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.

Electric field calculation and peripheral nerve stimulation prediction for head and body gradient coils.

PURPOSE: To demonstrate and validate electric field (E-field) calculation and peripheral nerve stimulation (PNS) prediction methods that are accurate, computationally efficient, and that could be used to inform regulatory standards. METHODS: We describe a simplified method for calculating the spatial distribution of induced E-field over the volume of a body model given a gradient coil vector potential field. The method is easily programmed without finite element or finite difference software, allowing for straightforward and computationally efficient E-field evaluation. Using these E-field calculations and a range of body models, population-weighted PNS thresholds are determined using established methods and compared against published experimental PNS data for two head gradient coils and one body gradient coil. RESULTS: A head-gradient-appropriate chronaxie value of 669 µs was determined by meta-analysis. Prediction errors between our calculated PNS parameters and the corresponding experimentally measured values were ~5% for the body gradient and ~20% for the symmetric head gradient. Our calculated PNS parameters matched experimental measurements to within experimental uncertainty for 73% of ∆Gmin estimates and 80% of SRmin estimates. Computation time is seconds for initial E-field maps and milliseconds for E-field updates for different gradient designs, allowing for highly efficient iterative optimization of gradient designs and enabling new dimensions in PNS-optimal gradient design. CONCLUSIONS: We have developed accurate and computationally efficient methods for prospectively determining PNS limits, with specific application to head gradient coils.