The prominent alpha peak in the power spectrum is the most visible difference between eyes open and eyes closed but the more interesting differences may be in the time domain.
Visual stimulus is perhaps the most encompassing and significant of all input to the brain. One would therefore expect that there would be substantial differences in the EEG activity when the eyes are open or closed. In this post we compare power spectral density (PSD) estimates and as well as various entropy measures using EEG data recorded with eyes closed and eyes open. We focus particularly on the variability between and within these conditions and what that means for our understanding of such ‘resting’ activity as a baseline. The EEG data was downloaded from this website and it comprises of 100 recordings of approximately 24 seconds in each condition from 5 different people.
The Alpha Peak in the Power Spectral Density (PSD)
The figure below shows the mean PSD plot for both eyes open and eyes closed condition for 100 EEG recordings in each condition, with the error bar representing standard error of mean. The alpha peak (7 to 15 Hz) that emerges with eyes closed is the best described difference in the literature and is pretty evident in the figure below. However, it is important to notice that while there is a clear difference between mean PSD between these two conditions in the alpha band, there is a lot of variability within the alpha-band for each condition. Furthermore, this variability extends into all bands of the power spectrum and we can see that the mean PSDs in these two conditions are not significantly different outside of the alpha range. (see related post Factors that Impact Power Spectral Density Estimation)
Variability within spectral bands
The variability is better illustrated by looking at the histogram of the overall power in each band across all of the 100 recordings in each condition (the error bar is the standard deviation of this histogram divided by sqrt(N=100) For instance, one can see that the log-PSD values have essentially the same overall range for most of the bands such as delta and beta with mostly comparable heights within each bin. The overlap between the distributions is evidently less in case of alpha band, which is well known, however, within each condition there is still quite a lot of variability in the distribution of the log-PSD as seen below. In case of the theta band as well, one can see that although the distributions when compared between conditions look different, the variability within each condition is still evident.
Overall the large range in each band suggests that spectral fluctuations within each condition over time must be considered when comparing between conditions. This is particularly important when using the resting eyes open or eyes closed conditions as a baseline for other task dependent studies. The fundamental implication is that while statistics across a large number of instances may yield significant spectral differences between two conditions, any individual period may not be representative of the overall range of resting fluctuation. This imposes a need for much greater statistical rigor to demonstrate true spectral differences. It also strongly suggests that the power in spectral bands is not particularly valuable as a real time predictor of any behavioral condition. Rather it is likely a composite derivative measure of other underlying features that may be more meaningful.
We do note however, that this analysis does not distinguish the results by channel and variability may be lower at the level of individual channels.
We next compare a few common entropy measures across these two conditions. Entropy can be considered a measure of diversity and/or predictability as previously described in this related post Measuring Entropy in the EEG. The below figure shows the distribution of both time-based entropy measures (Sample entropy and Approximate entropy) and frequency-based entropy measure (spectral entropy) across all the recordings for the eyes-open and eyes-closed conditions. The two time based measures assess diversity or predictability of temporal aspects of the signal while spectral entropy assesses the diversity of the spectral composition of the signal.
There are several interesting things to note here:
First one can clearly see that while the two entropy measures in the time domain are virtually identical, the spectral entropy distribution looks fundamentally different. Under both eyes open and eyes closed conditions, entropy in the time domain has much greater variability (the distribution is wider) whereas the spectral entropy is substantially narrower. What this says is that while the overall spectral compositions of the waveforms stay fairly similar from instance to instance (as you would expect since the shape of the overall power spectrum does not change all that much), the temporal characteristics change substantially more.
Second, there is a statistically significant shift of the distribution to the right from eyes closed to eyes open that is prominent in the time-domain entropy measures indicating that visual input imposes greater temporal disorder on the signal compared to our internal meandering. While some shifting is present in the spectral entropy distribution the primary peak of the data remains in the narrow range between 0.7 and 0.8.
Implications of the variability
What do these results really tell us?
- While the alpha band is a prominent statistical signature, the substantial variability within conditions precludes this feature (or any other spectral band power) as a reliable predictor of a behavioral condition.
- Despite the variability within bands the overall spectral entropy (which reflects the general shape of the PSD) does not vary much so spectral entropy cannot distinguish well between the conditions. (see related posts The Blue Frog in the EEG and Intra-person Variability in the EEG)
- On the other hand, entropy measures in the time domain show substantially more variability and are therefore likely to be a more interesting reflection of internal processes and a more useful predictive measure across condition (though not accurate on its own).
- Lastly, when there is so much variability within the EEG data in either the eyes-open or closed conditions, can this be considered a reliable baseline for comparison to some task-specific EEG? Significantly, it calls into question the reliability of changes that we observe between baseline and task condition and makes the case for longer baselines and/or bootstrapping approaches to effectively incorporate within condition variability into statistical tests.
Lastly, while this particular dataset does not distinguish recordings by individuals, it would be an interesting exploration. (See related post Intra-person Variability in the EEG)