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Correlated neuronal activity and the flow of neural information. Jaeseung Jeong, Ph.D Department of Bio and Brain Engineering. Nonlinear information transmission of the cerebral cortex. Conventional measure: cross-correlation.

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correlated neuronal activity and the flow of neural information

Correlated neuronal activity and the flow of neural information

Jaeseung Jeong, Ph.D

Department of Bio and Brain Engineering

nonlinear information transmission of the cerebral cortex
Nonlinear information transmission of the cerebral cortex

Conventional measure: cross-correlation

  • Cross-correlation is used for quantifying correlations between EEGs from different channels implying the information transmission between two cortical regions (coherence analysis).


Jelic V et al., Quantitative electroencephalography power and coherence in Alzheimer\'s disease and mild cognitive impairment. Dementia. 1996;7(6):314-23.

phase synchronization in chaotic systems
Phase synchronization in chaotic systems
  • Coupled chaotic oscillators can display phase synchronization even when their amplitudes remain uncorrelated (Rosenblum et al., 1996). Phase synchronization is characterized by a non uniform distribution of the phase difference between two time series. It may be more suitable to track nonstationary and nonlinear dynamics.
phase synchronization and interdependence
Phase synchronization and interdependence

Definition of synchronization: two or many subsystems sharing specific common frequencies

Broader notion: two or many subsystems adjust some of their time-varying properties to a common behavior due to coupling or common external forcing

Jansen et al., Phase synchronization of the ongoing EEG and auditory EP generation. Clin Neurophysiol. 2003;114(1):79-85.

Le Van Quyen et al., Nonlinear interdependencies of EEG signals in human intracranially recorded temporal lobe seizures. Brain Res. (1998)Breakspear and Terry. Detection and description of non-linear interdependence in normal multichannel human EEG data. Clin Neurophysiol (2002)

neural synchronization
Neural Synchronization
  • The brain can be conceived as a complex network of coupled and interacting subsystems. Higher brain functions depend upon effective processing and integration of information in this network. This raises the question how functional interactions between different brain areas take place, and how such interactions may be changed in different types of pathology.

Mutual information of the EEG

  • The MI between measurement xi generated from system X and measurement yj generated from system Y is the amount of information that measurement xi provides about yj.
  • J Jeong, JC Gore, BS Peterson. Mutual information analysis of the EEG in patients with Alzheimer\'s disease. Clin Neurophysiol (2001)

What is the resting state

as a reference baseline?

What does the brain do when not actively engaged in

goal-directed cognitive tasks –

when, for want of a better term, we might say it is at “rest”?

What functions does the ‘resting’ brain subserve

and how do these impinge on more general aspects of cognition?


Functional connectivity in the motor cortex of

resting human brain using MRI.

  • An MRI time course of 512 images in resting human brain obtained every 250 ms reveals fluctuations in signal intensity in each pixel that have a physiologic origin. Regions of the sensorimotor cortex that were activated secondary to hand movement were identified using functional MRI methodology (FMRI).
  • Time courses of low frequency (< 0.1 Hz) fluctuations in resting brain were observed to have a high degree of temporal correlation (P < 10(-3)) within these regions and also with time courses in several other regions that can be associated with motor function.
  • It is concluded that correlation of low frequency fluctuations, which may arise from fluctuations in blood oxygenation or flow, is a manifestation of functional connectivity of the brain.

(Biswal B., Yetkin F., Haughton V. and Hyde J., (1995) Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn. Res. Med. 34, 537–541)


Biswal et al. (1995) were the first to observe the coherence between such low frequency oscillations and widely distributed neuro-anatomical networks.

  • This issue has since been explored in a wide range of tasks (e.g. [Gusnard et al., 2001], [Kelly et al., 2008] and [McKiernan et al., 2006]), clinical pathologies (e.g. [Bluhm et al., 2007], [Castellanos et al., 2008], [Greicius et al., 2007], [Greicius et al., 2004], [Kennedy et al., 2006], [Lowe et al., 2002], [Tian et al., 2006] and [Tinaz et al., 2008]), and even in chimpanzees (Rilling et al., 2007).

