Ongoing physiological processes in the cerebral cortex
David A. Leopolda,b,⁎, Alexander Maiera,c
aSection on Cognitive Neurophysiology and Imaging, Laboratory of Neuropsychology, National Institute of Mental Health, National Institutes of Health, Department of Health and Human
Services, 49 Convent Dr. 1E-21, MSC 4400, Bethesda, MD 20892, USA
bNeurophysiology Imaging Facility, National Institute of Mental Health, National Institute of Neurological Disorders and Stroke and National Eye Institute, National Institutes of Health,
Department of Health and Human Services, 49 Convent Dr. 1E-21, MSC 4400, Bethesda, MD 20892, USA
cDepartment of Psychology, College of Arts and Science, Vanderbilt University, 111 21st Avenue South, 008 Wilson Hall, Nashville, TN 37240, USA
a b s t r a c t a r t i c l ei n f o
Received 17 June 2011
Revised 2 October 2011
Accepted 18 October 2011
Available online 25 October 2011
Functional magnetic resonance imaging (fMRI) has revealed that the human brain undergoes prominent, regional
hemodynamic fluctuations when a subject is at rest. These ongoing fluctuations exhibitdistinct patterns of spatio-
temporal synchronization that have been dubbed “resting state functional connectivity”, and which currently
serve as a principal tool to investigate neural networks in the normal and pathological human brain. Despite the
wide application of this approach in human neuroscience, the neural mechanisms that give rise to spontaneous
fMRI correlations are largely unknown. Here we review results of recent electrophysiological studies in the cere-
bral cortex of humans and nonhuman primates that link neural activity to ongoing fMRI fluctuations. We begin
by describing results obtained with simultaneous fMRI and electrophysiological measurements that allow for
that investigate the correlational structure of spontaneous neural signals, including the spatial variation of signal
coherence over the cortical surface,across cortical laminae,and between the two hemispheres. In the final section
inherent limitations of the fMRI correlation approach.
Published by Elsevier Inc.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neural correlates of resting-state fMRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Types of slow electrophysiological signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simultaneous fMRI and electrophysiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spatial characteristics of ongoing cortical activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surface correlation patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laminar organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The “global” resting state signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functional connectivity: speculations and caveats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
What neural processes give rise to functional connectivity? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The “inverse problem” of fMRI and its correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Drilling down while building up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
In1936 theNewYork Times rananarticleentitled “Inside telephones
in the brain”. The title referred to the brain's intrinsic connectivity, and
specifically to the experiments of J. G. Dusser de Barenne, the father of
chemical neuronography. Barenne and colleagues for the first time
NeuroImage 62 (2012) 2190–2200
⁎ Corresponding author at: Section on Cognitive Neurophysiology and Imaging,
Laboratory of Neuropsychology, National Institute of Mental Health, National Institutes
of Health, Department of Health and Human Services, 49 Convent Dr. 1E-21, MSC 4400,
Bethesda, MD 20892, USA.
E-mail address: firstname.lastname@example.org (D.A. Leopold).
1053-8119/$ – see front matter. Published by Elsevier Inc.
Contents lists available at SciVerse ScienceDirect
journal homepage: www.elsevier.com/locate/ynimg
used neural activity to infer large-scale connections between brain
areas. They placed a minute amount of the excitatory agent strychnine
on the cortex of experimental animals and then measured the resulting
spatial pattern of electrical responses over the cortical surface. This ap-
proach revealed, in their words, “the directed functional (and anatomi-
cal) relations between the various cortical areas” (Dusser de Barenne
and McCulloch, 1938; Hogenhuis, 2002). A decade and a half later Pri-
bram and MacClean used the same method to study the organization
of the limbic cortex (MacLean and Pribram, 1953; Pribram and
MacLean, 1953). They reported five distinct zones of reciprocal excita-
tion, which we would now call networks, that appeared strikingly sim-
ilar in cats and monkeys (Fig. 1). Prior to these experiments, the large-
scale organization of the mammalian brain had been a topic reserved
for anatomists working with fixed tissue or for neuropsychologists ap-
plying surgical ablation. Now for the first time neurophysiologists
were able to weigh in on this issue by charting “functional networks”
in the brain of live animals. Nonetheless, the application of chemical
neuronography was short-lived, perhaps due to technical hurdles or
perhaps because it was ahead of its time. Shortly after the experiments
of Pribram and MacLean, most electrophysiologists abandoned ques-
and describing the response patterns of isolated cells.
Only in the last decade has neural activity again taken center stage
in the study of the brain's large-scale architecture. Functional MRI is
now routinely used to identify and characterize networks in the
human brain. Unlike neuronography, which involves excitation of
brain tissue, the modern field of functional network mapping in the
human brain is noninvasive, and relies exclusively on the brain's en-
dogenous (spontaneous, or “ongoing”) hemodynamic fluctuations.
Based on first principles, there is no reason to suspect that these sig-
nals should yield much useful information. Until recently, most neu-
rophysiological studies have considered spontaneous neural activity
to be an irrelevant or even nuisance signal, representing “noise” in
the system that might interfere with sensory encoding or motor re-
sponses. According to this theoretical framework, ongoing fMRI fluc-
tuations might be, at best, a sluggish and imprecise approximation of
this undesirable neural activity. However, a wide range of studies
have now demonstrated that spontaneously occurring fMRI fluctua-
tions are not random, but instead have a high degree of spatiotempo-
ral organization. In fact, patterns of temporal correlation measured
between distant voxels, dubbed “functional connectivity”, exhibit
consistent spatial patterns that find striking agreement across exper-
iment, laboratories, and subject groups. As a result, functional con-
nectivity, measured in subjects at rest, has become the principal
means to investigate the integrity of large-scale functional networks
in the human brain. Thus while structured fMRI fluctuations could
not have been anticipated, and are in many respects still mysterious,
they have come to provide a new window on brain neurophysiology
that simply cannot be ignored.
