Introduction In recent years, the importance of measuring connectivity between spatially separate but functionally related brain areas has become of key interest in the study of brain function. Recruitment of multiple brain regions to form networks is thought to be integral to the way in which the brain processes information (Schnitzler and Gross, 2005; Uhlhaas and Singer, 2010) and abnormal recruitment of brain areas is thought to be implicated in pathologies such as schizophrenia (Friston, 1999; Phillips and Silverstein, 2003; Stephan et al., 2009). The study of functional connectivity (FC) is therefore of great importance to the field of neuroimaging. In most neuroimaging studies, the term functional connectivity has been used to indicate correlation between signals observed in spatially separate brain regions. Much progress in this area has evolved from the study of spontaneous fluctuations in blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) signals. Spontaneous BOLD fluctuations are observed during the resting state (Biswal et al., 1995) and superimposed onto task driven responses (Fox et al., 2006). The timecourses of resting state signals from spatially separate areas have been shown to be correlated in time (Biswal et al., 1995), the implication being that activity in these areas is linked, even in the absence of external stimuli. Such measurements have been termed functional connectivity MRI (fcMRI) and a number of data driven analysis techniques (e.g. seed based correlation and independent component analysis) have been applied to fcMRI data revealing the spatial signature of a number of resting state networks (Fox and Raichle, 2007; Laufs, 2008). Improvements in fcMRI measurement have been shown to result from the use of ultra high (7T) magnetic field. The BOLD response becomes more closely related to microvasculature as field strength is increased (Yacoub et al., 2001). Further, BOLD contrast to noise ratio (CNR) also increases with field and a recent study has shown that at 7T, fcMRI yields network measurements with improved spatial resolution and sensitivity (Hale et al., 2010). Unfortunately, all BOLD measurements (including those at ultra high field) are to some degree confounded since they are indirect assessments of brain activity; they relate to blood flow and not to electrical processes and are therefore limited by poor temporal resolution due to the protracted hemodynamic response. In addition, fcMRI is affected by non-neuronal physiological signals, e.g. the cardiac and respiratory cycles (Wise et al., 2004; Birn et al., 2006, 2008). Such artifacts worsen with field strength and add structured interference to fcMRI, potentially leading to spurious FC. Most importantly, the indirect nature of fcMRI means that the electrical mechanisms that mediate FC cannot be elucidated. As the importance of FC grows, the introduction of non-hemodynamic metrics and our ability to develop a complete understanding of brain network activity and connectivity will become a key goal in neuroscience. Neural oscillations have an established role in coordinating neural activity both in local networks (Gray et al., 1989; Womelsdorf et al., 2007) and over longer distances (von Stein et al., 2000). Such oscillations are thought to be intimately involved in network activity. Insight into the relationship between oscillatory processes and fcMRI network measurements has been gained from concurrent electroencephalography (EEG) and fMRI (Laufs, 2008). Some studies have shown that spontaneous fluctuations in α (8–13 Hz) band power (measured at an EEG electrode) is negatively correlated with BOLD signal changes in occipital and parietal cortices; other studies have reported positive correlations between α power and BOLD in the thalamus (Goldman et al., 2001; Moosmann et al., 2003; Mantini et al., 2007). Laufs et al. (2003) and Mantini et al. (2007) demonstrated that fronto-parietal network activity is associated with ongoing modulation of α power, implying that a single EEG frequency band can be associated with multiple brain areas. Further, Mantini et al. (2007) have shown that electrical activity in the β band is associated with resting state motor network activity identified using fcMRI. Unfortunately, most EEG/fMRI studies focus on EEG data in sensor space. It is well known that the inhomogeneous conductivity profile in the head means that patterns of electrical potential measured at the scalp are diffuse, and can be distorted. This makes the EEG signal at a single electrode an average of electrical activity across a large volume of tissue. Further, a single sensor most affected by a source doesn't necessarily directly overlay that source. It is therefore difficult to pinpoint the location of electrical oscillators using EEG. Most importantly, it is hard to disentangle two spatially separate sources that may