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A Mixed-Integer Programming Approach for the Design of Homogeneous Magnets

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T Chan

T Chan1*, I Dayarian2 , D Jaffray2 , T Stanescu2 , (1) University of Toronto, Toronto, ON, (2) Princess Margaret Cancer Centre, Toronto, ON


TU-FG-FS2-6 (Tuesday, August 1, 2017) 1:45 PM - 3:45 PM Room: Four Seasons 2

Purpose: Novel technologies aim at the integration of an MRI scanner with a therapy system to enable in-room MR guidance for improved soft-tissue radiotherapy targeting. The objective of this study was to develop a new optimization framework based on mixed-integer programming (MIP) for the design of realistic MR magnets with reduced footprint.

Methods: Assuming an arbitrary shape for the target MR imaging volume, the MIP model defines an objective function that minimizes the amount of material required by the magnet configuration to guarantee a desired degree of field homogeneity. MIP explicitly integrates thick coil field calculations, based on a semi-analytical formulation, and physical constraints imposed by coil thicknesses in a single model. Coil overlap issues common to linear programming (LP) based models are avoided by defining candidate cross-section values that each coil may take during the optimization process. Constraints are introduced to define the field homogeneity tolerance and limit the critical current density for the current-carrying coils. The modelling was set to provide extensive flexibility by allowing both asymmetrical and symmetrical coil configurations as well as to control the total number of coils in the final magnet design.

Results: The MIP model was investigated for multiple scenarios and compared to an LP model assuming the same simulation environment. Given the reduced size of the candidate coil domain, the LP formulation lead to significant coil overlaps making the solution unfeasible. In contrast, the MIP model provided realistic solutions with symmetry/asymmetry in the coil configurations for a given number of coils.

Conclusion: A novel MIP-based optimization approach was developed for magnet design that a) provides accurate field calculations, b) derives precisely the coils’ relative location, size, and currents, c) guarantees pre-defined field homogeneity inside the imaging volume, and d) produces configurations that satisfy reduced footprint feasibility constraints required for MR-guided therapy systems.

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