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Session: Particle Therapy [Return to Session]

ArcPT Plan Optimization: Thinking Out of the Box with Mixed-Integer Programming

S Wuyckens1*, M Saint-guillain2, G Janssens3, E Sterpin1,4, J Lee1, K Souris1, (1) UCLouvain / MIRO, Woluwe-saint-lambert, BE, (2) UCLouvain / ICTEAM, Louvain-La-Neuve, BE, (3) Ion Beam Applications SA, Louvain-la-neuve, BE, (4) KULeuven / Department of Oncology, Leuven, BE


MO-H345-IePD-F4-3 (Monday, 7/11/2022) 3:45 PM - 4:15 PM [Eastern Time (GMT-4)]

Exhibit Hall | Forum 4

Purpose: Arc Proton Therapy (ArcPT) uses the continuous rotation of the gantry to deliver the treatment following a series of control points, forming the arc. In several studies, this advanced delivery technique has shown multiple benefits over the conventional treatments delivered with 2 to 4 fixed-angle beams, such as improved robustness and LET distribution. However, the optimization of ArcPT plans raises new challenges, in particular one related to the beam delivery time (BDT) optimization. The BDT is mainly driven by the energy layer switching time (ELST) that increases linearly with the numbers of beams and energy switches. As classical algorithms are ineffective to solve the complexity of ArcPT planning, we propose a novel approach based on mixed-integer linear programming providing treatment and optimality proofs.

Methods: A mixed-integer program (MIP) is formulated with two sets of decision variables: the usual spot weights as continuous variables and binary variables determining whether some energy switch happens. Constraints are formulated to obtain target dose coverage but also specific energy sequences. The MIP is tested on a brain case with 2.5 mm dose grid resolution and compared to other modalities (VMAT, IMPT) and ArcPT algorithms (SPArcling).

Results: The MIP successfully optimized the treatment plan with a constraint of maximum 6 upwards energy switches to get a fair comparison with the SPArcling algorithm. While the target coverage was similar to other methods, the ArcPT plan generated with MIP obtains the best conformity index and better spares the brain stem by achieving 66 % of the dose limit set to 55 Gy versus 77% (SPArcling), 91.5 % (VMAT) and 80% (IMPT).

Conclusion: We presented a novel method based on a MIP formulation able to solve the complex ArcPT plan optimization problem. The preliminary results obtained with a brain case are encouraging and compete with existing modalities.

Funding Support, Disclosures, and Conflict of Interest: This research is conducted in collaboration with Ion Beam Applications s.a. (IBA) and is supported by the Walloon Region as part of the Arc Proton Therapy convention (Poles Mecatech et Biowin).


Treatment Planning, Protons, Optimization


TH- External Beam- Particle/high LET therapy: Proton therapy – treatment planning/virtual clinical studies

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