Erin Munro Krull’s research utilizes new mathematical technique

Erin Munro Krull, assistant professor of mathematics and the Mark and Janice Franzen Professor in Applied Mathematics, recently published an article in Frontiers in Neuroscience. With two colleagues in the field of computational neuroscience, Munro Krull applied a new mathematical technique called Independent Component Analysis (ICA) to neural recordings from rat auditory cortex.

Since ICA is a relatively new technique, there were only a few times it had been applied and interpreted on neural signals before this study. ICA takes simultaneous recordings from many sensors dispersed in different locations, and decomposes the recordings into signals produced by separate populations.

Munro Krull gives an analogy for how this works: “Imagine multiple microphones arranged in a room across a chorus of singers. ICA takes the recordings from all the microphones and decomposes them to give what each choral section is singing separately.”

She says this is a new method of analyzing brain waves and reveals two different modes of operation during slow-wave sleep. The study produced implications for how we understand sleep stages and what exactly the brain does during sleep stages. “In particular, non-REM sleep was previously thought to be relatively uniform, but our analysis reveals two distinct modes of operation within non-REM sleep,“ she says.

She said the theta oscillations they found previously had been associated with emotional processing, while the larger amplitude oscillations they saw when there were no underlying theta oscillations are known to occur earlier in sleep.

“The larger amplitude non-REM oscillations may be linked to restorative processes in the brain, such as restoring chemical balances and repair,” Munro Krull says. “So, we hypothesize that earlier non-REM sleep serves as a restorative process, while later non-REM sleep serves as emotional processing. There are implications for work-life balance and the amount of sleep you get, the quality of sleep, and possibly post-traumatic stress.

“On top of that, this study shows that you can get consistent results when you apply ICA to real data and that those results can reliably tell you more information on what is going on in the brain.”


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