The publication of this manuscript has been partially supported by the SFI FutureNeruro-Funded Investigator grant to DT.

The following experimental protocol is in accordance with all local, national, and international ethics guidelines for human research. The data used to test the protocol have been acquired with authorization of the Ethical Committee of region Tuscany-protocol 2018SMIA112 SI-RE.
NOTE: The scripts used for implementing the analyses described are available at https://github.com/conorkeogh/NetworkAnalysis.
1. Raw Data Collection
<ol>
	<li>Prep...

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L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=EEG+and+MEG+coherence:+measures+of+functional+connectivity+at+distinct+spatial+scales+of+neocortical+dynamics.">EEG and MEG coherence: measures of functional connectivity at distinct spatial scales of neocortical dynamics.</a> Journal of Neuroscience Methods. 166 (1), 41-52 (2007).</li><li>Bullmore, E., Sporns, O. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Complex+brain+networks:+graph+theoretical+analysis+of+structural+and+functional+systems.">Complex brain networks: graph theoretical analysis of structural and functional systems.</a> Nature Reviews Neuroscience. 10, 186-198 (2009).</li><li>Baccal&#225;, L., Sameshima, K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Partial+directed+coherence:+a+new+concept+in+neural+structure+determination.">Partial directed coherence: a new concept in neural structure determination.</a> Biological Cybernetics. 84, 463-474 (2001).</li><li>Sameshima, K., Baccal&#225;, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Using+partial+directed+coherence+to+describe+neuronal+ensemble+interactions.">Using partial directed coherence to describe neuronal ensemble interactions.</a> Journal of Neuroscience Methods. 94, 93-103 (1999).</li><li>Seth, A., Barrett, A. B., Barnett, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Granger+causality+analysis+in+neuroscience+and+neuroimaging.">Granger causality analysis in neuroscience and neuroimaging.</a> Journal of Neuroscience. 35, 3293-3297 (2015).</li><li>Hesse, W., M&#246;ller, E., Arnold, M., Schack, B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+use+of+time-variant+EEG+Granger+causality+for+inspecting+directed+interdependencies+of+neural+assemblies.">The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies.</a> Journal of Neuroscience Methods. 124, 27-44 (2003).</li><li>Nunez, P. L., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=EEG+coherency.+I:+Statistics,+reference+electrode,+volume+conduction,+Laplacians,+cortical+imaging,+and+interpretation+at+multiple+scales.">EEG coherency. I: Statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales.</a> Electroencephalography and Clinical Neurophysiology. 103, 499-515 (1997).</li><li>Nunez, P. 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The authors have nothing to disclose.

The described method allows the derivation of statistical maps of cortical network dynamics from non-invasive EEG data. This allows the investigation of phenomena not readily apparent on examination of simple time series data through assessment of how the recorded regions are interacting with each other, rather than evaluating what is happening in each individual location in isolation. This can reveal important insights into disease pathology18.
The essential aspect of ...

