Mixed integer programming with dose‐volume constraints in intensity‐modulated proton therapy

Zhang, Pengfei; Fan, Neng; Shan, Jie; Schild, Steven E.; Bues, Martin; Liu, Wei

doi:10.1002/acm2.12130

Cited by 9 publications

(11 citation statements)

References 16 publications

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“…Nonlinear programming based on quadratic objective functions (i.e., quadratic optimization) has been used in radiation therapy treatment planning for decades. Compared with linear programming, quadratic optimization usually generates plans with smoother dose–volume histogram curves . Furthermore, because of its simplistic formulations and the capability to use Quasi‐Newton optimization methods, it can achieve clinically acceptable plans much more quickly than linear programming .…”

Section: Discussionmentioning

confidence: 99%

“…51 Furthermore, because of its simplistic formulations and the capability to use Quasi-Newton optimization methods, it can achieve clinically acceptable plans much more quickly than linear programming. 51 Therefore, we believe that it is still valuable to develop a method which can integrate the minimum MU constraint into robust optimization for IMPT treatment planning using an optimization algorithm similar to PCS. Therefore, it can be more readily incorporated into the current IMPT treatment planning workflow (such as the most popular version of the optimization algorithm, PCS, in Eclipse TM ).…”

Section: Discussionmentioning

confidence: 99%

“…Compared with linear programming, quadratic optimization usually generates plans with smoother dose–volume histogram curves . Furthermore, because of its simplistic formulations and the capability to use Quasi‐Newton optimization methods, it can achieve clinically acceptable plans much more quickly than linear programming . Therefore, we believe that it is still valuable to develop a method which can integrate the minimum MU constraint into robust optimization for IMPT treatment planning using an optimization algorithm similar to PCS.…”

Section: Discussionmentioning

confidence: 99%

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Robust optimization in IMPT using quadratic objective functions to account for the minimum MU constraint

Shan

Bues

et al. 2017

Medical Physics

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Purpose: Currently, in clinical practice of intensity-modulated proton therapy (IMPT), the influence of the minimum monitor unit (MU) constraint is taken into account through postprocessing after the optimization is completed. This may degrade the plan quality and plan robustness. This study aims to mitigate the impact of the minimum MU constraint directly during the plan robust optimization. Methods and materials: Cao et al. have demonstrated a two-stage method to account for the minimum MU constraint using linear programming without the impact of uncertainties considered. In this study, we took the minimum MU constraint into consideration using quadratic optimization and simultaneously had the impact of uncertainties considered using robust optimization. We evaluated our method using seven cancer patients with different machine settings.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Robust optimization in IMPT using quadratic objective functions to account for the minimum MU constraint

Shan

Bues

et al. 2017

Medical Physics

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“…A large number of time-consuming computations were needed for this study. In order to speed up the calculation, we migrated our in-house developed treatment planning system (TPS) to a Graphic Processing Unit (GPU)-based computing platform, including the following three components: (a) a modified ray-casting-based dose and linear energy transfer (LET) calculation engine, 59,64 with the enhanced capability to account for inhomogeneity more accurately 65 ; (b) voxel- wise worst-case-based 3D, [10][11][12][13][14][15][16][17]20,[25][26][27][28]66,67,68 4D, 19 and LETguided 26,69 robust optimization; and (c) DVH-band method 20,61,63 to quantify plan robustness. The TPS was highly parallelized using Compute Unified Device Architecture (CUDA).…”

Section: C Graphic Processing Unit (Gpu)-accelerated Treatment Plamentioning

confidence: 99%

Intensity‐modulated proton therapy (IMPT) interplay effect evaluation of asymmetric breathing with simultaneous uncertainty considerations in patients with non‐small cell lung cancer

