Sleep spindles and spike–wave discharges in EEG: Their generic features, similarities and...

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Journal of Neuroscience Methods 180 (2009) 304–316

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Journal of Neuroscience Methods

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Sleep spindles and spike–wave discharges in EEG: Their generic features,similarities and distinctions disclosed with Fourier transform andcontinuous wavelet analysis

Evgenia Sitnikovaa,∗, Alexander E. Hramovb,1, Alexey A. Koronovskyb,1, Gilles van Luijtelaarc,2

a Department of Neuroontogenesis, Institute of Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences, Butlerova str., 5A, 117485 Moscow, Russiab Faculty of Nonlinear Processes, Saratov State University, Saratov, Astrakhanskaya str., 83, 410012 Saratov, Russiac Donders Center for Cognition, Radboud University Nijmegen, PO BOX 9104, 6500 HE Nijmegen, The Netherlands

a r t i c l e i n f o

Article history:Received 23 February 2009Received in revised form 8 April 2009Accepted 10 April 2009

Keywords:Absence epilepsyEEG pattern recognitionContinuous wavelet transformAdoptive waveletFFTGenetic model

a b s t r a c t

Epileptic activity in the form of spike–wave discharges (SWD) appears in the electroencephalogram (EEG)during absence seizures. A relationship between SWD and normal sleep spindles is often assumed. Thisstudy compares time–frequency parameters of SWD and sleep spindles as recorded in the EEG in theWAG/Rij rat model of absence epilepsy. Fast Fourier transformation and continuous wavelet transforma-tion were used for EEG analysis. Wavelet analysis was performed in non-segmented full-length EEG. Aspecific wavelet-based algorithm was developed for the automatic identification of sleep spindles andSWD.

None of standard wavelet templates provided precise identification of all sleep spindles and SWD inthe EEG and different wavelet templates were imperative in order to accomplish this task. SWD wereidentified with high probability using standard Morlet wavelet, but sleep spindles were identified usingtwo types of customized adoptive ‘spindle wavelets’. It was found that (1) almost 100% of SWD (but only50–60% of spindles) were identified using the Morlet-based wavelet transform. (2) 82–91% of sleep spin-dles were selected using adoptive ‘spindle wavelet 1’ (template’s peak frequency ∼12.2 Hz), the remainingsleep spindles with ‘spindle wavelet 2’ (peak frequency ∼20–25 Hz). (3) Sleep spindles and SWD weredetected by the elevation of wavelet energy in different frequencies: SWD, in 30–50 Hz band, sleep spin-dles, in 7–14 Hz. It is concluded that the EEG patterns of sleep spindles and SWD belong to differentfamilies of phasic EEG events with different time frequency characteristics.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Sleep spindles are abundantly preset in the electroencephalo-gram (EEG) during drowsiness and non-REM sleep in allmammalian species and in humans (reviewed in Jankel andNiedermeyer, 1985; De Gennaro and Ferrara, 2003). The name‘spindle’ refers to a characteristic EEG waveform: sleep spindlesare defined as “a group of rhythmic waves characterized by pro-gressively increasing then decreasing amplitude” (IFS, 1974). Theoccurrence of sleep spindles in the EEG is associated with lossof perceptual awareness and it is remarkable that this ‘low vigi-lance’ state is also favorable for the occurrence of absence epilepsy

∗ Corresponding author. Tel.: +7 495 334 70 61; fax: +7 495 338 85 00.E-mail addresses: [email protected] (E. Sitnikova), [email protected]

(A.E. Hramov), [email protected] (A.A. Koronovsky),[email protected] (G. van Luijtelaar).

1 Tel.: +7 8452 523864; fax: +7 8452 523864.2 Tel.: +31 0 24 3615612; fax: +31 0 24 3616066.

(e.g., a non-convulsive generalized epilepsy of unknown etiology).Typical absence seizures are characterized by bilaterally symmet-ric 3–5 Hz spike–waves complexes in the EEG (Panayiotopoulos,1999). Some inbred rat strains, such as Genetic Absence EpilepsyRats from Strasbourg (GAERS, Marescaux et al., 1992) and WistarAlbino Glaxo from Rijswijk (WAG/Rij, van Luijtelaar and Coenen,1986), have a genetic predisposition to absence epilepsy and exhibitspontaneously occurring spike–wave seizure activity in their EEGconcurrently with mild clinical concomitants (Coenen and vanLuijtelaar, 2003). Spike–wave discharges (SWDs) in these geneticrat models and spike-and-wave complexes in humans are similarin respect to their waveform, duration (1–30 s and mean 5 s) andfrequency dynamics (Midzianovskaia et al., 2001; Bosnyakova etal., 2007; Sitnikova and van Luijtelaar, 2007).

A generic relationship between sleep spindles and SWD hasbeen proposed and confirmed in the feline penicillin model alreadysome decades ago; in this model seizures were induced pharma-cologically by injections of penicillin (Gloor, 1968; Kostopoulos,2000). Previously, the EEG structure of sleep spindles and SWD inrats was investigated with the aid of traditional spectral analysis

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E. Sitnikova et al. / Journal of Neuroscience Methods 180 (2009) 304–316 305

(fast Fourier transform) and this method yielded rather ambigu-ous results. As compared to sleep spindles, SWD displayed a highertotal power and more beta activity (due to the presence of a strongharmonic component). In spite of that, both SWD and spindleswere regarded as rather similar EEG phenomena considering thesame peak frequency (Drinkenburg et al., 1993; Mackenzie et al.,2004)3. In addition to that, EEG of WAG/Rij rats showed ‘spiky’intermediate transients that were identified as not fully formedSWD (Drinkenburg et al., 1993). Recent studies of spontaneous SWDin GEARS and WAG/Rij rats requestioned the pro-epileptogenicnature of spindle oscillations (Pinault et al., 2001, 2006; Meerenet al., 2009). Our investigation in WAG/Rij rats suggest also thatsleep spindles and SWD are rather independent physiological phe-nomena (van Luijtelaar and Sitnikova, 2006). In order to betterunderstand a putative functional relationship between these twokinds of rhythmic oscillations, electroencephalographic features ofSWD and sleep spindles will be compared.

Sleep spindles are abundant during non-REM sleep, also SWDpreferably appear during the passive awaking state and dur-ing the transition between wakefulness and sleep (in WAG/Rijrats: van Luijtelaar and Coenen, 1986; Drinkenburg et al., 1991;in humans: Halász, 1991; Halász et al., 2002). SWD and sleepspindles show amplitude maximum in the frontal cortex (vanLuijtelaar and Coenen, 1986; Midzianovskaia et al., 2001; Terrierand Gottesmann, 1978) and both of them are dynamic oscilla-tions. This means that their frequency changes over time andrestricts applicability of traditional frequency–domain measures(such as fast Fourier transform), in which time–domain informa-tion is lost. In contrast, in wavelet decomposition the EEG signalcan be represented in two-dimensional time–frequency–domain,in which signal power changes as a function of time and frequencysimultaneously (Daubechies, 1993; Kaiser, 1994; Torresani, 1995;Koronovskii and Hramov, 2003). Wavelet transform employs wave-like scalable function (wavelet basis) that is well localized in bothtime and frequency. By selecting an optimal wavelet basis, weintended to retrieve earmarks of sleep spindles and SWD that havenot been previously detected.

