Article

Network dynamics of encoding and retrieval of behavioural spike sequences during theta and ripples in a CA1 model of the hippocampus

BMC Neuroscience (Impact Factor: 2.67). 07/2010; 11(Suppl 1). DOI: 10.1186/1471-2202-11-S1-P55
Source: DOAJ

ABSTRACT

The hippocampus is known to be involved in spatial learning in rats. Spatial learning involves the encoding and replay of
temporally sequenced spatial information. Temporally sequenced spatial memories are encoded and replayed by the firing rate
and phase of pyramidal cells and inhibitory interneurons with respect to ongoing network oscillations (theta and ripples).
Understanding how the different hippocampal neuronal classes interact during these encoding and replay processes is of great
importance. A computational model of the CA1 microcircuit [3], [4], [5] that uses biophysical representations of the major
cell types, including pyramidal cells and four types of inhibitory interneurons is extended to address: (1) How are the encoding
and replay (forward and reverse) of behavioural place sequences controlled in the CA1 microcircuit during theta and ripples?
and (2) What roles do the various types of inhibitory interneurons play in these processes?

Full-text

Available from: Vassilis Cutsuridis
Dynamics and Function of a CA1 Model of the
Hippocampus during Theta and Ripples
Vassilis Cutsuridis
and Michael Hasselmo
Center for Memory and Brain, Boston University, Boston, MA, USA
vcut@bu.edu
Abstract. The hippocampus is known to be involved in spatial learning
in rats. Spatial learning involves the encoding and replay of temporally
sequenced spatial information. Temporally sequenced spatial memories
are encoded and replayed by the firing rate and phase of pyramidal cells
and inhibitory interneurons with respect to ongoing network oscillations
(theta and ripples). Understanding how the different hippocampal neu-
ronal classes interact during these encoding and replay processes is of
great importance. A computational model of the CA1 microcircuit [3],
[4], [5] that uses biophysical representations of the major cell types, in-
cluding pyramidal cells and four types of inhibitory interneurons is ex-
tended to address: (1) How are the encoding and replay (forward and
reverse) of behavioural place sequences controlled in the CA1 microcir-
cuit during theta and ripples? and (2) What roles do the various types
of inhibitory interneurons play in these processes?
Keywords: Computational model, microcircuit, inhibitory interneurons,
STDP, calcium, theta, ripples, medial septum, CA1.
1 Int roduction
Spatial memories in the hippocampus are encoded (stored) and replayed by the
firing frequency and spike timing of pyramidal cells and inhibitory interneurons
during network oscillations. Theta oscillations (4-10 Hz) are observed in rats
during exploration and rapid eye movement (REM) sleep, whereas sharp wave-
associated ripples (100-200 Hz) are observed during immobility, slow-wave sleep
(SWS) and consummatory behaviours. During exploration hippocampal place
cells have been shown to systematically shift their firing phase with respect to
theta as the animal transverses the place field (a phenomenon known as phase
precession) [19].
Many theories have been proposed over the years trying to understand how
memories in the hippocampus are encoded and replayed during network oscil-
lations [7],[15]. Buzsaki’s two-stage memory model [15] hypothesized that both
theta and sharp-wave (ripple) states of the hippocampus are essential to mem-
ory trace encoding and replay. During theta (exploratory behavior) neocortical
Corresponding author.
K. Diamantaras, W. Duch, L.S. Iliadis (Eds.): ICANN 2010, Part I, LNCS 6352, pp. 230–240, 2010.
c
Springer-Verlag Berlin Heidelberg 2010
Page 1
Dynamics and Function of a CA1 Model 231
Fig. 1. (A) Pyramidal cell model with calcium detectors in distal and proximal den-
drites. (B) Entorhinal cortical (EC) and Schaffer collateral (CA3) inputs during theta
rhythm. (C) Forward replay of CA3 spatial memories used as inputs to CA1 during
ripple activity (location A in figure 2). (D) Reverse replay of CA3 spatial memories
used as inputs to CA1 during ripple activity (location B in figure 2).
information is transmitted to the hippocampus via the dentate gyrus, where it is
encoded by pyramidal cells via synaptic plasticity mechanisms. During the sharp-
wave associated ripple state the pyramidal cells initiate population bursts, which
then cause the already stored memories in the hippocampus to reach the neocor-
tex and hence to be replayed. Hasselmo’s and colleagues’ oscillatory model [7]
hypothesized that hippocampal theta rhythm (4-7 Hz) can contribute to mem-
ory formation by separating encoding (storage) and retrieval of memories into
independent functional sub-cycles. Recent experimental evidence has shown that
in the CA1 area of the hippocampus the same set of excitatory and inhibitory
cells, which fire at specific phases during theta, are active at completely different
phases during ripples [10], [11], [12]. Similarly, medial septal GABAergic neurons
differentially phase their activities with respect to theta and ripple [14], [17].
