Figure 3.

Time-dependent fluctuations of resistance of brain dynamics. (a) Temporal evolutions of dynamical resistance R (grey lines) from two subjects with epilepsy. Data are derived from $\mathcal{N}=6$ accessible dynamical regimes, and we find comparable time-dependent fluctuation with other number of accessible dynamical regimes (Supplementary Fig. S2). Smoothed temporal evolutions (moving average over 3 h) are shown as black lines; red vertical lines indicate times of seizure occurrence. Discontinuities in the temporal evolutions are due to recording gaps (colored khaki), and tics on x-axes denote midnight. (b) Temporal evolutions of dynamical resistance R when transiting into and out of epileptic seizures. Dynamical resistance values of the pre- and post-seizure period are rescaled to the value at seizure onset (t = 0). Decreasing values of resistance during the pre-seizure period (assumed duration: 4 h) are colored red and increasing values are colored blue. Means and standard deviations are shown by lines and shaded areas, respectively. (c) Periodograms⁶⁶ $\mathcal{P}(R)$ of temporal evolutions of dynamical resistance depicted in (a) showing subject-specific ultradian (less than 24 h) and circadian (around 24 h) peaks in periodicity as well as infradian contributions (larger than 24 h)⁶⁷. (d) Averaged periodogram $\overline{\mathcal{P}(R)}$ of temporal evolutions of dynamical resistance from all subjects showing a pronounced circadian peak in periodicity. Mean values and standard deviations are shown as solid lines and shaded areas, respectively.