Analysis of latency jitter requires single-trial data and a high signal-to-noise ratio. For this purpose, only data from the first block and the highest stimulus intensity was analyzed, since this block/intensity combination had the best signal-to-noise ratio. The data analyzed was a subset of the data published in Matre et al. (2015).

Latency jitter was measured by different methods. The MCD of inter-potential intervals is a method for evaluating latency variability between action potentials from two muscle fibers from the same motor unit (Ekstedt et al., 1974) and is routinely calculated in single fiber electromyography studies in patients with suspected neuromuscular transmission defects (Stalberg et al., 1974). We calculated a modified MCD for ERP as the average of the absolute time-differences between consecutive single-trial peak latencies. The procedure is illustrated in Figure 1. A larger MCD represents more jitter.

N2 (black) and P2 (white) peak latencies in consecutive single trials for all subjects (each horizontal “line” on the y-axis represents one subject). Habitual sleep on the left and sleep restriction on the right. Data from the first block and highest stimulus intensity were included in this analysis. ∗: Peaks used for example of calculation of mean consecutive difference in Figure 2.

Another measure of latency jitter is the phase locking value (PLV) (Mouraux and Iannetti, 2008). Phase locking occurs when an event resets the phase of ongoing EEG oscillations and transiently locks to the onset of the event. PLV is a measure of phase locking across trials in the time-frequency domain, as detailed below (Mouraux and Iannetti, 2008). A lower value represents more jitter.

After removal of segments with artifacts (15.3%), 3202 epochs were analyzed in STEP (Single Trial detection toolbox for Evoked Potentials), an open source toolbox running under the Matlab environment, for single trial peak detection (Hu et al., 2010, 2011a, 2011b). STEP was run with wavelet filtering and multiple linear regression with dispersion term. Search intervals were [50–200 ms] for the maximum negative peak (N2) and [150–500 ms] for the maximum positive peak (P2). No peaks were found in 2.6 % of the single trial epochs. Figure 1 shows the distribution of N2P2-peak latencies in single trials for each subject divided by habitual sleep and sleep restriction.

MCD was calculated for both N2 and P2 peak latency. If the STEP analysis was unable to find a peak (N2 or P2) in a given epoch, the corresponding epoch and the preceding epoch were removed. Statistically defined outliers exceeding ±3 standard deviations were removed, including the epoch preceding the epoch with the outlier. After removal of outliers, the N2 peak dataset consisted of 2988 peak values, and the P2 peak dataset consisted of 3003 peak values. For the first block and the highest stimulus intensity, 287 consecutive N2 peaks and 284 consecutive P2-peaks were used for the final MCD calculation.

Single trial responses were processed in the time frequency domain using custom written scripts (Hu et al., 2014; Zhang et al., 2012). Briefly, the power spectral density of each epoch was calculated with the Short-Time Windowed Fourier Transform (200 ms Hanning window). The average post-stimulus changes of EEG oscillation were found by averaging across trials. A percentage change in power for each time frequency point after stimulus (0–800 ms relative to stimulus onset) was calculated from a pre-stimulus reference interval [-900, -100 ms] in order to find the magnitude of event-related changes in oscillation amplitude (ER%). By combining bootstrapping (1000 times) and a paired t-test, a statistical map of p-values (threshold: p < 0.01, uncorrected) was produced, comparing each ER% time frequency point to the reference interval (Durka et al., 2004). The null hypothesis of this test would be no difference between the ER% time frequency point and the reference interval. A large cluster of significant p-values, corresponding to the N2- and P2-peaks in the time-domain average, were found in the [1–400 ms] and [1–25 Hz] range. Within this region of interest, the phase locking of the signal was estimated as the PLV (Mouraux and Iannetti, 2008; Zhang et al., 2012) using custom written Matlab scripts on the averaged waveforms. PLV for each time-frequency point (t, f) was calculated by the formula below (Eq. 1), where N is the number of trials and F is the phase information. Vertical bars indicate absolute values.

PLV will range from 0 to 1, where 1 means a constant phase between trials, and 0 means random phase between trials (Aydore et al., 2013). The mean within this region of interest was used as the dependent variable in a mixed model analysis. For a more thorough description of the PLV measure, see e.g (Lachaux et al., 1999; Mouraux and Iannetti, 2008; Zhang et al., 2012).

Data was analyzed by linear mixed models with maximum likelihood estimation. The independent fixed factor was sleep condition (sleep restriction vs. habitual sleep). Dependent variables were PLV, MCD for N2 peak latency (N2-MCD), and MCD for P2 peak latency (P2-MCD). Since PLV depends on ER%, the analysis of PLV included ER% as a covariate if it improved the model fit (Mouraux and Iannetti, 2008), based on the Akaike Information Criterion. Also, stimulus number (exact occurrence in the stimulus sequence) was included as a covariate to adjust for potential habituation or sensitization. The intercept was allowed to vary randomly in all models (random intercept). Random slope for sleep was added if it improved the model fit. Individual variation was accounted for by including participant as a random factor in the models.

Paired comparisons of sleepiness, sleep latency, response speed and number of hours slept were performed by Student's t-test or by the non-parametric Wilcoxon test, if data were non-normally distributed. Statistical analyzes were performed with IBM SPSS version 21 (IBM, Chicago, Illinois, USA). The significance level was set to 0.05.

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