exhibit FC since the same channels can be affected by both sources. Finally, EEG measurements at high magnetic field are limited by poor signal to noise ratio (SNR) and interference caused by the MR scanner. These effects combined limit the utility of concurrent EEG/fMRI. Magnetoencephalography (MEG) is a non-invasive technology in which the magnetic fields induced by neuronal current flow in the brain are measured above the scalp (Cohen, 1972). MEG has been shown to be an excellent means to measure neural oscillatory processes. Furthermore, unlike electric fields, magnetic fields are not distorted by inhomogeneous conductivity in the head. This, coupled with the high number of sensors (~ 300 in modern systems) and advanced source reconstruction algorithms (Robinson and Vrba, 1998; Zumer et al., 2007; Wipf et al., 2010), makes MEG data more appropriate for projection into source space. MEG studies performed in this way can exhibit vastly improved spatial resolution compared to EEG. For FC measurement, projection is advantageous (Schoffelen and Gross, 2009) since: 1) It limits the effect of field spread (a single source affecting multiple sensors) making results easier to interpret and allowing spatial comparison between FC maps generated independently using fcMRI and MEG; 2) The improved spatial resolution allows separation of signals originating from spatially separate brain locations; and 3) Projection allows for increased signal to noise ratio (SNR) (see for example Brookes et al., 2008a,b, 2009, 2010). These facts make MEG the most attractive non-invasive means to measure electrodynamic FC. However, care must be taken when making these measurements (Schoffelen and Gross, 2009) since the magnetic field induced from a single current source will affect multiple MEG sensors, and the ill posed nature of the inverse problem means that, while spatial resolution is improved compared to EEG, signals originating from spatially separate voxels in source space are not necessarily independent. Cross talk (or signal leakage) between voxel timecourses can therefore generate spurious connectivity measurement. Additionally, MEG is susceptible to interference from environmental noise which may also affect FC metrics. Despite difficulties a number of studies have employed MEG to measure FC in both sensor and source space and a variety of methodologies have been described. Dynamic imaging of coherent sources (Gross et al., 2001) is an elegant technique in which a frequency domain beamformer is employed to project MEG data; coherence between brain regions is subsequently measured. Other studies (e.g. Guggisberg et al., 2008) have employed time domain beamforming and imaginary coherence (imaginary coherence excludes coherent sources with zero time lag and therefore eliminates the effect of field spread and cross talk). Other metrics include phase lag index (Stam et al., 2007) (which quantifies asymmetry in the phase lag distribution (field spread and cross talk would cause a symmetric distribution and is therefore eliminated)) and synchronization likelihood (Stam and van Dijk, 2002) (which takes two separate electrical signals and looks for isochronous recurrence to a certain part of their (individually different) attractors). Interestingly, in a recent paper (Liu et al., 2010) Liu and colleagues employed a MEG sensor space ‘envelope correlation’ metric to show that inter-hemispheric connectivity (observed by fcMRI) is mirrored by inter-hemispheric neuromagnetic correlation (though no direct comparison was made). In the envelope correlation technique, data are frequency filtered to the band of interest and correlations between power envelopes of oscillatory timecourses from spatially separate brain areas are sought. The findings of Liu et al. are in agreement with papers showing that task driven changes in hemodynamics are related to fluctuations in the envelope of band limited oscillatory power (Singh et al., 2002; Brookes et al., 2005; Stevenson et al., 2011; Zumer et al., 2010). However, since measurements were made in sensor space, the spatial structure of connectivity inferred was unclear. In contrast to sensor space analyses, de Pasquale et al. (2009) used source space reconstructions with minimum-norm techniques and showed that the dorsal attention and the default mode networks, commonly observed using fMRI, are also observable in MEG, particularly using non-lagged correlations in short temporal windows. However, minimum-norm techniques are known to have poor spatial resolution and large reconstruction errors in time-course estimation. Nevertheless, these papers represent some of the first demonstrations of similarity between hemodynamic and electrical resting state FC measurements which we further investigate here. In this paper, we investigate techniques to measure resting state functional connectivity (defined as