<p>Synchronization between
coupled oscillators of whatever kind is known generally as synchrony or
coupling.&nbsp;In the context of human or animal consciousness, various kinds of neural and
electromagnetic field synchrony seem to play functional roles. The interaction
between oscillations at different frequency bands and at different phase slopes
is generally known as cross-frequency coupling (CFC).&nbsp;</p><p>Connectivity in EEG is measured by coherence, phase, and forms of cross frequency coupling.&nbsp;</p><h4>Coherence</h4><p></p><p>Coherence measures the stability of the phase
relationship between two time series, calculating the difference between two
signals measured at the scalp. &nbsp;Coherence
in excess is hypercoherence; coherence in deficiency is hypocoherence. Coherence measures do not
separate phase and amplitude.&nbsp;</p><p><img src="@@PLUGINFILE@@/erroneous%20coherences.png" alt="erroneous coherences" width="600" height="585" class="img-responsive atto_image_button_left"></p><p>Unfortunately, coherence measures are also apt to be spurious and false positives are likely. The image to the left is of Erroneous coherences.&nbsp; In EEG measures, a linked ears or mastoid reference
used can significantly alter the both the power and phase at each electrode
site, if a high amplitude source of EEG is at one or more of the temporal
electrodes. For similar reasons, any common reference coherence data must be
interpreted cautiously. Even in average references, spuriously large coherences
can occur from superficial dipoles at large interelectrode differences.&nbsp;&nbsp; Fein et al. (1988) argue the most diligent
way to measure coherences is with reference-free recording methods, while Nunez
et al (1997) agree, noting that Laplacians give the best intermediate spatial
range coherence estimates.&nbsp; Finally , of
import to valuation of synchrony measures offered, coherence measures do not
separate phase and amplitude.</p>When coherences are accurate (not false positives), they can indicate the followin<img src="@@PLUGINFILE@@/Coherence%20Images.png" alt="Coherence Measures" width="600" height="767" class="img-responsive atto_image_button_left">g symptoms. Hypercoherence
shows a lack of flexibility in the connection relationships; firings are locked
into the same rhythm. Imagine soldiers goose-stepping or a crowd clapping in
unison. Hypercoherence is problematic in the sense that it can create “tunnel
vision” or the inability to switch tasks readily. On the other hand, it may
lead to a sort of frenetic distractibility, where nothing gains the complete
attention and the individual always feels “scattered,” “distracted,” and
busied. The ways in which coherence manifests symptomatically are dependent upon the frequency band they manifest in. Hypercoherence in beta is very different than hypercoherence in alpha, for instance.&nbsp;<br><br><div><!--[if !supportFootnotes]--><h4>LORETA Coherence Measures</h4>

Loreta computes a&nbsp;<strong>three-dimensional distribution of 2394 voxels of 7x7x7 mm of the generating electric neuronal activity in the grey matter.</strong>&nbsp;A great advantage of this technique is that it isn’t restricted to a certain number of electrodes or electrode locations, and therefore it self-adapts to almost every electrode set-up and EEG measuring device.The measures of coherence and phase can also be taken from Low Resolution Electromagnetic Tomographical Analysis (LORETA), which is a weighted average and the best montage to glean coherences from. Unfortunately, using LORETA in a Z-scored format is a misuse, since inputting scalp z-transformed-maps will not output LORETA (current density) z-transformed-values. This invalid inputs to LORETA violate the mathematics and the physics underlying all computations.</div><div><img src="@@PLUGINFILE@@/LORETA%20Coherence%20.png" alt="LORETA Coherence" width="800" height="758" class="img-responsive atto_image_button_left"><br><hr align="left" size="1" width="33%">