et al. 2020

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Purpose Intensity‐modulated proton therapy (IMPT) is sensitive to uncertainties from patient setup and proton beam range, as well as interplay effect. In addition, respiratory motion may vary from cycle to cycle, and also from day to day. These uncertainties can severely degrade the original plan quality and potentially affect patient’s outcome. In this work, we developed a new tool to comprehensively consider the impact of all these uncertainties and provide plan robustness evaluation under them. Methods We developed a comprehensive plan robustness evaluation tool that considered both uncertainties from patient setup and proton beam range, as well as respiratory motion simultaneously. To mimic patients' respiratory motion, the time spent in each phase was randomly sampled based on patient‐specific breathing pattern parameters as acquired during the four‐dimensional (4D)‐computed tomography (CT) simulation. Spots were then assigned to one specific phase according to the temporal relationship between spot delivery sequence and patients’ respiratory motion. Dose in each phase was calculated by summing contributions from all the spots delivered in that phase. The final 4D dynamic dose was obtained by deforming all doses in each phase to the maximum exhalation phase. Three hundred (300) scenarios (10 different breathing patterns with 30 different setup and range uncertainty scenario combinations) were calculated for each plan. The dose‐volume histograms (DVHs) band method was used to assess plan robustness. Benchmarking the tool as an application’s example, we compared plan robustness under both three‐dimensional (3D) and 4D robustly optimized IMPT plans for 10 nonrandomly selected patients with non‐small cell lung cancer. Results The developed comprehensive plan robustness tool had been successfully applied to compare the plan robustness between 3D and 4D robustly optimized IMPT plans for 10 lung cancer patients. In the presence of interplay effect with uncertainties considered simultaneously, 4D robustly optimized plans provided significantly better CTV coverage (D95%, P = 0.002), CTV homogeneity (D5%‐D95%, P = 0.002) with less target hot spots (D5%, P = 0.002), and target coverage robustness (CTV D95% bandwidth, P = 0.004) compared to 3D robustly optimized plans. Superior dose sparing of normal lung (lung Dmean, P = 0.020) favoring 4D plans and comparable normal tissue sparing including esophagus, heart, and spinal cord for both 3D and 4D plans were observed. The calculation time for all patients included in this study was 11.4 ± 2.6 min. Conclusion A comprehensive plan robustness evaluation tool was successfully developed and benchmarked for plan robustness evaluation in the presence of interplay effect, setup and range uncertainties. The very high efficiency of this tool marks its clinical adaptation, highly practical and versatile nature, including possible real‐time intra‐fractional interplay effect evaluation as a potential application for future use.

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“…1,2 DVCs are either implemented as soft-DVCs that are desired by the optimization model but not guaranteed to be satisfied [3][4][5][6][8][9][10] or as hard-DVCs that are enforced by the model to ensure satisfaction. [12][13][14][15]17 A soft-DVC-based optimization model was first introduced by Bortfeld et al 3 This was followed by Wu et al, 4 who proposed a weighted non-convex DVC-based objective function to penalize the DVC violation. In their work, Newton's method was used for the optimization.…”

Section: Introductionmentioning

confidence: 99%

Integrating soft and hard dose‐volume constraints into hierarchical constrained IMRT optimization

et al. 2019

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Purpose Dose‐volume constraints (DVCs) continue to be common features in intensity‐modulated radiation therapy (IMRT) prescriptions, but they are non‐convex and difficult to incorporate. We propose computationally efficient methods to incorporate dose‐volume constraints (DVCs) into automated IMRT planning. Methods We propose a two‐phase approach: in phase‐1, we solve a convex approximation with DVCs. Although this convex approximation does not guarantee DVC satisfaction, it provides crucial initial information about voxels likely to receive doses below DVC thresholds. Subsequently, phase‐2 solves an optimization problem with maximum dose constraints imposed on those subthreshold voxels. We further categorize DVCs into hard‐ and soft‐DVCs, where hard‐DVCs are strictly enforced by the optimization and soft‐DVCs are encouraged in the objective function. We tested this approach in our automated treatment planning system which is based on hierarchical constrained optimization. Performance is demonstrated on a series of paraspinal, lung, oligometastasis, and prostate cases as well as a small paraspinal case for which we can computationally afford to obtain a ground‐truth by solving a non‐convex optimization problem. Results The proposed algorithm successfully meets all the hard‐DVCs while increasing the overall computational time of the baseline planning process (without DVCs) by 20%, 10%, and 11% for paraspinal, oligometastasis, and prostate cases, respectively. For a soft‐DVC applied to the lung case, the dose‐volume histogram curve moves toward the desired direction and the computational time is increased by 11%. For a low‐resolution paraspinal case, the ground‐truth solution process using mixed‐integer programming methods required 15 h while the proposed algorithm converges in only 2 min with a proximal solution. Conclusions A computationally tractable algorithm to handle hard‐ and soft‐DVCs is developed which is capable of satisfying DVCs without any parameter tweaking. Although the algorithm is demonstrated in our in‐house developed automated treatment planning system, it can potentially be used in any constrained optimization framework.

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Mixed integer programming with dose‐volume constraints in intensity‐modulated proton therapy

Cited by 9 publications

References 16 publications

Robust optimization in IMPT using quadratic objective functions to account for the minimum MU constraint

Robust optimization in IMPT using quadratic objective functions to account for the minimum MU constraint

Intensity‐modulated proton therapy (IMPT) interplay effect evaluation of asymmetric breathing with simultaneous uncertainty considerations in patients with non‐small cell lung cancer

Integrating soft and hard dose‐volume constraints into hierarchical constrained IMRT optimization

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