Name: microstate and omega complexity analyses of the resting-state electroencephalography
Uploaded: 2018-06-15T12:30:00
Description: Watch this Scientific Journal Video about Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography at JoVE.com

This article was supported by the National Natural Science Foundation of China (31671141).

This protocol was approved by the local ethical committee. All the participants and their parents signed an informed consent form for this experiment.
1. Subjects
<ol>
	<li>Only include 15 healthy male adolescent subjects, whose age ranges from 14 to 22 years (mean &#177; standard deviation: 18.3 &#177; 2.8 years). 
	NOTE: The current protocol to analyze the microstate and omega complexity has been developed for healthy subjects, but is not restricted to this group only.</li>
</ol>
<p c...

<ol>
	<li>Khanna, A., 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=Microstates+in+resting-state+EEG:+current+status+and+future+directions.">Microstates in resting-state EEG: current status and future directions.</a> Neurosci Biobehav Rev. 49, 105-113 (2015).</li><li>Chen, J. L., Ros, T., Gruzelier, J. H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Dynamic+changes+of+ICA-derived+EEG+functional+connectivity+in+the+resting+state.">Dynamic changes of ICA-derived EEG functional connectivity in the resting state.</a> Hum Brain Mapp. 34 (4), 852-868 (2013).</li><li>Imperatori, C., 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=Aberrant+EEG+functional+connectivity+and+EEG+power+spectra+in+resting+state+post-traumatic+stress+disorder:+a+sLORETA+study.">Aberrant EEG functional connectivity and EEG power spectra in resting state post-traumatic stress disorder: a sLORETA study.</a> Biol Psychol. 102, 10-17 (2014).</li><li>Gao, F., 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=Altered+Resting-State+EEG+Microstate+Parameters+and+Enhanced+Spatial+Complexity+in+Male+Adolescent+Patients+with+Mild+Spastic+Diplegia.">Altered Resting-State EEG Microstate Parameters and Enhanced Spatial Complexity in Male Adolescent Patients with Mild Spastic Diplegia.</a> Brain Topogr. 30 (2), 233-244 (2017).</li><li>Seitzman, B. A., 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=Cognitive+manipulation+of+brain+electric+microstates.">Cognitive manipulation of brain electric microstates.</a> Neuroimage. 146, 533-543 (2017).</li><li>Lehmann, D., Michel, C. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=EEG-defined+functional+microstates+as+basic+building+blocks+of+mental+processes.">EEG-defined functional microstates as basic building blocks of mental processes.</a> Clin Neurophysiol. 122 (6), 1073-1074 (2011).</li><li>Koenig, T., 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=Millisecond+by+millisecond,+year+by+year:+normative+EEG+microstates+and+developmental+stages.">Millisecond by millisecond, year by year: normative EEG microstates and developmental stages.</a> Neuroimage. 16 (1), 41-48 (2002).</li><li>Britz, J., Van De Ville, D., Michel, C. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=BOLD+correlates+of+EEG+topography+reveal+rapid+resting-state+network+dynamics.">BOLD correlates of EEG topography reveal rapid resting-state network dynamics.</a> Neuroimage. 52 (4), 1162-1170 (2010).</li><li>Musso, F., 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=Spontaneous+brain+activity+and+EEG+microstates.+A+novel+EEG/fMRI+analysis+approach+to+explore+resting-state+networks.">Spontaneous brain activity and EEG microstates. A novel EEG/fMRI analysis approach to explore resting-state networks.</a> Neuroimage. 52 (4), 1149-1161 (2010).</li><li>Strelets, V., 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=Chronic+schizophrenics+with+positive+symptomatology+have+shortened+EEG+microstate+durations.">Chronic schizophrenics with positive symptomatology have shortened EEG microstate durations.</a> Clin Neurophysiol. 114 (11), 2043-2051 (2003).</li><li>Kikuchi, M., 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+microstate+analysis+in+drug-naive+patients+with+panic+disorder.">EEG microstate analysis in drug-naive patients with panic disorder.</a> PLoS One. 6 (7), e22912 (2011).</li><li>Santarnecchi, E., 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+Microstate+Correlates+of+Fluid+Intelligence+and+Response+to+Cognitive+Training.">EEG Microstate Correlates of Fluid Intelligence and Response to Cognitive Training.</a> Brain Topogr. , (2017).</li><li>Schlegel, F., 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+microstates+during+resting+represent+personality+differences.">EEG microstates during resting represent personality differences.</a> Brain Topogr. 