Characterizing magnetic field coupling in MRI-guided radiotherapy by solving a Dirichlet problem with sparsely sampled boundary conditions.

Integrating medical linear accelerators and MRI scanners for MRI-guided radiotherapy (MRgRT) is complicated by mutual magnetic field coupling, making efficient field mapping crucial. This study proposes a computationally efficient methodology to characterize an MR scanner's magnetic fringe field by solving a boundary value problem (BVP) from sparsely sampled data. This approach accurately maps fields in free space and near ferromagnetic materials without requiring proprietary internal MR coil models or full-scale room simulations. Approach: A full-scale finite element method (FEM) model of a proximity-type MRgRT system, validated against experimental measurements, was used as the reference. A hybrid BVP methodology was developed where Laplace's equation was first solved using sparsely sampled magnetic field boundary conditions. To account for the linac, this free-space solution was subsequently used as an initial condition for a refined model that incorporated the ferromagnetic properties of the linac head and was solved using Maxwell's equations. Accuracy was assessed by comparing the BVP solutions to the full-scale FEM reference across various sampling resolutions. Main results: The BVP approach reconstructed the magnetic field to within 1G of the reference using a coarse 40 cm boundary sampling. The hybrid method successfully characterized field distortions from the linac; ignoring the ferromagnetic structure led to errors of -7G to 2G near the component, whereas including it reduced the discrepancy to within 1G. The methodology was efficient, reducing computation time from 2 hours for the full-scale model to under 10 minutes, while using a fraction of the memory. Significance: This study presents a validated, efficient, and accessible BVP-based methodology for magnetic field characterization in MRgRT systems. By enabling accurate field mapping from sparse data, accounting for ferromagnetic components, and drastically reducing computational demands, this approach offers a robust tool for rapid engineering assessments and serves as a practical alternative to complex full-scale simulations.&#xD.