correlation or coherence between signals from spatially separate brain regions) using MEG. We compare our results to those gained from fcMRI measurements in the same subjects. In fcMRI, we exploit the advantages afforded by ultra high (7T) magnetic field. In MEG, we apply envelope correlation and coherence techniques to brain space reconstructions of neuronal activity generated using adaptive beamformers and examine the relationship between the reconstructed neuronal activity and fcMRI. Our study has three specific aims: 1) To investigate the applicability of beamforming as a source space projection algorithm for FC measurement; 2) To compare multiple MEG metrics including envelope correlation, coherence and imaginary coherence; and 3) To compare the consistency in the spatial signature of motor network FC measured independently using fcMRI and MEG and to test the hypothesis that neural oscillatory processes are intimately related to hemodynamic FC. In what follows, the Methods section describes in detail our processes for measuring FC using MEG data, and testing the validity of those measurements. In the Results section we address individually each of the three aims stated above and we show that MEG represents a useful modality with which to investigate FC, with good agreement between measurements generated using these two disparate modalities. Finally, in the discussion, we examine the nature of the electrical effects that underlie hemodynamic FC. Methods Data acquisition Six healthy right handed subjects took part in the MEG experiments. Five of those six subjects took part in the fMRI experiments. The study was approved by the University of Nottingham Medical School ethics committee. MEG MEG data were recorded using the third order gradiometer configuration of a 275 channel CTF MEG system at a sampling rate of 600 Hz. The scanner is housed inside a magnetically shielded room (MSR) and a 150 Hz low pass anti-aliasing hardware filter was applied. All subjects underwent a single experiment which comprised two contiguous phases, a resting state phase and a localizer task. During the resting state phase, subjects were asked to lie in the scanner with their eyes open and relax while 300 s of resting state data were acquired. The localizer task comprised a total of 10 trials. A single trial comprised 30 s of left index finger movement, 30 s of right index finger movement, 30 s during which both left and right index fingers were moved together, and 30 s of rest. The movement itself comprised abductions and extensions of the index finger. The motor task was cued visually via projection through a waveguide in the MSR onto a back projection screen located 40 cm in front of the subject. During data acquisition the location of the subject's head within the scanner was measured by energizing coils placed at 3 fiducial points on the head (nasion, left preauricular and right preauricular). If any subject moved more than 5 mm during the experiment, data from that subject was discarded. Following data acquisition, the positions of the coils were measured relative to the subject's head shape using a 3D digitizer (Polhemus isotrack). An MPRAGE structural MR image was acquired using a Philips Achieva 3T MRI system (1 mm3 isotropic resolution, 256 × 256 × 160 matrix size, TR = 8.3 ms, TR = 3.9 ms, TI = 960 ms, shot interval = 3 s, FA = 8° and SENSE factor = 3). The locations of the fiducial markers and MEG sensors with respect to the brain anatomy were determined by matching the digitized head surface to the head surface extracted from the 3T anatomical MRI. fMRI fMRI data were acquired using a Philips Achieva 7T system. All subjects underwent a resting state and a localizer experiment (note, these data have previously been published in a study by Hale et al. (2010) comparing 3T and 7T fcMRI). In the resting state experiment, subjects were asked to lie in the scanner with their eyes open and relax while 300 s of BOLD data were acquired. The localizer experiment involved a visually cued finger movement. A single trial comprised 12 s of movement followed by 18 s rest. The experiment comprised 10 trials; during even numbered trials the subject moved their left index finger and during odd numbered trials the subjects moved their right index finger allowing both the right and left motor cortices to be identified. Echo planar images (matrix size 144 × 144, TE = 25 ms, SENSE factor = 3) were acquired with a voxel size of 1.5 mm × 1.5 mm × 3 mm. The TR was 2 s for the localizer, but reduced to 1.5 s for the resting state experiment to increase temporal degrees of freedom and therefore improve characterization of temporal correlation. To ensure a homogeneous B0, a parcellated shimming procedure (Poole and Bowtell, 2008) was employed. The flip angle was set to the Ernst angle (70°). 