Detection of Cortical Slow Waves in the Sleep EEG ... - IEEE Xplore

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 59, NO. 10, OCTOBER 2012

Detection of Cortical Slow Waves in the Sleep EEG Using a Modified Matching Pursuit Method With a Restricted Dictionary Antoine Picot∗ , Harry Whitmore, and Florian Chapotot∗

Abstract—In this paper, an innovative knowledge-based methodological framework to detect sleep slow waves (SSW) in the human sleep electroencephalogram (EEG) is proposed. Based on a restricted matching pursuit (RMP) algorithm, automatic pattern recognition of SSW is implemented using a small dictionary of Gabor functions modeling the target waveform morphological characteristics. The method describes EEG signals in terms of SSW properties and provides detection thresholds based on the largest MP coefficients. A computer software implementation of this new method was tested on a database of overnight polysomnographic recordings collected in 15 young healthy subjects and visually scored by a trained sleep expert. In addition to full automation and fast application, the results obtained from the RMP algorithm, and evaluated using a rigorous performance evaluation metrics, showed excellent agreement as compared with expert scoring, with 97% of correct detections and a concordance of 67% in SSW time position and duration. The performances demonstrated by this new method were superior to that of a canonical detection algorithm introduced earlier, with an equivalent sensitivity but a significant 12% increase in precision (p = 0.0002). By mimicking the way human processes information while scoring SSW, the RMP algorithm proves stable over time and sleep/wake states, and may thus be used with virtually no human intervention. Index Terms—Electroencephalogram (EEG), matching pursuit, pattern detection, sleep, slow waves.

I. INTRODUCTION OLYSOMNOGRAPHY (PSG) is a technique to explore sleep and brain activity. It is based on the collection and analysis of multiple physiological signals, including the electroencephalogram (EEG) recorded by means of surface electrodes placed at standard head positions. During the 24 h of a day, humans experience distinct vigilance states and express a set of recurrent spontaneous patterns of brain activity. Rechtschaffen and Kales (R&K) have described different states of vigilance in humans and proposed a scoring system for their classification using two main sleep states: rapid eye movement (REM)

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Manuscript received January 30, 2012; revised April 25, 2012 and June 29, 2012; accepted July 18, 2012. Date of publication July 31, 2012; date of current version September 14, 2012. This work was supported by the National Institute of Health under Grant PO1 AG-11412. Asterisk indicates corresponding author. ∗ A. Picot is with the Institut National Polytechnique (INP), Toulouse Cedex 4, France (e-mail: [email protected]). H. Whitmore is with the Sleep, Metabolism and Health Center, University of Chicago, Chicago, IL 60637 USA (e-mail: hwhitmor@medicine. bsd.uchicago.edu). ∗ F. Chapotot is with the Sleep, Metabolism and Health Center, University of Chicago, Chicago, IL 60637 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TBME.2012.2210894

sleep, and nonrapid eye movement (NREM) sleep, the latter subdivided into light (stages I and II) and deep sleep (stages III and IV). The R&K guidelines for visual analysis and staging of sleep/wake stages [1] were published in 1968 and became accepted as a standard reference. Although updated and replaced in 2007 by the American Academy of Sleep Medicine (AASM), most of the guidelines, remained unchanged, with efforts made only to simplify and clarify transitions between stages [2]. The function of sleep remains an open-question, yet tremendous progress has been achieved in the understanding of how the brain regulates vigilance and the alternation of sleep and wake states. While there is an increasing interest among neuroscientists in the study of the sleep EEG transient events as a window to brain mechanisms, the lack of automated and accurate detection tools still prevents or strongly limits the strength of large-scale cohort sleep studies. As one of the most salient features of sleep, slow EEG potentials of large-amplitude and low-frequency have been described long ago using a vast terminology such as cortical slow oscillation [3], [4], EEG delta waves [5], or sleep slow waves (SSW) [1]. This brain oscillatory activity that is unique to the sleep EEG is now seen as an alternation of up- and down-states in the cortical neuronal mantle reflecting basic neurophysiological processes currently investigated for their potential role in cognitive functions such as attention, learning, and memory [6], [7]. Slow wave activity (SWA), otherwise called EEG delta power, is a spectral measure of absolute power in the [0.5–4] Hz frequency range that has been validated as a biomarker of sleep depth and intensity [8], [9]. SWA is associated with virtually every physiological function including thermoregulation, energy metabolism, cardiovascular and respiratory functions, and is most likely influenced through neuro-endocrine and autonomic control [10]. The amount and quality of sleep impact not only cognitive and affective functions but also physiological and metabolic activities [11]. Health studies have demonstrated that lack of sleep, as often occurs in a growing number of situations, increases the risk of cardio-metabolic diseases [12], [13]. This evidence confirms the importance of sleep and stimulates the research community to further understand its functions. In complement to the results obtained from visual stage scoring, modern sleep investigations now also include quantitative measures of EEG background activity obtained from either an FFT-based power spectral analysis [8], or a period-amplitude analysis [5]. These two methods have considerable practical advantages but lack time resolution and precision in estimating sleep transient and oscillatory events. A novel approach based