The modern field of functional connectivity began in 1995. In that
year, Biswal et al. (1995) discovered that slow fMRI fluctuations in the
sensorimotor strip and several other regions of a resting subject's
the pattern of functional activation found during a more conventional
behavioral task. The authors suggested that the spontaneously occur-
ring correlations reflected the inherent functional organization of the
neural network itself, at the same time briefly reporting similar obser-
vations in auditory and visual networks. The immediate implication of
this findingwasthat thebasic properties of large-scale neuralnetworks
taneous hemodynamic signals in the absence of a task.
Biswal's seminal report launched a field of study which, sixteen
years later, has produced thousands of publications, and appears to
be growing at an exponential rate (Friston, 2011). Analysis of ongoing
Fig. 1. Chemical neuronography technique for evaluating widespread connectivity in the limbic system. (a) Strychninization of the posterior cingulate (black rectangle) in a ma-
caque led to strong (+) and weak (±) responses on a subset of electrodes placed on the cortical surface whereas others exhibited no (o) responses. (b) Circumscribed zones of
interconnectivity within the limbic cortex of the macaque and the cat brain. Note the five similar limbic networks identified in the two species.
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
fMRI signals in resting subjects consistently differentiates several dis-
tinct cortical and subcortical functional “networks”, or regions exhi-
biting high temporal covariation (Tomasi and Volkow, 2011). Such
networks are often compared across individuals (Biswal et al.,
2010), tracked through the course of development (Power et al.,
2010), and evaluated in patients with neuropsychiatric and neurode-
generative disease (Andrews-Hanna et al., 2007; Greicius, 2008).
precise, correspondence with structurally derived networks based on
fiber pathways revealed by diffusion tensor imaging (DTI) (Honey
et al., 2009). At present, resting state functional connectivity figures
prominently into the neuroscience community's ambitious effort to as-
semble a comprehensive network map of the human brain, or “connec-
tome” (Sporns, 2011).
In this article, we review electrophysiological characteristics of the
brain's spontaneous activity, focusing on features that are most perti-
nent to resting state functional connectivity measured with fMRI. We
focus on the cerebral cortex because both its resting state fMRI signals
and its spontaneous neural activity have been studied in greatest de-
tail. In the first section, we describe neural correlates of spontaneous
fMRI that have been established during simultaneous electrophysio-
logical and fMRI recordings. In the second section, we describe the
spatial organization of the candidate electrophysiological signals
gauged by the pattern of interelectrode correlation over the cortical
surface and across cortical laminae. In the third section, we speculate
on potential generative mechanisms for slow electrophysiological
fluctuations that might underlie hemodynamic functional connectiv-
ity, and we also offer important caveats concerning the inherent lim-
itations of inferring neural activity based on fMRI correlation. We will
not discuss methodological issues related to functional connectivity
analysis, nor survey specific functional networks, as these topics have
been reviewed elsewhere (e.g. Bullmore and Sporns, 2009; Cole et al.,
2010; Deco and Corbetta, 2011; Power et al., 2010). We will also leave
aside semantic issues, such as the inherent imprecision of the terms
“functional connectivity”, “network” and “resting state”, and mention
only that the growing terminology in this field needs to be matched
in the long term.
Neural correlates of resting-state fMRI
The simultaneous acquisition of electrophysiological and hemody-
namic signals provides the most direct assessment of neural process-
es that underlie resting state fMRI. This approach has been conducted
in both humans and laboratory animals. In humans, the noninvasive
scalp electroencephalogram (EEG) exhibits significant temporal cor-
relation with resting fMRI fluctuations (Laufs et al., 2003; Picchioni
et al., 2011; Ritter and Villringer, 2006). Likewise, in animals, direct
measures of intracranial neural activity covaries with hemodynamic
signals (Huttunen et al., 2008; Leopold et al., 2003; Lu et al., 2007;
Pan et al., 2011; Schölvinck et al., 2010; Shmuel and Leopold, 2008).
Here we focus on experiments from the nonhuman primate that es-
tablish specific neural correlates with spontaneous cortical fMRI sig-
nals. Because resting state functional connectivity draws upon very
slow fMRI fluctuations, we begin with a brief digression in order to
describe the derivation of electrophysiological signals whose time
course can evolve over similar time scales.
Types of slow electrophysiological signals
Electrical signals in the brain vary over behaviorally relevant time-
scales ranging from milliseconds to minutes. Neural activity involves
the dynamic redistribution of electrically charged ions across cellular
membranes, which can be measured with an electrode as time-
varying potentials. The fastest changing electric potentials in the
brain are millisecond-duration impulses, or spikes. Spikes represent
the direct, digital communication between neurons, often transmit-
ting information between brain areas over long axonal projections.
