Gradient coils

We compared the B-field, E-field, and the PNS oracle values generated through Equation 3 (Huygens’ surface representation) with that from the computationally intensive direct calculation to test how well the fast Huygens’ based solution approximates the expensive full model (EM simulation plus PNS oracle extraction). We assessed the accuracy of the approach for the female and male model in seven Siemens gradient coils (Siemens Healthineers, Erlangen, Germany): four whole-body gradients (Sonata, Quantum, Prisma, and Connectome) and three head-only gradients (AC84, AC88, and the more recent “Impulse” head gradient⁵⁴ ). We compared the estimates ${\tilde{B}}_C$ , ${\tilde{E}}_C$ , and ${\tilde{P}}_C$ with their directly computed counterparts B_C, E_C, and P_C (computed using full EM simulations from the coil windings) as follows:
$${\chi }_B=\text{max}\left\{\frac{\left|B_C-{\tilde{B}}_C\right|}{\left|B_C\right|}\right\}{\chi }_E=\text{max}\left\{\frac{\left|E_C-{\tilde{E}}_C\right|}{\left|E_C\right|}\right\}{\chi }_P=\text{max}\left\{\frac{\left|P_C-{\tilde{P}}_C\right|}{\left|P_C\right|}\right\}.$$
Note that we only assessed this metric in regions where the amplitude of the quantity is above 1% of its global maximum, as the metric is ill-posed in low-amplitude regions. We assessed the error as a function of the number of basis functions on the Huygens’ surface by randomly removing basis functions and reporting the resulting error. Truncation of the full Huygens’ basis sets was done randomly, and we report χ for the average of 200 such choices.