25 (1), 20-26 (2012).</li><li>Wackermann, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Beyond+mapping:+estimating+complexity+of+multichannel+EEG+recordings.">Beyond mapping: estimating complexity of multichannel EEG recordings.</a> Acta Neurobiol Exp (Wars). 56 (1), 197-208 (1996).</li><li>Jung, T. P., 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=Removing+electroencephalographic+artifacts+by+blind+source+separation.">Removing electroencephalographic artifacts by blind source separation.</a> Psychophysiology. 37 (2), 163-178 (2000).</li><li>Pascual-Marqui, R. D., Michel, C. M., Lehmann, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Segmentation+of+brain+electrical+activity+into+microstates:+model+estimation+and+validation.">Segmentation of brain electrical activity into microstates: model estimation and validation.</a> IEEE Trans Biomed Eng. 42 (7), 658-665 (1995).</li><li>Pascual-Marqui, R. D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Standardized+low-resolution+brain+electromagnetic+tomography+(sLORETA):+technical+details.">Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details.</a> Methods Find Exp Clin Pharmacol. 24, 5-12 (2002).</li><li>Hu, 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=The+primary+somatosensory+cortex+contributes+to+the+latest+part+of+the+cortical+response+elicited+by+nociceptive+somatosensory+stimuli+in+humans.">The primary somatosensory cortex contributes to the latest part of the cortical response elicited by nociceptive somatosensory stimuli in humans.</a> Neuroimage. 84, 383-393 (2014).</li><li>Murray, M. M., Brunet, D., Michel, C. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Topographic+ERP+analyses:+a+step-by-step+tutorial+review.">Topographic ERP analyses: a step-by-step tutorial review.</a> Brain Topogr. 20 (4), 249-264 (2008).</li><li>Van de Ville, D., Britz, J., Michel, C. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=EEG+microstate+sequences+in+healthy+humans+at+rest+reveal+scale-free+dynamics.">EEG microstate sequences in healthy humans at rest reveal scale-free dynamics.</a> Proc Natl Acad Sci U S A. 107 (42), 18179-18184 (2010).</li><li>Gonuguntla, V., Mallipeddi, R., Veluvolu, K. C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Identification+of+emotion+associated+brain+functional+network+with+phase+locking+value.">Identification of emotion associated brain functional network with phase locking value.</a> Conf Proc IEEE Eng Med Biol Soc. 2016, 4515-4518 (2016).</li><li>Wen, D., 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=Resting-state+EEG+coupling+analysis+of+amnestic+mild+cognitive+impairment+with+type+2+diabetes+mellitus+by+using+permutation+conditional+mutual+information.">Resting-state EEG coupling analysis of amnestic mild cognitive impairment with type 2 diabetes mellitus by using permutation conditional mutual information.</a> Clin Neurophysiol. 127 (1), 335-348 (2016).</li><li>Rosales, F., 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=An+efficient+implementation+of+the+synchronization+likelihood+algorithm+for+functional+connectivity.">An efficient implementation of the synchronization likelihood algorithm for functional connectivity.</a> Neuroinformatics. 13 (2), 245-258 (2015).</li><li>Jia, H., Peng, W., Hu, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+novel+approach+to+identify+time-frequency+oscillatory+features+in+electrocortical+signals.">A novel approach to identify time-frequency oscillatory features in electrocortical signals.</a> J Neurosci Methods. 253, 18-27 (2015).</li><li>Wackermann, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Global+characterization+of+brain+electrical+activity+by+means+of+the+&#937;+complexity+production+rate.">Global characterization of brain electrical activity by means of the &#937; complexity production rate.</a> Brain Topogr. 18, 135 (2005).</li><li>Wackermann, J., Putz, P., Ga&#223;ler, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Unfolding+EEG+spatial+complexity+as+a+function+of+frequency.">Unfolding EEG spatial complexity as a function of frequency.</a> Brain Topogr. 16 (2), 124 (2003).</li></ol>

In this article, two kinds of EEG analytic methods (i.e., microstate analysis and omega complexity analysis), measuring the temporal complexity and spatial complexity of human brain respectively, were described in detail. There are several critical steps within the protocol that should be mentioned. Firstly, the EEG data must be cleaned before the computation of the microstate and omega complexity. Secondly, the EEG data should be remontaged against the average reference before the computation of the microstate and omega...

