Assessing synchronized activity in the human brain through frequency-dependent covariance analysis

This year is the centennial anniversary of German psychiatrist Hans Berger’s invention of electroencephalography (EEG), a way to record electrical activity in the brain, now called brainwaves or neural oscillations. Amazingly, Berger was motivated after an incident in his military years when he believed he had spontaneously transmitted something from his brain to his sister during a sudden moment when he was nearly killed in an accident, and his sister several kilometers away insisted their father get in touch with him.

Years later Berger called it “spontaneous telepathy.”

Berger’s EEGs record electrical activity in the brain, enabling evaluation of brain activity that originates in neurons in underlying brain tissue, typically showing waves whose frequencies correlate with how awake a person is. The years since Berger’s invention and discovery have, of course, revealed a great deal about the activity and brainwave patterns in the brain.

It is believed that some biological neural networks operate very close to phase transitions between dynamical regions that are ordered or disordered. Called the critical brain hypothesis, it posits that avalanche criticality and edge of chaos criticality are especially important in studies of brain function and dysfunction.

Evidence suggests it is actually near-critical states, as opposed to a singular state of a strictly critical state, that may be closer to observations and a better explanation for how the brain operates; brain states on the verge of criticality enhance the capacity for the brain to process information, store information and transmit it.

Now a team from the University of Granada in Spain has presented a new framework to explore signs of criticality across different brainwave frequency bands and constructed a more comprehensive picture of brain activity. In doing so, they have seen significant differences in signatures of criticality between data on healthy patients and people with Parkinson’s disease.

Lead author Rubén Calvo and his collaborators’ work has been published in Physical Review Letters.

Earlier work to validate the critical brain hypothesis used statistical analysis—time-averaged neuron firing rates. Calvo and his team took a deeper look, analyzing the way the distribution of how the firings occur over time. In particular, they used a “covariance matrix” to flesh out patterns within the data using a statistical technique called principal-component analysis (PCA).

PCA is a widely used technique to explain data of many variables by calculating new variables that are linear combinations of the original variables; they best explain the variance in the data.

Transforming the data in this way will create a new coordinate system with the greatest variance lying along the first coordinate, the second greatest variance (after the first coordinate’s variance is removed) is along the second, and so on. PCA analysis simplifies the data structure while making the explanatory variables more obvious.

To minimize known limitations with the PCA technique, the Granada group used frequency-dependent PCA, where frequency is that of brainwaves, such as those in the classifications labeled gamma, beta, alpha, theta and delta. Brain activity presents as diverse, time-dependent oscillations across many frequency bands, together with more complex nonperiodic oscillations.

Together they describe short-lived synchronizations of neurons, which is crucial for transmitting and integrating information between regions of the brain. The effectiveness of this depends on the distance to the edge of instability/criticality in the frequency band, the distance being in frequency space (viz. after a Fourier Transform).

The covariance matrix is the correlation between the firing rates of the many pairs of neurons. Solving for the covariance matrix gives a list of eigenvalues and eigenvectors—the leading eigenvectors represent directions of maximum variability, and associated eigenvalues represent the distance along that eigenvector.

This allows the very complicated dataset of firing rates to be described in a much simpler, low-dimensional manner. With frequency-dependent firing rates, Calvo and his group showed that the spectrum of eigenvalues can be used to deduce the distance to criticality for any frequency band.

“Therefore,” they write, “the frequency-dependent covariance matrix allows us to observe fingerprints of criticality in datasets with a nontrivial temporal organization and unveil dynamical features that could not be uncovered through standard analyses of the integrated longtime covariance.” Switching to multi-frequency space reveals dynamical processes that static covariances cannot.

To test their methodology, they used firing rate data from patients with Parkinson’s disease, a movement disorder of the nervous system. Measuring the distances from criticality, they discovered that “there is a significantly broader interval of frequencies close to the edge of instability compared to the control group”—more frequencies close to the instabilities in frequency space.

The brainwaves of Parkinson’s patients have significantly different structures in space and time. They conclude that their decomposition of data on brain activity could be a “promising avenue” for future research in understanding the differences between healthy brain states and pathological states.

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