This method aims to produce statistical maps of cortical networks based on non-invasive electrode recordings using a clinically viable setup, to allow for investigation of nervous system pathology, the impact of novel treatments, and the development of novel electrophysiological biomarkers.
EEG offers great potential for the investigation of nervous system function and disease1,2. This technology is inexpensive, readily available in research and clinical settings, and generally well tolerated. The simple, non-invasive nature of recordings make clinical use straightforward, and the existing framework of clinical EEG departments allows for easy access to the technology for clinicians.
From a technical perspective, EEG offers excellent time domain resolution3. This is of great importance when investigating nervous system function due to the rapid timescales of nervous system interactions and network dynamics. While imaging methods such as functional MRI offer greater spatial resolution and easily interpretable images, they are far more limited in their ability to interrogate nervous system function on the fine time scales offered by electrophysiological recordings4,5,6.
There is a growing need for the ability to interrogate nervous system function to inform diagnosis, treatment, and prognostication of nervous system diseases. The role of cortical network dynamics in nervous system pathology is increasingly recognized7. Many pathologies of the nervous system produce no macroscopic structural lesions visible with traditional imaging, but the abnormalities produced at the network level may be apparent with appropriate functional analysis methods.
Unfortunately, current EEG analysis methods are greatly limited in this regard. Traditional methods involve the analysis of simple time series data from individual electrodes. These signals represent the summation of field potentials in large cortical areas3,8. Analysis of data from individual channels in isolation using either visual inspection or simple statistical methods limits the usefulness of these recordings to detecting gross electrophysiological abnormalities in discrete, individual locations. With the increasing recognition of the importance of network-level effects to nervous system function and pathology, these simple analysis methods are clearly deficient in that they will fail to detect subtle relationships between signals, representing abnormalities in how cortical areas are interacting with one another at the network level.
A method of deriving statistical maps of cortical network connectivity from low-dimensional electrode recordings is demonstrated. This method allows investigation of the dynamics of interactions between varying brain regions in a way that is not possible with traditional analysis techniques, as well as visualization of these network interactions. This opens the possibility for non-invasive investigation of network level effects at high time domain resolutions in ways not previously possible. This method is based on the derivation of measures of interelectrode coherence9,10. These measures allow the investigation of how two recorded regions are interacting by evaluating the statistical relationships between the recordings of these areas11. By assessing how each recorded area interacts with every other recorded area, a statistical map of electrophysiological networks within the recorded areas can be made. This allows for the discovery of functional relationships that are not apparent on evaluation of individual channel data in isolation.
The focus of this manuscript is on the use of coherence on neural time series. Currently, there are a number of techniques for investigating the relationships between time series data that can be applied to channels in a pairwise fashion to derive models of cortical connectivity. Some methods, such as the related partial directed coherence12,13, aim to infer the direction of influence of the pair of signals investigated in order to better characterize the structure of the underlying networks, while other methods, such as Granger causality14,15, attempt to infer functional relationships through the ability of one signal to predict the data in another. Methods such as these can be applied in similar ways to generate high-dimensional models of cortical networks. However, the advantages of coherence as a means of investigating relationships between neural signals lies in its lack of assumptions. It is possible to investigate statistical relationships between recordings at two sites without making statements about the functional basis of these relationships and to build up a model of cortical connectivity based purely on statistical relationships with minimal assumptions about the cortical networks generating these signals.
Due to the purely mathematical nature of these measures, the relationship between the coherence measures of electrode recordings at the scalp and the underlying neural activity is complex16,17. While these methods allow the derivation of statistical constructs describing relationships between the electrode recordings for comparison, making direct causal inferences about the activity of the specific underlying neural populations is not straightforward3,8,16,17. These approaches allow for comparison of the network-level activity between groups to identify potentially useful biomarkers but are limited in terms of drawing specific conclusions regarding the relationship of these markers to specific neural mechanisms. This is due to the large number of confounding factors influencing the recorded activity3, as well as issues with estimating the specific cortical source of electrical signals recorded at the level of the scalp8. Rather, these approaches can produce statistical models of activity that can be interrogated and compared between groups to determine that differences exist at the network level18 and can be leveraged to produce novel biomarkers based on these constructs. However, these methods alone have a limited capacity to relate the differences seen to specific mechanisms and neural activities due to the complexity of the underlying system.
The use of network measures such as coherence is well established in systems neuroscience16,17. The full potential of these approaches for modelling and investigating cortical function has been limited by a lack of exploitation of these high-dimensional data structures. This work demonstrates that it is possible to apply these measures to EEG channels in a pairwise fashion in order to map data onto a high-dimensional feature space based purely on the statistical relationships between the electrical activity in cortical regions. It also demonstrates that, using modern statistical techniques, it is possible to use the generated models of cortical function to investigate these models without losing the information gained in the modelling process.
This method is potentially valuable in expanding the scope of applications of existing EEG technologies, improving the ability to derive useful functional measures without requiring adaptations to existing recording equipment18,19. By improving the ability to model cortical function and interrogate these models, the questions that can be investigated using EEG data are expanded. This further opens the possibility of greater integration of functional and structural evaluations for investigation of neurological disease20,21. This approach, using technology that is already widely available clinically, would allow investigation of cortical pathologies with both high temporal and spatial resolution.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Electrode cap</td>
			<td>ElectroCap International</td>
			<td></td>
			<td>Or any suitable cap</td>
		</tr>
		<tr>
			<td>Conductive gel</td>
			<td>SignaGel</td>
			<td></td>
			<td>Or any suitable gel</td>
		</tr>
		<tr>
			<td>Pin-type electrodes</td>
			<td>BioSemi</td>
			<td></td>
			<td>Or any suitable electrode</td>
		</tr>
		<tr>
			<td>BioSemi Active Two recording system</td>
			<td>BioSemi</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>ActiView recording environment</td>
			<td>BioSemi</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>MATLAB software</td>
			<td>Mathworks</td>
			<td></td>
			<td></td>
		</tr>
	</tbody>
</table>