We chose the continuous wavelet transform (CWT) as an appro-priate method for time–frequency analysis of the EEG signal. A lackof the requirement of stationarity is an advantage of using the CWTfor the characterization of short non-stationary events in the EEG,such as episodes of spindle and spike–wave activity, in which thesignal-to-noise ratio is low (Jobert et al., 1994; van Vugt et al., 2007).The present study also address the problem of individual variabil-ity and irregularity of EEG pattern of SWD and sleep spindle eventsthat would be solved by selecting optimal template wavelet func-tions. From a technical point of view, our study provides a clue forthe selective identification, classification and statistical descriptionof several types of phasic events in the EEG.

2. Materials and methods

2.1. Animals, EEG data acquisition and description of EEG patterns

EEG activity was recorded in nine adult WAG/Rij male rats(11–12 months old, 310–345 g body weight). A recording elec-trode was implanted epidurally at the surface of the frontal cortex

3 Interestingly, different authors gave different names to ‘spike–wave’ discharges.Mackenzie et al. (2004) used the term ‘absence spindles’, Kandel and Buzsaki (1997)called them HVS, ‘high-voltage spike–wave spindles’, thus emphasizing close rela-tionship between SWD and spindles. The name ‘spindles’ does not seem appropriatefor absence-related EEG phenomena, because absence epileptic discharges areasymmetric, have a clear large amplitude spike and a slow wave component, more-over, they do not have the for spindles characteristic waxing–waning morphology.

(amplitude maximum of the investigated events, coordinates: AP+2 mm and L 2.5 mm relatively to bregma). Ground and refer-ence electrodes were placed over the two symmetrical sides ofthe cerebellum. EEG recordings were made in free moving ani-mals during the dark period of the light–dark cycle continuouslyfor 5–7 h. EEG signals were fed into a multi-channel differen-tial amplifier via a swivel contact, band-pass filtered between0.5 and 100 Hz, digitized with 1024 samples/second/per channel(CODAS software).

Sleep spindles were first selected visually in accordance toguidelines for clinical electroencephalography (Rechtschaffen andKales, 1968; IFS, 1974) by taking into account specificity of sleepspindle activity in rats (Terrier and Gottesmann, 1978; Steriadeet al., 1993; van Luijtelaar, 1997). Sleep spindles in the EEGwere recognized as a sequence of 8–14 Hz waves with a minimalduration of 0.4 s (e.g., at least four wave cycles in a sequence).Sleep spindles had waxing–waning morphology and were char-acterized by twofold increase in amplitude as compared to thebackground EEG. In order to facilitate expert’s estimations, EEGrecords were additionally band-pass 5–15 Hz filtered. Visual spin-dle detections were double checked and verified by anotherexpert.

SWD appeared in the EEG as a sequence of repetitive high-voltage negative spikes and negative waves that lasted longer than1 s (van Luijtelaar and Coenen, 1986; Midzianovskaia et al., 2001).SWD were first detected automatically with EEG slope method(Dr. PLC van den Broek, DCC, Radboud University Nijmegen, theNetherlands) that provided about 90% of correct detections andthan verified by two experts.

2.2. Power spectrum analysis

Power spectrum EEG analysis was performed in all nine rats.Hanning windowed fast Fourier transform (FFT) was applied tocompare frequency–domain features of sleep spindles and SWD(with 0.5 Hz resolution). Statistical analysis was performed in 1 sepochs (30–40 SWD per subject and 50 sleep spindles per subject)selected in the EEG during light non-REM sleep. If spindle durationwas shorter than 1 s, the starting point of time-window was put sothat the entire spindle was in the middle of the epoch. Power spectrawere averaged per event type and per animal. The following quan-titative parameters were computed and statistically compared: (i)duration, (ii) frequency and (iii) EEG power over the characteris-tic frequency bands: 1–4.5 Hz (delta), 5–8.5 Hz (theta), 9–13.5 Hz(alpha), 14–31.5 Hz (beta), 32–59.5 Hz (gamma1) and 60–100 Hz(gamma2).

2.3. Continuous wavelet transform: general aspects of automaticdetection of SWD and sleep spindles in EEG4

Step 1. Continuous wavelet analysis. It was carried on in five outof nine rats; in these subjects all episodes of SWD and all episodesof sleep spindles were marked in the full-length EEG (5–7 h).

The continuous wavelet transform, the CWT, W(s, �), was com-puted as a result of convolving of EEG signal, x(t), with wavelet basisfunction, �s, � (Eq. (1), ‘*’ denotes the complex conjugation):

W(s, �) =+∞∫−∞

x(t)ϕ∗s,�(t)dt (1)

4 Principles of the wavelet transform are given in papers and books Daubechies(1993), Kaiser (1994), Torresani (1995) and Koronovskii and Hramov (2003). Practicalissue on the application of wavelet transform in EEG can be found in Jobert et al.(1994), Durka (1996), Le Van Quyen et al. (2001) and Senhadji and Wendling (2002).


306 E. Sitnikova et al. / Journal of Neuroscience Methods 180 (2009) 304–316

ϕs,�(t) = 1√sϕ0

(t − �s

)(2)

where s is the time scale and � is the time shift of the wavelet trans-form. Frequently, the parameter s in this formula is substituted bya reciprocal parameter fs so that fs = 1/s.

Wavelet basis function,�s, � in Eq. (2), belongs to a family of pro-totype ‘mother’ wavelet,�o. The ‘mother’ wavelet can be either realor complex function and should satisfy several conditions, such ascontinuity, zero mean amplitude, and finite or near finite duration(Torresani, 1995; Koronovskii and Hramov, 2003).

Time (t) and time scales (s) (or corresponding frequencies, fs) inwavelet basis function are related through the uncertainty princi-ple, which states that it is impossible to extract the exact frequencyat the exact time. This implies that the finer the time resolution inthe CWT, the more coarse the frequency resolution, and vice versa.In the CWT, time–frequency resolution can be adjusted by chang-ing the inner parameters of the scalable wavelet basis function (e.g.,parameter ω0 in the complex Morlet wavelet, see below and alsoTorresani, 1995; Koronovskii and Hramov, 2003), therefore, we firstselect a wavelet basis which would provide an optimal (for our pur-poses) time–frequency resolution and allow to localize preciselysleep spindles and SWD in the EEG.

Step 2. The choice wavelet basis function. It is known that waveletcoefficients in the CWT represent the degree of correlation betweenmother (basis) wavelet function and the EEG signal x(t). Therefore,the choice of the wavelet basis is crucial for the accurate repre-sentation of the EEG signal in the wavelet space. Beforehand, wetested several basis functions in the CWT of the EEG signal, e.g., realand complex Morlet wavelets, Mexican hat and Paul wavelet, andwe obtained the best time–frequency resolution with the complexMorlet wavelet:

0(�) = 14√�e

jω0�e−�2/2 (4)

The complex Morlet wavelet (Kaiser, 1994) is a complex exponen-tial modulated Gaussian function, exp(jω0�), whereω0 is a specificparameter that defined the frequency of the complex exponential(Fig. 1). A Gaussian smoothing function, exp(−�2/2) enables high-resolution in both time and frequency domains.