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PICOT et al.: DETECTION OF CORTICAL SLOW WAVES IN THE SLEEP EEG

on time-domain and morphological analysis of EEG signals have been developed in order to detect SSW automatically [14]. Among the multiple automated algorithm variants implementing SSW detection, most are based on a canonical detection (CD) method, which tracks large-amplitude slow potentials by identifying zero-crossings and peaks in EEG signals filtered in the low-frequency range [14]–[17]. The existing algorithms diverge mainly in terms of the duration and/or amplitude criteria of the considered negative and/or positive signal half-waves. Several improvements to the CD method have been attempted, consisting of grouping and averaging multiple EEG channels into regions of interest [18], [19], using Hilbert transform to assess detection likelihood [20], or including additional criteria to discard spurious artifact detections [19], [21]. Bandpass filter cutoffs may also differ from one algorithm to the other with a high-pass cutoff varying between 0.016 and 0.5 Hz and a low-pass cutoff frequency between 1.67 and 4 Hz. Few methods have attempted to produce results comparable to those obtained from guidelines-compliant visual sleep stage scoring with the exception of Riedner et al. [16], who considered SSW in the [0.5–2] Hz frequency range (negative half-waves between [0.25–1] s). A surprisingly overlooked issue is the fact that none of these detection algorithms have been assessed pragmatically and validated in comparison to the reference of a human expert. As a consequence, the effectiveness of the CD method remains undeveloped and its usefulness is limited to experimental studies conducted under supervision of an EEG expert. Recent advances in computer science and signal processing have spurred the development of new concepts like time-scale methods featuring optimal description of signals such as the EEG during sleep and wakefulness. Although promising methods such as matching pursuit (MP) with time-frequency dictionaries [22] have been proposed as unified parametric tools in EEG analysis [23], [24], practical limitations and computing complexity have prevented widespread adoption of this technique. As a consequence, even the most advanced sleep research conducted today is limited by the lack of efficient methods for the systematic identification and quantification of the sleep microstructure and transient events. In the absence of a practicable alternative, the objectives of the present study was to establish and validate, in a well-characterized control group, a fast algorithm for the unsupervised detection of SSW using the MP concept to process single- or multichannel EEG in a way compatible with international sleep scoring guidelines. The original concept of the method described in this paper is to take advantage of the MP algorithm and to turn it into a pattern detector by using a small dictionary restricted to functions modeling the target waveform, instead of using MP to approximate the whole EEG signal as combination of elementary waveforms. II. MATERIAL AND METHOD A. Material A dataset made of PSG recordings collected in 15 different young healthy adults and representing a total of about 120 h of data has been used to evaluate the proposed method. Our group of volunteers (14 males, 1 female) was 23.8 ± 3.32 years

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old (mean ± standard deviation) with a body-mass index of 22.92 ± 2.01. PSG recordings were collected in standard laboratory conditions after one night of habituation during a night of undisturbed baseline sleep with about 8 h of recording per night. A PSG technologist performed the electrode hookup with cup-electrodes attached on the scalp at positions according to the 10/20 system [25]. A standard montage was used including the frontal, central, and occipital EEG channels, horizontal and vertical electro-oculograms (EOG), chin electromyogram (EMG) as well as other cardio-respiratory channels. All signals were collected using acquisition workstations equipped with the Polysmith software and the Neurofax EEG-2100 system with JE-425 amplifiers (Nihon-Kohden, U.S.). All EEG derivations were bandpass-filtered using a 300 Hz-cutoff frequency low-pass filter (−18 dB/octave attenuation) and a high-pass filter with a time constant of 10 s (equivalent cutoff frequency of 0.016 Hz). All signals were then stored into computer files using a 200 Hz sampling frequency and a 16-bit analogue-to-digital converter.

B. Sleep Stages and SSW Scoring A human expert reviewed the PSG recordings in 30 s epochs to visually score wake and sleep stages according to international standard guidelines [1], [2]. In addition to two EOG and chin EMG, the scoring montage included EEG derivations referenced to contra-lateral mastoids (F3-A2, F4-A1, C3-A2, C4-A1, O1-A2, O2-A1) and filtered in the [0.3–45] Hz frequency band using a 5th order Butterworth band-pass filter. The same human expert also scored SSW events based on a frontal derivation (F3-A2) where amplitude is usually maximal [1], [2], [15]. Regardless of the recording time and sleep/wake stages, SSW have been consistently identified throughout the recordings as EEG rhythmic waveforms with a frequency in the [0.5–2] Hz range and a peak-to-peak amplitude greater than 75 μV, as recommend in the guidelines. As they often occurred in bursts or trains of successive waves or oscillations, trains of SSW were marked in single events by the expert. The visual scoring of SSW was performed on a computer by reviewing all 30 s epochs and by tagging the portions of signals identified as SSW using the computer mouse. The scoring of signals sampled at 200 Hz and displayed into 30 s epochs combined with a screen resolution of 1024 × 768 pixels resulted in a scoring precision of about (1/30) s for the SSW onsets and offsets. The polysomnographic recording analyser (PRANA) software package (PhiTools, Strasbourg, France) has been used for the visual scoring of both sleep/wake stages and SSW events. A total of 6343 trains of SSW have been scored by the human expert, which is equivalent to 800 min of cumulative event duration. This dataset has been randomly split into two subsets in order to obtain 40% of the data in a training set and 60% in a testing set. The first dataset, called dataset 1, included data from 6 out of 15 subjects (2483 SSW trains—318 min of cumulative SSW) and was used to tune up some of the method parameters. The other dataset, called dataset 2, was composed of the remaining data of the other nine subjects (3860 SSW trains—482 min

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Fig. 1. Representation of the CD algorithm principle for the detection of SSW on an EEG signal filtered in the [0.2–4] Hz range.

