Treatment planning in arc proton therapy: Comparison of several optimization problem statements and their corresponding solvers

Wuyckens, S.; Saint-Guillain, Michael; Janssens, Guillaume; Zhao, Lewei; Li, Xiaoqiang; Ding, Xuanfeng; Sterpin, Edmond; Lee, John A.; Souris, Kevin

doi:10.1016/j.compbiomed.2022.105609

Cited by 23 publications

(35 citation statements)

References 32 publications

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“…Spot-scanning arc therapy is an emerging proton modality 56 and rapidly developing [57][58][59][60] as a viable alternative to fixed-beam IMPT that can potentially offer a combination of advantages in plan quality and delivery efficiency, compared to fixed beam IMPT. But currently fixed-beam IMPT remains to be the mainstream for proton treatments, for which BAO is still relevant.…”

Section: Discussionmentioning

confidence: 99%

Beam angle optimization for proton therapy via group‐sparsity based angle generation method

et al. 2023

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Background: In treatment planning, beam angle optimization (BAO) refers to the selection of a subset with a given number of beam angles from all available angles that provides the best plan quality. BAO is a NP-hard combinatorial problem. Although exhaustive search (ES) can exactly solve BAO by exploring all possible combinations, ES is very time-consuming and practically infeasible. Purpose: To the best of our knowledge, (1) no optimization method has been demonstrated that can provide the exact solution to BAO,and (2) no study has validated an optimization method for solving BAO by benchmarking with the optimal BAO solution (e.g., via ES), both of which will be addressed by this work. Methods: This work considers BAO for proton therapy,for example,the selection of 2-4 beam angles for IMPT. The optimal BAO solution is obtained via ES and serves as the ground truth. A new BAO algorithm, namely angle generation (AG) method, is proposed, and demonstrated to provide nearly-exact solutions for BAO in reference to the ES solution. AG iteratively optimizes the angular set via group-sparsity (GS) regularization, until the planning objective does not decrease further. Results: Since GS alone can also solve BAO, AG was validated and compared with GS for 2-angle brain, 3-angle lung, and 4-angle brain cases, in reference to the optimal BAO solutions obtained by ES: the AG solution had the rank (1/276, 1/2024, 4/10 626), while the GS solution had the rank (42/276, 279/2024, 4328/10 626). Conclusions: A new BAO algorithm called AG is proposed and shown to provide substantially improved accuracy for BAO from current methods with nearly-exact solutions to BAO, in reference to the ground truth of optimal BAO solution via ES.

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Section: Discussionmentioning

confidence: 99%

Beam angle optimization for proton therapy via group‐sparsity based angle generation method

et al. 2023

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“…Another benefit of our MIP formulation is its ability to interchange soft objectives with hard constraints, although this has not been exploited in the current article. As shown in Wuyckens et al's (2022), the ability to turn medical constraints, from soft to hard, is mandatory in order to compute solutions with strong treatment guarantees. Finally, the benchmark produced for this study including a conventional IMPT plan and a SPArc plan allows to make several statements.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, it mainly depends on whether each irradiation angle and energy layer is activated or not, introducing this temporal dimension turns our PAT problem into a discrete, integer problem. In a recent study (Wuyckens et al 2022), we proved in that the irradiation time only is responsible for the inherently complexity (i.e., the NP-hardness) of the PAT problem.…”

Section: Mip Modelmentioning

confidence: 96%

“…We choose to model and minimize the irradiation time (BDT ≈ ) using the reasonable approximation that it takes 1 s to deliver one energy layer, 5.5 s to increase the energy, 0.6 s to decrease it and 0.2 s when same energy is kept to deliver the next layer (Liu et al 2020). In a previous work (Wuyckens et al 2022), we showed that this approximation of irradiation time can be modeled as a convex linear objective provided integrality constraints resulting in a mixed-integer programming (MIP) problem statement. The MIP statement has been extended to frame the bi-objective optimization problem 1, the specific mathematical expression of which is A.1-A.6 in Appendix A.…”

Section: Mip Modelmentioning

confidence: 99%

“…From Wuyckens et al (2022), the proton arc therapy treatment optimization problem for finding a single optimal point on the Pareto front can be modelled as a weighted sum using a mixed-integer two-index flow formulation…”

Section: Appendix a Mip Modelmentioning

confidence: 99%

See 2 more Smart Citations

Bi-criteria Pareto optimization to balance irradiation time and dosimetric objectives in proton arc therapy

Wuyckens¹,

Zhao²,

Saint-Guillain³

et al. 2022

Phys. Med. Biol.

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Objective. Proton arc therapy (PAT) is a new delivery technique that exploits the continuous rotation of the gantry to distribute the therapeutic dose over many angular windows instead of using a few static fields, as in conventional (intensity-modulated) proton therapy. Although coming along with many potential clinical and dosimetric benefits, PAT has also raised a new optimization challenge. In addition to the dosimetric goals, the beam delivery time (BDT) needs to be considered in the objective function. Considering this bi-objective formulation, the task of finding a good compromise with appropriate weighting factors can turn out to be cumbersome. Approach. We have computed Pareto-optimal plans for three disease sites: a brain, a lung, and a liver, following a method of iteratively choosing weight vectors to approximate the Pareto front with few points. Mixed-Integer Programming (MIP) was selected to state the bi-criteria PAT problem and to find Pareto optimal points with a suited solver. Main results. The trade-offs between plan quality and beam irradiation time (static BDT) are investigated by inspecting three plans from the Pareto front. The latter are carefully picked to demonstrate significant differences in dose distribution and delivery time depending on their location on the frontier. The results were benchmarked against IMPT and SPArc plans showing the strength of degrees of freedom coming along with MIP optimization. Significance. This paper presents for the first time the application of bi-criteria optimization to the PAT problem, which eventually permits the planners to select the best treatment strategy according to the patient conditions and clinical resources available.

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FLASH instead of proton arc therapy is a more promising advancement for the next generation proton radiotherapy

Kang

Ding²,

Rong

2023

J Applied Clin Med Phys

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Treatment planning in arc proton therapy: Comparison of several optimization problem statements and their corresponding solvers

Cited by 23 publications

References 32 publications

Beam angle optimization for proton therapy via group‐sparsity based angle generation method

Beam angle optimization for proton therapy via group‐sparsity based angle generation method

Bi-criteria Pareto optimization to balance irradiation time and dosimetric objectives in proton arc therapy

FLASH instead of proton arc therapy is a more promising advancement for the next generation proton radiotherapy

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