To view the plugin source code, please visit the plugin’s GitHub repository.

(Click the cat to download presentation slides). The slides are from the 31st EEGLAB workshop, day two ‘Time-frequency and connectivity analysis’ (November 30, 2021). Artwork is by Mayumi and Makoto Miyakoshi. All rights reserved!

# The PowPowCAT plugin for EEGLAB

What it does:

- It computes within-IC cross-frequency power-power coupling (covariance) called ‘comodugram/comodulogram’ (see references below) for a single-subject continuous IC activation.
- The preprocessing pipeline is as follows:
- Performs Matlab spectrogram() (hence it requires Matlab Signal Processing Toolbox) to compute spectrogram and power spectrum density (PSD) as its temporal average using 1-s window with 50% overlap and with modified () logarithmically-spaced frequency bins.

```
deviationFromLog = 5;
freqBins = logspace(log10(1+deviationFromLog), log10([user_input_value]+deviationFromLog), 100)-deviationFromLog;
```

- Finds boundary event in EEGLAB and removes the chunks that contain boundaries.
- Compute median across all the chunks to compute robust spectra, and compute the variance to discard 20% of chunks for cleaning.
- Compute covariance matrices of cross-frequency power spectrum for all the ICs (hence pre-selecting ICs is recommended; see this page for how to perform it efficiently.)
- Performs permutation statistics by randomizing chunk (i.e. datapoint) indices differently for each frequency bin to build surrogate time-frequency data, apply the same covariance calculation, and repeat these processes for 5,000 times. Finally, the observed (i.e. the real) covariance values are tested against the surrogate distribution using non-parametric method, stat_surrogate_pvals(). For multiple comparison correction, false discovery rate (FDR) is computed across all ICs and all pixels.
- By using mouse cursor, one can explore the frequency-frequency plot interactively and intuitively. The combination of frequency ranges as well as the correlation coefficient of the selected combination are shown.
- The subsampled time-courses of the two frequencies are shown in the bottom left plot.
- The scatter plot of the two time-series data are shown.

# Reference paper and erratum

Here is an erratum: The equation (1) in the above paper misses the normalization term 1/k. Too bad I had not found it before I published it!

# How to use it

- On the top left panel, choose whether you analyze electrode data or ICA-decomposed data.
- Enter the upper frequency limit in Hz.
- Choose parametric method (Pearson’s correlation coefficient) or non-parametric method (Spearman’s correlation coefficient). The parametric method is sensitive but susceptible to outliers, while the non-parametric method is robust but less sensitive. For further details, please see our paper (Thammasan and Miyakoshi, 2020).
- Set the number of iteration for the permutation test. Default is 5,000.
- Press the button ‘Precompute’ to start precomputing. It may take while, depending on how long your data is and how many electrodes/ICs there are.
- (Optional) When precompute is done, you may press the button on the top middle panel to show the first 35 electrodes/ICs to see the overview of the results.
- On the top right panel, enter the index of electrode/IC to show the results in the main interactive plotting panels. You may show the raw correlation coefficients, those masked by p<0.05 and by p<0.01 after false discovery rate (FDR) correction.

# Batch process from command line

The plugin package contains calc_PowPowCAT() which takes EEG and other 4 parameters as input and outputs EEG structure which contains EEG.etc.PowPowCAT under which precomputed PowPowCAT variables can be found.

# Results comparison

These are the selected independent components (ICs) with ICLabel-generated probabilistic labels.

Here is the comparison between PPC Pearson’s correlation coefficient (left) with Spearman’s correlation coefficient (right). The input data was continuous. The comodulogram is thresholded at FDR-corrected p<0.01. In the comodulogram, 11.5Hz-23.0Hz is selected. Note Pearson’ correlation is slightly more sensitive. Pearson’s correlation is calculated after removing 20% of outliers, while Spearman’s correlation is robust so data rejection is not applied.

The same comparison with the same but epoched data. The comodulogram is thresholded at FDR-corrected p<0.05. In the comodulogram, 11.5Hz-23.0Hz is selected. Note that sensitivity is reduced in the epoched data analysis.

The difference between the continuous and epoched data analysis is that for the former, 1-s sliding window with overlap of 50% is applied to obtain spectrogram, while for the latter, each epoch served as windows to analyze. Generally, it is recommended that you go back to the continuous data and apply the analysis. The results from the sliding-window calculation capturing ‘boundary’ events are excluded to avoid the boundary effect.