of cumulative SSW) who were not included in dataset 1 and was used to evaluate detection performance. C. Canonical Detection of SSW The PRANA standard developer kit, available as a MATLAB (The MathWorks, Natik, MA, USA) toolbox, has been used to implement the automated SSW detection algorithms used in the present study. To compare the performance of the proposed method, a reference SSW detection algorithm featuring the CD method was used. It was based on the source code of the FAST toolbox [19] also referenced in [17] with significant variations from earlier algorithms. Since algorithm detections may depend on factors such as the signal filtering and considerations of various morphological aspects of the waveforms, the following settings were used: a [0.2–4] Hz bandpass filtering using a fifth-order Butterworth filter, a negative zerocrossing with a subsequent positive zero-crossing separated by [0.25–1.25] s, a negative peak between the zero-crossings with a voltage lower than −40 μV, a negative-to-positive peak-to-peak amplitude greater than 75 μV, and a full-wave maximal duration of 2 s. The rationale to use these settings was to adhere to the R&K paradigm based on a 75 μV amplitude criteria and a lower frequency limit of 0.5 Hz. The principle of the CD algorithm is depicted in Fig. 1. D. Performance Evaluation Metrics The proposed SSW detection method was developed and evaluated on a training dataset (dataset 1) in order optimize threshold parameters. The performance of both the RMP and the CD algorithms were then evaluated on a testing dataset (dataset 2) and the results compared to those obtained from the expert scoring. The assignment of individual data to one or the other dataset has been obtained by random drawing in order to obtain 40% of data in the training set and 60% in the testing set as explained in Section II-B. In order to achieve the most unbiased performance assessment of SSW detection algorithms, our study has been performed without supervision and independently of scored sleep/wake stages using the whole-night left frontal EEG channel (F3-A2). Cortical SSW events detected by the automated algorithms were compared one by one to the events scored by the expert. When an event detected by the algorithm was part of an event scored by the expert, it was considered as a correct detection or true positive, otherwise it was considered as a false detection or false positive. The scored SSW trains during which no event was detected by the algorithm were considered as missed detections or false negatives. Several metrics were then computed to evalu-

ate the accuracy of algorithm detections. The true positive rate (TPR), or sensitivity, i.e., the rate between the number of SSW correctly detected and the total number of SSW to detect, was computed according to (1). The positive predictive value (PPV) or precision, i.e., the rate between the number of SSW correctly detected and the total number of SSW detected, was computed according to (2). The closer to 100 these two metrics are, the more accurate is the detection. TP × 100 TP + FN TP PPV = × 100. TP + FP TPR =

(1) (2)

Since SSW represent only 10% of the database, the false alarm rate (ratio between the number of false detections and the total number of correct “not SSW” detections) was not considered relevant as it would always yield very low values (suggestive of very good performance) as compared to the total duration of data without SSW. However, SSW have been scored by the human expert as trains of successive events and generally but not systematically included several consecutive individual events. Since detecting only one SSW in a train or detecting all of its elementary events could yield the same result, standard performance metrics might thus not be fully relevant. An alternative indicator, the common event duration (CED), was then estimated in order to provide a more accurate performance measure of SSW detection. CED is defined as the percentage of the total duration of SSW correctly detected to the total duration of SSW trains scored by the human expert, and is computed as D(sw) × 100. (3) CED = sw ∈T D(sw) sw ∈E In (3), T is the set of SSW correctly detected by the proposed method and E the set of SSW scored by the expert, D(sw) is the duration of the SSW sw. The closer to 100 this metric is, the more accurate the detection. A series of one-tailed paired t-tests was performed on the principal measures of performance outcomes (TPR, PPV, and CED) in order to confirm superiority of the proposed method as compared to a CD algorithm. As an exploratory estimate of performance, the relative event occupancy (REO, total SSW duration in a scoring epoch expressed as a percentage of the scoring epoch duration) of detected SSW in every 30 s epochs was also computed. This temporal index allows representing the occurrence and proportion of detected and scored SSW at different times of the recording and within different sleep/wake stages. This was used in order to verify that, according to the R&K criteria, SSW detections occurred mainly in sleep stages II, III, and IV while virtually absent from wake, and sleep stages I and REM. E. RMP Detection of SSW 1) Matching Pursuit: Matching pursuit (MP) has been introduced by Mallat and Zhang [22]. This algorithm provides an approximation of a signal y as a linear combination of elementary waveforms, called atoms, chosen from a redundant


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dictionary D. In the first step of the MP, the atom w0 that best fits the signal y is selected from D. In each consecutive step, the atom wn that best fits the residual signal Rn (y) left after subtracting all previous iterations is selected. At each iteration, the atom selected is the one that maximizes the scalar product k = |wn , Rn (y)|. This algorithm is described as ⎧ 0 R (y) = y ⎪ ⎪ ⎨ n R (y) = Rn (y), wn wn + Rn +1 (y) (4) ⎪ ⎪ ⎩ wn = arg max |wi , Ri (y)|. w i ∈D

The process is iterated until some stopping criterion, such as minimal residual energy threshold, is reached. After M iterations, the approximation of y is obtained as follows: y≈

M

Rn (y), wn · wn

where

wn ∈ D.