Slower “field” potentials arise from a superposition of heterogeneous
neural processes and are most closely associated with synaptic activity
(Buchwald etal.,1966).These fieldpotentials includethe EEG,the elec-
trocorticogram (ECoG) and the local field potential (LFP), measured
from thescalp,pialsurface,and neuropil, respectively (Fig. 2a). Because
rents, field potentials are strongly influenced by both the geometric ar-
rangement and temporal synchronization of the cellular structures that
give rise to them.
In considering potential correlates of resting state fMRI activity, it
is necessary to identify neural processes that vary over the same time
scales as empirically observed slow hemodynamic fluctuations. Some
field potential components, such as the so-called slow cortical poten-
tial, evolve over many seconds or longer (Birbaumer et al., 1990), and
might thus serve as a direct correlate for spontaneous fMRI fluctua-
tions (He and Raichle, 2009). This hypothesis has not been directly
tested. Other field potential components, such as the gamma-range
(50–100 Hz) activity are too fast to compare directly to the fMRI sig-
nal but exhibit slow changes in their power. Thus a particularly im-
portant family of electrophysiological signals is derived from
computing the band-limited power (BLP), which allows for the eval-
uation of slow changes produced by fast components of the LFP. This
somewhat counterintuitive notion is explained in Fig. 2b. Briefly, the
raw LFP is first filtered into a particular frequency band in order to iso-
late a physiologically meaningful signal component. The resulting
band-limited LFP is then rectified, and often then smoothed, in order
to create a time-varying estimate of the signal power within that fre-
quency range, or BLP. Rectification is the important step for under-
standing the apparent contradiction of slow variation in a fast
signal: because rectification is a nonlinear operation, the frequency
spectrum of the rectified BLP differs entirely from that of the raw LFP
signal. In fact, the BLP signal can change arbitrarily slowly. Based on a
single raw LFP signal, the BLP can be computed for multiple passbands,
resulting in a family of slowly varying frequency band-specific signals
derived from a single measurement of the time-varying field potential
that bear different relationships to the underlying physiologically pro-
cesses and to the spontaneous fMRI signal.
tion” in the literature describing field potentials and fMRI signals, most
spontaneous neural signals are aperiodic rather than oscillatory. In the
frequency domain, that means that the signals are composed of a
broad range of frequencies rather than a narrow band of energy around
some obvious exceptions, such as the prominent alpha rhythm mea-
brain signals often obey a 1/fβspectral distribution, where β is the expo-
nent of a power law. This relationship, which presents as a linear func-
tion on a double logarithmic plot of power or magnitude versus
frequency, indicates that lower frequency components have proportion-
ally larger amplitudes than higher frequency components, but that no
particular frequency dominates the spectrum. The 1/fβspectral distribu-
tion characterizes spontaneous signals measured with fMRI, LFP, ECoG,
EEG, and magnetoencephalographic (MEG) recordings as well as the
BLP derived from these raw signals (de Pasquale et al., 2010; Dehghani
et al., 2010; He et al., 2010; Leopold and Logothetis, 2003; Leopold et
1995), suggesting that slow, intrinsic activity variation may impact the
brain's interaction with the environment.
Simultaneous fMRI and electrophysiology
Combined fMRI and electrophysiological measurements have
revealed multiple neural correlates of resting state hemodynamic
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
responses. In a pair of recent studies combining functional echoplanar
trophysiological signals showingthe strongestand mostconsistentcor-
relations with spontaneous fMRI fluctuations were neural spiking
activity and gamma-range BLP. In one study, Shmuel and Leopold
(2008) acutely recorded from area V1 in monkeys that were scanned
under general anesthesia. They found that the blood oxygen level-
dependent (BOLD) signal in V1 was coupled to changes in both spiking
rate and gamma-range BLP. Schölvinck et al. (2010) subsequently
recorded from multiple cortical areas in the awake monkey during
“resting-state” MRI scans using chronically implanted electrode arrays.
Instead of the BOLD signal, they measured changes in regional cerebral
blood volume (CBV) following the intravascular injection of monocrys-
talline iron oxide nanoparticles (MION). Like Shmuel and Leopold, they
found that the spontaneous fMRI signal closely followed fluctuations in
the gamma-range BLP. They also reported correlation with the BLP de-
rived from other,lowerfrequencyLFPcomponents,thoughthesecorre-
lations were less consistent than those derived from the gamma-range.
In that study, spiking activity was not measured.
In both studies, cross-correlation analysis between neural and
fMRI fluctuations near the recording electrode produced prominent
peaks, indicating that the spontaneous fluctuation of the neural and
fMRI signals were tightly coupled. The correlation peaks were not
centered at time-zero, but were instead offset by a few seconds,
with fMRI signal lagging the spiking and gamma-range BLP. Though
this measure only indicates a correlation rather than a causal relation-
ship, such lags would be expected if the hemodynamic fluctuations
were a direct consequence of the neural activity. By contrast, such a
pattern of correlation between the two signals would not be expected
to arise from chance fluctuations of either signal alone or by artifacts
that simultaneously affect both signals. It also is important to point
out that the highest correlation coefficients observed were approxi-
mately 0.5, which corresponds to 25% of the total variance. Thus
while a significant fraction of the resting state fMRI signal variance
can be attributed to a single measure of spontaneous neural activity,
the majority of its variance remains to be explained.
To summarize recent findings on the neural correlates of sponta-
neous fMRI fluctuations, simultaneous electrophysiological and fMRI
measurements in primates point to spiking and gamma-range BLP
signals as being the most reliable correlates of resting state fMRI ac-
tivity, though other potential candidates, such as slow cortical poten-
tials, have not yet been explored.