<!--[endif]-->

<div id="ftn1">

<p><br></p>

</div>

</div><br><p></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><h4><br></h4><h4>Phase</h4><p>Phase is any one point or portion in a recurring series
of changes, as in the changes of motion of one of the particles constituting a
wave or vibration. There are metrics of phase in EEG an Quantitative EEG, one of the more commonly used is "phase lag." We expect a certain amount of phase lag between oscillations of the brain (for instance, can you see the lag between all three lines below? The black is the first wave, followed by the dark blue and then the light blue. Phase lag metrics are measured by phase reset, which is&nbsp;<img src="@@PLUGINFILE@@/Phase.png" alt="Phase" width="600" height="409" class="img-responsive atto_image_button_left">the&nbsp;<span style="font-size: 1rem;">time it takes for phase to lock (come into coherence) and shift (fall out of coherence) and the begin to lock again. The measure of how long these mechanisms take are measures of phase lag, as seen in normative databases, such as the Neuroguide image of phase lag below.&nbsp;</span></p><p>Blue phase lag is considered "hypo phase lag" and that means there is not enough phase lag (too much phase lock), a very similar measure to hypercoherence.&nbsp;</p><p>Red phase lag is considered "hyper phase lag" and that means there is too much phase lag (not enough phase lock), very similar to hypocoherence.&nbsp;</p><p><img src="@@PLUGINFILE@@/Phase%20Lag.png" alt="Phase Lag" width="700" height="512" class="img-responsive atto_image_button_text-bottom"><br></p><p><br></p><h4>Other Forms of Cross Frequency Coupling (CFC)</h4><p>Cross-frequency couplings are assessed by computing complex-valued coherences between Fourier transform coefficients at different frequencies. This methods detects all forms of amplitude-amplitude, phase-amplitude, and phase-phase coupling / information flow.&nbsp;<br></p><h4>Phase-Phase Cross Frequency Coupling (PPC)</h4><p><img src="@@PLUGINFILE@@/Phase%20Phase%20Coupling%20%281%29.png" alt="" role="presentation"><p>Phase-phase coupling (PPC), also known as cross frequency
phase synchrony (CPS), is one type of CFC that is commonly focused upon as
functionally relevant for the workings of the brain and thus for consciousness
(Siebenhühner et al. 2020).
In phase-phase coupling, we see the phase of a slower carrier wave align with
and serve as the carrier mechanism for a faster wave. This has been seen widely
with theta carrier waves and gamma waves, a phenomenon that is thought to be
fundamental in the encoding of memory (Scheffer-Teixeira &amp; Tort, 2016) .
Phase-phase coupling is amplitude independent and is reflective of an
“autonomous continuous time system” (Rosenblum et al., 1996). PPC is thought to
be a frequent type of neural temporal coding (Jirsa and Muller, 2013).&nbsp;</p></p><h4>Amplitude-Amplitude Coupling (aka Power-Power Coupling)</h4><p><img src="@@PLUGINFILE@@/Amplitude%20Amplitude%20Coupling.png" alt="Amplitude amplitude coupling" width="300" height="154" class="img-responsive atto_image_button_left"><p>Most quantitative analyses of EEG and MEG use fast Fourier
transformation (FFT) to compute power spectral density (PSD). However, this
measure fails to show the fast temporal dynamics that EEG brain-imaging is
best-suited for. This temporal resolution issue has been resolved through calculating
the spectral covariance of power-power coupling (PPC). Power-power coupling reveals how
amplitude (power) modulations in one frequency are affected by amplitude modulations
in the other frequency. The coupling can be found within different frequencies,
or within the same frequency. The measurement of PPC is seen not through the quantitative
analysis of FFT, but can be seen through Independent Component Analysis (ICA) via
the -Power-Power Coupling Analysis Toolbox (PowPowCat), a free open-source
toolbox for EEGLAB (Thammasan &amp; Miyakoshi, 2020).</p>

<p>&nbsp;<img src="@@PLUGINFILE@@/powerpowercoupling.png" alt="poeerpowerciupling" width="700" height="480" class="img-responsive atto_image_button_left"></p>

<p>When oscillations of two different frequencies covary in
time, power-power coupling may occur. This measurement is depicted in a
comodulogram, also known as a comodugram (Figure xx). The other detail provided
via this software graphical user interface include the time series of the
combination of the two selected frequency bins (specified by cursor position);
the scatter plot of the power spectral diagram, the correlation coefficient of
the two chosen frequencies, and the power spectrum density by spectrogram. This
type of measurement is uniquely beneficial in detecting thalamo-cortical
dysrhythmias, as seen in Parkinson’s Disease, tinnitus, depression, and some
forms of neuropathic pain (Vanneste et al., 2018).</p><p><br></p><p><p><i>The above image shows the interactive graphical
user (GUI) interface of power-power coupling analysis toolbox (PowPowCat),
showing the spectral covariance in which cross-frequency points within an
independent component correlate via a correlation coefficient, “r.”</i></p><br></p></p><h4>Phase-Amplitude Coupling (PAC)</h4><p><img src="@@PLUGINFILE@@/Phase%20Amplitude%20Coupling.png" alt="Phase Amplitude Coupling" width="300" height="368" class="atto_image_button_left"><br></p><p><p>Phase is not the only important dynamic of coupled oscillatory
phenomena. The second key variable is amplitude, also known as power. Phase and
amplitude can be meaningfully correlated and are functionally relevant to the
workings of the brain and consciousness (Siebenhühner et al. 2020). PAC usually
refers to a correlation
between the amplitude of faster rhythms (high gamma range) and the phase of
slower rhythms (2-12Hz range) (Florin &amp; Baillet, 2015; Canolty et al.,
2006; Tort et al., 2008, 2009; Voytek et al., 2010).</p>

<p>Jensen
and Colgin (2007) believe, “gamma oscillations might emerge at a particular
phase of the theta cycle and thereby recruit cell assemblies involved in
processing at that time.”&nbsp;
In most cases of this phenomenon, the slower oscillation exerts influence and
modulates the amplitude of the faster oscillation. Lakatos et al. (2005)
hypothesized a “hierarchical” organization of EEG oscillations exists in this
regard. This
type of coupling is commonplace in computational neuroscience, second only to
phase-phase coupling and has been thought of as an “integration mechanism”
between rate and temporal coding—rate attributed to amplitude and temporal
attributed to phase (Jirsa et al., 2013).</p>

<p>An example of PAC has been found
between many frequencies. with gamma and theta band CFC. Bagur et al. (2018)
examines data suggesting that theta frequency band (slower) modulates gamma
frequency band (faster) amplitude, with each theta cycle comprising a single
packet of gamma information from the sensory cortex. Buzsaki (2010, 2012)
suggests that these gamma packets may comprise a kind of brain syntax for
ordering and integrating information from different parts of the brain, while
De Ridder (cite) postulates that memory and predictions are encoded in
oscillations (memory being the low frequency oscillations and prediction and
prediction error being the high frequency oscillations. Likewise, Lisman (1995)
and Jensen (2006) believe the nesting of fast frequencies into slower one
predicts memory, while others have postulated nesting permits prediction
(O’Keefe, 1993; Jensen, 1996). Another function tied to gamma band activity
synchronized with thalamo-cortical activity is conscious auditory perception (Crone,
2001, Joliot, 1994; Llinas, 1998).</p></p>