(5)

n =1

2) Dictionary Definition: Standard MP is well-known method used in combination with large redundant dictionary in order to approximate EEG signal as a linear combination of atoms [23], [24]. The obtained scalogram offers a representation of the time-frequency energy distribution of the analyzed signal, on the basis of which patterns can be identified using certain duration, amplitude, and frequency criteria. This technique is computationally very intensive by requiring a large number of iterations. In contrast, the originality of the present method is to take advantage of the pattern detection ability of MP algorithm and to use a small dictionary restricted to target waveforms (i.e., a lower number of atoms). In this way, MP should provide a precise detection of SSW and highly decrease processing time. Since there is no neurophysiologic and morphological model accounting for the wave shape of SSW, the construction of a specific dictionary to detect SSW was experimental. We decided to use real-valued Gabor functions taking advantage of their large number of control parameters (phase, amplitude, position, frequency, width) allowing to precisely describe SSW. It was indeed easy to obtain atoms resembling the typical waveform of a SSW and to reproduce most of the elementary morphological aspects of a SSW such as the wave polarity and length, which was not always possible with other atoms such as spline functions, complex exponentials, damped sinusoids or “Fonction d’Onde Formantique” (FOF). Furthermore, this family of basis functions offers an optimal time-frequency resolution as demonstrated in [22]. Real Gabor functions can be expressed as follows: gγ (t) = K(γ)e−π ((t−u )/s) cos(ω((t − u) + φ) 2

(6)

where K(γ) is such as gγ = 1 and γ = {u, ω, s, φ}. As we want to restrict the dictionary to specific atoms resembling the shape of the SSW, several criteria are applied on parameters γ = {u, ω, s, φ} depending on the SSW characteristics. First, the frequency of SSW must be between 0.5 and 2 Hz. So, the frequency parameter ω is defined according to ω(f ) = 2π

f Fs

(7)

where Fs is the sampling frequency of y and f ∈ [0.5–2] Hz the frequency of the Gabor function. In this way, the atoms frequency stays in the [0.5–2] Hz range. Then, a SSW represents one oscillation only as we want to detect each events separately. So, the scale parameter s is defined according to s(f ) =

Fs 2f

(8)

in order to adjust the exponential component to the frequency f of the cosine function. Thereby, for each value f ∈ [0.5–2] Hz corresponds a single value of ω(f ) and s(f ). Moreover, SSW exhibits both a negative and then a positive deflection. So, we fix the phase φ between π3 and 2π 3 , as described in π 2π − φ∈ . (9) 3 3 Restricting the phase of Gabor functions in this range makes sure that the negative and positive oscillations of the atom are large enough. At last, a SSW is centered on a zero-crossing corresponding to the passage from a negative to a positive deflection. So, we want the Gabor functions to have the same negative-to-positive zero-crossing. If z is a negative-to-positive zero-crossing in the signal, the Gabor functions will be centered on u(z, f, φ): u(z, f, φ) = z −

−φ . ω(f )

π 2

(10)

By so doing, only the signal negative-to-positive zero-crossings can be considered as candidates, instead of all the signal samples. A dictionary D containing only the atoms corresponding to SSW is then constructed using these different restrictions as defined in

π 2π − D = gγ (f ,φ) |f ∈ [0.5–2] Hz, φ ∈ (11) 3 3 where γ(f, φ) = {u(z, f, φ), ω(f ), s(f ), φ}. 3) Detection of SSW: The proposed method iteratively processes EEG segments of 30 s duration with an overlap of 2 s between consecutive segments to make sure all events positioned at the edges of a segment are taken into account. The EEG signal is first filtered in the wide [0.3–45] Hz frequency range using a fifth-order Butterworth filter. The use of an EEG wideband filtering is also recommended in the scoring of sleep/wake stages [2] and removes the continuous signal components and the high-frequency artifacts caused by muscles and electrical power lines. The first step of the detection method is to detect all negativeto-positive zero-crossings of the current EEG segment. A cortical SSW is always centered on a negative-to-positive zerocrossing. All the negative-to-positive zero-crossings of the signal are preselected as candidates. Moreover, one advantage of this selection is to obtain a finite number of candidates to prevent testing all the segment samples. For each candidate, the frequency of negative-to-positive zero-crossings fzero is computed on a window of 2 s centered on the candidate. If this value

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Fig. 3. Results of the SSW detection on dataset 1 in terms of correct detections (T P ra te ) and precision P P va lu e for different threshold values M and Z to l .

Fig. 2.

Diagram of the RMP algorithm for SSW detection.

is greater than a given threshold Ztol , the candidate is rejected. We consider that if there are too many zero-crossings in a short time, there are no slow oscillations and consequently no SSW. The value of Ztol is studied and discussed in Section III-A. The MP algorithm is then processed with the dictionary D defined in (11) for every candidate. Frequencies from 0.5 to 2 Hz are tested by step of 0.1 Hz. Phases from π3 to 2π 3 rad are tested by step of π6 rad. The candidate that maximizes the scalar product k defined in paragraph II-E1 is selected. If k is greater than a given threshold M , then the candidate is stored as a SSW, removed from the preselection list, and the MP is processed again. Otherwise, we consider that the candidate waveform does not represent a SSW and that there are no more SSW candidates. The whole process is then applied to the next 30 s-segment of EEG. The value of the threshold M is studied and discussed in Section III-A. The principle of the SSW detection method is presented in Fig. 2. Following each detection, the SSW-related EEG signal is filtered in the δ band in order to extract features as described in [15] (duration, amplitude, and slope of each phase of the detected waveforms). The onset of the waveform is considered as the first positive-to-negative zero-crossing before the center of the waveform and the offset as the subsequent positive-tonegative zero-crossing. If the peak-to-peak amplitude is less than 75 μV or the duration less than 0.5 s, the waveform is rejected. Otherwise, it is validated as a SSW. III. RESULTS A. RMP Algorithm Optimization The proposed method was tested on dataset 1 with a selection threshold M varying from 35 to 55 and the zero-crossing frequency threshold Ztol varying from 2 to 6. These thresholds are defined in Section II-E3 and the results are illustrated in Fig. 3, with TPR as a function of PPV. Samples with identical symbols

