Focusing on the Alpha waves

The alpha waves co-exist with many other signals in human brain recordings. Although they can be easily spotted, just by looking at the EEG, pulling them apart from other brain activity requires special analysis approaches.

The standard way of isolating and quantifying alpha waves to this day is based on methods developed by Fourier, a French mathematician and physicist, in the early 1800s. Applied to brain activity, Fourier-based methods use filters to measure how well the brain signals match periodic functions of different frequencies. To isolate alpha waves, filters look for periodicity of brain activity around 10 Hz (10 cycles per second). Fourier methods are powerful and applied across many fields of science. Yet, they do not capture the real biological shapes of alpha waves in the brain.

Real brain activity is not perfectly periodic and symmetrical. Their real shape results from biological interactions of excitatory and inhibitory transmission across cells in circuits of different lengths, as well as the temporal characteristics of the molecules that mediate those communications. So, how can we actually see the real shape of alpha waves?

A promising alternative to Fourier methods is Empirical Mode Decomposition (EMD), developed in 1998 by Norden Huang, a Taiwanese-American engineer[1]. The EMD provides a data-driven (empirical) method to separate brain activity into its constituent signals in different frequency ranges without assuming linearity or stationarity. Roughly, the method works by finding the maxima and minima within the signal, yielding an intrinsic mode function that captures the fastest changes in the signal. The mean values of this new function are subtracted from the original signal, and the process repeats until there are no more fluctuations in the signal. The process is akin to sifting the data for the various contributing frequency modes, from the highest frequencies to a straight line.

We were in a unique position to apply this better method to distil Sage’s alpha waves from her brain activity. Our group was collaborating with Norden Huang himself, to develop tools to apply EMD to human brain recordings. While the principles and concepts in the methods were simple and elegant, getting everything to work properly and keeping the different rhythms from getting tangled across the extracted modes was far from trivial. Andrew Quinn was leading the efforts and was in the thick of the methods-innovation work. By the time the building opened, Andrew had published his first papers and tutorials on the new method[2].

Immediately after the recordings, Andrew analysed the data. From Sage’s musings during the session, we selected two seconds of brain activity. We picked some nice segments, more or less at random, and sent them off to the architects so they could choose one that would work for the casting. Here are the contenders. As you see, none of them is perfectly regular, symmetrical, or stationary.  Can you identify the one that made it to the façade? They are coloured in “sage”, just for fun.

[1] Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N-C., Tung, C. C., & Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1971), 903-995.

[2] Quinn AJ, Lopes-dos-Santos V, Dupret D, Nobre AC, Woolrich MW. EMD: Empirical mode decomposition and Hilbert-Huang spectral analyses in Python. Journal of open source software. 2021 Mar 31;6(59):2977.