Here we investigate, via computer simulations, the biophysical mechanisms by
which encoding and replay of behaviourally relevant spatial memory sequences
are achieved by the CA1 microcircuitry. A model of the CA1 microcircuit [3], [4],
[5], [6] is extended that uses simplified biophysical representations of the major
cell types, including pyramidal cells (PCs) and four types of inhibitory interneu-
rons: basket cells (BCs), axo-axonic cells (AACs), bistratified cells (BSCs) and
oriens lacunosum-moleculare (OLM) cells. Inputs to the network come from the
entorhinal cortex (EC), the CA3 Schaffer collaterals and medial septum (MS).
Our model addresses three important issues: (1) How is the mechanism of phase
precession of place cells in the CA1 microcircuit achieved in presence of various
types of inhibitory interneurons? (2) How are the encoding and replay (forward
and reverse) of behavioural place sequences controlled in the CA1 microcircuit
Page 2
232 V. Cutsuridis and M. Hasselmo
during theta and ripples? and (3) What roles do the various types of inhibitory
interneurons play in these processes?
2 Model Architecture and Properties
The CA1 network model consisted of 4 pyramidal cells and four types of in-
hibitory interneurons: two basket cells, an axoaxonic cell, a bistratified cell and
an oriens lacunosum-moleculare (OLM) cell. Hodgkin-Huxley mathematical for-
malism was used to describe the ionic and synaptic mechanisms of all cells. All
simulations were performed using XPPAUT [20] running on a PC under win-
dows XP. The biophysical properties of each cell were adapted from cell types
reported in the literature [5], [9].
Pyramidal Cells. Each pyramidal cell consisted of 4 compartments: an axon,
a soma, a proximal dendrite and a distal dendrite. Active properties included a
fast Na
+
current, a delayed rectifier K
+
current, an LVA L-type Ca
2+
current,
an A-type K
+
current, and a calcium activated mAHP K
+
current. No recurrent
connections between pyramidal cells in the network were assumed.
Each pyramidal cell received proximaland distal excitation (AMPA and NMDA)
from the CA3 Schaffer collaterals and entorhinal cortex (EC), respectively, and
synaptic inhibition (GABA
A
)fromtheBC,AAC,BSC,andOLMcellsinthesoma,
axon, proximal dendrite and distal dendrite, respectively.
A mechanism for spike timing dependent plasticity (STDP) in each dendrite
was used to measure plasticity effects. The mechanism had a modular structure
consisting of three biochemical detectors, which responded to the instantaneous
calcium level and its time course in the dendrite [1]. The detection system con-
sisted of: (1) a potentiation (P) detector which detected calcium levels above
a high-threshold (e.g. 4µM) and triggered LTP, (2) a depression (D) detector
which detected calcium levels exceeding a low threshold level (e.g. 0.6µM), re-
mained above it for a minimum time period and triggered LTD, and (3) a veto
(V) detector which detected levels exceeding a mid-level threshold (e.g. 2µM)
and triggered a veto to the D response. Calcium entered the neuron through:
(1) voltage-gated calcium channels (VGCCs), and (2) NMDA channels located
at each dendrite. Calcium influx from neither channels alone elicited plasticity.
Plasticity resulted only from the synergistic action of the two calcium sources
(NMDA and VGCC). A graphical schematic of the model pyramidal cell and its
calcium detectors for STDP is shown in Figure 1A.