and colors correspond to the same value of Ztol . Samples further to the left correspond to higher and samples further to the right correspond to lower values of Ztol . As expected, there were more candidates selected using a higher Ztol and so more imprecision in the detection. On the corresponding curves, upper samples correspond to lower M values and lower one to higher M values. A higher selection threshold decreases the number of detection and consequently also decreases the number of correct detections. The values of M and Ztol were optimized from these results in order to obtain the best compromise with highest values for TPR, PPV, and CED. The couple (M, Ztol ) that maximized the average of these three indicators was chosen as the set of optimal thresholds and this was obtained with M = 45 and Ztol = 4, and the corresponding performance of TPR = 97.6%, PPV = 64.8%, and CED = 68.2%. This was in line with our expectations, revealing that the preselected candidates were rejected when there were more than four negative-to-positive zero-crossings per second. Considering a single negative-topositive zero-crossing is equivalent to limiting the detection to waveforms with four waves per second, i.e., to an oscillation frequency not greater than 4 Hz. This limit corresponds to the upper limit of the δ band defined in Section I. In the following sections, the RPM-based SSW detection method was processed with these threshold values of M = 45 and Ztol = 4. B. Performance of the RMP Algorithm The performance of the proposed method for SSW detection has been evaluated on dataset 2 using the left frontal EEG channel (F3-A2) in all subjects. The method correctly detected 16748 SSW, with 8416 false detections and missed 382 events in reference to the expert scoring. As illustrated in Table I, it is interesting to note that the overall performance of the RMP detection (TPR = 97.4%, PPV = 64.5%, and CED = 67.4%) is very similar to those obtained while optimizing the algorithm parameters (see Section III-A). As the subjects in dataset 2 were all different from those of dataset 1, it is likely that the threshold defined in Section III-A are mainly subject-independent.


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TABLE I RESULTS OF THE SSW DETECTION OBTAINED WITH THE RMP ALGORITHM IN TERMS OF SENSITIVITY (TPR), PRECISION (PPV), AND COMMON EVENT DURATION (CED)

TABLE III RESULTS OF THE SSW DETECTION OBTAINED USING THE REFERENCE CD ALGORITHM IN TERMS OF SENSITIVITY (TPR), PRECISION (PPV), AND COMMON EVENT DURATION (CED)

TABLE II RELATIVE EVENT OCCUPANCY (REO) OF SSW DETECTED IN EACH SLEEP STAGE WITH THE RMP ALGORITHM

TABLE IV COMPARISON OF THE SSW DETECTIONS OBTAINED USING THE RMP AND THE CD ALGORITHMS

Results of Table I indicate that the proposed method achieves a high rate of correct SSW detection with an overall TPR of 97.4%. Inspection of individual results indicate that, except for subject 3, the detection accuracy was never less than 96%. The overall precision of the RMP method in detecting SSW is given with a PPV of 64.5%, revealing that two detections out of three were correct. Except for subject 2, the overall precision fluctuated between 55% and 75%. From these results, the rate of false alarms, which is commonly used but represents a biased indicator in our study given the predominance of a signal with no SSW, would be around 6% with 13 252 s of false detection among 217 960 s of recording without SSW. Alternatively, the result of an overall CED of 67.4% indicates that two-thirds of the total duration of SSW trains marked by the expert were correctly detected. Thus, even with a dictionary limited to two-phase waveforms, SSW oscillations containing multiple elementary events can be detected correctly. In order to further illustrate the results of automated SSW detection, the REO (defined in Section II-D) of the events detected in each sleep stage is presented in Table II. These exploratory results confirm the overall good performance of the proposed method and reveal that SSW were detected mainly in NREM sleep stages III and IV, then in sleep stage II, and virtually absent in wake and in sleep stages I and REM. This distribution of SSW is consistent with the sleep/wake stages defined in international guidelines [1], with sleep stages III and IV described as containing more than 20% and 50% of SSW, respectively, and wake, sleep stage I and REM described by the absence of SSW. In sleep stage II, SSW detections with an REO lower than 20% is also a result in line with the stage scoring definitions. During wake, movement artifacts are the most prevalent, and the number of detected SSW should most likely reflect spurious detections.

dataset 2 using a CD method. The selection of a CD algorithm amongst another has been made in order to address the paradigm defined by the sleep scoring guidelines. Results obtained from the CD method consisted of 13 593 correct detections, 10 887 false detections, and 399 missed detections. The overall results of the CD algorithm are presented in Table III. The CD algorithm reached performance close to that of the RMP method in terms of sensitivity with an overall TPR of 96.6% for the former. Individual CD sensitivity results show slightly more variability than those of the proposed method but these differences were not statistically significant. The overall precision of the CD method was lower than for the RMP method with a PPV of 52.3%, indicating that almost one out of two event detected by CD represents a false detection. The CD algorithm also showed a lower CED with an overall value of 55.4%, revealing that half of the SSW trains scored by the sleep expert were actually detected by the algorithm. These differences in SSW detection performance between the two algorithms were both statistically significant for PPV (p = 0.0002) and CED (p = 0.035), representing a 12% increase in precision (as assessed from either PPV or CED) for the RMP-based method as compared to the CD method. Table IV summarizes the number of correct, false, and missed detections obtained from both algorithms. In the last column, the percentages of differences between the two methods are expressed with CD considered as the reference. It is notable that SSW detections were more accurate using the proposed method, with a 23.2% improvement in correct detections, and a number of false detections decreased by 22.7%, as compared to the CD method. The number of missed detections was similar for both methods and remained very low compared to the number of correct detections, which accounts for high TPR in both cases.

