A new approach to neuroimaging with magnetoencephalography

Abstract

We discuss the application of beamforming techniques to the field of magnetoencephalography (MEG). We argue that beamformers have given us an insight into the dynamics of oscillatory changes across the cortex not explored previously with traditional analysis techniques that rely on averaged evoked responses. We review several experiments that have used beamformers, with special emphasis on those in which the results have been compared to those observed in functional magnetic resonance imaging (fMRI) and on those studying induced phenomena. We suggest that the success of the beamformer technique, despite the assumption that there are no linear interactions between the mesoscopic local field potentials across distinct cortical areas, may tell us something of the balance between functional integration and segregation in the human brain. What is more, MEG beamformer analysis facilitates the study of these complex interactions within cortical networks that are involved in both sensory-motor and cognitive processes.

Figures

Figure 1

Schematics of source covariance matrices for different source reconstruction algorithms. Each element represents the covariance between a source and another source, with the distance to the sensors for each source increasing from top to bottom and from left to right. All panels have the same arbitrary scaling, with the blue‐yellow‐red colour scale representing increasing source covariance. Top left: The minimum norm approach assumes that no sources within the brain are linearly correlated, hence the diagonal source covariance matrix. Additionally, the increased weighting for deeper sources can be used to correct for the depth bias of minimum norm approaches. Although no correlation between sources is specified a priori, the minimum norm approach does not exclude correlated sources from the solutions. Top right: LORETA [Pasqual‐Marqui et al.,1994] assumes that active areas have a certain spatial extent that is represented by the “broad” diagonal of the source covariance matrix. Bottom left: Dynamic SPM [Dale et al.,2000] is based on the weighted minimum norm approach. Additionally, the source covariance for elements at fMRI hotspots (three hotspots in this illustration) can be increased to bring the MEG results in agreement with fMRI results. Bottom right: SAM [Robinson and Vrba,1999] assumes that no sources within the brain are linearly correlated, hence the diagonal source covariance matrix. The value of the diagonal elements is determined by the data covariance matrix [Mosher et al.,2003].

Figure 2

Diagonal elements of the SAM source covariance matrix for a set of target locations along a line. MEG data was simulated for two sources with different amounts of correlation between the respective time courses. This figure does not show actual source reconstructions, but simply the elements of the source covariance matrix that SAM assumes. It is clear that the assumption of uncorrelated sources, in combination with the fact that the source covariance matrix is determined by the data covariance [Mosher et al.,2003], modifies the source covariance matrix in such a way that perfectly correlated sources cannot be detected with SAM. However, it is also clear from this figure that partially correlated sources are not excluded from detection. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 3

Responses obtained from averaging 100 simulated, noise‐free epochs. The latency of each epoch was jittered by an amount taken from a Gaussian distribution (σ = 2, 5, or 10 samples) with zero mean. The inset shows the original epoch and the jittered epochs for the σ = 2 case. The effect of jitter depends on the width of the peak, and was chosen here to be representative for a typical, early latency, evoked response peak. Note the rapid decrease in the evoked response peak when the latency jitter increases. Acceptable levels of jittering are one or two samples, causing a reduction of 6–26% of the peak amplitude. This means that for MEG a jitter of 1–2 ms is acceptable and for BOLD fMRI the acceptable jitter is on the order of 1–2 s, assuming that the BOLD response is sampled at about 1 Hz. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 4

Results of group‐averaged MEG (top) and fMRI (middle) experiments for a covert letter fluency task, superimposed on a template brain and thresholded at P < 0.05 (corrected) [for details, see Singh et al.,2002]. The top panel displays the group SAM analysis of the MEG data, showing the peak power increase or decrease at each voxel in the brain, irrespective of which frequency band the power change occurred in. The blue‐purple‐white colour scale depicts decreases in signal power in the active phase, compared to the passive baseline. The middle panel shows group fMRI data. The red‐orange‐yellow colour scale depicts increasing BOLD amplitude. The bottom panel shows the peak group SAM (left) and fMRI (right) data superimposed on a slice through the template brain from the Montreal Neurological Institute (MNI) at a z coordinate of +35. Note the close spatial correspondence between the group MEG and fMRI results, despite the fact that two different imaging modalities were used and two different cohorts of subjects participated in the experiments.

Figure 5

Time–frequency wavelet plots (three panels on the left) computed for an active area (left caudolateral precentral gyrus, marked in the right panels) identified with the beamformer in two representative subjects. MRI‐SAM images (right panels) were computed for the water versus rest phase (25–40 Hz band) in a swallowing experiment [see Furlong et al.,2004 for details], with the blue‐purple‐white colour scale depicting decreases in signal power in the water phase compared to that in the rest phase. The central dividing line in the time–frequency plots indicates the end of the 5 s of the passive period and 0 s for the commencement of the 5 s of the active phase. Colours represent significant ERD/ERS, with blues/purples indicating a decrease in power (ERD) and reds/yellows an increase in power (ERS). ERD/ERS that was not significant (P > 0.05) was set to zero [Graimann et al.,2002]. This demonstrates that it is possible to localise non‐phase‐locked responses and get timing (and spectral) information. Note also that the time–frequency resolution can be optimised using wavelet analysis [see Fawcett et al.,2004].

Figure A1

Illustration of the design of a spatial filter for a source at a target location. The ideal transfer function in general can not be achieved because there are only a limited number of sensors (typically ∼150). However, an optimum transfer function can be obtained by applying a unity passband constraint in combination with a minimum output power constraint [van Veen et al.,1997]. The second constraint would without the first constraint result in a spatial filter that does not let any signal through, not even from the target location. The first constraint states that signal from the target location should be let through completely, so the only way to minimise the output power is to reduce the contribution from other sources to the spatial filter output, resulting in a narrowing of the passband of the spatial filter. The contribution to the beamformer output from sources away from the target location is small for the optimum spatial filter, whereas it can be large for a nonoptimum beamformer. Signal from the target location will be cancelled if it is correlated with signal from another location [van Veen et al.,1997; Vrba,2002], as is explained in the text. The main assumption underlying beamformer analysis is therefore that there are no correlated sources within the brain, an assumption that is not necessarily fulfilled when distinct areas are driven simultaneously by an external stimulus or another cortical area. However, it has been shown [van Veen et al.,1997] that the beamformer performance is relatively robust to correlated activity and induced activity is unlikely to be strongly correlated across the brain. Moreover, the effect of correlated activity at distant locations can be reduced by selecting only those sensors covering the target location.

Figure A2

Left: Power‐spectrum of the beamformer output for the peak activity in the somatosensory cortex to 3 Hz stimulation of the right index finger, showing a stimulus driven increase in power in the active period compared to that in the passive period (ERS) at 3 Hz and harmonics of 3 Hz. There is also an induced reduction in power around 12 Hz (μ‐rhythm) at the same location. The beamformer images (right) computed for the 2.95–3.05 Hz band and the 11.8–12.2 Hz band both show peaks in the somatosensory cortex.