24 axial slices were acquired with whole brain coverage. During all experiments the respiration and vector-cardiogram were recorded. Subject head motion was measured during post processing and if any subject moved more than the smallest voxel dimension (1.5 mm) during the experiment, data from that subject were discarded. Data analysis Analysis of localizer data fMRI localizer data were motion corrected (SPM5), corrected for physiological artifact using RETROICOR (Glover et al., 2000), and smoothed spatially using a 3 mm FWHM Gaussian kernel (SPM5). In order to identify areas exhibiting significant BOLD change during finger movement, data were processed using the general linear model implemented in SPM5 (http://www.fil.ion.ucl.ac.uk/spm/). Robust statistically significant (p 0.25 was 126 ± 15 cm3; this was compared to 155 ± 17 cm3 when weights were computed using resting state data only (results given as average and standard error across subjects). This highlights the advantage of judicious selection of a time frequency window for weights computation and shows that inclusion of data recorded during a task driven change in signal power can improve the spatial resolution of the beamformer. Figs. 2E and F show lead field correlation and weights correlation as a function of distance from the seed location respectively. Note the improved spatial resolution of weights correlation with respect to lead field correlation that is also apparent in Figs. 2A and B. (Note also that separate lead field correlations for different frequency bands appear because the source orientation (δ) is computed independently for each frequency band. Lead fields themselves do not change with frequency.) The ability of the beamformer to construct independent weighting parameters, even in the case of correlated lead fields, makes it advantageous compared to non-adaptive source localization algorithms which rely only on lead fields to reconstruct source space signals. This is true of all beamformer applications, but is particularly important for FC measurement since high values of FC will necessarily result from correlation between weights. Here, we are interested specifically in connectivity between the left and right motor cortices and, in all subjects, weights correlation did not extend from the seed in the right motor cortex to the left motor cortex. This is shown in Fig. 2G where weights correlation between locations of interest in left and right sensorimotor cortices is plotted as a function of frequency (average ± standard error across subjects). Notice that correlation between left and right sensorimotor cortices is low (~ 0.1) and shows no significant change across frequency bands. The graph also shows lead field correlation between the left and right motor cortices which also remains low for all frequencies. (Note again that the small variation in lead field correlation across frequencies is due to the slight difference in the estimation of δ for the frequency bands studied.) Investigating electrodynamic connectivity The results above show that beamforming is an effective source localization algorithm and further that since weights derived for the left and right sensorimotor cortices are independent, measurement of high FC metrics is likely to result in real, not spurious FC measurement. In this section we present the results of our investigation into electrodynamic connectivity between the left and right motor cortices. We exploit the direct nature of MEG, and the multiple FC metrics described, to investigate the electrodynamic processes that underlie FC. Fig. 3A shows an example of the Hilbert envelopes derived from locations of interest in the left (blue) and right (red) sensorimotor cortices. These timecourses were taken from a single subject; the locations were derived based on that subject's localizer analysis and the three panels show three separate 10 s segments of data. Fig. 3B shows an example of the averaged Hilbert envelope timecourses (Δ = 0.5 s) extracted from the left (blue) and right (red) sensorimotor cortex. Again this result is derived from a single subject and all 300 s of resting state data are shown. In both Figs. 3A and B, data have been filtered to the low β frequency band. Fig. 3C shows corrected AEC, CAE, Coh and ICoh, applied to signals extracted from the left and right motor cortices. Note in all cases that the locations of interest were derived individually for each subject based on the localizer analysis. The left hand column shows corrected AEC between the left and right motor cortices, plotted as a function of frequency. To derive the corrected value, the average AEC from simulated data was subtracted from that derived from real data, on a subject by subject basis. (In order to improve visualization of the characteristic frequency response, for this analysis, the high-γ frequency band (40–70 Hz) was split into two, 40–50 Hz and 50–70 Hz.) A threshold