C. Comparison With a CD Algorithm

D. Incorrect Detections and Expert Scoring

In order to compare the performance of both algorithms, the SSW detection results obtained from the application of the proposed method have been compared to those obtained on the same

In an effort to understand failures of the algorithms in detecting SSW, we have reviewed the recording portions with incorrect detections and compare the signals processed by the algorithms

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Fig. 4. Example of a false SSW detection (gray box) of the CD algorithm related to distortion of the signal by narrow-band [0.2–4] Hz filtering.

Fig. 6. Example of a missed SSW detection (gray box) of the CD method related to narrow-band [0.2–4] Hz filtering and its influence on the signal zerocrossings.

Fig. 5. Example of a missed SSW detection (gray box) of the CD algorithm related to distortion of the signal by narrow-band [0.2–4] Hz filtering. Fig. 7.

to those scored by the expert. The following observations, with examples of false (see Fig. 4) and missed (see Fig. 5) detections, illustrate the side-effects of the CD method narrow-band filtering on the signal morphology. A 30 s epoch of EEG signal recorded from the left frontal channel (F3-A2) during sleep stage II is shown in Fig. 4. The signal used in expert visual scoring and in RMP algorithm is filtered in the [0.3–45] Hz frequency band and displayed on top of the figure while, at the bottom, the same signal is represented filtered in the narrow δ[0.2–4] Hz band as processed with the CD algorithm. Although there was no SSW detected by the expert or by the RMP algorithm in the highlighted gray box, narrow-band filtering of the CD algorithm distorted the waveform thereby appearing more like a SSW with a negative then positive deflection and leading to a false detection (highlighted in light gray on the signal). Fig. 5, with a 20 s epoch of EEG from the F3-A2 channel, shows another example of a wrong decision of the CD method where narrow-band filtering alters the waveform preventing correct detection of SSW. In this case, as highlighted in dark gray on the signal, several SSW scored by the expert and detected by the RMP algorithm have been missed by the CD algorithm. The latter algorithm first detects the negative zero-crossings as the onset of the candidates. However, duration between the candidate onset and the subsequent positive zero-crossing was longer than the upper duration criteria and thereby was not validated as a SSW. Another example of a wrong decision is illustrated in Fig. 6. The CD algorithm did not consider this SSW scored by the expert and detected by the RMP algorithm because although the signal came close to it, it did not cross the zero-line at the onset of the wave, resulting in a missed detection (highlighted

Example of a train of SSW scored by the expert (gray box).

in the gray box). This SSW scored by the expert was detected by the proposed method as the scalar product between the wave candidate and the associated Gabor function was high. The significant disagreement between the results scored by the expert and those obtained by the algorithms led us to also inspect the expert-scored SSW trains in an attempt to elucidate discrepancies. In Fig. 7, a 30 s epoch of signals from the left (F3-A2) and right (F4-A1) frontal EEG channels is illustrated with an example of trains of SSW (in dark gray on the signals) scored by a sleep expert. As highlighted in the gray box, all waves of the train did not fulfill the 75 μV peak-to-peak amplitude criterion. IV. DISCUSSION The detection of typical EEG waveforms using standard MP algorithm operating on a large and redundant dictionary has been presented earlier [24]. In the present study, MP was used to specifically detect SSW, and this was achieved in a more efficient way by limiting the number of atoms in the dictionary and by selecting basis functions for their potential in accounting for the target waveform characteristics. Differences in this approach also lie in the way MP is processed and in the nature of the stopping criteria. Standard MP processes all the signal samples and minimizes the error between approximated and real signals. In our method based on a small and specific dictionary, MP is triggered by the detection of a negative-to-positive zero-crossing representing the SSW reference point and is then processed under control of a minimal amplitude stopping criteria. While the proposed RMP algorithm showed a sensitivity of 64.5–67.4% according to the metrics used in performance evaluation as compared to the expert scoring, Durka et al. obtained


a global concordance of 81% with the expert in scoring NREM sleep stages III and IV. When their analysis was limited to deep sleep, concordance dropped to 68% [24]. Besides differences in scoring stages versus events, the observed results seem quite comparable in terms of performance. However, the RMP algorithm takes about 20 min to analyze 8 h of EEG signal while standard MP requires about five days to process the same signal. The small size of our specific dictionary requires little iteration, which dramatically decreases computing time. From tests conducted on the same computer, the RMP algorithm for the detection of SSW was in the average 300 times faster than the greedy and time-consuming MP algorithm used in [24]. About 35% of SSW trains scored by the expert were not detected by the RPM and CD algorithms. According to [26], the global disagreement in scoring sleep stages is around 20%. Regarding the scoring of sleep stages III and IV in particular, an intra-class scoring concordance of 64% between two experts has been reported in [24]. Since the scoring of NREM sleep stages relies on the presence of SSW, an inter-expert variability in the same range is most likely to occur in the scoring of SSW events. Assuming similar inter-expert variability in the scoring of individual SSW and of NREM sleep stages, our unique results would indicate a level performance not far from that of the expert. This comparison with the inter-rater reliability in sleep stage scoring may not be fully appropriate, but unfortunately there is no reference data available regarding the scoring of SSW events. In our study, the sleep expert scored SSW as trains of successive individual events to mimic the task of assessing the abundance or percentage of time occupied by SSW within 30 s epochs, as recommended in the sleep scoring guidelines. However, a careful inspection of the recording portions scored by the expert indicated that not all SSW of a train necessarily fulfilled the 75 μV amplitude criterion. The exhaustiveness of this task may account for the lack of such data in the literature, and since visually scored SSW were available from a single expert, no inter-expert agreement can be calculated. This discrepancy and the lack of reference data clearly represent a limitation in our ability to assess the true performance of an algorithm. In the present study, the decision of using data from healthy young adults has been made deliberately in order to be able to first evaluate the method on a well-characterized dataset in which we would be sure to observe a significant amount of SSW. The purpose of this work was to present a method as standard as possible and compliant with R&K and AASM guidelines. As these guidelines provide a description of the sleep/wake stage scoring criteria in young healthy adults, it also appeared logical to us to evaluate the method on such a control dataset. From a similar standpoint, the reference CD algorithm was also selected in order to closely match the R&K paradigm. By imposing an explicit limit on the lower SSW frequency, our results may differ from those of other variants without full-wave duration criteria, such as in [15] and in [16]. However, the use of a less restrictive reference algorithm would have shown an increased number of detections, with its usual corollary of degraded precision. As shown in the present results, the number of missed detections was quite low for both the CD and the proposed methods, although the RMP algorithm showed better overall performance.

