Anatomical constraints on source models for high-resolution EEG and MEG derived from MRI

Abstract

Electroencephalography (EEG) remains the primary tool for measuring changes in dynamic brain function due to disease state with the millisecond temporal resolution of neuronal activity. In recent decades EEG has been supplanted by CT and MRI for the localization of tumors and lesions in the brain. In contrast to the excellent temporal resolution of EEG, the spatial information in EEG is limited by the volume conduction of currents through the tissues of the head. We have extracted source models (position and orientation) from MRI scans to investigate the theoretical relationship between brain sources and EEG recorded on the scalp. Although detailed information about the boundaries between different tissues can also be obtained from MRI, these models are only approximate because of our relatively poor knowledge of the conductivities of the different tissue compartments in living heads. We also compare the resolution of EEG with magnetoecephalography (MEG), which offers the advantage of requiring less detail about volume conduction in the head. The brain's magnetic field depends only on the position of sources in the brain and the position and orientation of the sensors. We demonstrate that EEG and MEG space average neural activity over comparably large volumes of the brain; however, they are preferentially sensitive to sources of different orientation suggesting a complementary role for EEG and MEG. High-resolution EEG methods potentially yield much better localization of source activity in superficial brain areas. These methods do not make any assumptions about the sources, and can be easily co-registered with the brain surface derived from MRI. While there is much information to be gained by using anatomical MRI to develop models of the generators of EEG/MEG, functional neuroimaging (e.g., fMRI) signals and EEG/MEG signals are not easily related.

Figure 1

Sources of EEG and MEG. a. Neocortical sources can be generally pictured as dipole layers (or “dipole sheets”, in and out of cortical fissures and sulci) with meso-source strength varying as a function of cortical location. EEG is most sensitive to correlated dipole layer in gyri (regions ab, de, gh), less sensitive to correlated dipole layer in sulcus (region hi) and insensitive to opposing dipole layer in sulci (regions bcd, efg) and random layer (region ijklm). MEG is most sensitive to correlated and minimally apposed dipole layer (hi) and much less sensitive to all other sources shown, which are opposing, random or radial dipoles. b. Source model obtained by segmenting MRI images (left hemisphere shown). The source model consists of more than 10⁶ vertices. The sources are assumed normal to the cortical surface.

Figure 2

Volume conduction models. a. Realistic shaped Boundary element Model (BEM) of the head. The brain and scalp boundaries were found by segmenting the images with a threshold, and opening and closing operation respectively, while the outer skull boundary was obtained by dilation of the brain boundary (ASA, Netherlands). b. Approximation to the scalp surface with an ellipsoid. As discussed in the text, the realistic BEM suffers a potentially fatal flaw by assuming increased thickness is related to increased resistivity. The brain surface was first approximated by an ellipsoid using principal components analysis, and confocal ellipsoids were fit to skull and scalp layers. This assures uniform thickness of the skull and scalp layers in the model. On the upper surface of the scalp, the error in the approximation is less than 10% at all scalp vertex positions.

Figure 3

Example sensitivity distributions of EEG and MEG (magnetometer). For convenience sensitivity is normalized to the source that contributes the largest potential or magnetic field at the EEG electrode shown in the inset figure. The MEG sensor at the position corresponding to the EEG electrodes is located 2 cm above the scalp, and is oriented towards the center of the brain. a: Sensitive distribution of EEG is shown on an inflated cortex. The grey regions indicate surfaces oriented parallel to the scalp. It is apparent that this electrode is most sensitive to both the gyral and sulcal surfaces below the electrode, but is also sensitive to distant gyral syrfaces. b: Sensitivity distribution of MEG. It is apparent that this sensor is entirely insensitive to the gyral surfaces that contribute to the EEG electrode, and is mainly sensitive to the sulcal walls. The orientation of the sulcal walls plays a critical role; opposing sulcal walls contribute opposite fields to the sensor.

Figure 4

Potential in a 4-sphere model due to a radial dipole source in the inner sphere, that is, the model brain. The three curves in each figure were obtained with the three brain-to-skull conductivity ratios. The model consists of four spherical layers: Sphere radii are (brain, CSF, skull, scalp) = (8.0, 8.1, 8.6, 9.2). Brain and scalp are assumed to have the same conductivity; CSF conductivity is 5 times brain conductivity; 3 brain-to-skull conductivity ratios are plotted (20, 40, 80). (Upper) Fall-off of potential through the thickness of the skull and scalp. Potential is plotted on a logarithmic scale. (b) Angular spread of potential in the skull and scalp. The curves represent the distance at which potential is 50% of its maximum directly above the dipole (θ = 0).

Figure 5

Simulations of sensitivity of potentials and surface Laplacian to dipole sources. Simulations were performed using a 4-sphere model of the head as described in Figure 4. The only parameter varied in these simulations is the brain-to-skull conductivity ratio from 20 to 160. (a) Dependence of potential on source depth for radial and tangential dipoles. Depth is calculated from the top of the brain sphere (r₁ = 8.0). (b) Dependence of surface Laplacian on source depth. (c) Dependence of outer surface (scalp) potential on the spatial extent of dipole layers composed of superficial radial dipole sources at a fixed radial location (r = 7.8). (d) Dependence of the Laplacian on the spatial extent of dipole layers composed of superficial radial dipole sources at a fixed radial location (r = 7.8).

Figure 6

Example half-sensitivity distributions of EEG versus surface Laplacian on the realistic source distribution for two electrodes. The electrode positions are shown in the inset; the electrodes are separated by 5 cm. a. Half-sensitivity distribution of the potentials for each electrode position shown by corresponding color coding (red or blue) on the inflated brain. Regions indicated in purple are contributing significant potentials to both electrodes. b. Sensitivity distribution of the surface Laplacian at the same electrode position. Note that distant sources, more than 2 or 3 cm away from the electrode no longer contribute significantly to the signal at each electrode. Thus, there are two distinct red and blue regions shown on the inflated cortex and no regions of overlap.