Measuring Coherence: I'm going to measure the spectral coherence of the EEG signals to see which signals are synchronized with each other (if any). Coherence is a comparison of two signals, so I'll be comparing pairs of EEG signals around the head.
Coherence Compares Amplitude and Phase: Coherence looks at any changes in amplitude and in phase between the two signals. For two signals whose amplitudes and phases change together, the coherence could reach up to a value of 1.0 (perfect coherence). Or, if the amplitude and phase changes are completely independent, it is possible for the coherence to reach down to 0.0 (no coherence).
Coherence vs Frequency: Coherence is computed in the frequency domain, which means that we can see which frequencies are coherent and which are not. I'm most interested in what happens to this meditator's Alpha waves (which we saw were centered on 11.7 Hz), so I'll be mainly looking at the coherence around that frequency.
Baseline Coherence: Let's start by looking at the coherence during the meditator's baseline recording. This is when he was sitting with his eyes closed and relaxing -- but not meditating. The figure below shows the coherence for different pairs of EEG electrodes around his head. Blue is low coherence (0.0) and red is high coherence (1.0). Again, I'm looking at the figures mostly around the Alpha waves (10-12 Hz).
|Mean-Squared Coherence For EEG Signals Recorded with Eyes-Closed But Not Meditating.|
Click to Enlarge.
Looking at his Alpha wave frequencies, I see that his Alpha are coherent on back-left side of his brain (between electrodes 5 and 7) and on the back-right side of his brain (between electrodes 6 and 8). I think that it is interesting that the Alpha waves are not coherent between the left and right sides (between electrodes 7 and 8). These three findings suggest that the back-left region of his brain is working as a unit (at these frequencies), that the back-right region of his brain is working as a unit, but that the left and right Alpha waves are being generated independently. Again, this is when he is simply relaxing with his eyes closed.
Coherence While Meditating: Below is a figure showing the results during meditation. The color scale is the same as for the plots above for the baseline recording. In this new figure, note the Alpha coherence on the back-right (electrodes 6 and 8) is still present but that the Alpha coherence on the back-left (electrodes 5 and 7) is now gone! This suggests to me that the meditation has somehow decoupled the brain centers on the back-left of his brain. Whoa. Cool.
|Mean-Squared Coherence For EEG Signals Recorded During Eyes-Closed Meditation.|
Click to Enlarge.
Quantifying the Change in Coherence: To make this change in coherence more clear, I collapsed these complicated spectrogram-like plots into a simple plot of coherence versus frequency. The simpler plots are shown below. This plot only includes data during the eyes-closed portion of each test. Because we should really only look at the coherence at frequencies where there is appreciable signal energy (and we should ignore other frequencies), I've highlighted the region of the Alpha waves (the only signal that is consistently present during these recordings) by using thicker lines.
|Comparing the Average Coherence Just When the Eyes Are Closed.|
The thicker lines highlight the Alpha wave frequencies.
Discussion: In the previous post, we saw Alpha waves throughout the back half of his head. It would be easy to assume that we were seeing the same Alpha wave throughout the back of his head. Today's analysis has shown that this is not the case. When merely relaxing, the coherence measurement suggests that the back-left and the back-right parts of his brain are generating their own Alpha rhythms independently of each other. When meditating, it looks like the back-left part of his brain further subdivides. Why? I don't know. To what effect? I don't know. Is it a good thing or bad thing? I don't know. All I know is that it is really cool to be able to objectively measure changes in brain activity due to conscious control.
Next Steps: I'm thinking that I now want to go back and measure the coherence of the signals that we recorded from the meditator at Maker Faire. I'm pretty sure that my two meditators were using different meditative techniques, so it would be interesting to see if the changes in coherence are the same or different between the two meditators. It would also be interesting to repeat these recordings to see if the changes are consistent between meditation sessions. Finally, these coherence results simply show that the signals became more independent. It doesn't actually tell me which specific properties of the signals (amplitude? phase?) became different. It would be cool to see which aspects of the signals changed due to meditation. The brain sure is a dark and mysterious place!
Follow-Up: The coherence pattern seen above when not meditating has been confirmed in data from another non-meditating friend.