Global sensitivity of EEG source analysis to tissue conductivity uncertainties

Abstract

Introduction: To reliably solve the EEG inverse problem, accurate EEG forward solutions based on a detailed, individual volume conductor model of the head are essential. A crucial-but often neglected-aspect in generating a volume conductor model is the choice of the tissue conductivities, as these may vary from subject to subject. In this study, we investigate the sensitivity of EEG forward and inverse solutions to tissue conductivity uncertainties for sources distributed over the whole cortex surface.

Methods: We employ a detailed five-compartment head model distinguishing skin, skull, cerebrospinal fluid, gray matter, and white matter, where we consider uncertainties of skin, skull, gray matter, and white matter conductivities. We use the finite element method (FEM) to calculate EEG forward solutions and goal function scans (GFS) as inverse approach. To be able to generate the large number of EEG forward solutions, we employ generalized polynomial chaos (gPC) expansions.

Results: For sources up to a depth of 4 cm, we find the strongest influence on the signal topography of EEG forward solutions for the skull conductivity and a notable effect for the skin conductivity. For even deeper sources, e.g., located deep in the longitudinal fissure, we find an increasing influence of the white matter conductivity. The conductivity variations translate to varying source localizations particularly for quasi-tangential sources on sulcal walls, whereas source localizations of quasi-radial sources on the top of gyri are less affected. We find a strong correlation between skull conductivity and the variation of source localizations and especially the depth of the reconstructed source for quasi-tangential sources. We furthermore find a clear but weaker correlation between depth of the reconstructed source and the skin conductivity.

Discussion: Our results clearly show the influence of tissue conductivity uncertainties on EEG source analysis. We find a particularly strong influence of skull and skin conductivity uncertainties.

Keywords: EEG; finite element method; forward modeling; sensitivity analysis; source analysis; uncertainty quantification.

Figure 1

Visualization of the FEM head model showing electrode positions (red) and (from outside to inside) skin, skull, CSF, gray matter, and white matter surfaces (left). Lateral and medial view of source depth (distance to inner skull surface) visualized on inflated left cortex surface (right).

Figure 2

Median and 50% confidence interval of first-order and skin-skull second-order (left) and full (right) Sobol indices for signal topography/RDM plotted as a function of source depth.

Figure 3

First-order and skin-skull second-order Sobol indices for signal topography visualized on inflated cortex surface; (fronto-)lateral (left column) and medial (right column) view. Please observe the different scalings of the colorbar.

Figure 4

Full Sobol indices for signal topography visualized on inflated cortex surface; (fronto-)lateral view.

Figure 5

Median and 50% confidence interval of first-order (left) and full (right) Sobol indices for signal magnitude/MAG plotted as a function of source depth.

Figure 6

Full Sobol indices for signal magnitude visualized on inflated cortex surface; (fronto-)lateral (left column) and medial (right column) view.

Figure 7

Average localization error (top) and the average ratio between the change in source depth and localization error (bottom) visualized on inflated cortex surface; (fronto-)lateral (left column) and medial (right column) view.

Figure 8

Average RDM (top) and correlation between RDM and localization error, i.e., distance between reconstructed and original source position, (bottom) visualized on inflated cortex surface; (fronto-)lateral (left column) and medial (right column) view.

Figure 9

Median and 50% confidence interval of the correlation coefficient between deviation of tissue conductivities from mean, |σ_i−(σ_max−σ_min)/2|, and distance to average source localization (left) and correlation coefficient between tissue conductivity and depth of localized source (right) plotted as a function of source depth.

Figure 10

Correlation coefficient between tissue conductivity and depth of source localization for skin (top) and skull conductivity (bottom) visualized on inflated cortex surface; (fronto-)lateral (left column) and medial (right column) view.