Minimax Current Density Extended to E-Gradient Coil Design

 In this study, an alternative gradient coil design method was developed to control the peak electric field induced in human tissues, and the trade-off between coil performance and winding complexity versus electric field control was investigated. The infinity norm of a current density induced in a highly conductive domain placed around the region of interest was minimized by using convex optimization. A set of transverse asymmetric and symmetric longitudinal gradient coils for head imaging was designed by varying the degree of electric field control over a highly conductive domain equivalent to a human head and torso. The coil performance, minimum gradient threshold stimulation, and electric field in a human model were used to assess the degree of electric field control versus coil performance. Transverse gradient coils with peak electric field control exhibited smaller concomitant fields than those without electric field control. The concomitant field remained unchanged for longitudinal gradient coils with electric field control. An overall reduction of 30% in the peak electric field in the human model was achieved by a transverse gradient coil, and a longitudinal coil achieved 18% reduction, while maintaining control over the winding complexity and coil performance. This study demonstrated the successful application of the minimax current density concept to control the peak electric fields in a human model induced by transverse and longitudinal head gradient coils.