Electroencephalography (EEG) has been widely used to record electrical activity of the human brain both in clinical diagnosis and scientific research, since it is noninvasive, low-costed and has very high temporal resolution1. In order to study the EEG signals in resting state, researchers have developed many EEG techniques (e.g., power spectrum analysis, functional connectivity analysis)2,3. Of these, microstate analysis and omega complexity analysis could make good use of the spatial and temporal information inherent in EEG signals4.
Previous researches have shown that although the topographical distribution of EEG signals varies over time in eye-closed or eye-open resting state, the series of momentary maps show discontinuous changes of landscapes, i.e., periods of stability alternating with short transition periods between certain quasi-stable EEG topographies5. Microstates are defined as these episodes with quasi-stable EEG topographies, which last between 80 and 120 ms1. Since different electric potential landscapes must have been generated by different neural sources, these microstates may qualify as the basic blocks of mentation and can be considered as &#34;atoms of thought and emotion&#34;6. Using modern pattern classification algorithms, four resting EEG microstate classes have been consistently observed, which were labeled as class A, class B, class C and class D7. Moreover, researchers revealed that these four microstate classes of resting EEG data were closely associated with well-known functional systems observed in many resting-state fMRI (functional magnetic resonance imaging) studies8,9.Thus, the microstate analysis provided a novel approach to study the resting state networks (RSNs) of human brain. In addition, the average duration and the frequency of occurrence of each microstate class, the topographical shape of the four microstate maps are significantly influenced by some brain disorders4,10,11, and are associated with fluid intelligence12 and personality13.
In the other aspect, traditional functional connectivity of multi-channel EEG could only describe the functional connections between two scalp electrodes, thus failed to assess the global functional connectivity across scalp or within a certain brain region. The omega complexity, proposed by Wackermann (1996)14 and calculated through an approach combining principal component analysis (PCA) and Shannon entropy, has been used to quantify the broad-band global synchronization between spatially distributed brain regions. In order to assess the omega complexity of each frequency band, Fourier transform was commonly conducted as an initial step25.
The microstates and omega complexity can be used to reflect two closely linked concepts, i.e., the temporal complexity and spatial complexity4. Since the microstate classes represent certain mental operations in human brain, they can reflect the temporal structure of neuronal oscillations. Lower duration and higher occurrence rate per second must indicate higher temporal complexity. The omega complexity is positively related with the number of independent neural sources in brain, thus are commonly considered as an indicator of spatial complexity4.
The current article describes the protocol of EEG microstate analysis and omega complexity analysis in detail. The EEG microstate and omega complexity analyses offer the opportunity to measure the temporal and spatial complexities of brain activity respectively.

<table>
	<tbody>
		<tr>
			<td>ANT 20 channels EEG/ERP system</td>
			<td>ASA-Lab, ANT B.V., Netherlands</td>
			<td></td>
			<td>company web address: 
			http://www.ant-neuro.com/</td>
		</tr>
		<tr>
			<td>EEGLAB plugin for Microstates</td>
			<td>Thomas Koenig</td>
			<td></td>
			<td>https://sccn.ucsd.edu/wiki/EEGLAB_Extensions_and_plug-ins</td>
		</tr>
		<tr>
			<td>sLORETA</td>
			<td>Roberto D. Pascual-Marqui</td>
			<td></td>
			<td>http://www.uzh.ch/keyinst/loreta.htm</td>
		</tr>
		<tr>
			<td>MATLAB 2010a</td>
			<td>The MathWorks Inc.</td>
			<td></td>
			<td>company web address: 
			http://www.mathworks.com/</td>
		</tr>
		<tr>
			<td>eeglab</td>
			<td>Swartz Center for Computational Neuroscience, University of California, San Diego</td>
			<td></td>
			<td>https://sccn.ucsd.edu/eeglab/index.php</td>
		</tr>
	</tbody>
</table>

microstate and omega complexity analyses of the resting-state electroencephalography

Microstate and omega complexity are two reference-free electroencephalography (EEG) measures that can represent the temporal and spatial complexities of EEG data and have been widely used to investigate the neural mechanisms in some brain disorders. The goal of this article is to describe the protocol underlying EEG microstate and omega complexity analyses step by step. The main advantage of these two measures is that they could eliminate the reference-dependent problem inherent to traditional spectrum analysis. In addition, microstate analysis makes good use of high time resolution of resting-state EEG, and the four obtained microstate classes could match the corresponding resting-state networks respectively. The omega complexity characterizes the spatial complexity of the whole brain or specific brain regions, which has obvious advantage compared with traditional complexity measures focusing on the signal complexity in a single channel. These two EEG measures could complement each other to investigate the brain complexity from the temporal and spatial domain respectively.

