Statistical method for detecting phase shifts in alpha rhythm from human electroencephalogram data

We developed a statistical method for detecting discontinuous phase changes (phase shifts) in fluctuating alpha rhythms in the human brain from electroencephalogram (EEG) data obtained in a single trial. This method uses the state space models and the line process technique, which is a Bayesian method for detecting discontinuity in an image. By applying this method to simulated data, we were able to detect the phase and amplitude shifts in a single simulated trial. Further, we demonstrated that this method can detect phase shifts caused by a visual stimulus in the alpha rhythm from experimental EEG data even in a single trial. The results for the experimental data showed that the timings of the phase shifts in the early latency period were similar between many of the trials, and that those in the late latency period were different between the trials. The conventional averaging method can only detect phase shifts that occur at similar timings between many of the trials, and therefore, the phase shifts that occur at differing timings cannot be detected using the conventional method. Consequently, our obtained results indicate the practicality of our method. Thus, we believe that our method will contribute to studies examining the phase dynamics of nonlinear alpha rhythm oscillators.

Figure 1

Result of applying the LP method to simulated data of P1. (a) Typical result of the LP method. The upper row indicates a single simulated trial. The lower row indicates the probabilities of the four states calculated by the LP method. The black (i), blue (ii), yellow (iii), and red (iv) lines indicate the probabilities of the four states of S1, S2, S3, and S4, respectively. (b) Estimated state of each trial at each time bin. Blue, yellow, and red dots indicate the three estimated states of S2, S3, and S4, respectively, and black area indicates the estimated state of S1.

Figure 2

Detection ratios of the phase shift using the LP method from the P2 simulated data. The upper row indicates a single simulated trial. The lower row indicates the detection ratios of the phase shift according to the amount of phase shift.

Figure 3

Detection ratios of the amplitude shift using the LP method from the P3 simulated data. The upper row indicates a single simulated trial. The lower row indicates detection ratios of the amplitude shift according to the amount of amplitude shift.

Figure 4

Comparison of the averaged instantaneous amplitudes over the detected trials and that over the undetected trials at the timing of the 4$\pi$/9 phase shift in P2. The error bars indicate the standard errors among the trials.

Figure 5

Typical results obtained by applying the LP method to experimental EEG data. The upper row indicates a single experimental EEG trial. The lower row indicates probabilities of the four states calculated by the LP method. The black (i), blue (ii), yellow (iii), and red (iv) lines indicate the probabilities of the four states of S1, S2, S3, and S4, respectively. The red line is mostly overlaid on the yellow line. Gray arrows indicate the timings when phase shifts are detected by the LP method. The time instant of 0 ms on the x axis indicates the flash stimulus onset.

Figure 6

Number of trials in which the phase shift was detected at each time bin. These data are the grand averaged data over all the subjects. The time instant of 0 ms on the $x$ axis indicates the flash stimulus onset.

Figure 7

Mean number of detected trials per time bin in the early latency, late latency, and prestimulus periods. The values are averaged over all eight subjects and the error bars indicate standard errors among the subjects. (a) Comparison between early latency and prestimulus periods. (b) Comparison between late latency and prestimulus periods.