In the complex Morlet wavelet family (Eq. (4)), parameter ω0determines the shape and the width of the wavelet function; there-fore, this parameter influences time and frequency resolution in theresultant CWT. Whenω0 <�, the temporal resolution was high, butfrequency resolution was too low (so that the frequency informa-tion of analyzed EEG events was lost) and vice versa, whenω0 > 4�,the frequency resolution was high, but the time resolution waslow. Value ω0 = 2� provided an optimal time–frequency resolu-tion of the EEG signal that was sufficient for both investigated EEG

phenomena (Koronovskii and Hramov, 2003). Another importantfeature of the complex Morlet wavelet is the lack of negative fre-quencies in Fourier space (�s(sω) in Fig. 1). This is profitable forthe time–frequency representation of the EEG signal in the waveletspace; the Presence of negative Fourier frequencies in some waveletbasis functions (e.g., in Paul wavelet) might embarrass extractingfrequency information from the analyzed signal and, thus, worsentime-scale resolution of the method.

In the complex Morlet wavelet family, the correspondencebetween time scales (s, in wavelet space) and frequencies (f, inFourier space) can be computed by the formula Eq. (5) (Koronovskiiand Hramov, 2003):

f = ω0 +√

2 +ω20

4�s(5)

whereω0 denotes the basis frequency of the Morlet mother wavelet.Noteworthy, forω0 = 2� the correspondence between s and f is sim-ple, s ≈ 1/f, but it is more complex for the other ω0.

Step 3. Qualitative analysis of wavelet power. The squared modulusof the CWT, E(t, fs), was used to measure instantaneous frequencyenergy at time � (Eq. (6)). The integral of E(t, fs) was averaged overtime to obtain the wavelet power spectrum (or scalogram), 〈E(fs)〉(Eq. (7)):

E(t, fs) = |W(t, fs)|2 (6)

⟨E(fs)

⟩= 1T

T∫0

|W(t, fs)|2dt (7)

The distribution of wavelet energy over the frequency scale wasvisually inspected in order to assess the frequency characteris-tic band, Fs ∈ (f1, f2), in which SWD (and sleep spindles) showedthe most clear differences from the background EEG (Fig. 2). Theninstantaneous wavelet power,w(t), was computed in the frequencyband Fs (Eq. (8)):

w(t) =∫FS

E(t, fs)dfs (8)

Step 4. Automatic detection of SWD and sleep spindles with the aid ofthe CWT (complex Morlet wavelet ω0 = 2�). SWD were recognizedautomatically when the wavelet energy, w(t), in the characteristicfrequency band FSWD ∈ 30–50 Hz exceeded the threshold Ek = 0.5 fora duration of 1 s and longer (Fig. 2). Sleep spindles were first selectedin the same EEG by an increased wavelet power in Fsp ∈ 8–14 Hz,but this approach was insufficient, and sleep spindles were oftenmixed up with SWD. In order to prevent error detections, seg-ments of previously selected SWD were set to zero (bottom platein Fig. 2). Despite this, only 40% of the sleep spindles were detected

Fig. 1. The complex wavelet Morlet (parameter ω0 = 2�) as represented in time–domain, 0(t/s), and in the frequency–domain, �0(sω). Solid line shows the real part anddotted line—the imaginary part.



Fig. 2. In the wavelet spectrum (complex Morlet wavelet ω0 = 2�), SWD (highlighted in grey) can be recognized by an increased power in frequencies >10 Hz. Note thecharacteristic dynamic of dominant frequency during SWD: at the beginning it was 12–14 Hz and decreased at the end (7–9 Hz). Dome-like curve in the wavelet spectrumoutlines a confidence (upper) area in which ‘boundary effects’ are significant (Torrence and Compo, 1998; Koronovskii and Hramov, 2003). Two bottom plates show principlesof automatic detection of SWD. SWD were recognized automatically based on the value of wavelet energy w(t) in the characteristic frequency band FSWD ∈ (30–50) Hz whenw(t)> Ek , where Ek is the threshold level (indicated by dashed line). Further, in order to avoid misapprehending of SWD as sleep spindles, EEG episodes with SWD were setto zero.

automatically and correctly (see Section 3.3). The quality of auto-matic detections of sleep spindles was slightly improved whenparameters Fsp and Ek were chosen individually (different valuesfor each rat), but the percentage of true detections was still low(∼60%, Table 2B). The best performance of wavelet-based automaticidentification of sleep spindles in EEG was achieved with the aidof specifically designed adoptive wavelet basis (‘spindle wavelets’,Section 2.3).

2.4. Construction of adoptive wavelet basis (‘spindle wavelet’) forthe automatic recognition of sleep spindles

An adoptive wavelet basis function (spindle wavelet) was builtusing sleep spindle prototype extracted from the native EEG (Fig. 3).The EEG signal was represented by the function g(t) and trans-formed into a complex form, g(�). Time shift between the real andimaginary parts was T0/4, where T0 denotes the typical period of asleep spindle oscillation (10):

g(�) = g(�) + jg(�+ T0/4), where j =√

−1 (10)

In order to construct a complex wavelet basis, s(�), g(�) was nor-malized with Gaussian function (11):

s(�) = ˛g exp

(−�2

2

), (11)

In this formula˛denotes the normalization factor, which was deter-mined using the normalization function:

+∞∫−∞

( s(�))2d� = ˛2

+∞∫−∞

g(�)2 exp(−�2)d� = 1. (12)

Both ‘spindle wavelets’ fulfilled the requirements for wavelet bases(e.g., continuity, zero mean amplitude, and finite or near finite dura-tion). Let us note that the same computational procedure is usedfor the harmonic, e.g., sin(ω0t) function, in order to construct thecomplex Morlet wavelet (4).

In order to select an optimal spindle template, 80 candidate spin-dle templates were chosen in five rats (15–22 spindles per rat). Eachspindle template was employed in the automatic detection systemand tested as a wavelet basis. Wavelet energy, w(t), was computedin the frequency band Fsp(type 1) ∈ 7–14 Hz and selections weremade ifw(t)> Ek for a minimal duration of 0.35 s. Finally, we chosea wavelet basis that provided the maximum number of positivespindle detections. This ‘spindle wavelet’ (type 1) yielded the bestperformance in all animals (87.4% of correct detections on average,Table 3A).

Sleep spindles that were missed by ‘spindle wavelet’ type 1 werecaptured with ‘spindle wavelet’ type 2. A basis function for ‘spindlewavelet 2’ had to be selected for each rat individually (4–9 spindlesper subject were tested as wavelet basis). Type 2 sleep spindles



Fig. 3. The algorithm used for constructing adoptive ‘spindle’ wavelets. Sleep spindle prototypes are selected in native EEG, g(t), converted into the complex form andnormalized with Gaussian function (see text for details).

revealed an increased wavelet energy, w(t), in the frequency bandFsp(type 2) ∈ 20–25 Hz.

