Fast realistic modeling in bioelectromagnetism using lead-field interpolation

• Published in: Human brain mapping Vol. 14; no. 1; pp. 48 - 63
• Main Authors: Yvert, Blaise, Crouzeix-Cheylus, Anne, Pernier, Jacques
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.09.2001; Wiley-Liss
• Subjects: Algorithms; BEM; Biological and medical sciences; dipole localization; ECG; EEG; Electrocardiography - methods; Electroencephalography - methods; forward problem; Humans; inverse problem; Investigative techniques, diagnostic techniques (general aspects); Magnetoencephalography - methods; MCG; Medical sciences; MEG; Models, Biological; Nervous system; numerical methods; Original; Radiation; Radiodiagnosis. Nmr imagery. Nmr spectrometry; realistic head model; Electrodiagnosis; Computation time; Electromagnetism; Magnetoencephalography; Exploration; Electroencephalography; Models; Computing method
• ISSN: 1065-9471; 1097-0193
• DOI: 10.1002/hbm.1041

The practical use of realistic models in bioelectromagnetism is limited by the time‐consuming amount of numerical calculations. We propose a method leading to much higher speed than currently available, and compatible with any kind of numerical methods (boundary elements (BEM), finite elements, finite differences). Illustrated with the BEM for EEG and MEG, it applies to ECG and MCG as well. The principle is two‐fold. First, a Lead‐Field matrix is calculated (once for all) for a grid of dipoles covering the brain volume. Second, any forward solution is interpolated from the pre‐calculated Lead‐Fields corresponding to grid dipoles near the source. Extrapolation is used for shallow sources falling outside the grid. Three interpolation techniques were tested: trilinear, second‐order Bézier (Bernstein polynomials), and 3D spline. The trilinear interpolation yielded the highest speed gain, with factors better than ×10,000 for a 9,000‐triangle BEM model. More accurate results could be obtained with the Bézier interpolation (speed gain ∼1,000), which, combined with a 8‐mm step grid, lead to intrinsic localization and orientation errors of only 0.2 mm and 0.2 degrees. Further improvements in MEG could be obtained by interpolating only the contribution of secondary currents. Cropping grids by removing shallow points lead to a much better estimation of the dipole orientation in EEG than when solving the forward problem classically, providing an efficient alternative to locally refined models. This method would show special usefulness when combining realistic models with stochastic inverse procedures (simulated annealing, genetic algorithms) requiring many forward calculations. Hum. Brain Mapping 14:48–63, 2001. © 2001 Wiley‐Liss, Inc.