Spatial characteristics of ongoing cortical activity
signals. As with fMRI, this aspect of spontaneous neural activity relies on
assessing the temporal correlation between sites. An obvious question is
whether the spatial pattern of neural correlations bears resemblance to,
and perhaps underlies, the pattern of fMRI correlations that constitutes
Rectification (e.g absolute value or square) and smoothing
Field Potentials (FP)
Local field potential (LFP)
Band-pass filter (e.g. gamma-range)
Fig. 2. Derivation of band-limited power (BLP) signal from local field potential (LFP) trace. (a) Using different methodologies, Field Potentials (FP) can be recorded from inside the
brain, from within the subcranial space or on the intact scalp. (b) A raw FP voltage trace is filtered into a given frequency range using a band-pass filter, typically within a narrow
frequency range less than 100 Hz (e.g. gamma range LFP, 50–100 Hz, or multiunit, 500–1500 Hz). The resulting band-limited signal is then rectified by one of a number of methods
(e.g. estimating the signal envelope or squaring the band limited signal) and then temporally smoothed. The resulting BLP signal is an estimate of the time-varying signal magnitude
or signal power. Owing to the non-linear nature of the rectification step, fluctuations can proceed over time scales that are much slower than the pass band used in the filtering step.
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
functional connectivity. While, the answer to this question is still one for
future research, a few studies have used cortical recordings from elec-
trode arrays to assess the spatial organization of spontaneous electro-
physiological signals over both small and large scales. Here we
separately review the surface, laminar, and global features such signals
in the cerebral cortex.
Surface correlation patterns
Optical imaging techniques provided the first glimpses of the spa-
tial organization of spontaneous neural activity over the cortical sur-
face. In 1995, the same year that marked the beginnings of fMRI
resting state functional connectivity, Arieli et al. (1995) were able to
visualize ongoing signals in the primary visual cortex of anesthetized
cats. They artificially incorporated a light-absorbing dye molecule
into the plasma membrane of cortical neurons whose fluorescence
varied linearly with the electric membrane potential. While imaging
voltage fluctuations, they also recorded spiking responses from single
cells from within the imaged field using a microelectrode. When they
compared the voltage changes at each spatial location to the spiking
of given cells, they found that action potentials were temporally
locked to the membrane voltage fluctuations over a spatially distinct
portion of the imaged field (Fig. 3). In doing so, they created a func-
tional map of membrane voltage fluctuations based on the spontane-
ous activity of single neurons. They found that two different neurons
measured from the same electrode were often coupled with voltage
changes in different spatial regions, suggesting the engagement of
the neurons with different components of the local functional archi-
tecture (see also Tsodyks et al., 1999). Finally, they demonstrated
that the spatial pattern of ongoing cortical activity just prior to visual
activation could reliably predict a significant proportion of the natural
variability in the stimulus-evoked responses (Arieli et al., 1996), a
finding that would later find parallels in human fMRI (Fox et al.,
2006). These seminal observations, which have yet to be demonstrated
in the awake preparation or in other species, opened the door to the
mapping of functional cortical networks using ongoing brain activity.
Subsequent neurophysiological studies examined the correlation
of field potentials between pairs of electrodes and found that the
level of LFP coupling falls off monotonically as a function of distance
along the cortical surface (Leopold et al., 2003). In one study, this fall-
off was so predictable that it was possible to determine the precise
position of a sulcus based on the sharply diminished correlation be-
tween electrodes positioned on opposite sides of the sulcal opening
(Leopold and Logothetis, 2003). TheLFPcorrelationfalloffwithincreas-
ing cortical distance varies as a function of frequency, as evaluated by
magnitude-squared coherence. Whereas gamma-range coupling falls
off within a few millimeters, lower frequency components fall off more
gradually (Leopold et al., 2003). Similar analysis was applied to the spa-
tial correlation of slow BLP fluctuations. Compared to the LFP coherence,
can be seen in Fig. 4. The discrepancy is largest between the gamma-
range LFP (LFPhigh) and the gamma-range BLP (BLPhigh), with the former
falling off abruptly and the latter remaining coherent over distances ex-
ceeding one centimeter (Leopold et al., 2003).
Measuring electrophysiological coherence over yet larger scales
with microelectrode arrays, such as those corresponding to the
same spatial scales measured with fMRI, is possible but technically
challenging since this approach requires the exposure of large areas
of the brain. Noninvasive techniques such as EEG and MEG provide
a wider coverage but face severe challenges associated with the so-
called inverse problem of source localization. The inverse problem
ambiguous combination of current sources originating from multiple
locations. This problem poses particular difficulties for methods based
on the correlation of independent neural signal sources, though there
has recently been progress in this field (Brookes et al., 2011; Ghuman
et al., 2011).
Subdural ECoG arrays implanted in human epilepsy patients pro-
vide an electrophysiological measure similar to the LFP and have
allowed for the evaluation of neural correlations over arrays spanning
several centimeters. In one study, He et al. (2008) investigated spon-
taneous activity within a large swath of the frontoparietal cortex.