Combined application of ‘spindle wavelets’ type 1 and type 2highly improved the quality of automatic detection of sleep spindlesin the EEG. Automatic selections of sleep spindles perfectly matchedselections made by experts (Fig. 4). From a technical point of view,‘spindle wavelets’ encouraged automatic recognition of sleep spin-dles and provided better results as compared to what has beenobtained using the standard complex Morlet wavelet (ω0 = 2�).

2.5. Statistical analysis of automatically recognized SWD andsleep spindles

The performance of wavelet-based detection method was eval-uated by measuring the percentage of true positive/negativedetections, false positive/negative and by computing sensitivity andspecificity.

True positive (TP) was computed as percentage of correctdetections of SWD (or sleep spindles). True negative (TN) is thepercentage of correct rejections of SWD (or sleep spindles). Falsepositive (FP) represented the percentage of incorrect automaticdetections of SWD (or sleep spindles). False negative (FN), percent-age of events missed by the automatic wavelet-based method.

The accuracy of automatic recognition was computed as = (TP/Ne) × 100% (where TP was the number of true positivedetections and Ne the number of expert selections). SWD denotesthe accuracy of SWD detection and SS the accuracy of spindledetection. The sensitivity and specificity were assessed using theformulae:

sensitivity = TP(TP + FN)

× 100%

specificity = TN(TN + FP)

× 100%.

The software for the wavelet analysis was specifically designedat the Faculty of Non-linear processes, Saratov State University(Russia). Power spectrum analysis was performed using BrainVision Analyser software (BrainProducts© GmbH) and Spectranes

software (Dr. PLC van den Broek and Dr. J van Egmond, UMC©, SintRadboudsoftware). ANOVA (Fisher test for post hoc analysis) andt-test for related samples were used for the statistical analysis.

3. Results

Various oscillatory patterns were encountered in the EEG ofour subjects, WAG/Rij rats, during drowsiness and non-REM sleep;here we statistically analyzed spike–wave discharges (SWD) andsleep spindle oscillations (Fig. 5), but disregarded intermediateoscillatory waveforms or so-called ‘spiky oscillations’5 (Fig. 5). Ascompared to sleep spindles, SWD lasted ten times longer, theiramplitude was twice as low and their mean frequency was signifi-cantly lower (Table 1).

3.1. Sleep spindles and SWD in Fourier space

The fast Fourier transform (FFT, frequency–domain measure),which is traditionally used for time–frequency analysis of the EEG,has serious disadvantages that limits its application for analysis ofSWD and spindle events. An obstacle that we faced in the Fourieranalysis was the necessity of fixing the time-window length.Duration of the investigated events varied from half a second(mean duration of sleep spindles) to tens seconds (SWD) (Table 1).For example, Fig. 3 shows that time-window 7 s was too narrow forSWD, but it is definitely too broad for sleep spindles and for spikyoscillations (the latter patterns were not included in the furtheranalysis).

In FFT, time–domain information is missing, and short-lastingchanges are disregarded in the Fourier space. This seriously limitsthe applicability of this method for the time–frequency EEG analy-sis and this enforced us to use the CWT in the current study as theoptimal method of analysis of the time–frequency peculiarities ofthe phasic EEG events (Torresani, 1995; Koronovskii and Hramov,2003).

5 ‘Spiky oscillations’ were first described in EEG of WAG/Rij rats by Drinkenburget al. (1991).



Fig. 4. Automatic recognition of sleep spindles with the aid of two ‘spindle wavelets’. (A) An example EEG with sleep spindle oscillations. (B) Distribution of wavelet energyw(t) as obtained with type 1 and type 2 ‘spindle wavelets’ in the characteristic bands (Fsp). Type 1 ‘spindle wavelet’ sleep spindles in Fsp(‘type 1’) = 7–14 Hz with thresholdEk = 12.4; Fsp(‘type 2’) = 20–25 Hz, threshold Ek = 21. (C) Automatic spindle detections match experts’ selections.

The power spectrum of SWD contained a harmonic componentat 20 Hz (shown by arrows in Fig. 5) that replicates its mean fre-quency (10 Hz). This 20 Hz harmonic component is likely to beelicited by the regular ∼10 Hz spikes. The other spectral compo-

nents (peaks in 24 and in 35 Hz) do not fit to the expected 30and 40 Hz harmonics, suggesting that epileptic discharges do notrepresent a single rhythm. SWD display in the EEG regularly modu-lated rhythmic activity and it is characterized by complex frequency

Fig. 5. EEG during slow-wave sleep EEG in WAG/Rij rat. Epileptic discharges (SWD), normal sleep spindles and intermediate spiky phenomena are characterized by differentwaveforms and different power spectra.



Table 1Basic characteristics of sleep spindles and SWD (epoch length = 1 s; mean ± S.D.).

Number of EEG samples Duration (s) Mean frequency (Hz) Total power (�V2)

Sleep spindles 445 0.68 ± 0.08 11.14 ± 1.02 11.3 ± 1.7SWD 297 6.71 ± 0.58* 9.14 ± 0.47a,* 24.8 ± 6.5*

* Significant differences between sleep spindles and SWD (t-test, p < 0.05).a As measured in a period 0.5–1.5 s after the onset.

dynamics. Noteworthy is that the ∼8 Hz frequency component andit’s harmonic (16 Hz) were also found in Fourier spectrum of ‘spikyoscillations’.

3.2. Power spectrum analysis of sleep spindles and SWD

Both sleep spindles and SWD displayed peaks around 9–12 Hz(Fig. 6A) in their power spectra, suggesting that both EEG phe-nomena were characterized by the same rhythmic component inthe alpha frequencies. In spite of that, the power spectra of sleepspindles and SWD displayed principal differences:

(i) In SWD, the amplitude of the spectral peak in the mean fre-quency ∼9 Hz was several times higher as compared to the∼10–11 Hz peak in sleep spindles. The ∼9 Hz peak in the spec-trum of SWD was sharp and had high power, it represents theperiodicity of the high-voltage spike and wave component. Asmooth ∼11 Hz peak in the spectrum of sleep spindles may beaccounted for considerable frequency variability within spin-dle sequences.

(ii) The mean peak frequency of SWD was lower than in sleepspindles (the difference was ∼2 Hz, Table 1).

(iii) In contrast to the spectrum of SWD, the power spectrum ofsleep spindles displayed relatively high power in delta frequen-cies (1–4 Hz).

(iv) In contrast to sleep spindles, power spectrum of SWD showedadditional peaks in harmonic frequencies, 16–20 Hz. These har-monic frequency components in the power spectrum wereconsidered as a manifestation of the sharp and regular spikesin SWD.

Statistical analysis of the distribution of spectral power overthe characteristic frequency bands revealed significant differencesbetween sleep spindles and SWD (ANOVA; F = 38.9; d.f. = 1.107;p < 0.0001, Fig. 6B). SWD had significantly more power in alpha, betaand gamma bands (e.g., in frequencies from 8.5 to 100 Hz) and lesspower in the delta band, as compared to sleep spindles (p < 0.05).

