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 < 0.05
FWE corrected) activation was observed in all subjects in the left and right sensorimotor
cortices. The peak in BOLD activity in the right sensorimotor cortex was used to define
a seed location for subsequent fcMRI analyses. The 7T EPI localizer data and associated
functional images were co-registered to the 3T anatomical MPRAGE image of each individual
subject using the fMRIB linear image registration tool (FLIRT) in FSL (http://www.fmrib.ox.ac.uk/fsl/).
Functional images were then co-registered to the standard brain (i.e. MNI space),
using FLIRT.
Synthetic aperture magnetometry (Robinson and Vrba, 1998) was applied to the MEG localizer
data in order to localize left and right sensorimotor cortices. An ‘active’ time window
was chosen as the period during which subjects moved both their left and right index
fingers. A ‘control’ window was defined as the rest period for each trial. Pseudo-T-statistical
functional images were constructed by contrasting beamformer projected oscillatory
power in the active window with that in the control window (regularization parameter
μ = 4; for definition of μ, see below). This resulted in a volumetric image showing
the spatial distribution of oscillatory power change. In agreement with previous literature
(see e.g. (Stevenson et al., 2011) robust task induced loss in β (13–30 Hz) band oscillatory
power was found localized to primary sensorimotor cortices. These locations were later
used to define locations of interest in the left and right sensorimotor cortices for
MEG FC analysis. MEG localizer images were co-registered to the MNI brain using FLIRT.
Analysis of resting state fcMRI data
Resting state fMRI data were motion corrected (SPM5), corrected for non-neuronal physiological
artifact using RETROICOR (Glover et al., 2000), and smoothed spatially (SPM5) using
a 3 mm FWHM Gaussian kernel. A seed based correlation technique (as described in Biswal
et al., 1995) was employed to assess resting state connectivity. An average BOLD seed
timecourse was derived from the peak voxel in right sensorimotor cortex, defined from
the localizer experiment, and its 26 nearest neighbors. The Pearson correlation coefficients
between the seed timecourse, and all voxels in the brain were computed resulting in
a volumetric image of correlation coefficients. Correlation coefficient images were
thresholded at a value corresponding to p < 0.05 Bonferroni corrected for multiple
comparisons (Hale et al., 2010). Again, the 7T EPI data and BOLD FC images were co-registered
to the 3T anatomical MPRAGE image of each individual subject, and to the standard
MNI brain, using FLIRT.
Analysis of resting state MEG data
MEG data were mean corrected and frequency filtered into seven bands of interest using
a finite impulse response filter in NUTMEG (http://nutmeg.berkeley.edu) (Dalal et
al., 2004). The frequency bands used were δ (1 Hz–4 Hz), θ (4 Hz–8 Hz), α (8 Hz–13 Hz),
low β (13 Hz–20 Hz), high β (20 Hz–30 Hz), low γ (30 Hz–40 Hz) and high γ (40 Hz–70 Hz).
FC was measured using a three step process: A) application of spatial filters to project
data into source space; B) application of the FC metric; and C) weights correlation
computation and simulation to assess the statistical significance of the FC metric
used. These three steps are described in detail in the following three sections.
A)
Application of spatial filters
Frequency filtered MEG data were projected into source space using a scalar beamformer.
The electrical source amplitude,
Q
ˆ
θ
t
at a predetermined location was estimated as:
(1)
Q
ˆ
θ
t
=
W
θ
T
m
t
where m(t) is the vector of magnetic field measurements made at M MEG sensors at time
t. Wθ is a vector of weighting parameters tuned to location and orientation θ = [r, δ],
where r represents location, and δ is the angle of the source with respect to the
azimuthal direction. W
θ
was computed based on minimization of output signal variance, with a linear constraint
that signal power originating at θ remains in the output signal (Van Drongelen et
al., 1996; Van Veen et al., 1997; Robinson and Vrba, 1998), mathematically:
(2)
W
θ
T
=
L
θ
T
C
+
μ
σ
I
−
1
L
θ
−
1
L
θ
T
C
+
μ
σ
I
−
1
where L
θ
represents the lead fields, C represents the M × M data covariance matrix, μ is the
matrix regularization parameter, σ is an estimate of uncorrelated noise power and
I is the identity matrix. The lead fields L
θ
were computed using a multi-sphere head model (Huang et al., 1999) and the forward
calculation described by Sarvas (1987). The angle δ was found independently at each
r using a non-linear search to compute the orientation of maximal variance. The noise
estimate (σ) was computed as the minimum singular value of the covariance matrix and
μ = 4 in all cases. The channel level data covariance matrix C was computed in two
ways: in the first case, only those data acquired during the resting state phase of
the experiment were used. In the second case, data from the entire experiment were
used. It is well known that the spatial resolution of beamformer imaging is inhomogeneous
across the head, with the highest spatial resolution being in regions of high power
(Barnes and Hillebrand, 2003). During the resting state phase, brain areas may exhibit
little power and undergo no modulation, meaning that spatial resolution may be low
and homogeneous. However, using covariance computed over the entire experiment, spatial
resolution would be expected to improve, partly due to increased amount of data (Brookes
et al., 2008a,b), but also particularly in the motor network which will undergo power
change due to the localizer task. This implies that covariance computed over longer
windows is advantageous; however in doing this one necessarily assumes that sources
of interest are stationary throughout the whole experiment. Beamformer weights W
θ
T
and associated timecourses
Q
ˆ
θ
t
were computed for locations placed at the vertices of a regular 5 mm grid spanning
the entire brain. A separate set of beamformer weights was computed for each frequency
band in order to optimize beamformer sensitivity to effects of interest in that band
(Brookes et al., 2008a,b, 2009, 2010).