Detection of functional connectivity using temporal correlations in MR images. Michelle Hampson, Bradley S. Peterson, Pawel Skudlarski, James C. Gatenby, John C. Gore, Human Brain Mapping 15(4):247 - 262, 2002

what is default mode network
What is default mode network?
  • The default mode network (DMN) is a network of brain regions that are active when the brain is at rest, which is characterized by coherent neuronal oscillations at a rate lower than 0.1 Hz.
  • The DMN includes the posterior cingulate cortex (PCC) and the adjacent precuneus, the medial prefrontal cortex (MPFC), and the medial, lateral and inferior parietal cortex.
  • Although deactivated during task performance, this network is active in the resting brain with a high degree of functional connectivity between regions. This resting state activity has been termed the default-mode of brain activity to denote a state in which an individual is awake and alert, but not actively involved in an attention demanding or goal-directed task (Raichle et al., 2001).
Key neuroanatomical components of anti-correlated task positive and task-negative networks of the resting brain default network
low frequency oscillation of fmri signal and spontaneous activity at rest
Low frequency oscillation of fMRI signal and spontaneous activity at rest
  • When a long MRI time series data are analyzed in terms of frequency distribution, one can see the oscillation power is largely in the low frequency region, far below respiration rate. There are some peaks at 0.1Hz or at a lower frequency.
  • Such 0.1Hz oscillations used to be attributed to so-called vaso-motion, of the sort seen in in-vivo optical measurements. Any vascular modulation could lead to CBF variations. If this is the case, the modulation is not likely due to the local neuronal activity, but some signal to the vascular system from remote areas.
  • However, the presence of connectivity between functionally related sites was shown by correlations between these low frequency oscillations in time series MRI data at resting state (Biswal et al 1995). Furthermore, there is a slow modulation of the power of neural oscillations in the gamma range; such modulations can induce low frequency BOLD signal variation (Leopold et al 2003).
the blood oxygen level dependent bold signal in dmn
The blood oxygen level dependent (BOLD) signal in DMN
  • Empirical research has largely focused on the functional connectivity of the DMN within the parameters of functional magnetic resonance imaging (fMRI) data and the blood oxygen level dependent (BOLD) signal; an indirect measure of neuronal activity reflecting changes in blood oxygen level contrasts within the brain (Fox and Raichle, 2007).
  • Low-frequency oscillations are likely associated with connectivity of larger scale neuronal networks, while higher frequencies are constrained in smaller networks, and may be modulated by activity in the slower oscillating larger networks ([Buzsáki and Draguhn, 2004], [Fox and Raichle, 2007] and Penttonen and Buzsáki, 2003]).
eeg and dmn
  • Researchers have examined DMN activity in terms of traditional bands of EEG activity (Chen et al., 2008), and in terms of very slow EEG frequencies ([Helps et al., 2008] and [Vanhatalo et al., 2004]).
  • Vanhatalo reported pervasive very low frequency oscillations (0.02–0.2 Hz) across diverse scalp regions, in combination with evidence of robust phase-locking between these low frequency oscillations and traditional EEG bands of activity.

Chen et al. (2008) compared the spatial distribution and spectral power of seven bands of resting state EEG activity, in an eyes closed and eyes open condition:

