  Purpose: To demonstrate and validate E-field calculation and 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 669us
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 deltaGmin 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.
