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 mu s was determined by meta-analysis. Prediction errors between our calculated PNS parameters and the corresponding experimentally measured values were similar to 5% for the body gradient and similar to 20% for the symmetric head gradient. Our calculated PNS parameters matched experimental measurements to within experimental uncertainty for 73% Delta G(min) 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.