Inhibitory Interneurons. All inhibitory interneurons consisted of a single
compartment (soma). Active properties of BC, AAC and BSC included a fast
Na
+
, a delayed rectifier K
+
and a type-A K
+
currents [5]. Active properties
of the OLM cell included a fast Na
+
current, a delayed rectifier K
+
current, a
persistent Na
+
current and an h-current [9]. During theta, axoaxonic and basket
cells received excitatory inputs from the EC perforant path and the CA3 Schaffer
Page 3
Dynamics and Function of a CA1 Model 233
Fig. 2. Virtual linear track paradigm used. The rat must transverse the track starting
from location A and stopping at location B. Gray lled ellipses represent the place
fields (PF) of three pyramidal cells (PCs) in the network. Note their fields are non-
overlapping. As the rat transverses the PF, each PC shifts its firing to earlier phases
of the theta rhythm. At locations A and B the rats retrieve either the track locations
to be transversed or the track locations already transversed, respectively.
collateral, inhibition from the medial septum, and recurrent excitation from the
pyramidal cells. Basket cells recurrently inhibited each other and received addi-
tional inhibition from the bistratified cells. Bistratified cells were excited by the
CA3 Schaffer collateral input only, inhibited by the medial septum, synaptically
excited by PC recurrent excitation and synaptically inhibited by the basket cell.
OLM cells received recurrent excitation from the PCs and forward inhibition
from the medial septum. During ripples, the AAC, BC and BSC were excited
only by the CA3 Schaffer collaterals and inhibited by the MS cells (see MODEL
INPUTS subsection for details). The OLM cell was excited by the PCs and
inhibited by the MS cells (see MODEL INPUTS subsection for details).
Model Inputs. Excitatory inputs (spikes) to network cells originated from the
entorhinal cortex (EC) and CA3 Schaffer collaterals, whereas external inhibitory
one from the medial septum (MS). During theta, the EC and CA3 inputs were
continuously present, but at different frequencies (see Figure 1B). The interspike
interval of the EC input was set to 10ms (100Hz), whereas the ISI of the CA3
input was set to 20ms (50Hz) [22]. Both EC and CA3 inputs arrived at the same
time in the CA1-PC dendrites. The MS inputs were modelled as burst cells,
which fired at specific phases of the theta rhythm. One MS burst cell fired at the
peak of the extracellular theta (type 1) [14], whereas the other one at its trough
(type 2 ) [17]. MS cells inhibited only the network inhibitory interneurons.
Page 4
234 V. Cutsuridis and M. Hasselmo
During ripples, the CA1 PCs received forward or reversed excitatory rippled
input only from the CA3 Schaffer collaterals (see Figure 1C and 1D) [15], [21].
The inhibitory inputs from the MS cells were of two types: (1) a cell with a theta-
like oscillation during the ripple-centered epoch, pausing its activity before the
ripple peak and increasing its firing right after the ripple peak (type 1 ) [17], and
(2) a cell that paused its activity during the ripple episode (type 2)[17].
3Results
3.1 Virtual Linear Track
Our virtual linear track consisted of a rat running from station A to station B
(see Figure 2). In stations A and B the rat was allowed to stand still awaiting
for the GO signal to transverse the linear track. The linear track consisted of
four non-overlapping place field representations of equal dimensions ( 25cm).
The virtual rat took 2.25 sec (9 theta cycles) to tranverse through one place
field. Figure 4 shows the firing activities of two place cells (PC 1 and PC4) and
all inhibitory interneurons in two place fields (PF1 and PF4 in Figure 2). Each
place field was encoded by the firing of a single pyramidal cell, whose phase of
firing shifted with respect to the external theta rhythm [19]. As the rat entered
a place field (first theta cycle) of a given pyramidal cell, the first spikes occured
close to the trough of the theta cycle. As the rat was approaching the end of the
field (last theta cycle), they occured near the peak of the cycle, having precessed
almost 180 degrees over the course of 9 theta cycles (see figure 4) [23]. This was
accomplished by the constantly increasing strength of the proximal synapses
due to the STDP learning rule, which increased the tendency of PCs to fire
at earlier theta phases in the presence of a constant level inhibitory threshold
(BSC inhibition) (simulation result not shown). Once the rat reached station B,
it was rewarded and allowed to be engaged into consummatory behaviours. At
the stations A and B, our hippocampal simulation entered a different state of
waking without theta rhythmic oscillations, where sharp wave associated ripple
activity dominated the input and output of CA1 [16], [18]. As experimental
studies have shown at station A the rat experienced forward replay of neural
activity coding the track locations to be transversed [16], whereas at station B
the rat experienced reverse replay of neural activity coding the track locations
it has just tranversed [18].
