Sleep spindles occurrence correlates with the consolidation of recently acquired information. The memory consolidation literature supports that there are more sleep spindles after a learning task. Thus, the detection of them does not only allow the classification of the N2 sleep stage, further provides a quantification value of memory replay and memory consolidation during sleep. Event detection is an important processing step performed in the analysis of diverse kinds of waveforms. The short and long term average ratio is the most widely used event detection approach to analyze passive seismic data and trigger the storing or discarding of data. Its popularity comes from its simplicity and the usage of a fixed threshold determined by the intention of the data usage and not based on the signal dynamics. This work explores the usage of this event detection approach on the online detection of sleep spindles. The advantages of the detection performance with this feature over using the same binary classification method using other fast calculation features come from its statistical properties. The classification features compared are the root mean square amplitude, relative spindle power, and the Teager-Kayser energy operator.
Sleep spindles are short-duration events (0.5-2 s) in the specific frequency range of 11-16 Hz that
occur during the NREM sleep and they are detectable in EEG registers. The principal characteristic
of the N2 sleep stage is the high presence of these events
Classification algorithms have the assumption that there is some space of features where the patterns are separated. Online or real-time applications require fast computation of these features. Thus, it is a great achievement if this separation is notorious in a small dimensional space or even in just one dimension.
This work takes this last approach. The proposed algorithm does a binary classification (spindle or not spindle) using only an extracted feature from the input signal. Then it also annotates the time of occurrence of each spindle to make a detector.
This work uses a single feature from the EEG signal as many previous methods of spindles detection
The use of a public database is important to compare the results of different methods. In that
sense, this work use the same dataset used by
Data The event detection methods were evaluated over a synthetic EEG signal and also in a real EEG dataset. The baseline of the synthetic signal has a frequency spectrum slope of í f 3 typical of slow-wave sleep. It is generated with a sum of sinusoidal signals:
xEEG.t/ = 4918 ³nn==4299 .0:1n/13_.fs/ ^cos..2 .1 + . f /rf /.0:1n/t + .1 + rp.t///; (1) where fs = 100Hz is the sampling frequency, f = 0:01 is the standard deviation given to the central frequencies of the expression 1, rf is a random number, and rp.t/ is a random time series generated from a normal Gaussian distribution. The baseline signal adds with a spindles signal: xspindle.t/ = 16 ³k fspindle.t/ < p.t * k/ xsigma.t/; xsigma.t/ = ³m=^*1;0;1` .1 * ðmðda/cos.2 .12 + 0:5m/.1 + sf1/t/ + . ù1.2/ * ðmðda/cos.2 .24 + m/.1 + sf2/t/ ; (2) where da is the amplitude difference of the main lobe with the lateral lobes, sf1 and sf2 are random deviations for the main frequency of 12Hz and its first harmonic for spindles. fspindle.k/ is a triangular envelope defined by the expression (3) with a duration tspindle = 0:75s. Expression (4) defines the probability of occurrence of spindles where U .t/ is a random time series uniformly distributed between [0,1].
h tspindleaspindle + aspindlet fspindle.t/ = n 2 l ntspindleaspindle * aspindlet t g tspindle_2 j t < tspindle_2 ; (3) nh1 U .t/ > 0:998 p.t/ = nl0:01 0:99 < U .t/ < 0:998 ; (4) nn0 U .t/ f 0:99 j The tested synthetic EEG signal has 8 segments of 300s with different values for aspindle: 0.125, 0.250, 0.375, 0.5, 0.625, 0.750, 0.875, and 1.0.
The real EEG signals come from the DREAMS dataset
General Procedure The event detection methods in this work use a general framework of a single dimension signal and a single threshold to classify a sample as forming part of an event occurrence. Consecutive samples classified as spindles must exceed the minimum duration to finally designate a section of the input signal as an event. A time for possibles gaps is also included to actuate as replace of an hysteresis mechanism.
A common procedure before any step is to obtain the z-score value of the signal. Given that there is not any assumption about the signal properties, the mean value and the standard deviation are calculated at each sample, then there is the need of advance in various samples to achieve consistency in these statistical estimators. The z-scored signal x.t/ is band-pass filtered in the sigma band (11-16Hz) with a Chebyshev type I fourth order filter to obtain x .t/. The calculation of features at each sample uses both signals. The detection follows the procedure show in Algorithm 1. Algorithm 1 Spindle Detection Algorithm Inputs: feature.t/, tmin, tgap Outputs: thresholdfeature.t = tfinal/, is_spindle(t), count_spindles 1: if f eature.t/>thresholdfeature.t/ then 2: if hold==False then 3: start=t; 4: end if 5: hold=True; 6: else if hold==True then 7: gap=gap + 1; 8: if gap>tgap then 9: gap=0; 10: hold=False; 11: if t * start>tmin then 12: count_spindles=count_spindles + 1; 13: is_spindle.start : t/=1; 14: end if 15: end if 16: end if . The threshold could be time dependent
The short and long term ratio was compared with other features. The short-time and the ratio were predefined for calculation of each feature. ST is the length in samples of selected short-time, LT = ST is the length in samples of selected long-time. ST A0.n/ is the ratio feature using as ratio long-time all past samples, ST A1.n/ uses as short-time a single sample. ST A0.n/, ST A1.n/, and T eager.n/ pass through a moving average filter of length ST .