Electrodes were first conceptually divided into distinct sensorimotor
and nonsensorimotor (control) regions based on previous clinical
mapping and resting state fMRI correlation patterns. High correlation
was found for ongoing activity between electrodes within the senso-
rimotor region, but not between the sensorimotor and control re-
gions. Furthermore, this region-specific correlation was only present
for the lowest frequency range of the raw voltage signal (b4 Hz) but
not the gamma-range BLP, suggesting that the slowest LFP compo-
nents most directly underlie the specificity of fMRI functional connec-
tivity (He et al., 2008). In a different study, Nir et al. (2008) used a
stimulus-evoked STAspontaneous STA
Fig. 3. Spatiotemporal coherence pattern between single neurons and membrane potentials measured with voltage sensitive dye in the visual cortex of an anesthetized cat.
(a) Spike triggered average (STA) evoked by a visual stimulus. The STA was evaluated between a cell isolated in area 17 (E = electrode) and the membrane potential over several
square millimeters of cortex. The chamber spanned a portion of area 17 and area 18 (see inset). (b) STA evaluated during spontaneous ongoing activity, triggered to the same spike
as in (a). This STA showed a pattern of covariation that was restricted to a particular spatial zone within the field of view. (c) Two single neurons measured from the same electrode
gave very different spatial patterns in their spike-triggered average, suggesting that they were engaged in different functional networks.
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
similar preparation but reached a somewhat different conclusion re-
garding the frequency range carrying spatially specific information.
They found that spatial specificity of interelectrode correlations was
highest in the gamma-range BLP of the ECoG signal. They evaluated
the correlation of spontaneous signals measured simultaneously
from the two hemispheres and found that only the gamma-range
BLP showed strong spatial specificity between corresponding homo-
topic regions of the cortex in the two hemispheres. While lower fre-
quency signals showed coupling
correlations were unspecific and did not exhibit peaks in symmetrical
regions of the two hemispheres.
The finding of homotopic specificity in spontaneous neural activi-
ty patterns may be particularly important, since this is a feature com-
mon to nearly all resting state fMRI studies (e.g. Smith et al., 2009).
The axonal fibers passing through the corpus callosum are likely to
support interhemispheric neural correlation to some extent, as sup-
ported by decreased symmetry in a patient following a callosotomy
(Johnston et al., 2008). However, it is also clear that some parts of
the brain showing strong functional connectivity across the two
hemispheres are not directly connected by callosal fibers, including
both cortical (Vincent et al., 2007) and subcortical (Di Martino et al.,
2008) structures. Moreover, a recent study comparing spontaneous ac-
monkeys (Matsui et al., 2011) found that interhemispheric correlation
was not well predicted by the pattern of microstimulation-induced fMRI
ly observed in studies of fMRI functional connectivity remains somewhat
of a mystery.
The cerebral cortex is a laminar structure whose superficial
(layers 1–3), middle (layer 4 with its various sublayers), and deep
layers (5 and 6) are distinct in their anatomical connections and
functional responses. To what extent does ongoing neural activity
vary as a function of cortical layer? In a third important study from
1995, Snodderly and Gur (1995) examined this question by measuring
the ongoing spiking rate of neurons in different layers of V1 in the
awake macaque. They found a striking difference in the spontaneous
neural spiking rates measured from different layers of animals sitting
in complete darkness. Neurons in layers receiving direct input from the
principal layers of the lateral geniculate nucleus (cortical layers 4C, 6,
and 4A) showed high spontaneous firing. By contrast, neurons in other
layers (cortical layers 2/3, 4B and 5) were nearly silent. While that
study did not measure field potentials, a recent study found a similar
laminar distribution of gamma-range BLP (Maier et al., 2010). Impor-
tantly, most efferent V1 corticocortical projections originate in the silent
layers, with layers 2/3 giving rise to the majority of feedforward connec-
neurons is puzzling, since they would be the best candidates to support
rebral hemispheres during the resting state.
In a rather different exploration of spontaneous activity across
cortical laminae, Maier et al. (2010) simultaneously measured field
potentials within different layers using a multicontact microelec-
trode. Parallel recordings allowed for the evaluation of LFP coher-
ence and BLP coherence between different layers. Analysis of
pairwise LFP coherence between electrodes revealed two prominent
laminar zones, one superficial (layers 1–4) and one deep (layers 5
and 6). Coherence measured between electrodes situated in the
same zone showed high coherence, whereas the coherence mea-
sured between electrodes situated on opposite sides of the boundary
between the zones (between cortical layers 4C and 5) fell to near
zero. Maier et al. speculated that this compartmentalization might
reflect a differential engagement of superficial layers with other cor-
tical areas and deeper layers with subcortical areas, which is roughly
suggested by the anatomical projection pattern. Importantly, a sim-
ilar segregation was present in the slow fluctuation of gamma-range
BLP signals, which, as described above, is a strong correlate of
frequency (Hz) interelectrode distance E1 to E2 (mm)
Fig. 4. SpectralandspatialcharacteristicsoflowfrequencyLFPandBLPcoherence inmonkeyvisualcortexduringrest.(a)Themeanpair-wise LFPcoherence amonganarrayofelectrodesis
shown as a function of frequency (black). In addition, coherence of the BLP is shown for two frequency ranges (blue and red traces indicating low and high frequencies, or 5–8 Hz and
50–100 Hz, respectively). Note that the high frequency BLP exhibited a strong coherence, even though the underlying fast voltage fluctuations did not. (b) Coherence drop-off as a function
of electrode separation. The magnitude-squared coherence of the LFP (closed circles, solid lines) and BLP (open circles, dashed lines) are shown for the frequency ranges highlighted in (a),
with thesame color assignments. The coherence of the BLP for thetwo frequencybandsis computed over the frequency range 0.05–0.1 Hz, correspondingto thegreen box in (a). Note that
the high frequency BLP falls off very gradually, remaining high at cortical distances exceeding 10 mm. This is in contrast to the coherence of the low frequency BLP andthe coherence of the
LFP in either frequency range.
