Table 2 Field error values from Eq. (6) for the mid-surface between gray and white matter.

From: A fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation

Error type and percentage values

SimNIBS Ernie model (%)

4 Connectome models, averaged headreco seg

4 Headreco models, averaged FreeSurfer seg

FMM LU precision: 1e−4: Field FMM precision: 1e−4

\({Error}_{total}\) for entire midsurface/BEM-FMM LU versus iterative sol

0.10

0.11%0.02%

0.12%0.02%

\({Error}_{total}\) for 4 cm ROI under coil/BEM-FMM LU versus iterative sol

0.03

0.03%0.03%

0.05%0.02%

\({Error}_{mag}\) for entire midsurface/BEM-FMM LU versus iterative sol

0.08

0.08%0.01%

0.09%0.01%

\({Error}_{mag}\) for 4 cm ROI under coil/BEM-FMM LU versus iterative sol

0.03

0.02%0.005%

0.05%0.02%

FMM LU precision: 1e−4: Field FMM precision: 1e−1

\({Error}_{total}\) for entire midsurface/BEM-FMM LU versus iterative sol

0.37

0.38%0.02%

1.34%0.29%

\({Error}_{total}\) for 4 cm ROI under coil/BEM-FMM LU versus iterative sol

0.15

0.16%0.02%

0.40%0.08%

\({Error}_{mag}\) for entire midsurface/BEM-FMM LU versus iterative sol

0.28

0.27%0.02%

1.00%0.15%

\({Error}_{mag}\) for 4 cm ROI under coil/BEM-FMM LU versus iterative sol

0.15

0.14%0.01%

0.28%0.03%

FMM LU precision: 1e−3: Field FMM precision: 1e−1

\({Error}_{total}\) for entire midsurface/BEM-FMM LU versus iterative sol

1.35

1.46%0.29%

0.90%0.98%

\({Error}_{total}\) for 4 cm ROI under coil/BEM-FMM LU versus iterative sol

0.40

0.42%0.16%

0.20%0.21%

\({Error}_{mag}\) for entire midsurface/BEM-FMM LU versus iterative sol

1.05

1.04%0.19%

0.61%0.69%

\({Error}_{mag}\) for 4 cm ROI under coil/BEM-FMM LU versus iterative sol

0.39

0.37%0.18%

0.15%0.16%

  1. The FMM-LU is tested with different values of FMM precision for (i) LU matrix decomposition and; (ii) field computations. Four Connectome models (with both FreeSurfer and Headreco segmentations, respectively) are tested along with the default Ernie model of the SimNIBS FEM software. The superscript denotes standard deviation.