Supporting Text
Further Details About the DC Stable Electroencephalogram (EEG) Recording Technique. Direct current (DC) stable recording requires (i) a genuine DC amplifier with sufficiently high input impedance and a wide enough dynamic input range to tolerate offset voltages, as well as (ii) a DC stable skin-electrode interface. In the present study, we used both a custom made and a commercial DC amplifier (see Methods). A DC stable skin-electrode interface was obtained in the following way: we used sintered Ag/AgCl electrodes (electrode elements bought from In Vivo Metric, Healdsburg, CA, and Biomed) embedded in an isolating plastic housing produced in our laboratory. The plastic housing was firmly attached to the skin with collodion to minimize drying of the gel, which would cause marked baseline drifts due to changes in electrode potentials. The electrode gel can be any chloride-containing product (in our study, Signa Gel, Parker Laboratories, Fairfield, NJ). The skin beneath the electrode was scratched with a tiny needle through the basal lamina to short-circuit skin-generated potentials (see refs. 1-3). After allowing 10-15 min for stabilization, baseline drift was always unidirectional and <500 m V per hour.
Filtering. For filtering of the infraslow oscillation (ISO), please see Methods. Higher frequencies for the phase locking analysis were bandpass filtered with paired [highpass (hp) and lowpass (lp)] finite impulse response (FIR)-filters: 0.5-1 Hz was obtained with hp 0.6 Hz [passband, stopband (sb) was at 0.3 Hz] and lp 0.8 Hz (sb 1.6Hz), 1.5-4 Hz with hp 1.5 Hz (sb 0.75 Hz) and lp 3 Hz (sb 6 Hz), 4-8 Hz with hp 2.5 Hz (sb 5 Hz) and lp 6 Hz (12 Hz), and 7-18 Hz with hp 4 Hz (sb 8 Hz) and lp 12 Hz (sb 24 Hz). For the amplitude correlation analysis, we used bandpass filters: frequency band 0.5-1 Hz was obtained with a center frequency (cf) of 0.8 Hz (pb ±0.2 Hz and sb ±0.3 Hz), 8-11 Hz with cf 9 Hz (pb ± 1 Hz and sb ± 2 Hz), 11-15 Hz with cf 13 Hz (pb ± 1.5 Hz and sb ± 3 Hz). For amplitude correlation, 1-100 Hz band was obtained with a hp 2 Hz (sb 1 Hz) and lp 100 Hz (sb 160 Hz).
Artifact Controls. Artifact controls consisted of the following: skin potentials were short-circuited by scratching the skin beneath the electrodes (1, 2). Body and eye movement artifacts were visually distinguished by their appearance in the EEG, and eye channels were added to exclude the possibility that pendular eye movements of early stage I sleep would cause interfering EEG fluctuation in frontal areas. Artifacts related to respiration were excluded by adding respiration channels (thermocouple monitoring nasal airflow; Fig. 4). By performing all analyses also using median filtering before FIR-lowpass filtering, we also confirmed that the high-amplitude, monophasic waveforms (e.g., K complexes of delta wave bursts) did not introduce artefactual ISO deflections.
Phase Locking. We used the phase-locking factor (PLF) to evaluate the uniformity of phase difference (Fig. 2) and phase of occurrence (Fig. 3) distributions. For N complex numbers (e.g., the phase differences or the phases of occurrence) z, i = 1¼ N, with unit modulus, the PLF is given by |1/N S zi|. The PLF attains a value of 1 for perfect phase ordering and approaches 0 for a uniform phase distribution when the number of samples approaches infinity. For analyses of epochs containing <100 cycles of ISO (as in Fig. 2), the temporal correlations among nearby samples could have been significant, and we therefore obtained the confidence limits by estimating the distribution of surrogate PLFs with 200 time-shifted epochs. It turned out that the surrogate PLFs obeyed the Rayleigh distribution very well and hence PLFs obtained for real data were conveniently expressed as normalized with the mean of the surrogate PLFs (PLFreal/PLFshuffled, mean ( = l /l m ) >1.95 corresponds to P < 0.05, >2.41 corresponds to P < 0.01, and >2.96 corresponds to P < 0.001). The time points (with their corresponding phase values) of the occurrence of K complexes and interictal epileptiform events (IIEs) (Fig. 3) were sampled so far apart that they were effectively temporally independent, and thus the Rayleigh test itself was used to estimate whether the phase values were randomly distributed. Altogether, 37,494 s (average 4,686 s per patient, range 800-7,600 s) of sleep records were used for the phase locking analysis of IIEs, hence the mean interval of 238 IIEs was 158 s.
Cortical Current Density Reconstruction. Cortical current density reconstruction was generated with minimum-norm estimation method using BESA 5.0 analysis environment (MEGIS Software, Grafelfing/Munchen, Germany). We used a realistic head shape model with the minimum L2 norm method, both with and without depth weighting (results were qualitatively similar in both; Movie 1 is constructed without weighting). Before this computation, the EEG signal was filtered with a median lowpass filter (1-s window), and down-sampled at 10 Hz, followed by a linear interpolated finite impulse response (IFIR) filter at 0.1 Hz to obtain ISO waveforms. Movie 1 shows sequential cortical current density maps at a speed that equals to real time course of ISOs.