Realistic spatial sampling for MEG beamformer images

Abstract

The spatial resolution achievable using magnetoencephalography (MEG) beamformer techniques is inhomogeneous across the brain and is related directly to the amplitude of the underlying electrical sources [Barnes and Hillebrand, Hum Brain Mapp 2003;18:1-12; Gross et al., Proc Natl Acad Sci USA 2001;98:694-699; Van Veen et al., IEEE Trans Biomed Eng 1997;44:867-860; Vrba and Robinson, Proc 12th Int Conf Biomagn 2001]. We set out to examine what an adequate level of spatial sampling of the brain volume is in a realistic situation, and what implications these inhomogeneities have for region-of-interest analysis. As a basis for these calculations, we used a simple retinotopic mapping experiment where stimuli were 17-Hz reversing gratings presented in either left or right visual hemifield. Beamformer weights were calculated based on the covariance of the MEG data in a 0-80 Hz bandwidth. We then estimated volumetric full-width half-maximum (FWHM) maps at a range of sampling levels. We show that approximately 10% of the 1 mm cubic voxels in the occipital volume have a FWHM smoothness of <5 mm, and 80% <10 mm in three subjects. This was despite relatively low mean signal-to-noise ratios (SNR) values of 1.5. We demonstrate how visualization of these FWHM maps can be used to avoid some of the pitfalls implicit in beamformer region-of-interest analysis.

Figure 1

A: Estimates of FWHM (broken lines) at the simulated source location are plotted against grid spacing for dipole moments of 0.2 (up triangles), 0.6 (diamonds), 1.2 (squares), 1.8 (down triangles) and 3.2 nAm (circles). The larger the dipole moment, the smaller the FWHM. For low dipole moments (0.2 and 0.6 nAm), the smoothness estimate is independent of spatial sampling as the source space is sampled adequately at all levels. As dipole moment increases (1.8 and 3.2 nAm), however, it is clear that the smoothness estimate saturates at the Nyquist limit (solid line) for coarse grid spacing (6 and 8 mm). Only when grid spacing is sufficiently fine does the smoothness estimate diverge from saturation to its true value. B: The beamformer estimate of spectral power change (active/baseline) in the 0–140 Hz band for different source amplitudes from three orthogonal views. The dark contour shows the measured FWHMs for these images. FWHM estimates from A (which are averages across all three dimensions) are based only on the weight vectors relating to the central voxel and its immediate neighbors; however, they accord well with those observed in the volumetric power change image.

Figure 2

A: FWHM estimates for four axial slices at 1.2‐cm separation (z axis) through the occipital lobe of subject K.D.S. The calcarine sulcus extends medially from x = −0.07 on slice z = 0.022 up to x = −0.04 on slice z = 0.034. It can be seen that FWHM tends to increase toward the head center, reflecting the decrease in MEG system sensitivity to sources in this area. The smallest FWHM values, however, are not simply distributed at the scalp surface, as one would expect if FWHM were related directly to sensitivity alone. Histograms of the per‐voxel FWHM for subjects K.D.S. and A.S. are shown in B and C, respectively. In both cases the median FWHM is around 8 mm extending down to 2 mm (the minimum we could measure) and up to 20 mm. D: Cumulative FWHM counts for 3 subjects (K.D.S., crossed; A.S., dotted; A.W., solid) are shown. In this case, the FWHM count is shown as a fraction of total volume. For example, for subject K.D.S. (dotted), 20% of voxels have an FWHM below 6 mm, and 80% less than 10 mm.

Figure 3

A: The upper panel shows a single axial slice (z = 2.4 cm) of the FWHM image for subject A.S. based on the covariance window of 0–80 Hz. The lower panel shows the 32–36 Hz mw‐SPM for the same axial slice. The stimulus was in the right visual field and there is clear contralateral visual cortex activation. Comparing upper and lower panels, it seems that regions of low FWHM correspond to regions of high SPM gradient. The line on the SPM is for reference to B. B: Enlargement of A marked with a track of 20 virtual electrode locations extending from the SPM peak (location 0) and spaced at 1.4 mm. Highlighted locations are at 0, 14, and 17 mm from the peak. C: The square of the Pearson correlation coefficient (i.e., fraction of variance explained) between location 0 and all other locations is plotted for both weight vectors (diamonds) and virtual electrode time series (dotted, circles). FWHM estimate (see scale at right) at each voxel along the line is also plotted (solid, squares). Arrows mark distances 0, 14, and 17 mm from the peak. The trough in FWHM estimate corresponds to the sharp fall‐off in the degree of relationship between virtual electrodes. D: Spectral power estimates at virtual electrode locations 0 (dotted, circles), 14 (dashed, green), and 17 mm (solid) are shown. The visual cortex is clearly being driven at 34 Hz by the 17‐Hz reversing checkerboard. As the virtual electrode locations cross the low FWHM boundary, the signal rapidly (over the space of 3 mm) disappears.