RMS.n/ = v ³nk=n*ST x .k/2
ST ; Short and long-time average ratio (STA/LTA) ðx .k/ð ST A0.n/ = 1 ³n n k=0 ðx .k/ð ðx .k/ð ST A1.n/ = 1 ³n
LT n=n*LT ðx .k/ð
ST A_LT A.n/ = S11T ³³nnk=n*ST ðx .k/ð
LT k=n*LT ðx .k/ð ; (5) (7) (8)
T eager.n * 1/ = .x.n * 1/2 * .x.n * 2/x.n///;
The detection metrics employed here are the same as used by
d = P ^y f ` * PP ^^yy ff `` ++ PP ^^yy >> `` * P ^y > ` = 12+.P.P^y^yff ``**PP^y^yff `/`/ ; (9) where is the threshold value, y is the distribution of the detection feature when there is a spindle and y the distribution of feature values when there is not a spindle. The best threshold, known the probability distributions fy and fy, is which maximizes this metric. The maximum value is 1 and it is achieved only if the pdf’s have disjointed domain and the threshold value is in the gap between them.
Statistical analysis The probability density function (pdf) of samples of an EEG signal is assumed to be Gaussian and reinforced by the histograms in Figure 1 C. Thus, the features calculations perform those operations to a normal aleatory variable. Then, the root mean square (RMS) should have a Chi pdf, short and long-time average (STA/LTA) and relative spindle power (RSP), as calculated here, should have a Fractional Gamma pdf, and the Teager-Kaiser energy operator should have a Chi-squared pdf.
The probability density function of samples of an EEG signal is Figure 1 D shows the histogram of the values of the features calculated from spindles and not spindles samples. The first 3 seconds of the synthetic signal were removed because the z-score is badly estimated for the first samples. The mean and standard deviation are still not consistent. The first 30 seconds, the first epoch, are removed from real signals for the same reason. The distance between the means of each distribution and the length of the tails say something about the classification difficulty using a single threshold. The metric d allows the selection of a better threshold. However, it needs caution because the features depend on the length of the time window and the metrics are threshold dependent (Figure 2). Figure 1 E shows the classification performance with different thresholds. The most classical performance metrics have their best value at threshold values above the preferable threshold selected with d .
Figure 2 A presents ROC curves that are another perspective of the results of Figure 1 C. An additional short-time value and an additional ratio were included to show the different behavior of the detection performance. Figure 2 B shows the maximum value achieved for d occurring with STA/LTA at the short-time window of 0.05 seconds and a ratio equal to 0.001.
The proposed spindle detection method considers a single EEG channel and a single extracted
feature. This consideration could be a weakness in typical EEG studies where multiple channels
are recorded and more sophisticated analyses could be performed
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the other hand, it is a necessary alternative in studies where recording devices of few channels are
available like the OpenBCI, Emotiv EPOC
The STA/LTA feature performs better with the smallest ratios for the real signals dataset. That does not occur in the synthetic signals, where the Teager-Kaiser energy operator features performs the better. This could indicate that there is a need for more pre-processing of the input signal to remove noise and other physiological artifacts not considered in the construction of the synthetic signals like ECG, EMG and, ocular movements. Without any other pre-processing another good performance feature is RMS.
The accuracy metric goes near to 1 with higher thresholds due to the best classification of True Negatives samples that are much higher in quantity than True Positive samples. Interestingly, Cohen- and F1 metrics have better values for higher thresholds than for the d metric (Figure 1 E). Furthermore, all metrics are consistent in performance between cases. The ROC curves allow having another perspective than a simple value, although they represent the same information, and clarifies why the common choice of the RMS feature over another feature in the task of spindle detection. The maximum of the d metric occurs at a similar threshold value for the RMS feature in any combination of short-times and ratios. The threshold value that gives the best d metric for STA/LTA is more variable across cases (we do not show but the behavior of probability distributions in Figure 1 D explain it).