was derived using the statistical distribution of AEC values from simulated data (see Methods section) and corrected AEC values above a threshold corresponding to p = 0.05 were taken to be significant. (These regions are shaded in gray.) The 5 rows of Fig. 3C show the case for Δ = 0.5 s, 1 s, 4 s, 6 s and 10 s respectively. The second column of Fig. 3C shows corrected CAE between the left and right motor cortices as a function of frequency (again Δ = 0.5 s, 1 s, 4 s, 6 s and 10 s are shown and correction is performed in the same manner as for AEC). The third column shows corrected Coh values between the left and right motor cortices and the final column shows corrected ICoh values. In all cases the red line shows the result (average and standard error across subjects) while the green line the 95% confidence limit based on simulations. In the case of ICoh, the blue line shows the 90% confidence limit, based on simulation. Raw values of AEC, CAE, Coh and ICoh, applied to real and simulated MEG data, are shown in Appendix 4. Results show that the group average AEC values derived from real data (Δ = 1 s, 4 s, 6 s and 10 s) are significantly larger than those derived from the simulated data, implying significant connectivity between the left and right motor cortices. The group average CAE values derived from real data (all Δ) also exhibit statistical significance. For both AEC and CAE, a clear frequency band response is observed with the highest FC metrics observed in the low β band (13–20 Hz). This is not surprising since oscillatory effects in the β band are well known to play a fundamental role in the motor network and these effects have been previously reported (Mantini et al., 2007; Liu et al., 2010). Interestingly, the size of the effect observed depends on the time scale (Δ) on which the measurements of correlation are made. This effect provides information on the time scale of functional connectivity and this is addressed in more detail in the discussion below. The Coh measurements showed no significant effect in any frequency band. ICoh values were extremely small in magnitude, and did not reach significance (p = 0.05). However, the frequency signature of ICoh mirrored that shown by the AEC and CAE metrics with the highest ICoh being observed in the β band. In addition (for Δ = 4 s), ICoh values exceeded a 90% confidence limit. The results shown in Fig. 3C represent FC averaged over a 300 s window. However, recent interest has grown in dynamic FC measurements (Chang and Glover, 2010). Fig. 4 shows that dynamic measurements of electrodynamic FC can be obtained using our ICoh and AEC techniques. For both metrics, n FC measurements are made using n time windows, enabling a timecourse of FC to be derived whose temporal scale is determined by Δ. Fig. 4A shows two such timecourses, the upper panel shows ICoh while the lower panel shows AEC (Δ = 10 s in both cases and 13 Hz–20 Hz filtered data are used). Notice that the ICoh values, peaking at around 0.07, are much smaller than the AEC values which peak around 0.4. Notice also that there is a large variation in FC over time, with AEC values ranging from 0 to 0.4. Fig. 4B shows correlation between ICoh and AEC FC timecourses as a function of frequency for Δ = 1 s, 4 s, 6 s and 10 s. The red line shows the result for real data while the black line shows the result derived from simulated data. Notice that for Δ > 4 s, a peak is observed in the β frequency band which is only apparent for real data. These peaks do not reach statistical significance (p = 0.05 derived using the simulated data) across the subject group. However, the trend observed does imply that, in the β band, a degree of similarity exists between AEC and ICoh and that coherent activity (with a non-zero time lag) may underlie envelope correlation. Cross-modal comparison A comparison between resting state FC measured using fcMRI and MEG was undertaken based on the similarity between FC images derived from the two modalities. Since our CAE metric yielded the highest temporal correlation coefficients, this metric was used exclusively for the cross-modal comparison. Fig. 5 shows FC images acquired in a single subject. Fig. 5A shows the fcMRI result, with a seed in the right motor cortex yielding significantly (p 0.4 for CAE; > 0.08 for AEC compared to ~ 0.02 for ICoh). A likely reason is that envelope correlation approaches are less affected by noise, external interference and temporal jitter in MEG signals (this is particularly true of CAE), making them a more stable FC metric than coherence based approaches. Amplitude correlation metrics should not however be considered an improvement over coherence approaches since the latter are likely to be less sensitive to third party and common mode modulations. For example, given two systems with similar characteristic time scales, they are unlikely to appear as