In general, sleep spindles and SWD were characterized byremarkable differences in the frequency–domain. Although themean of the peak frequencies of sleep spindles and SWD appeared

in alpha band (11 Hz versus 9 Hz, respectively), SWD demonstratedhigher power in 9–100 Hz and lower power in 1–4.5 Hz, as com-pared to sleep spindles. This difference in frequency composurebetween SWD and sleep spindles closely links with differences intheir EEG waveforms. This issue was further examined with the aidof continuous wavelet transform (Section 3.3).

3.3. Sleep spindles and SWD in the wavelet space

Preliminary time–frequency analysis of sleep spindles was per-formed using CWT with the complex Morlet wavelet (ω0 = 2�).Based on the distribution of wavelet energy over the frequencyscale, we specified frequency bands (FSWD and Fsp), in which spin-dles and SWD could be best discriminated from the backgroundEEG. Selection criteria for the automatic recognition of SWD andsleep spindles were obtained by measuring wavelet energy,w(t), inFSWD (and Fsp), so that w(t)> Et (Section 2.2). In total, our analysiswas performed in full-length EEG (5–7 h) in five rats (66–249 sam-ples of SWD per subject and 1305–2341 samples of sleep spindles,Table 2).

3.3.1. Epileptic discharges, SWDIn the wavelet spectrum (the CWT with the complex Morlet

ω0 = 2�), SWD showed a vast increase of energy in frequenciesabove 10 Hz (Fig. 2) and SWD could be identified in the waveletspace by the presence of high wavelet power in the >10 Hz fre-quency band. The repetitive spikes in SWD corresponded to theisolated bursts in the high-frequency part of its wavelet spec-trum. In addition, the wavelet spectrum revealed a characteristicfrequency dynamics during SWD (Fig. 2). At the beginning, SWDshowed a maximum wavelet energy at ∼13 Hz and this maximumwas gradually shifted to 7 Hz at the end of SWD. The same frequencydynamics in SWD was demonstrated in WAG/Rij rats and in humanpatients (Bosnyakova et al., 2007).

In the wavelet-based automatic recognition system, it appearedthat almost all SWD in all animals were identified correctly by hav-ing high wavelet power in frequency band FSWD ∈ 30–50 Hz andwith the energy threshold set at Ek = 0.5 (Fig. 2). Table 2A shows thatthe accuracy of detections (SWD), selectivity and specificity werehigh and almost reached 100%. Incorrect detections (false positive,

Fig. 6. Results of power spectrum analysis of sleep spindles and SWD (n = 9 rats). (A) Mean power spectrum of SWD differs form that in sleep spindles by having large peak in9–10 Hz and additional component in harmonic beta frequencies. (B) ANOVA analysis of EEG power in the selected frequency bands (asterisks show significant differences,p < 0.05).



Table 2Results of automatic identification of SWD (under part, A) and sleep spindles (under part, B) using the CWT with the complex Morlet wavelet (ω0 = 2�).

A. SWD## Rat NN Visual detections, Ne Automatic detections PerformanceTP FP FN Accuracy S , % Sensitivity % Specificity %

1 105 105 0 0 100.0 100.0 100.02 81 79 2 1 97.5 98.8 97.53 249 247 1 2 99.2 99.2 99.64 120 117 1 3 97.5 97.5 99.25 66 65 2 1 98.5 98.5 97.0

Mean ± S.D. 124 ± 73 123 ± 73 1.2 ± 0.8 1.4 ± 1.4 98.5 ± 1.1 98.8 ± 0.9 98.7 ± 1.3

B. sleep spindlesa

Rat NNVisualdetections, Ne

Automatic detections Parameters Performance

TP FP FN Ek f1 (Hz) f2 (Hz) Accuracy S (%) Sensitivity (%) Specificity (%)

1 2341 1358 894 1359 1.5 6.25 12.5 58.0 47.7 60.32 1381 856 599 855 1.4 8.3 16.6 62.0 54.1 58.83 1491 999 772 1002 1.8 5.5 12.5 67.0 57.9 56.44 1305 718 505 720 2.2 6.25 16.6 55.0 48.6 58.75 1598 1007 866 1015 1.9 6.25 12.5 63.0 57.1 53.8

Mean ± S.D. 1623 ± 416 987 ± 239 727 ± 169 990 ± 239 1.7 ± 0.3 6.5 ± 1.1 14.1 ± 2.3 61.2 ± 4.7 53.2 ± 4.8 57.7 ± 2.5

## SWD detections were made when wavelet energy in frequencies FSWD ∈ (30, 50) Hz exceeded the threshold level, Ek = 0.5 (the same parameters FSWD and Ek were usedfor all animals). TP, true positive detections: the percentage of correct automatic detections from the total amount of visually detected events; FP, false positives: thepercentage of incorrectly identified events from the true positive detections; FN, false negatives: the percentage of missed events from the true negative detections. Accuracy = (TP/Ne) × 100%. Sensitivity = TP/(TP + FN) × 100%. Specificity = TN/(FP + TN) × 100%.

a Sleep spindles were detected using individual parameters FSWD and Ek .

FP or error type 1) were rare (0–1.8%). All this suggests that SWD canfaithfully be distinguished from non-epileptic background EEG byhaving sustained increase in power in the gamma frequency band.

3.3.2. Sleep spindlesAs compared to SWD, sleep spindles showed a greater vari-

ability in shape and their electroencephalographic pattern wasless stereotypic. This embarrassed the automatic detection of sleepspindles. The CWT with complex Morlet wavelet ω0 = 2� (Fig. 7A)was used for time–frequency representation of sleep spindles. Itappeared that the distribution of wavelet energy over the frequencyscale varied from spindle to spindle, indicating a wide variabil-ity of the frequency content of EEG spindle events. Despite that,sleep spindles were characterized by the presence of strong 8–14 Hzcomponents (Fig. 7A) that met the definition of sleep spindles asshort-lasting sinusoidal 8–14 Hz oscillations.

The detection of sleep spindles with the aid of Morlet-basedCWT was facilitated by an increase of the threshold of the waveletenergy in 8–14 Hz, however this was not sufficient. A maximum of38–45% of correct detections of sleep spindles (TP, data not shown)was obtained when a fixed threshold of the wavelet energy in8–14 Hz (Ek = 0.025) was applied to the Morlet-based wavelet spec-trum. Automatic detection was improved when parameters, suchas the frequency band (f1, f2) and threshold value (Ek), were chosenfor each rat individually. Even though, only 55–67% of sleep spin-dles were identified correctly (Table 3B) by having higher waveletpower in frequencies from 6.5 to 14.1 Hz (mean values of f1 andf2). Most likely, sleep spindles bear similarities with other alphaoscillations in the EEG and, therefore, they could not be easily dis-tinguished from non-spindle oscillatory activity with the aid of thestandard wavelet basis function. In order to improve the quality ofsleep spindle detection and subsequently to extract generic proper-ties of sleep spindles, we designed adoptive ‘spindle wavelet’ basisfunctions (Sections 2.3 and 3.3.3).

3.3.3. Identification of two spindle types with the aid of twoadoptive ‘spindle wavelets’

Although the variability in the waveform of sleep spindles wasrather high, spindle sequences were characterized by some sharedelements (Fig. 8A). Sleep spindles showed different degrees of con-formity to two types of spindle wavelets, e.g., ‘spindle wavelets’ type

1 and type 2 (see Section 2.3). When ‘spindle wavelet 1’ was usedfor the automatic recognition of spindle events, about 87.4% of sleepspindles (so-called type 1 sleep spindles) were identified correctlyin the frequency band Fsp(type 1) ∈ (f1, f2) = (7, 14) Hz (Table 3A).

