implemented to solve the fluence intensity and aperture shapes simultaneously. Single arc comVMAT plans, utilizing 180 beams with 2• angular resolution, were generated for a glioblastoma multiforme case, a lung (LNG) case, and two head and neck cases-one with three PTVs (H&N 3PTV ) and one with foue PTVs (H&N 4PTV )-to test the efficacy. The plans were optimized using an alternating optimization strategy. The plans were compared against the clinical VMAT (clnVMAT) plans utilizing two overlapping coplanar arcs for treatment.Results: The optimization of the comVMAT plans had converged within 600 iterations of the block minimization algorithm. comVMAT plans were able to consistently reduce the dose to all organs-at-risk (OARs) as compared to the clnVMAT plans. On average, comVMAT plans reduced the max and mean OAR dose by 6.59% and 7.45%, respectively, of the prescription dose. Reductions in max dose and mean dose were as high as 14.5 Gy in the LNG case and 15.3 Gy in the H&N 3PTV case. PTV coverages measured by D95, D98, and D99 were within 0.25% of the prescription dose. By comprehensively optimizing all beams, the comVMAT optimizer gained the freedom to allow some selected beams to deliver higher intensities, yielding a dose distribution that resembles a static beam IMRT plan with beam orientation optimization. Conclusions: The novel nongreedy VMAT approach simultaneously optimizes all beams in an arc and then directly generates deliverable apertures. The single arc VMAT approach thus fully utilizes the digital Linac's capability in dose rate and gantry rotation speed modulation. In practice, the new single VMAT algorithm generates plans superior to existing VMAT algorithms utilizing two arcs. C 2016 American Association of Physicists in Medicine. [http://dx

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“…Besides these two main directions, the research done by Hoegele et al [11] proposes a quadratic programming model and develops an algorithm based on projection method to solve the model. Cheng et al [6] introduces a variational method to construct the VMAT problem. The binary level-set method is used to model apertures and a fast sweeping method is used to model beam intensity constraints.…”

Section: Introductionmentioning

confidence: 99%

Treatment Planning for Volumetric-Modulated Arc Therapy: Model and Heuristic Algorithms

Song

Shi

Sun

et al. 2015

IEEE Trans. Automat. Sci. Eng.

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In this paper, we study the radiation treatment planning optimization for Volumetric-Modulated Arc Therapy (VMAT). A nonlinear mixed integer programming model is formulated, then the linearization technique is used, and the resulting mixed integer programming model is solved by a heuristic approach based on the Nested-Partitions framework. The approach partitions the feasible region iteratively and constructs a feasible solution by solving the LP relaxation of the original problem. We design two partition strategies: partition by column and expansion from center of aperture. Numerical results with clinical cases show the efficiency of the proposed model and algorithm.Note to Practitioners-VMAT delivers a dose in a continuous manner which requires the dose intensity and aperture shape to be optimized simultaneously. The resulting treatment planning problem becomes very difficult to solve. In this paper, we develop a nonlinear mathematical model based on control points. The frequently used clinical setting such as dose-limit and dose volume constraints as well as multi-leaf collimator (MLC) constraints are considered in the model. We then use a linearization technique to transform the nonlinear treatment planning model to an equivalent mixed integer linear programming (MILP) model. The objective of the MILP model is a penalty function of target underdose and organ at risk (OAR) overdose. Based on the property of the MILP treatment planning problem, an effective heuristic method based on Nested-Partitions framework is developed to solve the MILP problem. The output of the model includes the dose intensity and aperture at each control point. As the prescription dose limit and feasibility of change between adjacent control points are ensured in the model, the output is deliverable through a planning system. Index Terms-Heuristics, nonlinear mixed integer programming, radiation therapy planning, volumetric-modulated arc therapy (VMAT).

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Binary Level-Set Shape Optimization Model and Algorithm for Volumetric Modulated Arc Therapy in Radiotherapy Treatment

Cited by 8 publications

References 62 publications

A continuous arc delivery optimization algorithm for CyberKnife m6

A continuous arc delivery optimization algorithm for CyberKnife m6

A comprehensive formulation for volumetric modulated arc therapy planning

Treatment Planning for Volumetric-Modulated Arc Therapy: Model and Heuristic Algorithms

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