B)
Resting state functional connectivity metrics
Having projected MEG data into the brain, the second step involves application of
FC metrics. In the following description, the beamformer weights (and therefore estimation
of δ for each voxel) were computed from the entire dataset (thus allowing optimal
spatial resolution). However, in all cases FC metrics were only applied to data acquired
during the resting phase (i.e. first 300 s) of the MEG experiment, meaning that we
only compute resting state connectivity between brain regions. For all computations,
a seed voxel was chosen in the right sensorimotor area, as defined individually for
each subject using the MEG localizer results.
Four separate FC metrics were applied; two based on envelope correlation—termed Average
Envelope Correlation (AEC) and Correlation of Averaged Envelopes (CAE); and two based
on coherence termed coherence (Coh) and Imaginary Coherence (ICoh). In all cases,
connectivity was measured between the projected signal at the seed voxel, and that
from all other (test) voxels in the brain. The four connectivity metrics were computed
as follows:
1.
AEC: The timecourses of bandpass filtered electrical activity at the seed and test
voxels were Hilbert transformed to obtain the analytic signal. The absolute value
of the analytic signal was then determined in order to give the envelope of oscillatory
power in the frequency band of interest. This we term the Hilbert envelope and this
technique has been used extensively in previous MEG studies (for a mathematical description
see Brookes et al., 2004). The Hilbert envelopes for the seed and test voxels were
divided into n time segments of equal length Δ. The Pearson correlation coefficient
between seed and test Hilbert envelopes was computed within each segment. This gave
n correlation values, one for each time segment. These were then averaged across segments
yielding a single average value which we term Averaged Envelope Correlation (AEC).
2.
CAE: The timecourses of electrical activity at both the seed and test voxels were
Hilbert transformed and the Hilbert envelopes computed. The Hilbert envelopes were
divided into n time segments of equal length Δ and the average value of the envelope
computed within each time window. This resulted in two new temporally averaged Hilbert
envelope timecourses, each comprising n points (we term these the ‘averaged envelopes’).
The Pearson correlation between these averaged envelopes was then computed as a measure
of FC which we term Correlation of Average Envelopes (CAE).
3.
Coh: The filtered projected electrical timecourses (not the Hilbert envelopes) from
the seed and test voxels were divided into n time segments of equal length Δ. Coherence
between seed and test timecourses was computed within each segment giving n values,
one for each time segment. These were then averaged across segments yielding an average
coherence value (Coh). (Coherence within a single segment, k, was computed as
C
XY
(
f
)
=
X
k
(
f
)
Y
k
*
(
f
)
/
X
k
(
f
)
2
Y
k
(
f
)
2
for a single frequency bin (f) where X
k
(f) and Y
k
(f) are the Fourier transformed segment (k) of the virtual time series and * indicates
the complex conjugate. Coherence values for frequency bands were computed from the
sum of autospectra and cross spectra in the corresponding frequency bins (Guggisberg
et al., 2008)).
4.
ICoh: As above, the projected electrical timecourses (not the Hilbert envelopes) from
the seed and test voxels were divided into n time segments of equal length Δ. The
imaginary part of coherence between seed and test timecourses was computed within
each segment. The absolute value of imaginary coherence was then computed and averaged
across segments (ICoh). (Imaginary Coherence within a single segment was computed
as
I
XY
(
f
)
=
Im
X
k
(
f
)
Y
k
*
(
f
)
/
X
k
(
f
)
2
Y
k
(
f
)
2
and values for frequency bands were computed from the sum of autospectra and cross
spectra in the corresponding frequency bins (Guggisberg et al., 2008). The absolute
value of imaginary coherence was computed since we were interested in the magnitude
of FC, not the directionality).
As mentioned above, previous work (Singh et al., 2002; Brookes et al., 2004; Winterer
et al., 2007; Stevenson et al., 2011; Zumer et al., 2010) has shown a close relationship
between task driven fluctuations in oscillatory power and the hemodynamic response.
Further, papers investigating MEG FC and its relationship to fcMRI (de Pasquale et
al., 2009; Liu et al., 2010) have both employed amplitude envelope based measurements.
This motivated the use of the AEC methodology described above. CAE employs MEG time
series that are temporally collapsed. This makes correlation results less sensitive
to phase jitter in the Hilbert envelope, and to noise. The CAE measurement is also
similar to that used by de Pasquale et al. (2009) however it does sacrifice some temporal
resolution. Coherence and imaginary coherence have been applied in previous MEG studies.
