Electro- and magnetoencephalography (EEG, MEG) are methods to study electrical brain activity by recording scalp potentials and extra-cranial magnetic fields [Cohen and Halgren, 2003
; Gevins et al., 1995
; Hämäläinen et al., 1993
]. EEG and MEG provide excellent time resolution for noninvasive detection of human brain activity, and estimates of the locations of the underlying sources can be constructed on the basis of the spatial distribution of the EEG and MEG [Baillet et al., 2001
]. In part, the spatial resolution in EEG and MEG source estimates is limited by the spatial spread of the signal patterns generated even by focal sources. The spread depends on the distance between the sources and the sensors; the minimum distance is limited by the thickness of the skull and scalp, and, in the case of MEG, the thickness of the Dewar vessel containing the superconducting SQUID sensors. When multiple sources are simultaneously active, their overlapping signal patterns are superimposed, and cancellation of signals of opposite polarity may occur. Cancellation reduces the overall signal-to-noise ratio, thereby contributing to the difficulty of source estimation. In general, when interpreting EEG and MEG data, it is important to take into consideration the overall pattern of simultaneous activation across the brain. This is different from such techniques as functional magnetic resonance imaging (fMRI) in which the signals from individual voxels can be observed largely independently. Here, we attempt to characterize cancellation effects in EEG and MEG signal patterns.
The sources of EEG and MEG signals are described in terms of primary currents [Plonsey, 1969
; Tripp, 1983
]. The active primary currents give rise to the electric potential distribution, which can measured on the scalp using EEG. In addition, in a conductive medium, there will be associated passive volume currents at locations where the gradient of the electric potential differs from zero. However, the primary currents, together with the conductivity geometry of the head, determine the electric potentials and the volume currents; therefore, it is convenient to express the signals conceptually as functions of the primary currents. The main contribution to the primary currents detectable with EEG and MEG comes from ionic currents in the apical dendrites of cortical pyramidal cells, which are mostly aligned perpendicular to the local cortical surface [Hämäläinen et al., 1993
; Lopes da Silva, 1991
; Okada et al., 1999
]. These currents result from both post-synaptic and active trans-membrane currents [Murakami and Okada, 2006
]. For symmetry reasons, the signals from other types of active currents at the cellular level are expected to cancel out macroscopically or generate electric potentials and magnetic fields which fall off rapidly with distance. These invisible currents include those from trans-membrane currents themselves, post-synaptic currents in stellate cells or in the basal dendrites of pyramidal cells, as well as the quadrupole-like current patterns associated with action potentials [Humphrey, 1968a
; Humphrey, 1968b
; Lorente de No, 1947
]. Therefore, it is reasonable to assume that the primary currents underlying the extracranial EEG and MEG signals are located in the cortical gray matter, oriented perpendicular to the cortical surface.
In EEG and MEG source analysis, the basic element for the primary current distribution can be taken to be a current dipole, which summarizes the net effect of the microscopic currents within a volume of a few cubic millimeters, or a few square mm of cortical surface. At the intermediate spatial scale of about 1 cm and above, the folding of the cerebral cortex adds a macroscopic geometric factor, which can be examined using the detailed anatomical information provided by structural MRI. For example, the spatial frequency spectrum of cortical gyrification has been related to the pattern of spatial coherence in scalp EEG [Freeman et al., 2003
]. Cancellation of the EEG and MEG signals occurs when the cortical activity extends over a region where the surface normal, and therefore, also the orientation of the source elements, changes. In particular, cancellation occurs when the activation involves opposing walls of a sulcus or a gyrus. depicts simulated EEG and MEG signals from two current dipoles of opposite direction in the primary visual cortex in the calcarine region, which mostly cancel out when active simultaneously. Even at the spatial scale of several centimeters, corresponding to activity distributed over multiple regions across the whole cortex, large amount of cancellation of spatially overlapping EEG or MEG signal patterns can occur. Partial cancellation is illustrated in with sources in the inferior occipitotemporal region of the left and right hemispheres.
Figure 1 Examples of cancellation of EEG and MEG signals. (A) Simulated data generated by two current dipoles in the primary visual cortex of the left and right hemispheres. The maps depict spatial patterns of signals over the occipital region when each dipole (more ...)
We refer to local patches of activity as extended
sources, whereas distributed
source patterns may consist of multiple local foci or patches of activity in separate regions of the cortex. This terminology is useful also in the context of source estimation: on one hand, a single equivalent dipole is usually an adequate model, not only for very small foci, but also for moderately extended source patches, such as those corresponding to various types of sensory evoked responses. On the other hand, distributed source models are particularly useful for widely spread activation that consists of multiple simultaneously active functional areas, as is often the case, e.g., with language-related activity. In the present study we explore the cancellation effects in EEG and MEG signals using a realistic reconstruction of the cortical surface [Dale et al., 1999
; Dale and Sereno, 1993
; Fischl et al., 1999
]. For quantitative analysis, we calculated a measure of cancellation for multiple randomly distributed foci of simultaneous activity across the cortex as well as for locally extended patches of activity.