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
spontaneous fMRI fluctuations. Taken together, these results suggest
that the upper and lower layers contribute differently to measures of
resting state fMRI functional connectivity. A recent finding demon-
strating layer-specific fMRI coupling between anatomically con-
nected cortical areas in humans supports this possibility (Polimeni
et al., 2011).
The “global” resting state signal
Above we described neural correlates of fMRI fluctuations based
on simultaneous neural measurements within a delimited cortical re-
gion or between interhemispheric homologues. Functional MRI
correlations with neural activity have also been observed far away
from the recording site. Specifically, in a study by Schölvinck et al.
(2010) gamma-range BLP fluctuations from recording sites in the oc-
cipital, parietal, and frontal cortex of resting monkeys were all corre-
lated with hemodynamic fluctuations over large regions of the
cortical mantle (see Fig. 5a). Coupling to the locally measured neural
signal was prominent throughout nearly the entire cortex, but was
not observed in either subcortical structures or the white matter.
While there are various interpretations of this result, one obvious
one is that global correlations are driven by local neurovascular cou-
pling to widespread neural synchrony. Preliminary support for this
interpretation comes from paired neural recordings in resting
pariental electrode (L)
frontal electrode (R)
time lag (S)
neuro / neuro
neuro / MRI
monk1 V1 electrode
monk2 V1 electrode
monk1 frontal electrode
monk1 parietal electrode
Avg (24 sessions)
time lag (s)
Fig. 5. Widespread correlation of spontaneous activity in the monkey cerebral cortex. (a) Correlation between gamma range LFP power fluctuations measured at an electrode site in
the macaque frontal cortex and fMRI signals throughout the brain. Strong correlations were observed in sensory, motor, and associative cortex, but were absent in the white matter
and in large subcortical structures such as the thalamus, striatum, and cerebellum (not depicted here). Note that in this example the weaker correlation strength in the anterior
cortex is a consequence of a lower signal-to-noise ratio in the MR images resulting from the particular coil used in the fMRI acquisition. (b) Two example sessions demonstrating
the correlated spontaneous fluctuations measured in distant cortical electrodes in the macaque brain. Thedatawere collectedduringwhole-brainfMRIdataacquisition.Fluctuationsin
the gamma range LFP power over a 10-minute period are shown from a right frontal electrode andleft parietal electrode for each session.Power was estimated each 2.6 s, correspondingto
fMRI activity took the form of punctate events rather than slow oscillations.
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
animals in our laboratory. Even electrodes in non-homotopic regions
of opposite hemispheres display a strong correlation in the gamma-
range BLP, with a prominent zero-lag peak (Fig. 5b). This observation
has important implications for the interpretation of resting state func-
tional connectivity. In particular, the global fMRI signal correlation
reported by Schölvinck et al. is commonly observed, yet frequently dis-
carded in functional connectivity analysis, a practice that can introduce
artifacts (Fox etal.,2009;Murphyet al.,2009).Thefactthatthisregion-
ally unspecific component of resting state functional connectivity re-
flects genuine neural activity raises further questions about this
practice (Schölvinck et al., 2010).
To summarize this section on the spatial nature of spontaneous
neural activity, correlation and coherence measurements in humans
and animals demonstrate a high degree of spatial organization over
the cortical surface and across cortical laminae. In addition, a signifi-
cant component of the global fMRI signal appears to be driven by neu-
ral activity fluctuations that are themselves coordinated over large
regions of the cerebral cortex.
Functional connectivity: speculations and caveats
It is by now well established that spontaneous fMRI activity gives
rise to consistent correlational patterns, which are used to study the
large-scale organization of the human brain. As reviewed above,
while the neural underpinnings of specific "networks" are still out
of reach, it is clear that spontaneous neural activity is organized at
multiple spatial scales and is often coupled with resting fMRI signals.
In this section we step back from the data to consider fundamental
questions about spontaneous brain activity, including its possible
physiological origins, and we also discuss fundamental limits on the
power of fMRI correlational methods.
What neural processes give rise to functional connectivity?
Questions surrounding the interpretation of functional connectiv-
ity usually focus on whether or not it is an accurate reflection of direct
anatomical connections (see, for example, Fox and Raichle, 2007).