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The choice of the reference algorithm used in this study is thus likely to represent a fair selection in our comparative approach since a lower precision of the CD algorithm would have been a further advantage in favor of the method developed. In the existing algorithm implementing SSW detection based on a CD method, the way the signals are processed and the candidates are selected presents a major disadvantage. While special care is usually given to prevent phase distortion (by applying filters in both the forward and backward directions), the narrow-band filtering of EEG signals in a low-frequency band impacts the analyzed signals by distorting waveforms in shape and amplitude. As shown in the present study, these features of the CD algorithms may lead to incorrect or missed SSW detections. A reason that is likely to account for the superiority of the RMP approach in detecting SSW is that EEG signals are filtered in a wide [0.3–45] Hz frequency band, thereby preventing waveform distortion. By relying more on the overall shape of the analyzed waveforms, it is also less sensitive to the waveform baseline magnitude and to the zero-crossings defining both SSW phases. Instead of using a set of strict duration and amplitude criteria, the only fiducial point that matters in the RMP algorithm is the central negative-to-positive zero-crossing of the SSW. As shown by the PPV and CED metrics, the RMP algorithms significantly improves the accuracy of SSW detection as compared to the CD method, confirming the results of our preliminary study on the training dataset [27]. The results obtained on the testing set introduced in the present study indicate a slight increase in variability as compared to [27]. Nevertheless, the threshold parameters being optimized on the first set of PSG recordings and the stable performance obtained here, with nine subjects absent from the training set, illustrates the robustness of the method. By examining the distribution of the detection results by sleep/wake stages, it appears that there were a small number of SSW incorrectly detected by the RMP algorithm during wake and in sleep stages I and REM. In this regard, we have demonstrated that the lower accuracy of the CD method results in more false detections within these particular vigilance states [21]. In practice, the detection of SSW in neurophysiologic studies was based on multiple variants of the CD algorithm and performed under the supervision of a sleep expert in order to select the recording portions to analyze, i.e., NREM sleep epochs exclusively [15], [17]–[19]. As a matter of fact, the improbable detection results obtained during wake and in sleep stage I and REM suggest spurious detections related to an increased prevalence of movement artifacts during activated states. The superior detection accuracy of the RMP algorithm, combined with a simple movement artifact detector is thus likely to represent a suitable solution for large-scale analyses of sleep in ambulatory PSG recordings. Another interesting application of this study is the characterization of sleep in aging. Since the amplitude of SSW seems to decrease with age, the visual scoring of sleep stages with a strict adherence to the guidelines criteria often results in a reduced number of sleep transient events [28] and in a loss of deep sleep [29]. While the threshold used in this study was optimized for the detection of SSW as defined in the R&K guidelines, a possible application would be to adapt the stopping criteria of the

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RMP algorithm in order to detect and quantify low-amplitude SSW. To date, there is no reference to a clinically validated method for the detection of individual SSW. The only mention of a potential clinical application comes from a recent study based on a refined multichannel version of the CD method and based on the analysis of data obtained during the first sleep cycle in one subject with altered sleep after intense and prolonged physical exercise [20]. This refinement relies on the availability of a large number of EEG channels and requires that at least one instance in the detection results fulfill the amplitude criteria of the CD method. This limitation may well restrict the method’s effectiveness in situations such as in the elderly where the whole EEG amplitude is attenuated to such an extent that no SWS can be visually identified, unless the SSW minimal amplitude rule of the scoring guidelines is modified. In contrast, our method can operate on single-channel EEG recordings, and it is based on more fuzzy morphological criteria with an amplitude criteria set at a lower threshold, which may overcome problems related to the important individual variability in the amplitude of the sleep EEG. Further work based on the proposed method, by exploring various dictionaries and control parameters, may attempt to extend the RMP applications to the detection of additional transients such as K-complexes, sleep spindles, and micro-arousals. In this regard, the results of [24] on sleep spindles detection using standard MP are encouraging. The availability of a methodological framework that allows for the precise detection of sleep transients and for the characterization of their associated waveforms within the millisecond range paves the way for new research on the neuronal processes of sleep. In particular, new and more precise markers of sleep quality and sleep intensity could be developed based on our work. The possibility of detecting and characterizing every individual SSW should lead to more accurate results than by estimating SWA from FFT spectral power in the delta frequency band [9]. In this respect, SWA and traditional power spectral measures blindly compute EEG activities regardless of whether they are related to the occurrence of sleep SSW or from a different origin. V. CONCLUSION An original algorithm to specifically detect cortical SSW in single-channel EEG has been designed and evaluated. The method is based on the use of the MP algorithm with a minimal dictionary restricted to atoms capable of reproducing the target waveform morphology. By doing so, MP was successfully used as a pattern recognition algorithm detecting cortical SSW in PSG nocturnal recordings without supervision. The RMP algorithm operates in a way similar to a human expert in processing visual information for the scoring of SSW. In preventing waveform distortion as a consequence of narrow-band signal filtering, the algorithm focuses mainly on the shape of the target waveform rather than to apply strict duration and amplitude criteria as implemented in the existing CD algorithms. The RMP algorithm has been optimized and evaluated independently using a database of human PSG recordings from