3.2 Encoding of Spatiotemporal Memories during Theta
Figure 3 depicts the encoding process of spatiotemporal memories during theta.
During theta, input from EC enters the distal dendrite of the CA1 PC cells,
whereas input from CA3 Schaffer collaterals enters the proximal dendrite of
the PC cells. On their own, the EC inputs generate dendritic spikes in the distal
dendrites, which get attenuated on their way to the soma (see figure 3A) [2]. The
CA3 inputs generate excitatory postsynaptic potentials (EPSPs), which fail to
Page 5
Dynamics and Function of a CA1 Model 235
Fig. 3. Schematic of encoding of spatiotemporal memories during the theta rhythm
(see text for details)
Fig. 4. (Left) Firing activities of pyramidal cell 1 and all inhibitory interneurons with
respect to theta rhythm. (Right) Firing activities of pyramidal cell 4 and all inhibitory
interneurons with respect to theta rhythm. Vertical arrows indicate phase precession
ofpyramidalcellfiringsinevery theta cycle. Nine theta cycles comprise a pyramidal
cell’s (place cell’s) place field.
generate somatic action potentials, because they are presynaptically inhibited by
GABA
B
(see figure 3B) [8]. The presynaptic GABA
B
inhibition in CA1 cyclically
changed its strength with respect to theta (active during the first half of theta,
inactive during the second half) [8]. During the first half of theta, the strength
of CA3 input to PC proximal dendrites was reduced by 50%. When the EC and
CA3 inputs were concident in the proximal dendrites of the PCs, then action
potentials are generated in the PC somas (figure 3C).
Page 6
236 V. Cutsuridis and M. Hasselmo
Figure 3D-F depicts which cells are active during theta. Figure 4 depicts the
firing activities of all network cells during theta. During the first half-cycle of
theta (0-180 degrees), we propose the following: the coincident EC and CA3
inputs cause first the AAC to fire action potentials with interspike interval (ISI)
equal to 20ms, which inhibit the PCs at their axons and prevent them from firing
APs (Figure 3D) [11]. Once the AAC stops firing, BCs, which are modeled as
slow integrators [11], start to fire due to the coincident EC and CA3 inputs to
their somas. Because of their mutual recurrent inhibition, each BC fires every
40ms as in [11]. The role of BCs is to inhibit the PCs and prevent them from
firing, pace subthreshold theta oscillations in PCs [13] and prevent the BSC from
ruining learning in the PC proximal dendrite by inhibiting it (Figure 3E). BSC,
along with the OLM cell, is also inhibited by the type 2 MS cell (Figure 3E).
The type 2 MS cell also inhibits the type 1 MS cell, which in turn disinhibits the
AAC and BCs and allows them to fire and carry-on with their inhibitory duties
(Figure 3E).
Figure 3F depicts the second sub-cycle of theta, which begins as the presynap-
tic GABA
B
inhibition to CA3 Schaffer collateral input to PC synapses declines
and type 1 MS cell approach maximum activity. Because of this septal input,
the basket and axoaxonic cells are now inhibited, releasing pyramidal cells, bis-
tratified cells and OLM cells from inhibition. Pyramidal cells may now fire more
easily, thus, allowing previously learned memories to be recalled. Type 1 MS cell
also inhibits the type 2 MS cell, which in turn disinhibits the BSC and OLM
cell. To ensure the correct place memory of the sequence is recalled, the disin-
hibited BSC broadcasts to all PCs a non-specific inhibitory signal, which allows
the PCs that learned the place memory to recall it, while quenching all other
spurious places memories (e.g. subsequent memories in the sequence). The OLM
cell, which gets activated by the PCs, in turn send an inhibitory signal to the
distal PC dendrite, which prevents the EC input from interfering with the recall
of the pattern.