EEG microstate
Grand mean normalized microstate maps are displayed in Figure 1. The electric potential landscapes of these four microstate classes identified here are very similar to those found in previous studies4.
The mean and standard deviation (SD) of microstate parameters of the healthy subjects were shown in <st...

Watch this Scientific Journal Video about Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography at JoVE.com

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

This article describes the protocol underlying electroencephalography (EEG) microstate analysis and omega complexity analysis, which are two reference-free EEG measures and highly valuable to explore the neural mechanisms of brain disorders.

Microstate and omega complexity are two reference-free electroencephalography (EEG) measures that can represent the temporal and spatial complexities of ...

This semester have answered 10 questions in the field of brain disorder, such as how to identify an efficient pair of markers to a code of bios in today's diagnosis. The main advantage of this technique is that it could emanate as a reference of the pending problem when you're adhering to traditional EEG analysis. The applications of this technique extend toward our understanding of resting-states networks of human brain.To begin this procedure, import the raw EEG data to the EEG lab software. Next, load the channel location file into the EEG lab software to obtain the spatial locations of these electrodes. To remove the reference electrodes, an option of Select data in channel range of the popup dialog box, select only the recording electrodes, and do not select the reference electrodes so that the reference electrodes can be removed.To band pass filter the EEG data between 0.5 and 80 hertz, in the popup dialog box, choose 0.5 for the lower edge of the frequency pass band hertz and choose 80 for the higher edge of the frequency pass band hertz. Then click Ok.To remove the powerline noise with a notch filter between 49 and 51 hertz, in the popup dialog box, choose 49 for the lower edge of the frequency pass band hertz and choose 51 for the higher edge of the frequency pass band hertz. Then select the option of Notch filter the data instead of pass band, and click Ok.To remove eye movements, click on Tools, then click Artifact removal using AAR 1.3, and EOG removal using BSS.To remove EMG, click Tools, then click Artifact removal using AAR 1.3 and EMG removal using BSS. Next, segment the preprocessed continuous EEG data into epochs with an epoch length of two seconds. A window will pop up that allows the saving of the segmented EEG data.Then import the segmented EEG data to the EEG lab software and reject EEG epochs with amplitude values exceeding plus or minus 80 microvolts at any electrode. Next, save the preprocessed EEG data. In this procedure for each subject, load the preprocessed EEG data, convert reference channels to common average reference, and band pass filter the EEG data between two and 20 hertz.Next, identify the four microstate maps in each subject. In the popup dialog box, choose three for the min number of classes, choose six for the max number of classes, choose 50 for the number of restarts, choose max number of maps to use, and select the options of GFP peak only, and No polarity. Then, click the Ok button.Subsequently, save the EEG data of each subject after identifying its own microstate maps. Import the EEG data sets of all subjects saved in the last step at once. Then identify the group level microstate maps.In the popup dialog box, select the data sets of all subjects in the option, Choose sets for averaging. In the option, Name of mean, give a name for the group level microstate maps, then click the button Ok.This will create a new data set named as GrandMean which stores the group level microstate maps. Manually sort the order of four group level microstate maps according to their classic order.In the popup, select More, and then the number of maps shown becomes four. After that, select Man sort. In the popup dialog box, enter the new order of four group level microstate maps and click Close.Following that, sort the order of the four microstate maps of each subject, save the microstate parameters for each subject which will invoke two popup dialog boxes sequentially. In the first dialog box, select the data sets of all subjects. In the second dialog box, select 4-Classes for option, Number of classes.Select the options of Fitting only on GFP peaks and Remove potentially truncated microstates. Next, choose 30 for the label smoothing window, ms, and choose One for the the Non-Smoothness penalty, then click Ok.A CSV file which stores submicrostate parameters will be saved on the computer. These images show that microstate Class A and B have a right frontal to left occipital orientation, and a left frontal to right occipital orientation respectively.Microstate Class C and D have symmetric topographies but prefrontal to occipital orientation, and front to central to occipital orientation were observed respectively. This table shows the mean and standard deviation of microstate parameters of the healthy subjects. Once mastered, this technique can be done in one hour if it is performed properly.While attempting this procedure, it's important to remember that the EEG data should be preprocessed carefully. Following this procedure, other methods like source localization can be performed in order to answer additional questions such as where these microstate maps come from. This technique paved a way for researchers in the field of brain science to expose disease as in human brain.

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