Here they are employed as a comparison to amplitude envelope based measurements, and
to investigate the nature of electrodynamic connectivity. For example, strong agreement
between Coh and AEC might imply that phase locking between large cell populations
was underlying changes in oscillatory amplitude and driving amplitude based FC measurements.
High ICoh values would show that an observable phase lag was apparent between network
nodes. Variation of Δ and computation of FC timecourses enable important information
about the time scale FC to be generated. Use of the metrics in this way was therefore
expected to exploit the direct nature of MEG and provide information on the electrical
processes mediating FC.
C)
Weights correlation, simulation and statistical significance
Source reconstruction of MEG data limits the effect of field spread since it enables
visualization of FC in source space. However, the inverse problem is ill posed and
the estimated timecourses of electrical activity at separate MEG voxels are not necessarily
independent. In other words, it is possible to get signal leakage between spatial
filters. Independence of two spatial filters can be assessed by examining correlation
between beamformer weights. If the weights for two spatially separate voxels are correlated
(as is likely to be the case for nearby voxels) then the projected signals will also
be correlated and this may appear as spurious FC in the beamformer based FC images.
If, however, the beamformer weights for two voxels are completely independent, but
the timecourses from those voxels are highly correlated, it is more likely that genuine
FC exists between those two brain locations. In order to assess the weights correlation
problem, correlation coefficients between beamformer weights at the seed location,
and all other voxels in the brain were computed in order to create volumetric images
of weights correlation. These were constructed for all subjects and all frequency
bands (note, the absolute value of weights correlation was computed in all cases).
Correlation between beamformer weights was compared to correlation between lead field
patterns in order to assess the advantages of beamforming over non-adaptive algorithms
(e.g. dipole fitting) in which lead fields are used directly for source reconstruction.
Both weights correlation and lead field correlation were plotted against distance
between the seed and test voxel in order to examine the extent of spurious connectivity
around the seed region.
While weights correlation is a useful metric for visualization of signal leakage,
it cannot be used to assess directly the statistical significance of FC and for this
purpose, simulated MEG data were generated. On each iteration of the simulation, two
dipolar sources were simulated in the brain, the first at the seed location, and the
second at a test location. The timecourses for these two sources comprised Gaussian
random noise which was colored by frequency filtering to the band of interest. No
significant correlation existed between simulated seed and test timecourses. The source
orientations and the variance of the source timecourses were equivalent to those derived
by application of the beamformer to the real MEG data for the same subject, location
and frequency band. The simulated timecourses were multiplied by lead fields for the
two locations/orientations and 300 s of simulated MEG data were constructed (taking
into account the third order gradiometer sensor configuration). 300 s of MEG data
were acquired (using the third order gradiometer configuration of the 275 channel
system at a sampling rate of 600 Hz) with no subject in the scanner. These noise data
were added to the simulated data resulting in a simulated MEG dataset.
The simulated data were used repeatedly in order to assess statistical significance
of measured FC values throughout this paper. On each repetition of this simulation,
different seed and test timecourses were employed. Simulated MEG data were projected
into the brain using the same beamformer weights derived from and applied to the real
MEG data. Since our simulated data were designed to be similar to the real resting
state data, beamformer reconstruction of the simulated source timecourses was successful.
However no correlation between simulated sources was introduced, meaning that following
beamformer projection, if FC analysis of simulated data implied high levels of FC
between sources, this was entirely spurious and could be due to either weights correlation,
field spread between the two sources or real correlated noise across MEG sensors.
Two separate strategies were employed to identify areas of statistically significant
FC in MEG images; the first technique was applied to individual subject data and the
second to group data. In both cases, volumetric images containing simulated FC values
were employed and for every FC image created using real MEG data, an equivalent simulated
FC image was created. (Note: in creating the simulated FC image, on each iteration
of the simulation, the test voxel was moved to a different location, meaning that
a single MEG dataset was simulated for every voxel.)
In order to derive statistical significance in a single subject the following process
was employed: 1) voxels were binned according to their weights correlation (bin width
0.05) and the mean value of simulated FC was computed within each bin; 2) The mean
simulated FC values within each bin were subtracted from values derived from real
and simulated data on a voxel by voxel basis—the result being two corrected images,
one based on real data, the other on simulated data; and 3) The distributions of corrected
simulated FC values across all voxels were computed and used to threshold corrected
FC images derived from real data. Only those voxels in the upper fifth percentile
of the corrected simulated distribution were said to exhibit statistically significant
FC.
In order to assess statistical significance of FC across the subject group, FC images
were co-registered to the standard brain using FLIRT. Following co-registration, in
a single frequency band, for every voxel in MNI space, six real and six simulated
FC values were available (one value per subject). These two sets of numbers were averaged,
and the statistical significance of the difference between them was computed using
a non-parametric Wilcoxon signed rank test, implemented in Matlab (Mathworks). Under
a null hypothesis, one would expect no significant difference between the real and
the simulated data. Voxels in which a statistically significant (p < 0.05) difference
between the real and the simulated images was observed were said to exhibit significant
FC at the group level.