Based both on first principles and on its correspondence with ana-
tomical imaging techniques such as diffusion tensor imaging (DTI)
and direct tract tracing, it is reasonable to assume that functional cor-
relations are shaped by constraints imposed by directanatomicalcon-
nections (Bullmore and Sporns, 2009; Heinzle et al., 2011; Krienen
and Buckner, 2009; Vincent et al., 2007). At the same time, spontane-
ous activity correlation is frequently observed in areas without direct
ical connectivity from mere activity correlation (Di Martino et al.,
2008; Krienen and Buckner, 2009; Margulies et al., 2009; Vincent
et al., 2007; Zhang et al., 2008) (for a review, see Sporns, 2011). In
such discrepancies are even more apparent than in humans (Adachi
et al., in press). Activity correlations that arise in the absence of direct
anatomical connections are sometimes euphemistically described as
Whence come the activity fluctuations? It must be stated that one
can easily imagine a system of anatomical interconnections that is not
marked by slow, coherent neural or hemodynamic activity changes. In
the absence of a solid theoretical framework within which to under-
stand observed spontaneous activity patterns, the field of resting state
functional connectivity retains its germinal quality as a thoroughly em-
pirical science (Biswal et al., 2010). In the long run, determining the or-
igin and significance of spontaneous neural and hemodynamic signals
tion than is the purely empirical characterization of hemodynamic cor-
Early studies were more probing with respect to the phys-
iological origin of resting fMRI correlations, with some investigators
questioning whether they may be entirely attributed to spontaneous
vasomotor oscillations (Mitra et al., 1997). While vascular effects may
contribute to the overall variance, it is now clear that neural processes
play a critical role, not only because of the neural correlates described
above, but also because resting state fluctuations are metabolically
demanding (Fukunaga et al., 2008). Why should there be any partic-
ular spatial organization to spontaneous neural activity, and what
might be its consequence for normal brain function? On these points
we can only speculate at present.
One possibility is that slow, coordinated activity changes of the
brain are related to the establishment or maintenance of synaptic
connections between neurons. As during development, spontaneous
neural activity could act to stimulate synaptic connections (Katz and
Shatz, 1996), or to reinforce them during network formation and ho-
meostasis (Sur and Rubenstein, 2005; Turrigiano and Nelson, 2004).
It is known that spontaneous activity influences dendritic spine struc-
ture and number in adults (Sur and Rubenstein, 2005; Trachtenberg
et al., 2002), and lack of spontaneous activity can lead to cell pathology
(Fishbein and Segal, 2007). Over long time scales, such processes could
manifest as an ongoing activity correlation between synaptically con-
nected neurons—a slow, continual “handshaking” of sorts between
structurally interconnected areas. Synaptic modification made during
tern of spontaneous activity associated with sleep (Tononi and Cirelli,
However attractive, models of functional connectivity that rely on
direct anatomical connections cannot account for all the data, such as
the known functional covariation between anatomically unconnected
areas described above. A somewhat different possibility, though not
mutually exclusive, is that spontaneous activity fluctuations reflect
ascending neuromodulation from the brainstem or interplay between
the cortex and other forebrain structures, such as the basal ganglia or
thalamus. While there is presently not much direct evidence in sup-
port of this hypothesis, it is clear from other spontaneous physiolog-
ical phenomena, such as sleep, that ascending mechanisms can have
a strong impact on the cortex. In fact, recent work by Tononi and col-
leagues raises the possibility that sleep itself, or closely related physi-
activity patterns (Huber et al., 2006; Nir et al., 2011; Vyazovskiy et al.,
2011). Sleep, which has traditionally been considered to affect the cor-
tex as a whole, can be highly regional, can involve local changes in
chemical neuromodulators such as acetylcholine and norepinephrine,
and can influence neural activity over both short and long time
scales. Moreover, certain features of regional sleep activity can ap-
pear during waking, and may thus contribute, under some condi-
tions and in some individuals, to resting state correlations. It is
therefore interesting to consider that the brain's intrinsic mecha-
nisms for sleep, including ascending subcortical pathways, could
generate a dynamic and coordinated cortical mosaic of activity
that shapes the pattern of temporal correlation observed in fMRI
functional connectivity (see Drew et al., 2008). In addition, numer-
ous other factors could potentially contribute to specific fMRI corre-
lations measured in functional connectivity, including circulating
hormones (Joëls and Baram, 2009), direct innervation of the vascu-
lature (Hamel, 2006), or spatiotemporal waves of cortical activity
(Massimini et al., 2004; Wu et al., 2008).
The “inverse problem” of fMRI and its correlations
The multiple candidate neural and vascular contributors to fMRI
signal variation described above pose two distinct challenges for
interpreting functional connectivity. The first challenge is the de-
generate nature of the fMRI signal, whether BOLD or CBV, within a
given voxel in the brain. From electrophysiology experiments
reviewed here, it is clear that spontaneous neural activity is coordi-
nated at multiple spatial scales, from microscopic to global. It is also
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
clear that the perfusion and oxygenation status of a voxel, which de-
termines the measured “activity” level during fMRI can be simulta-
neously shaped by diverse physiological processes during each
time point. Such a convergence of influences onto a single, unitless
scalar intensity value places severe limits on the precision by
which one may ascribe an fMRI measurement to any particular neu-
rophysiological process, particularly during the unconstrained con-
ditions of the resting state. In this sense, fMRI has its own type of
inverse problem, which pertains not to the localization of underlying
events (as in EEG and MEG), but to the decomposition of its underly-
ing neural events. In other words, a spontaneous rise or fall in
the fMRI signal can never be uniquely attributed to a specific type
of neural event, since blood flow regulation is the final common
pathway of a very large number of heterogeneous physiological
The second, and possibly more severe, challenge for interpreting
functional is that the contribution of the various neural constituents
in any pair of hemodynamic signals tends to vary over time. Comput-
ing the correlation between two fMRI signals, in effect, summarizes
the temporal covariation between two signals over a window of
time and typically assumes stationarity during that period. Increasing
evidence suggests that this assumption is ill founded, as it is clear that
the correlational structure of resting state networks changes substan-
tially over a period of minutes (Chang and Glover, 2010). In other
words, the fundamental inverse problem of fMRI is compounded
when temporal correlations are computed. Not only is the neural con-
tribution to each voxel ambiguous, but the relative neural contribu-
tion of each signal to the intervoxel correlations varies over time.