The remaining sleep spindles, which failed to be captured with‘spindle wavelet 1’, were selected using ‘spindle wavelet 2’ inFsp(type 2) ∈ (f1, f2) = (20–25 Hz). It was found that type 2 sleepspindles comprised 7.9% from the total number of sleep spindles(Table 3B).

3.4. Two types of sleep spindles and their relevance to SWD

There was a clear inconsistency in our population of sleep spin-dles: those that matched ‘spindle wavelet 1’ failed to be capturedby ‘spindle wavelet 2’. In order to understand better a physiologi-cal meaning of this divergence of sleep oscillations, we performeda power spectrum analysis of the two spindle prototypes. ‘Spindlewavelet 1’ had a fundamental frequency of 12.2 Hz that correspondsprecisely to the mean frequency of sleep spindles in rats (Terrier andGottesmann, 1978), in addition to that, it showed a peak in 7 Hz andelevations around 2 and 26 Hz.

In contrast to the spectrum of ‘spindle wavelet 1’, the spec-trum of ‘spindle wavelet 2’ was more complex and it’s majorpeak appeared with a frequency of 21 ± 3 Hz. Typically, ‘spindlewavelet 2’ showed several sharp peaks in 1, 3, 16.7 and 21.3 Hz andmoderate elevations in 8.5, 11, 24.5 and 27 Hz. It can be concludedthat atypical ‘type 2’ sleep spindles can be distinguished from thecommon ‘type 1’ sleep spindles: a powerful beta-component canbe considered as a hallmark of ‘type 2’ spindles by having a largerindividual variation.

The occurrence of ‘type 2’ sleep spindles with the strong16–25 Hz component might be accounted by processes of epilep-togenesis taking place in our subjects. Previously, by means ofcoherence analyses of EEG, we showed (Sitnikova and van Luijtelaar,2006) that the frequency spectrum of SWD was characterized byfundamental and harmonic frequencies (10–12 and 20–24 Hz), butalso that the onset of SWD was characterized by an increased syn-chronization in 15–16 Hz between bilaterally symmetric corticalareas. In the present study, peaks with the same frequency (16.7and 21.3 Hz) were detected in ‘type 2’ sleep spindles. It is thereforelikely that neuronal synchrony in 16.7 and 21.3 Hz is common for



Fig. 7. Continuous wavelet transform (CWT) in EEG with sleep spindles (in squares). (A) The complex Morlet perfectly represents time–frequency characteristics of sleepspindles. In wavelet spectrum, a hallmark of spindles events was an increased energy in alpha band (8–14 Hz). (B–C) In the Morlet-based wavelet spectrum (top plates),‘type 2’ sleep spindle demonstrates high energy in frequencies <16 Hz, but in ‘type 1’ spindle these frequencies are hardly present. The CWT with two adoptive ‘spindlewavelets’ (bottom plates) poorly represents time–frequency structure of EEG signal. Despite good performance in localizing sleep spindles, ‘spindle wavelets’ are not suitablefor time–frequency analysis (they are not capable for extracting frequency–domain information).

SWD and for ‘type 2’ sleep spindles. ‘Type 2’ sleep spindles mightbe considered as a transitory oscillatory waveform between spindleand SWD in the EEG of WAG/Rij rats.

Sleep spindles and SWD were considered as alpha-band oscil-lations: they both demonstrate an elevation of power in 8–14 Hzin Fourier and wavelet space; SWD were mistakenly recognized

as sleep spindles in EEG before decomposition (bottom graphin Fig. 2 and ‘step 4’ in Section 2.2). On the other hand, theywere best localized in the wavelet spectrum in non-overlappingfrequency bands (Fsp and FSWD). Besides that, different wavelettemplates were necessary to extract EEG patterns of sleep spin-dles and SWD. The complex Morlet wavelet displayed a good

Table 3Automatic identification of sleep spindles with the aid of adoptive wavelet templates.

A. Type 1 ‘spindlewavelet’a Rat NN

Visual detections, Ne Automatic detections Parameter Performance

TP FP FN Ek Accuracy S (%) Sensitivity Specificity

1 2341 2130 23 281 12.4 91.1 88.4 98.92 1381 1132 28 110 14.2 82.2 91.2 97.63 1491 1312 30 149 14.9 87.8 89.8 97.84 1305 1096 39 104 13.6 83.9 91.3 96.65 1598 1422 16 144 16.4 88.9 90.8 98.9

Mean ± S.D. 1623 ± 416 1418 ± 419 27 ± 9 157 ± 72 14.3 ± 1.5 86.8 ± 3.7 90.3 ± 1.2 97.9 ± 1.0

B. Type 2 ‘spindlewavelet’b Rat NN

Spindles missed by‘type 1’ wavelet

Automatic detections Parameters Performance

TP TN FP FN Mean freq.c Ek Accuracy S (%) Sensitivity Specificity

1 211 140 2154 70 22 23 ± 3 21.0 66.3 96.9 86.42 249 110 1215 69 21 24 ± 4 23.5 44.2 94.6 84.03 179 164 1327 30 15 19 ± 2 18.8 91.6 97.8 91.64 209 117 1175 26 18 17 ± 2 18.5 56.0 97.8 86.75 176 112 1454 48 14 22 ± 2 18.5 63.6 96.8 88.9

Mean ± S.D. 205 ± 30 129 ± 23 1465 ± 400 48.6 ± 20.8 18 ± 6 21 ± 3 20.1 ± 2.1 64.3 ± 17.5 96.8 ± 1.3 87.5 ± 2.9

a Basis function ‘spindle wavelet 1’ was the same in all animals. Detections of ‘type 1 spindles’ were made if the wavelet power, w(t), in frequency band Fsp(type 1) ∈ (f1,f2) = (7, 14) Hz exceeded the threshold Ek .

b Basis function ‘spindle wavelet 2’ was chosen for each animal individually. ‘Type 2 spindles’ were detected when wavelet power, w(t), in frequencies Fsp(type 2) ∈ (f1,f2) = (20–25 Hz) exceeded the threshold Ek .

c Averaged peak frequency of ‘spindle wavelet 2’ basis (±S.D.).



Fig. 8. EEG waveforms of sleep spindles in WAG/Rij rat. (A) Native EEG in which the majority of sleep spindles comprised characteristic repetitive elements that matchspindle type 1. Sleep spindles type 2 display larger inter-subject variability and complex structure. (B) Frequency profiles of ‘spindle wavelets’ types 1 and 2 and standardMorlet wavelet. ‘Type 1’ spindle wavelet is characterized by predominant 8–14 Hz frequency component (spindle range). ‘Type 2’ spindle wavelet frequency consists of severalfrequency components in spindle and non-spindle range.

affinity to SWD (it was successfully used for extracting almost100% of SWD), but a low affinity to sleep spindles (it yielded50–60% of true spindle detections). All this point towards a fun-damental difference between EEG features of sleeps spindles andSWD.