15 different subjects visually analyzed by a registered sleep technologist according to international guidelines recommendations. As compared to the scoring of the expert, the algorithm demonstrated an overall performance with a sensitivity of 97% and a precision of 65–67% according to the evaluation metrics. Comparison of these results with those obtained from a CD algorithm revealed a 20% increase in the number of correct SSW detections while decreasing the number of false detection to a similar extent. The rigorous performance evaluation metrics used in this study leads to the conclusion that, even though the sensitivity of both the RMP and CD methods were comparable, with a slightly lower variability for RMP, the RMP algorithm achieves a more accurate detection of SSW. The analysis of SSW detections in each sleep stage, with most detections occurring during NREM sleep, was in fair agreement with the expert results of visual sleep stage scoring and suggest that a combined use with a movement artifact detector may further improve performance. In sleep research, investigators have used conventional measurement methods providing nonspecific markers of EEG activity in a given frequency range and quantifying indiscernibly the number, amplitude, and shape of transient events such SSW. Traditional quantitative EEG tools such as spectral power analysis lack accuracy and temporal resolution in their characterization of the brain activity accompanying sleep microstructure. The present methodological framework not only features an automated and robust pattern recognition of the cortical SSW, it also enables a characterization of the associated EEG waveforms, which opens a new avenue in the study of sleep-related neuronal processes and in the diagnosis of neuropsychiatric disorders. ACKNOWLEDGMENT The authors are thankful to Dr. H. Merica for her advice on the manuscript and to Dr. E. Van Cauter for providing the raw data used in this study. REFERENCES [1] A. Rechtschaffen and A. Kales, A Manual of Standardized Terminology, Techniques and Scoring System for Sleep Stages of Human Subject. Washington, DC: US Government Printing Office, 1968. [2] C. Iber, S. Ancoli-Israel, J. AL. Chesson, and S. Quan, The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications. Westchester, IL: AASM, 2007. [3] F. Amzica and M. Steriade, “Electrophysiological correlates of sleep delta waves,” Electroencephalogr. Clin. Neurophysiol., vol. 107, no. 2, pp. 69– 83, 1998. [4] M. Steriade, “Grouping of brain rhythms in corticothalamic systems,” Neuroscience, vol. 137, no. 4, pp. 1087–1106, 2006. [5] I. Feinberg, J. March, G. Fein, T. Floyd, J. Walker, and L. Price, “Period and amplitude analysis of 0.5–3 c/sec activity in NREM sleep of young adults,” Electroencephalogr. Clin. Neurophysiol., vol. 44, no. 2, pp. 202– 213, 1978. [6] G. Tononi and C. Cirelli, “Sleep function and synaptic homeostasis,” Sleep Med. Rev., vol. 10, no. 1, pp. 49–62, 2006. [7] G. Tononi, “Slow wave homeostasis and synaptic plasticity,” J. Clin. Sleep Med., vol. 5, no. 2, pp. 16–19, 2009. [8] A. Borbély and P. Achermann, “Concepts and models of sleep regulation: An overview,” J. Sleep Res., vol. 2, no. 1, pp. 17–29, 1992. [9] P. Achermann and A. Borbély, “Mathematical models of sleep regulation,” Front Biosci., vol. 8, pp. 683–693, 2003.


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Antoine Picot graduated from the Telecom Department, Institut National Polytechnique (INP) Grenoble, Grenoble, France, in 2006. He received the M.D. degree in signal, image, speech processing, and telecommunications, in 2006, and the Ph.D. degree in automatic control and signal processing, in 2009, from both from the INP Grenoble. He was a postdoctoral fellow at the University of Chicago, Chicago, IL. He is currently an Associate Professor at the INP Toulouse, Toulouse, France. His research interests include monitoring and diagnosis of complex systems with signal processing and artificial intelligence techniques.

Harry Whitmore received the B.A. degree in psychology from Knox College, Galesberg, IL, in 2001. He started his career in sleep medicine, in 2001, at the Sleep Disorders Center, Evanston Hospital. He became a Registered Technologist, in 2003, and joined the University of Chicago, Chicago, IL, in 2005. Mr. Whitmore is a member of the American Association of Sleep Technologists (AAST) and serves as the Vice Chair of the Program Committee for the AAST. He is also the Technical Director for the American Academy of Sleep Medicine’s ASTEP course.

Florian Chapotot graduated from the Universit Louis Pasteur, Strasbourg, France, and from the Universit Claude Bernard, Lyon, France. He received the Master’s degree in molecular biology and pharmacology, in 1995, a Graduate Certificate in statistical methodology, in 1997, a Ph.D. degree in cognitivebehavioral neurosciences, in 2000, and a postgraduate training as a Clinical Trial Investigator, in 2004, all from the Universit Louis Pasteur. He was a Research Scientist in the Human Factor Department, Armed Forces Health Services Research Center, La Tronche, France. He co-founded PhiTools, a University-sponsored start-up company developing software for bio-signal processing and analysis. He is currently an Assistant Professor at the University of Chicago, Chicago, IL. His research interests include the neurobehavioral regulation and mathematical modeling of sleep and vigilance. He also developed a computational approach based on signal processing, data mining, and machine learning to improve psychophysiological monitoring and diagnosis systems.