Investigating electrodynamic connectivity
FC between the left and right motor cortices is a well known effect in fcMRI. For
this reason, investigation into the nature of inter-hemispheric connectivity was undertaken
by measurement of FC between 2 locations; a seed in the right motor cortex and a test
voxel in the left motor cortex. Both locations were defined independently for each
subject based on the results of the MEG localizer analysis. Beamformer spatial filters
were derived for both locations and resting state data were projected into the brain.
AEC, CAE, Coh and ICoh were computed between locations in left and right motor cortex
(as described above). This was done independently for all frequency bands and subjects;
Δ was varied, taking values of 0.5 s, 1 s,4 s, 6 s and 10 s.
To test the significance of FC between the two locations, 100 simulated MEG datasets
were constructed (as described above) with simulated seed and test sources in the
right and left motor cortices respectively. (Again this was done for each frequency
band and subject, with source orientation and amplitudes matched to those measured
from real data.) Simulated datasets were projected through the same spatial filters
as those used for real data and 100 simulated values of AEC, CAE, Coh and ICoh were
derived (again for varying Δ). The mean of the simulated values was subtracted from
values derived from real data on a subject by subject basis yielding corrected AEC,
CAE, Coh and ICoh values. These corrected values were then averaged across subjects
and standard error computed. Finally, the simulated values were mean corrected (on
a subject by subject basis) and concatenated (across subjects) to create a distribution
comprising 600 points for each of the four connectivity measures and each of the seven
frequency bands. The 95% confidence limit was computed and used to assess statistical
significance of the measured FC. Using the null hypothesis, one would expect no significant
difference between AEC, CAE, Coh and ICoh values derived using real and simulated
data.
Previous results (de Pasquale et al., 2009) have shown that the time at which FC is
measured can have an important effect on the results obtained. In their paper de Pasquale
et al. show that cross hemisphere FC was better observed in carefully selected short
time windows than it was using their entire MEG dataset. In order to assess this effect
in our study, the timecourses of FC between left and right sensorimotor cortices were
assessed. As described above, AEC, Coh and ICoh were computed within n time windows
of length Δ. This enabled visualization of the timecourse of FC, with temporal resolution
determined by Δ. The AEC, Coh and ICoh timecourses were plotted in order to gage the
variation of the FC metric. In addition, FC timecourses enabled an interesting comparison
between our metrics since agreement (or disagreement) between metrics would provide
valuable information about the relationship between, for example, envelope correlation
and coherence. For this reason, the correlation between FC timecourses measured using
AEC, Coh and ICoh was computed allowing a numerical measure of the similarity between
metrics and enabling us to probe the relationship them.
Cross modal comparison
A comparison between fcMRI and fcMEG was undertaken by assessment of the similarity
of FC images derived using the two modalities. Initially, a visual comparison was
made between FC images generated using fcMRI and MEG. The locations of statistically
significant correlated areas were recorded, and the similarity between peak locations
measured. This was undertaken for each of the 7 frequency bands used in MEG analysis
and allowed a visual comparison of those MEG frequency bands most closely related
to FC measured using fcMRI.
In order to obtain a numerical value for the spatial similarity between MEG and fcMRI,
a spatial correlation coefficient metric was introduced. Initially, the fcMRI maps
(in MNI space) were smoothed using a Gaussian smoothing kernel (FWHM 8 mm) (this was
to account for the intrinsic differences in image smoothness between MEG and fcMRI
measurements) and averaged across subjects. The map was then reshaped into a one dimensional
vector. Unthresholded MEG FC maps (also in MNI space) were reshaped into one dimensional
vectors and the Pearson correlation coefficients between fcMRI and MEG derived vectors
were computed to give a numerical measure of the spatial similarity between maps.
This metric, which we term spatial correlation, was calculated for all frequency bands
on a subject by subject basis. Values were averaged across subjects and plotted as
a function of frequency. The motivation for this measurement was to see which MEG
frequency band best represented the spatial signature of BOLD connectivity. In order
to assess significance, the same spatial correlation metric was repeated using FC
images derived using simulated MEG data and statistical significance between spatial
correlation values computed using real and simulated data was assessed
Finally, the spatial overlap of significantly connected regions, derived from thresholded
fcMRI and fcMEG images was computed as a function of frequency.
Results
The Results section is split into 5 parts. In the first part, we investigate spatial
correspondence between fMRI and MEG localizers. In the second part, we address the
confounds of MEG FC measurement due to signal leakage between voxels in source space.
In the third part we use MEG data to investigate electromagnetic FC between the left
and the right sensorimotor cortices. In the fourth part, we undertake a quantitative
spatial comparison between fcMRI and fcMEG. In the final part, we address limitations
of our simulation approach to eliminating spurious FC.