# Demonstration

EEGLAB workshop tutorial data ‘stern_125.set’ was analyzed. The continuous 71-ch data were low-pass filtered at 50Hz, and non-brain ICs were rejected manually. The overall results are shown below.

For example, IC6 and IC8 look similar in terms of their scalp topography and frequency spectra. However, when you compare their cross-frequency power correlations, the difference is clearer. Compare the difference of 10Hz-20Hz peak in the bottom-left box bewtween IC6 and IC8.

The analysis revealed complex cross-frequency power coupling structure in IC15 and IC21. For example, IC15 showed 11Hz, 22Hz, 33Hz, and 44Hz peaks as 2nd, 3rd, and 4th harmonics. Note that the 4th harmonics can be seen more clearly in the correation coefficient plot than that in the PSD plot, indicating better sensitivity of this method to detect cross-frequency power-power coupling structure.

# Group-level analysis (12/29/2021 added)

Nick Dogris hired me to develop this part of the extention. He donated it for public use (Thanks Nick!) The first step is to apply a batch process on multiple .set files. This can be done using a batch mode. From PowPowCAT menu, click the second item.

It opens the following sub-window.

At this stage, both electrode data and ICA-decomposed data are available. The results from the calculation is stored under EEG.etc.PowPowCAT. Note that this batch process overwrites the exising .set files. Note also that the target .set files must be in the single folder.

When the batch process is finished, go to the next step. Note that from now on, only ICA-decomposed results are supported because the solution uses dipole density plots.

In this sub-window, first push the top button. This promptes the user to select all the pre-computed data. By selecting all the data you want to include, it automatically starts the next calculation for optimum clustering. It may take a few minutes. Then the following result report pops up.

These plots show results from evalution of optimality when the numbers of the clusters are varied from 5 to 15. There are three popular criterion used for the k-means algorithm. The optimum points are highlighted with blue dots. In this example, I choose 11 because Silhouette index shows a slight peak there. Based on this decision, the default number is changed from 5 to 11. If you want, a part of the result we will see can be exported in an Excel file format by specifying the output folder (the bottom pushbotton and the edit box).

By pressing ‘Visualizee the results’ button, it generates the clustering results.

Note that it generates Matlab variable PowPowCAT in the base workspace by default. This is a structure variable which contains basically all the results for the user-defined optimum number of clusters. If the optional file export is also requested, it save to the part of the output: dataset ID, within-subject IC indices, and the corresponding cluster indices.

# Reference

Llinás RR, Ribary U, Jeanmonod D, Kronberg E, Mitra PP. (1999). Thalamocortical dysrhythmia: A neurological and neuropsychiatric syndrome characterized by magnetoencephalography. *Proc Natl Acad Sci USA*. 96:15222-15227

Sterman MB, Kaiser D. (2000). Comodulation: A new QEEG analysis metric for assessment of structural and functional disorders of the central nervous system. *Journal of Neurotherapy*. 4:73-83.

Buzsaki G, Buhl DL, Harris KD, Csicsvari J, Czeh B, Morozov A. (2003). Hippocampal network patterns of activity in the mouse. *Neuroscience*. 116:201-211.

Csicsvari J, Jamieson B, Wise KD, Buzsaki G. (2003). Mechanisms of Gamma Oscillations in the Hippocampus of the Behaving Rat. *Neuron*. 37:311-322.

Thatcher RW, Biver CJ, North DM. (2004). EEG and Brain Connectivity: A Tutorial. *Unpublished manuscript, PDF available online*.

Sullivan D, Csicsvari J, Mizuseki K, Montgomery S, Diba K, Buzsaki G. (2011). Relationships between hippocampal sharp waves, ripples, and fact gamma oscillation: infludence of dentate and entorhinal cortical activity. *The Journal of Neuroscience*. 31:8605-8616.

Buzsaki G, Wang X-J. (2012). Mechanisms of Gamma Oscillations. *Annu Rev Neurosci*. 35:203-225.

Jirsa V, Mueller V. (2013). Cross-frequency coupling in real and virtual brain networks. *Frontiers in Computational Neuroscience*. 7:78.

Zobay O, Adjamian P. (2015). Source-Space Cross-Frequency Amplitude-Amplitude Coupling in Tinnitus. *BioMed Research International*. 2015:489619.

Yeh C-H, Lo MT, Hu K. (2016). Spurious cross-frequency amplitude-amplitude coupling in nonstationary, nonlinear signals. Physica A. 454:453-150.

# Acknowledgement

I express my gratitude to Drs. Gyorgy Buzsaki and Tim Mullen for informative communication.

(This page was written by Makoto Miyakoshi)