3.3 Forward and Backward Replay of Memories during Ripple
Activity
Figure 5 depicts the replay processes during a ripple episode. In contrast to theta
(figure 4), during the ripple episode (forward or reverse) the firing patterns of
inhibitory interneurons in the network change (figure 6) [11], [12]. During ripple
activity what was loca lly learned during theta oscillations, it is now retrieved
by the subiculum, entorhinal cortex and the neocortex, where it reached con-
sciousness [15]. The synaptic weights of the proximal dendrite are now fixed (no
changing). Forward and reverse replay activity arise from the highly synchronous
activity of the CA3 PCs [15], [21]. This highly synchronous activity excites first
the AAC, which is disinhibited by the type 1 MS cell (as we mentioned before
the type 1 MS cell pauses its activity for about 25ms before the peak of the
ripple episode and increases it right after it), and in turn inhibit the axons of all
CA1 PCs in the network. The duration of this axonal inhibition is short (less than
Page 7
Dynamics and Function of a CA1 Model 237
Fig. 5. Schematic of the forward and backward replay processes of spatiotemporal
memories during ripple activity (see text for details). Vertical dashed gray line indicates
the peak of the ripple episode.
Fig. 6. Firing activities of all network cells with respect to ripples during both forward
and reverse replay of spatiotemporal memories. Dashed yellow line indicates peak am-
plitude of ripple episode. Axoaxonic, basket, bistratified and OLM cells fire the same
way during both forward and reverse replay of memories [11], [12]. During forward re-
play, pyramidal cells fire in a specific order: black, blue, red, and green. During reverse
replay the order is reversed: green, red, blue, and black.
Page 8
238 V. Cutsuridis and M. Hasselmo
25 ms), since the AAC pauses its firing right after the peak of ripple episode due
to increased activity of the type 1 MS cell. The role of the AAC is to silence the
CA1 network and prepare it for the appropriate retrieval of information based
on the current context. Similar firing activity has the OLM cell in the network,
because it is also (dis)inhibited by a type 1 MS cell. The role of the OLM cell is
to prevent the EC input from interfering with the recall of the memory.
Next, BCs and BSC, which were inhibited by the type 2 MS cells during the
start of the ripple episode are now disinhibited by them and become active from
the highly synchronous CA3 input. The role of the BSC is to provide a non-
specific inhibition to all PCs, allowing this way only the ”appropriate” PCs that
learned the pattern(s) to recall it(them). The role of the BCs is to maintain the
highly syncronous ripple activity of the PCs. A similar role is played by the gap
channels in the PC axons [24].
4Conclusion
A reduced version of a previously published CA1 microcircuit model [3], [4],
[5], [6] is extended to simulate how spatiotemporal patterns are encoded and re-
trieved in the CA1 area of the hippocampus during theta and ripples. Our model
demonstrates: (1) How is phase precession of place cells in CA1 achieved in the
presence of various types of inhibitory interneurons? and (2) How are encoding
and replay (forward and reverse) of behavioural sequences of spatial memories
controlled in CA1 during theta and ripples in the presence of various types of
inhibitory interneurons. Much more work is needed to further explore why the
model place cells don’t precess beyond 180 degrees with respect to theta. Does
a full 360 degrees phase precession result from the interactions of a larger and
noiser network of cells or is it driven by phase precessed CA3 inputs? How does
a larger number of simulated theta cycles contribute to phase precession? Also,
what happens to network dynamics and its ability to learn when the presenta-
tion frequencies of inputs change? Finally, what role does dopamine in CA1 play
in binding together temporally sequenced spatial memories?
Acknowledgement. This work was funded by NSF Science of Learning Center
CELEST grant SMA 0835976, NIMH R01 MH61492, NIMH R01 MH60013 and
NIMH Silvio Conte Center grant P50 MH71702.
