Measuring functional connectivity in MEG: a multivariate approach insensitive to linear source leakage

Abstract

A number of recent studies have begun to show the promise of magnetoencephalography (MEG) as a means to non-invasively measure functional connectivity within distributed networks in the human brain. However, a number of problems with the methodology still remain--the biggest of these being how to deal with the non-independence of voxels in source space, often termed signal leakage. In this paper we demonstrate a method by which non-zero lag cortico-cortical interactions between the power envelopes of neural oscillatory processes can be reliably identified within a multivariate statistical framework. The method is spatially unbiased, moderately conservative in false positive rate and removes linear signal leakage between seed and target voxels. We demonstrate this methodology in simulation and in real MEG data. The multivariate method offers a powerful means to capture the high dimensionality and rich information content of MEG signals in a single imaging statistic. Given a significant interaction between two areas, we go on to show how classical statistical tests can be used to quantify the importance of the data features driving the interaction.

Fig. 1

Two interacting sources: Seed based analysis using a multivariate approach. The seed is in the right hemisphere (left hand side of the image as shown in yellow). The interacting source is in the left hemisphere at the location marked by the green dot. Panel A shows multivariate analysis without subtraction of linear interactions. [Note, this has been windowed to show the interaction; a large peak is observed precisely at the seed location which is not visible here due to windowing]. B) The equivalent case with subtraction of linear interaction. Note that seed blur has been eliminated completely. Note also that in both cases the interacting source is successfully located. C) A visualisation of X and Y, extracted from the two simulated source locations and showing sinusoidal interactions in the 20–40 Hz band. D) Visualisation of H, the variance explained as a function of frequency, showing interaction between the simulated sources in the 20–40 Hz band as expected.

Fig. 2

Result of testing for false positive rate in simulated data. Panel A shows the actual false positive rate (generated from the simulation) plotted against the expected false positive rate. Crosses show the case for simulations with 1 source. Circles show the case for 2 simulated sources with no interaction. Panel B shows the false positive rate for a simulation in which connectivity images are reconstructed on a 2 cm grid and 4000 realisations are performed. C) The spatial locations of maxima in 500 realisations of the two source simulation. D) The spatial locations of maxima in 500 realisations of the single source simulation.

Fig. 3

Further simulation results: The number of false positives achieved (out of 250) for different values of α_FWE (indexed by colour) over tests with different numbers of features. Ideal rates are given by dashed lines of the same colours.

Fig. 4

Resting state motor cortex connectivity delineated in the 4 Hz–80 Hz range in a single subject. A–D show the case for real data: A) Multivariate approach with correction for signal leakage thresholded at α_FWE < 0.05. B) The equivalent image without correction for signal leakage. C) Difference in χ² between the corrected (A) and uncorrected (B) images. D) Beamformer weights correlation image. E–G show the case in which empty room noise data are projected through the same beamformer spatial filters as those derived from real data. E) Multivariate approach with correction (thresholded at α_FWE < 0.05; as expected no voxels were significant). F) Multivariate approach without correction (thresholded at α_FWE < 0.05). G) Difference in χ² between corrected (E) and uncorrected (F) images.

Fig. 5

Assessing the contribution of the 5 features to connectivity between the left and right motor cortices for the first eigenmode. A) Contribution of each of the 9 frequency bands to the 5 orthogonal features (U_X, upper panel, U_Y lower panel, colours represent magnitude of the elements of U_X and U_Y). Note that the dominant mode (1) in both cases is a mixture of 8–13 Hz and 20–30 Hz power (mu rhythm). B) Canonical vectors a₁ (green) and b₁ (blue) from the first eigenmode showing the linear combinations of the features in Y and X respectively which maximally correlate. C) Bar chart showing the log probability that a model with h + 1 features improves on a model with h features. Values above 3 indicate that the more complex model is approximately twenty times more likely. Note that there is no evidence that including the second feature of X (predominantly 4–8 Hz power) improves the prediction of Y. D) Eigenmode timecourses for the first canonical variates x₁′ (blue) and y₁′ (green). The correlation (Pearson correlation 0.44) between these two linear mixtures of X and Y is known as the canonical correlation (Soto et al., 2010).