4. Discussion

The present study distinguishes two types of self-sustainedthalamo-cortical oscillations: sleep spindles during drowsiness andsleep and pathological SWD, also preferentially occurring in thesame vigilance states. We have applied Fourier transform andcontinuous wavelet transform in order to characterize amplitude-frequency parameters of spontaneous SWD and sleep spindles inthe WAG/Rij rat model of absence epilepsy. We report differencesbetween SWD and sleep spindles in respect to their EEG power anddegree of conformity with basis wavelet functions.

4.1. Application of wavelet transform for the identification ofoscillatory patterns in EEG

In the field of EEG research, the CWT is basically usedfor two purposes: first, time–frequency analysis, in particu-

larly, time–frequency analysis of SWD in patients with absenceepilepsy and in WAG/Rij rats (Bosnyakova et al., 2007) and,second, for extracting EEG features and automatic recognitionof patterns such as epileptiform discharges and sleep spindlesin humans (Jobert et al., 1994; Senhadji and Wendling, 2002;Khan and Gotman, 2003; Schonwald et al., 2003; Latka et al.,2005). Here we develop a wavelet-based algorithm for the auto-matic identification of spindle events and SWD in non-segmentedfull-length EEG data. In order to optimally localize the investi-gated EEG patterns in the time–domain, we used the complexMorlet wavelet and specific spindle wavelet functions. Our strat-egy (we call it ‘adoptive wavelet matching’) is to some extentcomparable with the matching pursuit technique (Durka, 1996,2003; Durka et al., 2005; Zygierewicz et al., 1999), in which atemplate function is chosen from a stochastic library that con-tains a set of Gabor, Dirac and Fourier basis waveforms. In thepresent study, we do not use a preset templates, but our ‘spindlewavelet’ basis functions are adopted directly from the EEG sig-nal.

The best performance of automatic recognition of SWD andsleep spindles is, in our case, achieved after selecting the opti-mal wavelet template and adjustment of the optimal amplitude(Ek) and frequency (Fs) parameters. It appeared that the variabil-ity of sleep spindles was high; therefore, a probability of correct



detection with the aid of standard wavelet functions was low.Almost all sleep spindles (95.5%) were extracted by the joint appli-cation of two different types of adoptive ‘spindle wavelets’. Type1 sleep spindles (85–90%) were recognized with the aid of onecommon template (‘spindle wavelet 1’) by having high power in6.25–16.6 Hz. In contrast to type 1 spindles, type 2 sleep spindles(10–15%) revealed high individual variability (‘spindle wavelet 2’had to be chosen individually) and showed high power in frequen-cies 20–25 Hz.

The ‘spindle wavelet’ functions displayed a complex profilein the Fourier space as compared to standard wavelet functions(Fig. 5B). The ‘spindle wavelets’ showed negative Fourier frequen-cies (negative frequencies were absent in complex wavelets, butpresent in real wavelets). Positive and negative Fourier frequenciesdid not mirror each other in the ‘spindle wavelets’, as they did in realstandard wavelets. This suggests a complex correlation betweenthe real and imaginary parts in the ‘spindle wavelets’. There-fore, the CWT with the ‘spindle wavelets’ combined features ofthe complex transform (required for the adequate time–frequencyrepresentation of sleep spindles) and some features of the realtransform (necessary for waveform extraction). As a result, ‘spin-dle wavelets’ were particularly good in extracting characteristicEEG features of each spindle type, but they were not suitablefor time–frequency analysis. It is concluded that a combinationof standard and adoptive wavelet transforms is favorable for dis-crimination and description of sleep spindles and epileptic EEGevents.

4.2. Epileptic activity (SWD)

We found that a robust increase of high frequencies was typi-cal for SWD; moreover, it was a distinguishing signature of seizureactivity. An increase in wavelet energy in 30–50 Hz was a reliablecriterion by which we identified almost 100% of seizures withoutfalse alarms. A similar method has been proposed for detectingepileptic episodes in the EEG (Khan and Gotman, 2003). They useda discrete wavelet transform and relied upon energy estimationin seizure-specific frequency scales (6–12 and 12–25 Hz), result-ing to 86% sensitivity and 14% of false alarms. We could detectSWD accurately based on energy in the gamma frequency band(30–50 Hz) and this was several times higher than the energy inthe mean interspike frequency of SWD (8–12 Hz). Our result isin full agreement with other indications that fundamental fre-quencies and harmonic spectral components are elevated duringabsence seizures (Van Hese et al., 2003; Drinkenburg et al., 1993).All this suggests that SWD (and probably also other kinds of epilep-tic discharges with monotonous spikes) can be clearly identifiedby a robust increase in wavelet energy in frequencies severaltimes higher than the mean frequency of discharges, i.e., harmonicfrequencies.

4.3. Non-epileptic oscillations (sleep spindles)

In the current paper it is found that sleep spindles represent avery heterogeneous group of oscillations and this causes difficultieswith extraction and recognition of spindle events in the EEG. In allour rats, almost all sleep spindles (95.5%) are extracted with jointapplication of two different types of adoptive ‘spindle wavelets’.‘Spindle wavelets’ are adopted from spindle prototypes, i.e., fromsleep spindle events in the EEG, and therefore they hold the mosttypical (or generic) features of sleep spindles. A frequency profile ofthese two spindle prototypes is crucially different (it can be seen inFourier spectrum of ‘spindle wavelets’ type 1 and type 2 in Fig. 8B).‘Type 2’ spindle wavelet is characterized by a strong harmonic com-ponent (20–25 Hz). The same harmonic component is present inSWD and it is likely to be elicited by spikes; spikes could be also

present in ‘type 2’ spindle sequence. Altogether this led us to thefollowing general conclusions:

• A majority of sleep spindles (85–90%) is selected by CWT with‘spindle wavelet’ type 1. This spindle type is referred to as ‘type1’, it has high power in frequencies 6.25–16.6 Hz and is, based onits EEG features, considered as normal spindle oscillations.

• A minority of sleep spindles (10–15%), which are missed by ‘spin-dle wavelet’ type 1, are captured with ‘spindle wavelet 2’. Thesespindles have high power between 20 and 25 Hz. These ‘type 2’sleep spindles show a deviant spindle-waveform and they mightbe considered as pro-epileptic events (a transitory waveformbetween spindles and SWD).

The average power spectrum of sleep spindles, as measured inthe frontal EEG as we did here (Fig. 6A), fits well with the Fourierspectrum of ‘type 1’ spindle wavelet (Fig. 8B), but it remarkably dif-fers from the Fourier spectrum of ‘type 2’ spindle wavelet. Accordingto the power spectrum analysis of sleep spindles in Wistar–Kyotorats (a strain with absence seizures) by Mackenzie et al. (2004) andin WAG/Rij rats (Drinkenburg et al., 1993; Sitnikova, 2008), sleepspindles display a peak in 11.4 Hz, have a short duration and do nothave sharp rhythmic components (otherwise they would have har-monic components in their Fourier spectrum). All these features arein agreement with the features of ‘type 1’ sleep spindles, therefore,it is likely that the earlier reports were concentrated in the largepopulation of ‘type 1’ sleep spindles, but that the minor populationof ‘type 2’ sleep spindles has not been described in the literature.