The reduction of this information into an r-value ranging from −1
to +1, as is the common practice in functional connectivity analysis,
thus results in an irretrievably ambiguous combination of neural and
Consider, then, how to interpret a change in functional connectiv-
ity, either over time or between groups of individuals. An increase in
fMRI correlation might occur because there is a subtle but consistent
increase in phase locking of the underlying neural signals. Alterna-
tively, it might result from a smaller number of prominent, coincident
events, of either neural or non-neural origin, affecting two regions.
There are multiple other possibilities. Likewise, a decrease in function-
al connectivity might stem from an inverse of either of the above
mechanisms. Alternatively, it might arise because one region abruptly
exhibits an additional, superimposed signal component that is absent
in another region. While mathematical methods such as independent
component analysis (Beckmann et al., 2005) and multivariate autore-
gressive models (Rogers et al., 2010) help to disentangle some
sources of shared variance, no computational method can precisely
separate the physiological contributors to hemodynamic signals, nor
isolate elements of shared temporal structure that correspond to dis-
tinct neural processes.
The unpalatable realities described here leave the practitioner of
functional connectivity facing a number of problematic questions:
Should one regress out the global cortical fMRI signal before evaluat-
ing specific correlations, even though a significant portion of the glob-
al signal is correlated with neural activity? What is the appropriate
duration of a “resting state” fMRI scan, given that the magnitude of
functional connectivity varies over time? To what extent can one rea-
sonably interpret differences in the mean resting state fMRI correla-
tion value between patient groups? Can fMRI correlation values be
taken as building blocks upon which to build large-scale network
models of the human brain? None of these questions has an easy an-
swer, let alone a "correct" one. Researchers must simply be aware of
the limitations of their method when designing their experiments,
when analyzing their data, and particularly when interpreting their
findings. The community must come to accept that the inverse prob-
lem of fMRI exists, and that it is particularly devastating for resting
state functional connectivity.
Drilling down while building up
When it comes to understanding the brain's spontaneous signals,
we have just scratched the surface. Despite this necessary conces-
sion, resting state fMRI functional connectivity has proven to be a
powerful method and has exhibiting a striking level of consistency
between laboratories and studies. Correlational fMRI approaches
yield repeatable brain network models and show promise for estab-
lishing biomarkers for the diagnosis of neurological and psychiatric
disease. Improved spatial resolution and analysis methods promise
to deliver further organizational features that will advance our un-
derstanding of the human brain.
It is vital that during the process of attempting to map the net-
work structure of the brain, we simultaneously dig deeper into the or-
igins of the brain's endogenous physiological processes. What drives
spontaneous neural fluctuations during rest? What is the relation be-
tween the ongoing neural activity, synaptic function and homeosta-
sis? Does spontaneous activity correlation capture the integrity of
functional networks, as many fMRI studies suggest? To what extent
does spontaneous activity contribute to the brain's enormous energy
expenditure? On this last point, it is known that metabolic energy is a
costly commodity in evolution, and the brain expends 20% of the
body's energy despite accounting for only 2% of the body's mass. Ap-
proximately 80% of this expenditure is thought to be related to the
maintenance of homeostasis (Hyder and Rothman, 2010; Raichle,
2006; van Eijsden et al., 2009). The contribution of spontaneous ac-
tivity variation to the brain's resting energy consumption may be
considerable, which further underscores the importance of under-
standing its essence.
Once regarded as irrelevant “noise”, endogenous neural activity is
now respected as a legitimate product of the brain. At present, resting
empiricism, with the pair-wise correlations of spontaneous activity be-
tween fMRI voxels taken as building blocks for constructing elaborate
brain networks. However, spontaneous activity must ultimately be un-
derstood on its own terms. The consistent patterns observed in func-
tional connectivity suggest that spontaneous activity is fundamental
to the functioning of the brain. Whether this role lies in homeostasis,
synaptic maintenance, information processing, neurovascular regula-
tion, or consciousness (Shulman et al., 2009) are important questions
for the future.
The fact that the spatial pattern of resting state correlations
show such striking consistencies across individuals (Biswal et al.,
2010), brain states (Vincent et al., 2007) and even species (Moeller
et al., 2009; Zhang et al., 2010) may be seen as a testament to the
importance of spontaneous physiological activity. As the field of
resting state functional connectivity grows faster than anybody
could have possibly imagined only a few years ago, systems neuro-
scientists must consider their priorities. The existence of functional-
ly connectednetworks in the mammalian brain has been
recognized since even before the work of Pribram and MacClean.
Functional MRI allows researchers to noninvasively characterize
and track correlational structures that resemble functional net-
works in humans, which holds great neuroscientific and clinical
promise. However, in order to truly understand the meaning of
fMRI-based networks, their variability, and their degeneration in
disease, human studies must be complemented by invasive studies
in animals. We must discover why slow ongoing neural activity ex-
ists in the first place, what dictates its spatial organization at multi-
ple scales, why certain networks are temporally synchronized over
long time scales, and how such correlational patterns relate to other
aspects of brain physiology such as sleep, learning, and interplay
between the hemispheres. Spontaneous activity is in some ways
D.A. Leopold, A. Maier / NeuroImage 62 (2012) 2190–2200
the most ubiquitous and obvious product of the brain; however, de-
spite its recent popularity it remains an aspect of brain function we
know very little about.
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