Localizer analysis
Fig. 1 shows the results from the MEG and fMRI localizer analyses. Fig. 1A shows decrease
in β band power in the left and right motor cortices in response to the finger movement
task, for a single representative subject. Fig. 1B shows the corresponding increase
in BOLD signal, again in a single subject, which also highlights left and right sensorimotor
cortices. Figs. 1C and D show equivalent results averaged across the subject group;
panel C shows β band power decrease while panel D shows corresponding BOLD increase.
Note that good spatial agreement is observed between β band power loss and increased
BOLD signal. The average MNI coordinates for the peaks in β band power loss were (− 41 ± 3, − 25 ± 6, 49 ± 9) mm
(left motor cortex) and (34 ± 8, − 31 ± 10, 49 ± 9) mm (right motor cortex). The average
locations of the peaks in BOLD response were (− 41 ± 4, − 21 ± 8, 53 ± 6) mm (left
motor cortex) and (42 ± 8, − 19 ± 10, 51 ± 9) mm (right motor cortex). (Note that
all measurements are quoted as mean ± standard deviation across subjects.) Given the
error bounds quoted, the spatial location of the peak BOLD and β band responses were
not significantly different. The mean Euclidean distance between β band and BOLD peaks
was 17 ± 7 mm. This level of spatial correspondence is in agreement with previously
published work (Brookes et al., 2005; Winterer et al., 2007; Stevenson et al., 2011).
Discrepancies could be the result of inaccurate coregistration, inaccuracies in MEG
inverse modeling, or they may reflect genuine spatial differences brought about by
the fundamental differences between these two disparate measurements. For the connectivity
results that follow, seed locations for MEG FC analysis were based on each individual's
MEG localizer analyses; seed locations for fcMRI were based on each individual's fMRI
localizer analyses. In all cases, seed locations were in the right sensorimotor cortex.
Spatial filter properties
As stated above, beamformer spatial filters, derived for spatially separate brain
locations, are not necessarily independent and cross talk between voxels could cause
spurious FC measurement. It is therefore important to determine accurately the properties
of spatial filters prior to FC computation. Fig. 2A shows a volumetric image of Pearson
correlation between lead fields at the seed location (at the cross hairs) and lead
fields at all other source space voxels. This is shown for a single subject, with
the source orientation for each voxel derived as the orientation of maximum signal
variance. Pearson correlation coefficients are thresholded at 0.5 for visualization.
Figs. 2B and C show volumetric images of correlation between beamformer weights at
the seed location and at all other voxels in the brain. (Weights correlation images
are computed using 13 Hz–20 Hz filtered MEG data.) Fig. 2B shows weights correlation
in a case where covariance is based on all available MEG data (i.e. contiguous resting
state and localizer data); Fig. 2C shows weights correlation in a case where covariance
is based on resting state data only. Images are thresholded at 0.5. Notice here that
weights correlation is far less widespread than lead field correlation, an effect
of the adaptive nature of beamforming which shows that, even if lead fields are correlated,
beamformer weights can remain independent.
Demarcation between lead field and weights correlation is confirmed in Fig. 2D which
highlights (for all frequency bands) the non-linear relationship between the two.
Again, this shows that high correlation between lead fields does not necessarily imply
high correlation between beamformer weights. This effect is affected by signal power;
the beamformer is able to separate two voxels with overlapping lead fields only if
significant signal power originates at those two voxels. This has been addressed in
previous work (Barnes and Hillebrand, 2003; Brookes et al., 2008a,b, 2009, 2010).
It is important to note that using covariance based on all data (i.e. resting state
and localizer data), the total volume of cortex with weights correlated at r > 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 < 0.05) correlated voxels in left primary sensorimotor cortices
and supplementary motor area (SMA). The strongest correlation was in left primary
sensorimotor cortices. Fig. 5B shows an equivalent result derived using MEG. Here
CAE (Δ = 0.5 s) is applied to low β band filtered MEG data. As with fMRI, a seed in
right sensorimotor cortex yields significant correlation with voxels in the left primary
sensorimotor area (p < 0.05). In Fig. 5B, the red–yellow overlay shows raw correlation
values while the green overlay shows those correlation coefficients that are significantly
higher than equivalent correlation values computed in simulation. Note that the highly
correlated diffuse region around the seed in right sensorimotor cortex is a result
of signal leakage between voxels and can be explained by weights correlation; the
region in left sensorimotor cortex cannot be explained by leakage and therefore represents
genuine connectivity. Given the fact that no a-priori fcMRI based information was
used in the MEG source reconstruction, or connectivity analyses, the level of spatial
agreement between these images is compelling.
A high level of spatial agreement between FC images was observed across the subject
group in both the low β and the high β MEG frequency bands. Table 1 shows the MNI
coordinates of the highest peaks in the left sensorimotor area derived from fcMRI
and fcMEG images. Note that since the best spatial agreement between fcMRI and fcMEG
was observed in the β band, results are shown for the 13–20 Hz and the 20–30 Hz bands
only. These results are averaged across subjects and mean ± standard deviation is
reported. The localizer results are also shown for comparison.
