Minimum electric‐field gradient coil design: Theoretical limits and practical guidelines

PURPOSE: To develop new concepts for minimum electric‐field (E‐field) gradient design, and to define the extents to which E‐field can be reduced in gradient design while maintaining a desired imaging performance. METHODS: Efficient calculation of induced electric field in simplified patient models was integrated into gradient design software, allowing constraints to be placed on the peak E‐field. Gradient coils confined to various build envelopes were designed with minimum E‐fields subject to standard magnetic field constraints. We examined the characteristics of E‐field‐constrained gradients designed for imaging the head and body and the importance of asymmetry and concomitant fields in achieving these solutions. RESULTS: For transverse gradients, symmetric solutions create high levels of E‐fields in the shoulder region, while fully asymmetric solutions create high E‐fields on the top of the head. Partially asymmetric solutions result in the lowest E‐fields, balanced between shoulders and head and resulting in factors of 1.8 to 2.8 reduction in E‐field for x‐gradient and y‐gradient coils, respectively, when compared with the symmetric designs of identical gradient distortion. CONCLUSIONS: We introduce a generalized method for minimum E‐field gradient design and define the theoretical limits of magnetic energy and peak E‐field for gradient coils of arbitrary cylindrical geometry.