phase locked without being truly coupled. However, slower fluctuations in the amplitude may be caused by third party modulation or common mode effects. We therefore stress that envelope correlation and coherence based approaches are complementary and are likely to represent fundamentally different underlying physiological processes. In Fig. 4 we show the time evolution of AEC and ICoh FC metrics and it is interesting to note a marked change in FC over 5 minute resting state recordings. Recently, interest has grown in dynamic FC measurements made using fcMRI (Chang and Glover, 2010) and interpreting large FC changes offers the potential for a better understanding of how these effects affect behavior. The current paper is limited since all FC measurements were made in the resting state, making FC change hard to interpret (see also below). However, Fig. 4 shows that dynamic FC measurements are possible using electromagnetic data; such measurements complement dynamic fcMRI metrics and this offers exciting opportunities to measure the time evolution of task induced change in FC. Finally, there was some agreement between imaginary coherence and amplitude correlation metrics. Figs. 3 and 7 show that ICoh measurements peak in the β band, and at its maximum exceeds a threshold corresponding to p < 0.1. Fig. 4B shows correlation measured between dynamic ICoh and AEC metrics; with quantitative analysis showing that correlation is strongest in the β band. We might then speculate that amplitude correlation is driven by coherent bursts of synchronized activity in spatially separate cell assemblies. Since the imaginary part of coherence is implicated, this is known to exhibit a non-zero phase lag. In all ICoh measurements the absolute value of imaginary coherence was computed and no agreement was found without this step. The phase of coherent bursts may therefore change in different time windows leading to positive and negative imaginary coherence values. That said, correlation between ICoh and AEC timecourses was small (and did not reach statistical significance). It therefore remains likely that these measurements generate complementary information and that both should be considered in future studies. Cross-modal comparison The cross hemisphere correlation results were supported by our cross modal comparison. The spatial agreement between FC measurements made using MEG and fMRI data is compelling. Results showed that the spatial signature of motor network connectivity can be measured independently using MEG and fMRI, and further that the location of peaks in correlation measured using fcMRI were similar to those measured using CAE applied to MEG data. (Note, AEC yielded similar peak positions, but due to the larger correlation coefficients observed, CAE results were presented.) Significant left hemisphere connectivity was observed in the θ, α, β and low γ frequency bands with the best spatial agreement in the β band. This is shown in Fig. 6 and supported by our quantitative analyses where spatial correlation between MEG and fcMRI derived FC maps is maximal in the β band. While some degree of overlap between FC measurements was observed for the α, β and low γ bands, the theta band showed FC that was spatially distinct from that in fcMRI. This could be a result of mislocalization (spatial filters are constructed independently for each frequency band and their accuracy depends on SNR. The θ band SNR is low potentially leading to mislocalization) or it could be indicative of a spatially distinct network mediated by θ oscillations. This warrants further investigation. It is unsurprising that β oscillations were most strongly implicated in motor cortex FC. Previous work (Salmelin et al., 1995; Stancak and Pfurtscheller, 1995; Pfurtscheller et al., 1996; Toma et al., 2000) has highlighted the role of β oscillations in the motor system and a close spatial relationship between β oscillations and the BOLD response has also been observed (Stevenson et al., 2011). Our results are in good agreement with other published work employing both concurrent EEG/fMRI and MEG (Mantini et al., 2007; Liu et al., 2010) and add further weight to a growing body of literature suggesting a close relationship between neural oscillations and BOLD. The strong agreement between the spatial signature of FC measured using MEG and fcMRI acts to reduce confounds associated with either technique when used alone. The spatial accuracy of MEG is known to be limited by the ill posed inverse problem and the spatial similarity observed helps to validate the beamformer spatial filter approach. However, of more importance is validation of the observed BOLD correlations. Our data show that there is a sound electrophysiological basis for BOLD correlation between the left and right motor cortices. Such correlation could alternatively be due to one (or a combination) of