  • In the eyes closed condition, the authors report delta (0.5–3.5 Hz) activity in the prefrontal area, theta (4–7 Hz) activity at frontocentral sites, and alpha-1 (7.5–9.5 Hz) activity distributed in the anterior–posterior region. Further, alpha-2 (10–12 Hz) and beta-1 (13–23 Hz) activity were evident in posterior regions, and high frequency beta-2 (24–34 Hz) and gamma (34–45 Hz) in the prefrontal area.
  • Comparatively, in the eyes open condition, delta activity was enhanced, and theta, alpha-1, alpha-2 and beta-1 were reduced in the respective regions.
  • They term this defined set of regional and frequency specific activity, the EEG default-mode network (EEG-DMN), and propose that the EEG-DMN should now be examined in the context of task-induced demands and in patient groups.
when is the dmn formed
When is the DMN formed?
  • The limited evidence of DMN in the infant brain (Fransson et al., 2007), fragmented connectivity between DMN regions during rest in young children (7–9 years; Fair et al., 2008), and more consistent DMN connectivity in children aged 9–12 years (Thomason et al., 2008), suggests that this network of spontaneous low frequency activity undergoes developmental change and maturation.
properties of default mode networks
Properties of Default mode networks
  • Research has concentrated on the patterns of activity within and interconnectivity between DMN brain regions during rest, and the impact that the commencement of goal-directed activity has on this.
  • Significantly, DMN activity is attenuated rather than extinguished during this transition between states, and is observed, albeit at lower levels, alongside task-specific activations ([Eichele et al., 2008], [Fransson, 2006], [Greicius et al., 2003] and Greicius and Menon, 2004).
  • The more demanding the task the stronger the deactivation appears to be ([McKiernan et al., 2006] and [Singh and Fawcett, 2008]).
  • Increased PCC activity, or reduced deactivation, systematically preceded and predicted response errors in a flanker task, up to 30 s before the error was made (Eichele et al., 2008).
a notable exception to this general pattern of deactivation during goal directed activity
A notable exception to this general pattern of deactivation during goal-directed activity
  • Attenuation of the ventral MPFC occurred with tasks involving judgments that were self-referential, while activity in the dorsal MPFC increased for self-referential stimuli, suggesting the dorsal MPFC is associated with introspective orientated thought (Gusnard et al., 2001).
  • Working memory tasks differentially deactivate the PCC. One study observed a signal increase and spatial decrease in the PCC and a signal decrease but spatial increase in the ACC with increasing working memory load in an n-back task (Esposito et al., 2006).
  • In contrast, earlier research reported a significant task-related decrease in PCC (Greicius et al., 2003), and although Hampson et al., (2006) did not find functional connectivity between the ventral ACC and PCC to differ between rest and a working memory task, performance was positively correlated with the degree of ventral ACC and PCC connectivity.

The issue of how different brain regions are connected functionally, that is, how the interplay of different areas subserves cognitive function, has become a key concern in neuroscience.

anti correlated task positive and task negative resting networks
Anti-correlated task-positive and task-negative resting networks
  • The DMN has been described as a ‘task-negative network’ given the apparent antagonism between its activation and task performance.
  • A second network also characterized by spontaneous low frequency activity has been identified as a task-positive network. This network includes the dorsolateral prefrontal cortex (DLPFC), inferior parietal cortex (IPC) and supplementary motor area (SMA).
  • Interestingly, the task-positive network and the DMN are temporally anti-correlated, such that task-specific activation of the task-positive network is affiliated with attenuation of the DMN.

This has led to a certain confusion with regard to terminology.

Should only the task-negative network be termed the DMN and contrasted with the task-positive network?

Or should both task-positive and task-negative networks be regarded as elements of the DMN?

task positive and negative components
Task-positive and negative components
  • The case for including task-positive and negative components as part of the same default-mode network system is supported by a considerable amount of evidence. Fox et al., 2005)
  • This proposition allows for naturally occurring competition between the task-negative and task-positive component, such that spontaneous anti-correlated interactions between the networks will result in periodic task interference, and importantly, does not necessitate the involvement of a central executive.
  • Indeed, it has been suggested on a number of occasions that the anti-correlation between the two networks may prove to be functionally more important, than DMN activity itself ([Fox et al., 2005]).
  • We use the DMN term to describe the task-negative network specifically. We use the term Low Frequency Resting State Networks (LFRSN) to describe both the task-positive and task-negative networks.
the functional significance of dmn activity
The functional significance of DMN activity
  • PCC (and adjacent precuneus) and MPFC, are the two most clearly delineated regions within the DMN in terms of their functional roles (Raichle et al., 2001).
  • PCC appears to serve an important adaptive function and is implicated in broad-based continuous sampling of external and internal environments (Raichle et al., 2001).
  • Reduced connectivity with anterior DMN regions in attention deficit/hyperactivity disorder (ADHD) participants ([Castellanos et al., 2008] and [Uddin et al., 2008a]) suggests that this region may be implicated in working memory orattention dysfunction.
  • Finally, PCC and retrosplenial cortex are also associated with the processing of emotionally salient stimuli, and may play a role in emotional processing related to episodic memory (Maddock, 1999).
  • MPFC has been associated with social cognition involving the monitoring of ones own psychological states, and mentalising about the psychological states of others ([Blakemore, 2008], ).