statistical modelling of cortical connectivity using non-invasive electroencephalograms

Non-invasive electrophysiological recordings are useful for the evaluation of nervous system function. These techniques are inexpensive, fast, replicable, and less resource-intensive than imaging. Further, the functional data produced have excellent temporal resolution, which is not achievable with structural imaging.
Current applications of electroencephalograms (EEG) are limited by data processing methods. Standard analysis techniques using raw time series data at individual channels are very limited methods of interrogating nervous system activity. More detailed information about cortical function can be achieved by examining relationships between channels and deriving statistical models of how areas are interacting, allowing visualization of connectivity between networks.
This manuscript describes a method for deriving statistical models of cortical network activity by recording EEG in a standard manner, then examining the interelectrode coherence measures to assess relationships between the recorded areas. Higher order interactions can be further examined by assessing the covariance between the coherence pairs, producing high-dimensional &#34;maps&#34; of network interactions. These data constructs can be examined to assess cortical network function and its relationship to pathology in ways not achievable with traditional techniques.
This approach offers greater sensitivity to network level interactions than is achievable with raw time series analysis. It is, however, limited by the complexity of drawing specific mechanistic conclusions about the underlying neural populations and the high volumes of data generated, requiring more advanced statistical techniques for evaluation, including dimensionality reduction and classifier-based approaches.

Measurements of the spectral power will produce n measures for each frequency band measured, where n is the number of channels recorded. These measures will be in decibels for the overall power. Measures of power within individual frequency bands should be expressed as relative power (i.e., the proportion of overall power represented by power within that band) to allow accurate comparisons between groups and conditions.
An example of visualiza...

Watch this Scientific Journal Video about Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms at JoVE.com

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Standard EEG analysis techniques offer limited insight into nervous system function. Deriving statistical models of cortical connectivity offers far greater ability to investigate underlying network dynamics. Improved functional assessment opens new possibilities for diagnosis, prognostication, and outcome prediction in nervous system diseases.

Non-invasive electrophysiological recordings are useful for the evaluation of nervous system function. These techniques are inexpensive, fast, replicable, ...