the many possible sources of common mode influences on hemodynamics (for example, overlap of capillary beds, draining veins, pulsation and breathing). The fact that there is agreement in MEG suggests a neuronal and not a hemodynamic basis to fcMRI. It remains to be seen whether FC observed using fcMRI in other brain networks (e.g. the default mode, attention and salience networks) can also be substantiated using MEG. Limitations and future study The measurement of functional connectivity using MEG is an interesting field that has potential to overcome many of the limitations of hemodynamic approaches. However, it remains a complex methodological problem and a complete solution is beyond the scope of a single paper. Here we present compelling evidence for the existence of electrophysiological FC, but these results must be taken at face value; they are valid within the limitations of the techniques used. It is well known that the SNR of MEG changes with frequency and is low for frequencies in the high γ band. This means that the FC values computed could be affected since high correlation or coherence in the gamma band may be masked by poor SNR. Here signal to noise ratio peaked in the alpha and β range (e.g. in left motor cortex signal variance was 18 ± 4 nA m, 31 ± 9 nA m, 29 ± 6 nA m, 24 ± 5 nA m and 7 ± 1 nA m for the θ, α, low-β, high-β and the low-γ frequency ranges respectively). There was some demarcation between FC results and SNR since, while SNR was high in the α-band, there was little spatial agreement between fcMEG and fcMRI measurements (Fig. 7B). However, the fact that FC metrics will be more accurate in bands exhibiting high SNR remains a potential confound. Despite the effectiveness of our simulations to test for spurious connectivity, some limitations remain. In our appendices we show that the beamformer effectively attenuates interference from a third brain source. However this was limited since only a single location for that source was chosen. It is conceivable that, had a different location been chosen, FC might have been affected. We also show effective attenuation of cardiac interference, however results presented do not prove categorically that the ECG or respiration has no effect on FC. In future studies, we advise measurement of physiological parameters (i.e. cardiac and respiratory cycles) alongside MEG. This would enable correlation of physiological parameters with MEG Hilbert envelope metrics in order to quantitatively assess the contribution of such interference. The simulation approach is flexible and it is possible to include interference sources in the simulation model; for example it may be possible to construct simulated data based on singular value decomposition of the real covariance matrix. However, this would rely on the explicit assumption that spatially separate sources exhibiting real FC would be represented by separate singular vectors in the SVD. An alternative approach would be to employ ICA; one might expect real functional networks and spurious networks elicited by interference to be separated by ICA, if they have an uncorrelated spatio-temporal signature. Judicious selection of independent components would thus eliminate spurious connectivity. These extensions should be the topic of future. The way in which data were segmented for computation of FC should also be addressed. The reason for segmenting data was to investigate the time scale of connectivity and our results show similarity with previous work. The segmentation strategy also enabled us to examine the time evolution of FC and enabled comparison of envelope correlation and imaginary coherence FC metrics (Fig. 4). However there is bias in our segmentation strategy. For our AEC metric, the accuracy of the correlation coefficient is dependent on the time-frequency window in which the measurement is made, and the number of measurements averaged; error in the correlation coefficient is therefore dependent on the duration (Δ), the number of segments, n, and the bandwidth of the Hilbert envelope signal. For our Coh/ICoh metrics, coherence and imaginary coherence were computed within each segment (i.e. the cross-spectrum was measured for each segment and then averaged over segments). This technique is also known to exhibit bias for small data segments. Our real and simulated data are processed in the same way, and so differences between AEC, Coh and ICoh values for real and simulated data (Fig. 3) are not affected by bias due to data segmentation. However, Δ does change for separate rows in Fig. 3C and so, as stated above, the reader must exercise caution when interpreting the time scale of connectivity. For example, AEC for Δ = 0.5 s exhibits no significant results; this could mean that no correlation is observed on that time scale or it could result from poor estimation of correlation coefficients using data