The spatial agreement, highlighted in Table 1, is also shown in Fig. 6. Fig. 6A shows
the group average FC map derived from fMRI (thresholded at a correlation coefficient
of 0.2). Figs. 6B–H show CAE analysis (Δ = 0.5 s) applied to MEG data for all frequency
bands: B: 1 Hz–4 Hz; C: 4 Hz–8 Hz; D: 8 Hz–13 Hz; E: 13 Hz–20 Hz; F: 20 Hz–30 Hz;
G: 30 Hz–40 Hz; and H: 40 Hz–70 Hz. In all fcMEG images, the green overlay shows voxels
in the left hemisphere exhibiting statistically significant (p = 0.05) correlation
with the seed in the right hemisphere. Note that significance is assessed across the
subject group employing simulated data and a non-parametric Wilcoxon signed rank test.
For all of the images shown, the cross hairs are at the same location in MNI space
(− 40, − 26, and 52) mm. Functional images are not corrected for multiple comparisons.
Significant left hemisphere connectivity is observed in the θ, α, β and low γ bands,
however the best spatial agreement between fcMRI and fcMEG is seen in the β band,
with the most focal region of high correlation observed in the high β (20–30 Hz) frequency
band. Note that connectivity in the θ band is spatially distinct and does not overlap
with that observed using fcMRI.
Fig. 7 shows results of a quantitative comparison of the similarity between fcMEG
and fcMRI images. Fig. 7A shows the spatial correlation coefficient derived between
the unthresholded fcMEG images and the unthresholded average fcMRI image for each
frequency band studied. The red line shows spatial correlation between CAE images
derived from real MEG data and fcMRI, while the blue line shows spatial correlation
between CAE images derived using simulated data and fcMRI. Here, spatial correlation
has been computed on a subject by subject basis and the result averaged across subjects.
Note that in the low β band, images derived from real data exhibit significantly (p = 0.0312)
higher spatial correlation than those derived using simulated data. In addition, spatial
correlation between fcMEG and fcMRI derived using the 13 Hz–30 Hz band data is significantly
(p < 0.05) higher than equivalent spatial correlations derived using the 1 Hz–4 Hz
and 40 Hz–70 Hz MEG data. Fig. 7B shows the volumar overlap between significant connectivity
in left hemisphere identified using fcMRI and fcMEG with overlap peaking in the low
β band. In general, deriving active cortical volumes based on beamformer based images
is confounded since beamforming is unable to provide an accurate measure of source
extent. Here we use this metric to show that while overlap is observed in the α and
β bands, no overlap is observed in δ, θ or γ. These quantitative results are in agreement
with the images in Fig. 6, and show that the best agreement between FC images derived
using fcMRI and fcMEG occurs when MEG data are frequency filtered into the β band.
This point will be addressed further in the discussion.
Remaining issues
There are 2 key questions that remain to be addressed in regarding the results of
this study. Firstly, how does the frequency content of the Hilbert envelope affect
FC metrics? Secondly, how does interference from other biomagnetic sources, either
in the brain or elsewhere, affect FC metrics? These issues are dealt with in Appendices 1–3;
The key results are given here.
A potential limitation of our simulations lies in the generation of the source timecourse
data. The white noise data employed for timecourse simulation contains no temporal
structure in its envelope. The Hilbert envelopes of the true β band data may therefore
contain frequency components that are not contained in the simulated data. As a result,
the differences between real and simulated data in Fig. 3C could be interpreted as
true bivariate coupling, or alternatively a difference in univariate data statistics.
If the latter was the case, then the results presented in Figs. 5, 6 and 7 would suggest
that those differences (temporal structure vs. no temporal structure) are not a general
cortical phenomenon, but only occur in the motor cortices and occur maximally in the
β band, making this interesting in itself, but not truly reflective of FC. This ambiguity
can however be lifted by a modification to the simulations whereby the frequency content
of the real and simulated Hilbert envelope data is matched. In Appendix 1 we undertake
this measurement; we show that when the frequency content of envelope signals is matched,
FC values are largely unaffected suggesting that the effects observed in Fig. 3 reflect
true bivariate coupling.
Our simulation approach to removing spurious connectivity, while effective and more
conservative than other approaches, does not represent a perfect solution to eliminate
all spurious connectivity. The simulations account for spurious FC resulting from
beamformer weights correlation (i.e. cross talk between spatial filters), field spread
between the two sources of interest or external interference correlated across sensors.
The simulations do not account for interference from other biomagnetic sources; for
example, it is possible that a third source (located in the brain and not accounted
for in simulation) may interfere with both the seed and test sources and thus cause
spurious connectivity. It is also possible that non brain sources (e.g. cardiac/respiratory
sources) may also interfere and lead to spurious FC. We assume that these additional
biomagnetic sources are eliminated by the beamformer. Previous work (Sekihara et al.,
2004, 2006; Brookes et al., 2008a,b, 2009, 2010) has shown that beamforming represents
an effective interference suppression tool and so this assumption is reasonable. In
Appendix 2, we apply a simple modification to our simulations to examine the effect
of a third brain source located midway between the left and right motor cortices;
results show that beamforming does effectively suppress this source and FC results
are unaffected. In Appendix 3 we also show that interference due to the cardiac cycle
is dramatically reduced by the use of a beamformer spatial filter.