In the context of DMN activity, MPFC is thought to mediate a dynamic interplay between emotional processing and cognition functions which map on to the ventral and dorsal regions, respectively ([Gusnard et al., 2001], [Raichle et al., 2001] and [Simpson et al., 2001]).

the significance of tnn and tnp
The significance of TNN and TNP
  • Slow oscillations of power may reflect long range coordination in a functional network. Spontaneous fluctuations of fMRI signals at resting state have been explored to find functional networks among functional sites on the basis of the connectivity.
  • It is thought that the TNN corresponds to task-independent introspection, or self-referential thought, while the TPN corresponds to action, and that perhaps the TNN and TPN should be considered elements of a single default mode network with anti-correlated components.
one hypothesis for dmn and task positive network
One hypothesis for DMN and task-positive network
  • One hypothesis is that task-positive activity is thought to be associated with preparedness for unexpected or novel environmental events.
  • According to this account the reciprocal relationship between the task-positive component and DMN has been described as low frequency toggling between a task-independent, self-referential and introspective state and an extrospective state that ensures the individual is alert and attentive to unexpected or novel environmental events ([Fox et al., 2005], [Fransson, 2005] and Fransson, 2006).
the functional role of low frequency oscillations
The functional role of low frequency oscillations
  • The functional role of low frequency oscillations coherent across resting state networks, and particularly the DMN, remains speculative.
  • Possible candidates include the temporal binding of information (Engel et al., 2001), particularly related to the coordination and neuronal organisation of brain activity between regions that frequently work in combination (Fox and Raichle, 2007);
the functional role of dmn
The functional role of DMN
  • The ability to maintain attentional focus and resist distraction or lapses of attention is conventionally considered to underlie higher order top–down control.
  • Attentional lapses during goal-directed action may be a result of interference arising from spontaneous, and most likely self-referential, thought.
  • The degree and maintenance of attenuation in DMN will relate specifically to both state factors such as motivation, and trait factors, such as disorder.
mental disorders and dmn
Mental disorders and DMN
  • In mental disorder, the absence of, or reductions in, the anti-correlation between the DMN and task-positive network manifest as reduced introspective thought (ASD) and attentional lapses (ADHD); while excessive antagonism will likely result in zealous toggling between extrospective and introspective processes (Schizophrenia).
  • Second, the integrity of the DMN is affected by reductions in connectivity, and is associated with deficits in attention and working memory (Alzheimer’s disease, ADHD, schizophrenia), as well as problems with self-referential and introspective mental processing (ASD).
  • In contrast, increased connectivity has been associated with maladaptive emotional and introspective processing (depression, schizophrenia).
mental disorders and dmn1
Mental disorders and DMN
  • Third, altered patterns of DMN functional connectivity commonly characterize dysfunctional introspective processing – connectivity in the DMN is negatively related to the positive symptoms of schizophrenia, while enhanced connectivity in the subgenual cingulate is associated with the length of depressive episode.
  • Finally, altered patterns of connectivity, atypical anti-correlations between the DMN and task-positive network, and reduced integrity of DMN functions, observed in a range of mental disorders, are all potential and pervasive sources of interference during goal-directed activity.
information processing of the brain for binding problem
Informationprocessing of the brain for binding problem
  • The BINDING PROBLEM, the receptive fields of two visual neurons were stimulated in two conditions, one in which a single object was presented, and another in which two objects were presented, but in a way that evoked practically the same firing rates as the single stimulus.
  • In this case, the synchrony between pairs of neurons reflected whether one or two stimuli were shown, even when both firing rates did not vary across conditions.
cross correlogram
  • A popular analytical tool used by neuroscientists to study the joint activity of neurons is the cross-correlation histogram or cross-correlogram.
  • It is constructed from the spike trains of two neurons, and shows the probability (or some quantity proportional to it) that neuron B fires a spike milliseconds before or after a spike from neuron A; is called the time shift or time lag.
  • When the two spike trains are independent, the cross-correlogram is flat; if there is any covariation in the spike trains, one or more peaks appear.
  • For instance, a peak at zero time shift means that the two neurons tend to fire at the same time more often than expected by chance.
  • Usually, cross-correlograms are corrected so that peaks caused by covariations in mean firing rate, computed over several tens or hundreds of milliseconds, are eliminated.
coincidence detection
Coincidence detection
  • In theory, neurons might be exquisitely sensitive to certain temporal input patterns. The classical mechanism proposed for this is coincidence detection, which occurs when a neuron is sensitive to the arrival of spikes from two or more inputs within a short time window.
  • There are examples, most notably in the auditory system, in which highly accurate coincidence detection takes place, but the question is whether this mechanism is commonly used throughout the cortex.