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  • Source
    • "The neuronal diversity, morphology, ionic, and synaptic properties, connectivity , and spatial distribution closely followed known experimental evidence of the hippocampal microcircuitry (Cutsuridis et al., 2010). In a subsequent modeling study, Cutsuridis et al. (2010) extended the model of the CA1 microcircuitry to test its recall performance of new and previously stored static patterns as well as its memory capacity in the presence/absence of various inhibitory interneurons. "
    [Show abstract] [Hide abstract] ABSTRACT: Successful spatial exploration requires gating, storage, and retrieval of spatial memories in the correct order. The hippocampus is known to play an important role in the temporal organization of spatial information. Temporally ordered spatial memories are encoded and retrieved by the firing rate and phase of hippocampal pyramidal cells and inhibitory interneurons with respect to ongoing network theta oscillations paced by intra- and extrahippocampal areas. Much is known about the anatomical, physiological, and molecular characteristics as well as the connectivity and synaptic properties of various cell types in the hippocampal microcircuits, but how these detailed properties of individual neurons give rise to temporal organization of spatial memories remains unclear. We present a model of the hippocampal CA1 microcircuit based on observed biophysical properties of pyramidal cells and six types of inhibitory interneurons: axo-axonic, basket, bistratistified, neurogliaform, ivy, and oriens lacunosum-moleculare cells. The model simulates a virtual rat running on a linear track. Excitatory transient inputs come from the entorhinal cortex (EC) and the CA3 Schaffer collaterals and impinge on both the pyramidal cells and inhibitory interneurons, whereas inhibitory inputs from the medial septum impinge only on the inhibitory interneurons. Dopamine operates as a gate-keeper modulating the spatial memory flow to the PC distal dendrites in a frequency-dependent manner. A mechanism for spike-timing-dependent plasticity in distal and proximal PC dendrites consisting of three calcium detectors, which responds to the instantaneous calcium level and its time course in the dendrite, is used to model the plasticity effects. The model simulates the timing of firing of different hippocampal cell types relative to theta oscillations, and proposes functional roles for the different classes of the hippocampal and septal inhibitory interneurons in the correct ordering of spatial memories as well as in the generation and maintenance of theta phase precession of pyramidal cells (place cells) in CA1. The model leads to a number of experimentally testable predictions that may lead to a better understanding of the biophysical computations in the hippocampus and medial septum.
    Full-text · Article · Jul 2012 · Hippocampus
  • Source
    • ", [7]. Active properties of the OLM cell included a fast Na + current, a delayed rectifier K + current, a persistent Na + current, a leakage current and an h-current [7], whereas those of the NGL cell included a fast Na + current, a delayed rectifier K + current and a leakage current. "
    [Show abstract] [Hide abstract] ABSTRACT: The hippocampus plays an important role in the encoding and retrieval of spatial and non-spatial memories. Much is known about the anatomical, physiological and molecular characteristics as well as the connectivity and synaptic properties of various cell types in the hippocampal circuits [1], but how these detailed properties of individual neurons give rise to the encoding and retrieval of memories remains unclear. Computational models play an instrumental role in providing clues on how these processes may take place. Here, we present three computational models of the region CA1 of the hippocampus at various levels of detail. Issues such as retrieval of memories as a function of cue loading, presentation frequency and learning paradigm, memory capacity, recall performance, and theta phase precession in the presence of dopamine neuromodulation and various types of inhibitory interneurons are addressed. The models lead to a number of experimentally testable predictions that may lead to a better understanding of the biophysical computations in the hippocampus.
    Full-text · Conference Paper · Jul 2011
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    [Show abstract] [Hide abstract] ABSTRACT: Coordination of neocortical oscillations has been hypothesized to underlie the "binding" essential to cognitive function. However, the mechanisms that generate neocortical oscillations in physiological frequency bands remain unknown. We hypothesized that interlaminar relations in neocortex would provide multiple intermediate loops that would play particular roles in generating oscillations, adding different dynamics to the network. We simulated networks from sensory neocortex using nine columns of event-driven rule-based neurons wired according to anatomical data and driven with random white-noise synaptic inputs. We tuned the network to achieve realistic cell firing rates and to avoid population spikes. A physiological frequency spectrum appeared as an emergent property, displaying dominant frequencies that were not present in the inputs or in the intrinsic or activated frequencies of any of the cell groups. We monitored spectral changes while using minimal dynamical perturbation as a methodology through gradual introduction of hubs into individual layers. We found that hubs in layer 2/3 excitatory cells had the greatest influence on overall network activity, suggesting that this subpopulation was a primary generator of theta/beta strength in the network. Similarly, layer 2/3 interneurons appeared largely responsible for gamma activation through preferential attenuation of the rest of the spectrum. The network showed evidence of frequency homeostasis: increased activation of supragranular layers increased firing rates in the network without altering the spectral profile, and alteration in synaptic delays did not significantly shift spectral peaks. Direct comparison of the power spectra with experimentally recorded local field potentials from prefrontal cortex of awake rat showed substantial similarities, including comparable patterns of cross-frequency coupling.
    Full-text · Article · Apr 2011 · Frontiers in Computational Neuroscience
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