Discussion
In this paper, we have described methodologies for measurement of resting state functional
connectivity in the brain using MEG data. We have shown that it is possible to reconstruct
resting state connectivity patterns using MEG that mirror those results obtained using
fcMRI. From a MEG methodological point of view, we have shown that beamforming provides
an excellent means to measure FC in source space. However, care must be taken when
making such measurements since cross talk between voxels can potentially lead to spurious
connectivity and this effect must be taken into account in all studies of this type.
The spatial agreement between FC measured using MEG and fcMRI has shown that β band
effects are implicated in inter-hemispheric motor cortex connectivity. This spatial
agreement 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 an electrodynamic metric confirms
the neural basis of fcMRI measurements. Finally we have demonstrated the application
of multiple MEG FC metrics (CAE, AEC, Coh, and ICoh). These methods should not be
considered as competing techniques but rather complementary methodologies that outline
the potential of MEG as a tool to move beyond hemodynamic responses and gain a better
understanding of the electrical nature of brain FC.
Beamformer methodology and FC measurement
The technique described for MEG based FC measurement is centered on the application
of a beamformer spatial filter. The suitability of beamforming for FC measurement
has been highlighted in studies involving DICS (Gross et al., 2001). A distinct advantage
of beamforming is that it is an adaptive source localization algorithm and signals
that do not originate from the brain (i.e. those signals whose spatial profile at
the sensor level cannot be explained by a dipolar source inside the head) are suppressed.
This gives beamforming an interference rejection property which is not mirrored by
non-adaptive algorithms. Interference rejection has been discussed in previous papers
(e.g. Brookes et al., 2009, 2010). In Appendix 3 of this paper we highlight a single
example showing rejection of cardiac interference. Using channel level analyses, spurious
FC measurement could result directly from cardiac interference since the artifact
affects a large number of sensors. However, correlation between beamformer projected
MEG data and the ECG is small showing that cardiac interference is greatly reduced
and so unlikely to affect left–right sensorimotor cortex connectivity. This example
represents only one of a number of interference fields; including low frequency respiratory
artifacts, the magnetomyogram and environmental noise. All interference fields are
actively suppressed by beamforming and this makes it a more attractive artifact rejection
technique than alternative methods such as ICA which are subjective since noise components
are often manually selected and eliminated.
A major difficulty in measurement of source space FC comes as a result of cross-talk
(or signal leakage) between voxels in source space. The ill posed nature of the inverse
problem means that voxels are not necessarily independent and as a result, signals
from spatially separate brain locations can become correlated even if no genuine connectivity
exists. Here, we highlight this by examining both lead field correlation and beamformer
weights correlation. If the beamformer weights from spatially separate voxels are
correlated, then the reconstructed signals from those voxels will also be correlated
(see Eq. (1)) and this will lead to spurious FC. Fig. 2 shows examples of both lead
field and weights correlation images. Notice the anisotropic nature of the spatial
profile of correlation in both cases; highly correlated regions appear that are distal
to the seed location and could easily be mistaken for spatially separate connected
brain areas. However, the beamformer weights correlation affects significantly less
cortical volume than lead field correlation; this demarcation between lead field and
weights correlation is highlighted in the non-linear relationship between the two
metrics shown in Fig. 2D. The fact that independent weights can result from correlated
lead fields gives beamforming its distinct advantage when compared to non-adaptive
algorithms.
Weights correlation can be minimized by judicious paradigm design. Beamformer spatial
resolution inhomogeneous, with highest spatial resolution achieved around areas of
high signal (Barnes and Hillebrand, 2003). Here weights were constructed using covariance
based on 300 s of resting state data and contiguous data recorded during the finger
movement paradigm. The increased amount of data, coupled with the high power changes
induced in sensorimotor cortices during the finger movement allowed optimal spatial
resolution in brain regions identified with the motor network. However, it should
be pointed out that even with optimized paradigm design, weights from a significant
volume of brain tissue remained correlated with the seed and such effects must be
taken into account in future studies (systematic evaluation of nulling beamformer
approaches (Dalal et al., 2006) may be of some value here). It also should be appreciated
that in constructing weights based on the entire dataset we make the critical assumption
that sources in regions of interest are stationary, meaning that source orientation
does not change between the resting state and the task. Finally, we should note that
while weights correlation has been used here as an informative measure of spatial
specificity, this is not the only means to make such measurements. The resolution
kernel (see Sekihara et al., 2005 for a complete description) is a means to assess
the contribution of distant sources to the estimated activity at a predetermined location.
This makes it potentially useful for investigation of signal leakage and hence for
future studies addressing new methodology for FC measurement in MEG.