a | All input spike trains were independent. In the middle traces, both postsynaptic neurons are shown to fire at about 30 spikes s-1.

  • b | Excitatory inputs were synchronous, with 10% shared inputs, as in Fig. 1a. Balanced and unbalanced neurons fired at 67 and 45 spikes s-1, respectively.
  • c | Inhibitory inputs oscillated with an amplitude equal to 50% of the mean rate, as in Fig. 1e. Balanced and unbalanced neurons fired at 59 and 30 spikes s-1, respectively.
  • d | All inputs were synchronous, with 10% shared inputs. Balanced and unbalanced neurons fired at 31 and 41 spikes s-1, respectively. For comparison, broken lines in the input–output rate plots (b–d) are the curves obtained with independent inputs (a). The balanced neuron is much more sensitive to correlations than the unbalanced one.

The y axis indicates the rate of spike coincidences when the spike trains from the two neurons are shifted in time by the amount shown on the x axis. These correlograms have been normalized so that a zero rate corresponds to independent spike trains. The three panels correspond to three different pairs.

  • Red traces were calculated from trials in which the monkey paid attention to a ‘tactile stimulus’ (the cross on the table); blue traces were calculated from trials in which the same tactile stimulus was presented, but the monkey had to pay attention to a visual stimulus on the screen.

In the top two examples, more synchrony was observed when attention was focused on the tactile stimuli; this was the more prevalent effect. An example of lower synchrony with attention on the tactile stimulus — the less frequent effect — is shown in the lower plot.


Monkeys were trained to fixate on a central spot and to attend to either of two stimuli presented simultaneously and at the same eccentricity.

  • One of the stimuli fell inside the receptive field of a neuron, the activity of which was recorded.
  • So, the responses to the same stimulus could be compared in two conditions, with attention inside or outside the neuron\'s receptive field.

a and b | The continuous traces show the stimulus-driven local field potentials (LFPs). The spikes below were recorded simultaneously from different electrodes.

  • c and d | Spike-triggered averages (STAs) computed during the stimulus presentation period. The STA corresponds to the average LFP waveform that is seen at the time of a spike. The y axes indicate the mean LFP; the x axes indicate time relative to the occurrence of a spike.
  • e | Power spectra of the two STAs shown in c and d. When attention is focused inside the receptive field, the recorded neuron tends to fire more in phase with the frequency components around 50 Hz, and less so with respect to the frequencies around 10 Hz.