segmented within a 0.5 s window. Future work should aim to employ multi-taper spectral methods; these techniques do not rely on data segmentation and therefore do not exhibit the same bias as conventional the more spectral analysis used here. Throughout this manuscript, we only measure resting state FC and this has proved interesting to compare MEG and fcMRI based metrics. However, future work should look to task driven changes in order to gain a more complete understanding of how FC changes with activity, and the relationship between metrics. For example, a direct comparison of the time evolution of imaginary coherence and envelope correlation between regions (as presented in Fig. 4) would be more meaningful if one knew that those brain areas were undergoing modulation. I.e. the peaks in the timecourses of FC (Fig. 4) could be better interpreted if they could be linked with a specific event (e.g. movement). However, care must be taken in using such measurements. Introducing a task will cause marked changes in cortical oscillatory power. Such changes, which occur in multiple brain areas, will illicit correlation between envelope signals from those areas. This would appear as an increase in FC, but could be due entirely to task driven change in separate unimodal brain regions. This is a limitation associated with all correlation approaches including those used in fcMRI. (Although such effects can be minimized by judicious selection of the time over which FC is measured (i.e. Δ).) In addition, changes in cortical oscillatory power cause changes in signal to noise ratio that can also result in spurious metrics of connectivity change (Schoffelen and Gross, 2009) (e.g. coherence measures become more reliable as SNR is increased and so an increase in SNR can appear as increased coherence, hence FC). Again such effects must be carefully considered in future studies examining task related FC changes. Finally, the term ‘functional connectivity’ has been used to describe temporal correlation or coherence between signals from spatially separate brain areas. However, the fact that two signals are correlated does not necessarily mean that the brain areas from which they originate are functionally related. For example correlation could be driven by a third brain region and could be caused by changes in attention or arousal. In fact, work in monkey LFP (Leopold et al., 2003) concluded that envelope correlations most likely do not represent functional communication but common modulation due to spontaneous fluctuations in the arousal and attention systems. It is possible that the fluctuations observed in the present paper result from similar underlying mechanisms to those observed in monkey and this could be investigated further using task positive paradigms. Conclusion In recent years, measurement of FC using fMRI has become a popular and important research area and to date has revealed the spatial signature of a number of hitherto unknown neural networks. However, the technique is fundamentally limited since fMRI is an indirect measure of brain activity. If the electrodynamic mechanisms underlying hemodynamic connectivity are to be elucidated, a multi-modal methodology will be key. In this paper, we have investigated resting state FC using fcMRI and MEG. We have shown that beamforming provides a suitable means to investigate FC in source space using MEG data. However, care must be taken when interpreting these measurements since cross talk between voxels in source space can potentially lead to spurious connectivity and this effect must be taken into account in all studies of this type. We have shown good spatial agreement between FC measured using MEG and fcMRI; FC between sensorimotor cortices was observed using both modalities, with the best spatial agreement when MEG data are filtered into the β band. This finding helps to reduce the potential confounds associated with each modality alone: while it helps reduce the uncertainties in spatial patterns generated by MEG (brought about by the ill posed inverse problem), addition of electrodynamic metric confirms the neural basis of fcMRI measurements. Finally, we have shown that multiple FC metrics can be applied to MEG data in order to investigate the nature of electrodynamic connectivity. Our results further those from previous studies and add weight to the argument that neural oscillatory processes are intimately related to both functional connectivity and the BOLD response. The clinical utility of MEG recordings has been highlighted in a number of recent papers (for example see Guggisberg et al., 2008; Stoffers et al., 2008) in which resting state measurements provide a protocol to differentiate patient groups. Here, we present a framework of doing source localization and FC measurement under resting state conditions. This could have great impact in future clinical work.
