Motion-induced fields near an idealized actively shielded MRI magnet: a reproducible reduced-order framework for scaling and sensitivity from 1.5 to 7 T.

PURPOSE: To present a transparent reduced-order electromagnetic framework for examining how an explicitly specified magnet geometry, movement trajectory, and body-conversion model affect movement-induced field estimates near MRI systems. The framework distinguishes dependencies imposed by the equations from spatial and sensitivity results computed from the field map.

METHODS

An idealized actively shielded magnet was represented by primary and opposing coaxial solenoids. A 7-T reference system was calibrated at two axial points; 1.5 T and 3 T cases were then generated by matched-geometry ampere-turn scaling as a controlled thought experiment. Movement-induced dB/dt was calculated from the directional derivative v·∇|B|. The primary whole-trunk screening estimate used an ellipsoidal conversion coefficient of 0.16 V m-1 (T s-1)-1, whereas a 0.15-m-radius circular-loop estimate, corresponding to 0.075 V m-1 (T s-1)-1, was evaluated as a sensitivity case. Additional analyses varied active-shield geometry, movement-field alignment, and hypothetical 10 T and 14 T matched-geometry cases.

RESULTS

Along the specified axial path, the peak dB/dt at 1.5 m s-1 was 3.17, 6.33, and 14.78 T/s for the matched-geometry 1.5 T, 3 T, and 7 T cases. The corresponding ellipsoidal trunk estimates were 0.51, 1.01, and 2.36 V m-1; circular-loop estimates were 0.24, 0.48, and 1.11 V m-1. At 7 T, varying the idealized active-shield geometry changed peak dB/dt from 13.12 to 16.70 T/s, and the directional term could range from the worst-case envelope to zero for locally orthogonal motion. A heart-specific E99 context, where E99 denotes the 99th-percentile induced electric-field magnitude in the myocardium in published anatomical simulations, was 0.42-1.23 V m-1 for the 7 T brisk-motion case; this was not interpreted as a cardiac stimulation prediction. A conceptual minimax schedule reduced the modeled peak by 77%, but is presented only as a mathematical demonstration.

CONCLUSION

This reproducible reduced-order framework quantifies how active-shield geometry, movement direction, and body-conversion assumptions shape motion-induced field estimates near an idealized MRI magnet. The calculations expose substantial sensitivity to the body model, shield geometry, and trajectory, providing a transparent basis for education, model verification, and the design of scanner-specific dosimetric studies. Translation to regulatory compliance or operational guidance requires measured or vendor-provided fringe-field maps, anatomically resolved dosimetry, waveform analysis, and local safety procedures.