While weights correlation can test the independence of spatial filters, it cannot
be used to test directly the validity of FC measurement. It is important to note that
weights correlation is certain to result in high FC values, however low correlation
between weights does not guarantee complete elimination of spurious FC. With this
in mind, in order to test the validity of FC measurement in this paper we employed
simulations. In our approach, dipolar sources were simulated at the seed and test
locations. These simulated sources had equivalent orientation and amplitude to those
measured using the real data; however, their timecourses were random and uncorrelated.
Simulated MEG data from these two sources were added to genuine noise data; the resulting
sum was projected through the same spatial filters as used to project the real data,
yielding beamformer reconstructions of the simulated sources. Connectivity between
the seed and test locations was measured using our simulated data. High levels of
FC measured using simulated data would be entirely artifactual and a result of either:
1) signal leakage due to correlated beamformer weights; 2) spatial spread of magnetic
field induced by current at the two source locations (i.e. the magnetic field from
the first source overlapping with sensors used to reconstruct the second source, or
vice versa); or 3) correlated MEG noise at the sensor level. All of these effects
could result in spurious FC measurement in real MEG data.
The accuracy of our simulations is shown to some degree by Fig. A7; notice the good
agreement between the real and simulated data in frequency bands, metrics and at time
scales (Δ) not exhibiting FC. However, there are potential limitations to our simulation
approach. Firstly, simulating data is computationally demanding and while it proved
possible for 300 s resting state studies, the approach may be impractical for longer
studies. Secondly, since no subject was present during the MEG noise recording, our
simulations account for environmental noise, but not for interference from non-neuronal
physiology or other brain sources; such effects must therefore be assumed to be attenuated
by beamforming (see also Appendix 2). Thirdly, simulated timecourse data were based
on white noise meaning that the frequency content of the simulated Hilbert envelope
data may differ from that of the real data (see also Appendix 1). There are alternative
approaches to testing statistical significance and these usually involve construction
of surrogate data directly from the real data. For example, an attractive technique
involves randomizing the phase of MEG data acquired at each sensor. This results in
a set of surrogate MEG signals with the same power spectrum as the real signals, but
randomized phase means that all genuine FC will be destroyed. Projecting these surrogate
data through the beamformer spatial filters will result in a methodology for measurement
of spurious connectivity. However, this technique, and those that involve switching
segments of data in time, necessarily assumes that MEG noise is uncorrelated across
sensors. Further the effects of field spread are not taken into account. Therefore,
while this approach is potentially useful, it should be investigated before being
used to assess the significance of resting state FC and it is likely that our simulation
approach is more conservative. For studies investigating a change in connectivity
between two or more conditions, computing the difference of connectivity values between
conditions may negate the need for simulation. However, FC changes can also be affected
by SNR (Schoffelen and Gross, 2009) and care must be taken in using such an approach.
Investigating electrodynamic connectivity
The utility of MEG as a means to measure FC lies in its ability to assess the nature
of electrodynamic connectivity. In this work we considered 4 different metrics for
FC measurements, two based on envelope correlation, and two based on coherence. Our
primary aim was to assess whether electrodynamic FC underlies fcMRI based metrics;
envelope correlation is conceptually more similar to fcMRI than coherence based methodologies
and results showed that correlation between left and right sensorimotor cortices peaks
in the β frequency band (although significant correlation was also observed at higher
frequencies (up to 40 Hz)). Interestingly, the time scale (Δ) on which connectivity
is measured appears to be of some importance. Results in Fig. 3 show that AEC measured
in 0.5 s time windows exhibits no significant correlation; significance increases
with Δ and is maximum for a 10 s time window. Conversely, when computing CAE, segmenting
envelopes into 10 s time windows resulted in significant inter-hemispheric correlation
in the low β band only. Significance was increased as Δ was reduced and was maximal
for Δ = 0.5 s. This provides information on the time scale of the correlation observed
and these results are in agreement with those previously published by Liu et al. (2010)
who, using channel space measurements, show that coherence between Hilbert envelope
signals from opposite hemispheres peaks in the 0–0.1 Hz range. These analyses implicate
a similar time scale to that of the fMRI BOLD response and this warrants further investigation.
We should however state that as Δ is reduced, the reliability of correlation (and
coherence) measurements is also reduced and care must be taken in interpretation of
these results (see below). In general the CAE approach elicited higher correlation
metrics than AEC; this is unsurprising since CAE effectively amounts to a low pass
filter on the Hilbert envelope data, this elevates the signal to noise ratio and thus
increase correlation coefficients measured.
Our inter-hemispheric measures of coherence and imaginary coherence between beamformer
projected signals in the left and right sensorimotor areas yielded no values above
our chosen 0.05 significance level. This could be to be due to the nature of coherence
and the way in which it was measured. It is unlikely that electrical signals from
two brain areas will remain coherent for long periods of time. Brain regions are more
likely to exhibit transient coherence (Varela et al., 2001; Hadjipapas et al., 2004).
In this work, we compute coherence averaged across a 300 s time window. It is therefore
unsurprising that resulting values are small. Conversely our envelope correlation
based approaches yielded much higher connectivity values (> 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.