Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

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.