This protocol is significant as it allows the investigation of cortical networks by modeling how regions interact with one another to reveal differences not evident with standard analysis techniques. The main advantage of this technique is that it allows us to investigate network functions using widely available equipment so we can obtain non-invasive electrical recordings without the need for specialized materials. This technique allows the non-invasive investigation of neuropsychiatric diseases by examining network structures facilitating the development of novel diagnostic methods and therapeutic biomarkers.This method has a broad range of applications within the clinical neurosciences particularly as the role of network function in disease becomes increasingly relevant. For data collection, attach the electrode cap to the patient's head taking care to ensure a correct alignment. Inject conductive gel into each of the electrode ports beginning at the scalp and slowly withdrawing to the cap surface to establish electrical contact with the scalp and to improve the signal-to-noise ratio.Then use a predetermined electrode montage based on the 10-20 system to attach the electrodes to the electrode cap and secure the appropriate ground electrodes. To set up the EEG, connect all of the electrodes to an electrophysiological recording system and link the recording system with an appropriate digital recording environment. Examine all of the recording channels to ensure that the offset is within an appropriate range and to avoid excessive channel noise.The algorithm will produce results regardless of the data quality so the recordings should be performed under strict data quality conditions and should be analyzed prior to their use. Then instruct the patient that recording has started and to avoid all unnecessary movements before conducting a short test recording to verify appropriate recording quality. At the end of the analysis, load the EEG data and any additional script libraries as necessary into a suitable data analysis environment.Discard the first and last five minutes of each recording to reduce the contamination of any movement artifacts and split the data into epochs based on task or if it is a resting state recording predetermined duration. To prepare the data, correct the baseline of the recordings by subtracting the mean of all of the channels from the recordings to avoid the impact of any baseline wandering during prolonged recordings. Rereference all of the channels to an appropriate reference.Then digitally filter all of the channels to isolate the frequencies of interest. To calculate the overall power spectra of the data, perform a Fourier transform of each channel being analyzed across the whole frequency range to be assessed. To assess the activity of individual frequency bands, isolate the theta band at four to eight hertz, the alpha band at eight to 12 hertz, the beta band at 12 to 30 hertz, the delta band at 0.5 to four hertz, and the gamma band at greater than 30 hertz.To evaluate the interactions between the first electrode pair, derive a measure of inter-electrode coherence. To assess the coherence, map the measurements of the inter-electrode coherence to be visualized onto a two-dimensional data structure where each column is an electrode location, each row is an electrode location, and each cell is the coherence between the corresponding electrode pair and map the coherence values to between zero and one colors. Then export a color map visualizing the inter-electrode coherence between each electrode pair within the frequency limits used.To visualize higher order interactions between cortical areas and to map out network dynamics, calculate how each electrode pair coherence measure covaries with those of every other unique electrode pair across the overall spectrum and within specific bands. Then map these covariance measures to colors and export a color map visualizing the network dynamics within and across frequency bands. To perform a dimensionality reduction, derive measures for comparison between the groups that represent the overall network dynamics within the statistical models generated using the principle component analysis.Instruct a covariance matrix for the pair-wise coherence measures to allow visualization of the high level network relationships and decompose the covariance matrix into eigenvectors and corresponding eigenvalues to allow identification of the axis within the model feature space that contain the greatest variance without being bounded by the existing measures. Rank the eigenvectors by their corresponding eigenvalues to identify those accounting for the greatest proportion of variance within the model. Then compare the first principle components derived from the network models.To select a functional region of interest, isolate the coherence data within the frequency bands of interest. Perform a principle component analysis to derive measures of overall network activity within the bands of interest. Then compare the measures between the groups to evaluate the network differences at specific oscillatory frequencies.To perform unsupervised learning using a distance metric such as Euclidean distance, compute the measures of distance between subjects within the space defined by the network model. Then use a clustering algorithm such as k-nearest neighbors to identify the groups within the data based on the model parameters. The spectral power can be visualized interpolated across the scalp allowing a limited estimation of the source of activity.Each of the inter-electrode electrode measure indicates the extent to which the activity in one area changes depending on the activity in another area allowing for differences in the direction of the interaction and time lag. Higher values of inter-electrode coherence suggest interactions between areas from which it is apparent that the recorded areas are communicating with each other. By measuring the interactions between every unique electrode pair, a statistical map of how the recorded channels are interacting can be constructed allowing investigation of how the areas are communicating rather than focusing on individual areas of isolation.The visualization of higher order network dynamics facilitates the recognition of the kinds of interactions being compared by a principle component analysis or a classifier-based technique to evaluate how the coherence measurements at one electrode pair relate to changes in coherence at another pair. For example, here we can visualize differences evident in the network mapping between two subjects with different clinical phenotypes of a neuropsychiatric disorder affecting cortical function where there were no statistically significant differences using standard analysis methods. Following the derivation of network measures using this procedure, machine learning techniques can be employed to leverage the data-rich models produced to allow more sophisticated diagnostic and prognostic analyses.This technique has allowed the investigation of disease subtypes in Rett syndrome, a pediatric neuropsychiatric disease, as well as the prediction of responses to novel treatments and epilepsy status.

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5.5K Views.  University Hospital Limerick. This protocol is significant as it allows the investigation of cortical networks by modeling how regions interact with one another to reveal differences not evident with standard analysis techniques. The main advantage of this technique is that it allows us to investigate network functions using widely available equipment so we can obtain non-invasive electrical recordings without the need for specialized materials. This technique allows the non-invasive investigation of neuropsychiatric dise...