In the current paper we describe EEG events as recorded inthe frontal cortex. In fact, we deal with anterior spindles, whichdiffer from posterior sleep spindles (Terrier and Gottesmann,1978). Both anterior and posterior spindles occur in humans andin rats and their features are known (Terrier and Gottesmann,1978; Jankel and Niedermeyer, 1985; Zygierewicz et al., 1999).In healthy humans, sleep spindles are recognized as “bursts at11–15 Hz, but mostly at 12–14 Hz” (IFS, 1974, p. 547), however, sleepspindles are usually identified in wider frequencies, from 11 to16 Hz (Zygierewicz et al., 1999; Huupponen et al., 2007). We had toexpand an initially predetermined spindle frequency band (from8–12 Hz to 5.5–16.6 Hz (Morlet-based wavelet detections). This isin agreement with the literature: in mammalian species, includingrats, sleep spindles appear in frequencies from 5 to 15 Hz (Gandolfoet al., 1990; Drinkenburg et al., 1993; Kandel and Buzsaki, 1997;Mackenzie et al., 2004).

In the current paper we found that the complex Morlet wavelet(ω0 = 2�) was not effective for automatic recognition of sleep spin-dles: only about 50% of sleep spindle events was detected correctlyand 39% of the spindles were missed; and the situation did notimprove after careful adjustment of recognition parameters, suchas the frequency band (Fsp) and the threshold (Ek). The low affinityof the complex Morlet wavelet to sleep spindles disagrees withresults obtained by Latka et al. (2005). These authors applied suc-cessfully the Morlet wavelet for the identification of sleep spindlesand concluded: “It is apparent that the complex Morlet wavelet mim-ics wave-packet behavior of sleep spindle and provides a mathematicalequivalent of the phenomenological description” (Latka et al., 2005, p.16). The disagreement with our results may lie in a different designof the experiments and in a species difference. We included inour analysis sleep spindles recorded during sleep, drowsiness andwakefulness (hundreds of sleep–wake cycles), while in humanssleep spindles are restricted to non-REM sleep and exclude wakingEEG. Sleep spindles in rats tend to occur as sleep deepens, butspindle-like events in the alpha frequency range are also presentduring passive wakefulness (Fanselow et al., 2001). Another limi-tation of our study is that our analyses was restricted to the frontalEEG, other locations might have resulted in distinct outcomes.



4.4. Distinctions between SWD and sleep spindles

The present results cast some doubts about the similaritybetween sleep spindles and SWD. First, their basic parameters aredifferent: SWD last ten times longer than anterior spindles, theiramplitude is nearly two times higher and their mean frequency isabout 2 Hz lower (as measured in a period 0.5–1.5 s after seizureonset).

Second, power spectrum analysis demonstrates that SWD arecharacterized by higher power in 9–100 Hz and lower power indelta as compared to sleep spindles. This difference in frequencycomposure correlates with the difference in their EEG waveformsthat has been demonstrated with CWT. It is also shown here thatthe EEG pattern of SWD is not comparable with that in sleep spin-dles: (i) different wavelets are necessary for the identification ofSWD and spindles; (ii) SWD are identified in the EEG with the aidof the standard Morlet wavelet, but sleep spindles can be identifiedonly with a high accuracy with the aid of two types of customizedadoptive ‘spindle wavelets’; (iii) spindle and SWD are detected withdifferent frequencies FSWD and Fsp SWD have high power between30 and 50 Hz, sleep spindles – between 6 and 14 Hz. Besides that itis found that SWD represent one family, but sleep spindles – twofamilies.

Previously, Drinkenburg et al. (1993) performed spectral anal-ysis of sleep spindles, SWD and intermediate ‘spiky’ activity andfound a striking resemblance between all these EEG events inrespect to their frequency content and peak frequencies. AlsoMackenzie et al. (2004) indicated that SWD have more power intheir frequency spectrum than normal spindle oscillations. Wecan add that sleep spindles possess high inter- and intra-subjectvariability and their time–frequency characteristics were more het-erogeneous than that of SWD; the EEG pattern of sleep spindles wasless stereotyped and less uniform compared to SWD.

The above-mentioned dissimilarities between sleep spindlesand SWD support the notion that the neurophysiological sub-strate of spindle oscillations and SWD is not the same. Ascompared to SWD, spindle oscillations are less generalized, theyare rather local oscillations (Terrier and Gottesmann, 1978; Jankeland Niedermeyer, 1985; De Gennaro and Ferrara, 2003), and theirEEG waveform is less regular (our own data). Previously we showedthat that sleep spindles and SWD are controlled by different age-related mechanisms (van Luijtelaar and Bikbaev, 2007). Moreover,lesions of the lateral thalamus including the caudal RTN, thoughtto be the pacemaker of sleep spindles, showed opposite effects onSWD and sleep spindles in WAG/Rij rats (Meeren et al., 2009). Com-prehensive in vivo and in vitro neurophysiological examinations inGAERS demonstrate that SWD do not originate from sleep spindles,but have 5–9 Hz oscillations as a plausible source (Pinault et al.,2001, 2006).

The genetic rat models of absence epilepsy (i.e., GAERS andWAG/Rij) are fundamentally different from the feline generalizedpenicillin epilepsy (Gloor, 1968; Kostopoulos, 2000) in a sense thatabsence seizures occur spontaneous in rodents, and are not chem-ically induced. It is, e.g., on the outcomes of the penicillin modelthat the theories on the close relation between SWD and sleepspindles emerged. We propose that sleep spindles in rodents arenot related to SWD, as it was demonstrated in cats. An exceptionmight be made for the rarely occurring type 2 sleep spindle. It has astrong beta component in SWD-harmonic frequency (∼21 Hz) andin the middle frequency (∼16 Hz) and this might be considered asa sign indicating a pro-epileptic nature of these oscillations. There-fore, type 2 sleep spindles could be considered as a deviant spindleform. It is assumed that ‘type 1’ spindles are normal oscillatory phe-nomena (with no aberrant features), while ‘type 2’ is an aberrantspindle type that appears in epileptic animals due to an impairmentof thalamo-cortical network mechanisms. This agrees with results

of neuronal modeling, indicating that sleep spindles and SWD canbe simulated in a common cortical neuronal model (Sargsyan etal., 2007); therefore, both spindles and SWD can appear in EEG asa manifestation of synchronization processes taking place in thesame thalamo-cortical circuit during low vigilance state. It seemsthat, besides SWD, the EEG of epileptic rats might exhibit vari-ous intermediate electroencephalographic patterns, such as type2 sleep spindles and spiky EEG events (mentioned by Drinkenburget al., 1991) which are not present in non-epileptic rats.

Acknowledgements

This research was supported by U.S. Civilian Research and Devel-opment Foundation for the Independent States of the Former SovietUnion (CRDF), grant REC-006; the Supporting program of Doctor ofScience (project MD-1884.2007.2) (grant to A. Hramov) and RussianFoundation for Basic Research (projects 07-02-00044 and 09-04-01302).

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Sleep spindles and spike–wave discharges in EEG: Their generic features, similarities and...

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