MODEL-BASED QUANTIFICATION OF THE TIME- VARYING MICROSTRUCTURE OF SLEEP EEG SPINDLES: POSSIBILITY FOR EEG-BASED DEMENTIA BIOMARKERS

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1 MODEL-BASED QUANTIFICATION OF THE TIME- VARYING MICROSTRUCTURE OF SLEEP EEG SPINDLES: POSSIBILITY FOR EEG-BASED DEMENTIA BIOMARKERS P.Y. Ktonas*, S. Golemati*, P. Xanthopoulos, V. Sakkalis, M. D. Ortigueira, H. Tsekou*, M. Zervakis, T. Paparrigopoulos*, and C. R. Soldatos* *Sleep Research Unit, Department of Psychiatry, National University of Athens, Greece Department of Electronic and Computer Engineering, Technical University of Crete, Greece UNINOVA, and Department of Electrical Engineering, Univ. Nova, Lisbon, Portugal Keywords: Sleep spindles, AM-FM signals, instantaneous envelope, instantaneous frequency, dementia. Abstract The time-varying microstructure of sleep EEG spindles may have clinical significance in dementia studies and can be quantified with a number of techniques. In this paper, the sleep spindle is modeled as an AM-FM signal in terms of six parameters, three quantifying the instantaneous envelope (IE) and three quantifying the instantaneous frequency (IF) of the spindle model. An application of such parameterization is proposed, in search of EEG-based biomarkers in dementia. The IE and IF waveforms of actual sleep spindles were estimated using the time-frequency technique of Complex Demodulation (CD). Sinusoidal curve-fitting using a matching pursuit (MP) approach was applied to the IE and IF waveforms, from which the six model parameters were subsequently estimated. Preliminary results indicate that the proposed parameterization may be promising, since it quantified specific differences in sleep spindle instantaneous frequency dynamics between spindles from dementia subjects and spindles from normal controls. 1 Introduction The sleep spindle waveform is a characteristic transient event of human stage 2 sleep EEG. It is defined by a group of rhythmic waves within the frequency range of Hz, exhibiting a progressively increasing, then gradually decreasing, amplitude, which gives the waveform its characteristic name. It is usually of sec duration, and it may be present in low-voltage background EEG, or superimposed on delta EEG activity, or temporally locked to a K complex [5]. Sleep spindles are generated by corticothalamo-cortical neuronal networks, and they are hypothesized to play an active role in inducing and maintaining sleep [6]. They are affected by cerebral impairment, as well as by normal and pathological aging [1]. With normal aging, sleep spindles are less numerous and less well-formed. In neurodegenerative disorders leading to dementia, the sleep EEG patterns suggest accelerated aging, as they appear to be an exaggeration of normal aging patterns. Accordingly, sleep spindles may become even less numerous, and their morphology appears to deteriorate further [4]. This paper presents preliminary results on the use of six parameters, based on an AM-FM model and quantifying the time-varying microstructure of sleep spindles, as EEG-based biomarkers in dementia. Specific differences in spindle instantaneous frequency dynamics are reported in terms of these parameters in a small sample of dementia subjects when compared to controls. 2 Methods 2.1 Assumed Model for a Sleep Spindle Sleep spindles can be modeled as AM-FM signals and can be expressed as [3]: f (t) = A(t) cos[g(t)]; A(t) 0 (1) where, A(t) = A 0 + k a cos(2πf a t + θa ), as a simple approximation, is a model for the instantaneous envelope (IE), and g(t) = 2πf 0t + k b cos(2πf b t + θ b ), as a simple approximation, is a model for the instantaneous phase [2]. The instantaneous frequency (IF), in rads/sec, is the time derivative of g(t). Figure 1a shows an example of the above model (simulation), while Fig. 1b shows a real sleep spindle. Observe that the time-varying morphology of the real spindle justifies the chosen model. Given the known neurophysiological mechanisms for sleep spindle generation [6,7], one may hypothesize that A(t) and its defining parameters (A 0, k a, f a ) model primarily cortical processes, while g(t) and its defining parameters (f 0, k b, f b ) model primarily thalamic processes. Accordingly, A 0, k a and f a may reflect dynamics of spatio-temporal summation of cortical post-synaptic potentials, resulting from thalamo-cortical neural activity and contributing to the power in the spindle signal (quantified by A 0 ). Similarly, f 0, k b and f b may reflect dynamics of reticular neural circuits in the thalamus, which are involved in the generation of the spindle frequency spectrum (11-15 Hz). The model in Equation (1) was assumed in this work. Accordingly, since sleep spindle morphology appears to

2 deteriorate in dementia, and dementia may be viewed as a result of cortical or sub-cortical pathology [4], one expects that this change in spindle morphology could be reflected in the model parameters. (a) Figure 1. Simulated sleep spindle (a) produced with the model of Eq 1, and real sleep spindle after bandpass filtering (5-22Hz). 2.2 Time-Frequency Analysis: Estimation of IE and IF Waveforms Previous work has compared several time-frequency methods for the estimation of IE and IF waveforms [8, 9]. Accordingly, methods based on the Hilbert transform (HT), Complex Demodulation (CD), Matching Pursuit (MP) and Wavelet transform (WT) were analyzed and compared as to their efficacy in estimating the six parameters (A 0, k a, f a, f 0, k b, f b ) of the proposed AM-FM model for a sleep spindle. Although HT was found to be quite accurate, it caused distortion to the IE and IF waveforms. Thus, part in the beginning and end of these waveforms (about 200 data points in total) had to be removed before further analysis. For a sampling rate of 512 Hz (needed for detailed quantification of the spindle morphology, and used in this work), this would lead to a removal of about 0.4 sec, which may cause a problem if the spindle is less than one sec in length. The same was found to be true for MP. On the other hand, CD, while exhibiting a relatively small estimation error for the parameters (less than 10% in simulated data), required the removal of about 0.24 sec of data due to distortion. Although WT was found to cause about the same amount of distortion as CD, it turned out to be quite erroneous in estimating the parameters (more than 15% error in simulated data) [9]. Due to the above reasons, CD was used in this study, in case the spindles (especially those obtained from dementia patients) were of a relatively short duration [4]. Before applying CD, the spindle data were filtered through a band-pass FIR filter of order 128, with frequency cut-offs at 5 and 22 Hz, designed using MATLAB s FIR1-command and then implemented in a zero-phase version using the filtfiltcommand. The cut-offs were chosen so that the spindle waveform components in the pass-band of Hz were passed with unity gain. Since the distortion introduced by the band-pass filtering was found to involve about 50 samples at the beginning and at the end of the band-passed signal, no data removal due to band-pass filtering was implemented because the distorted data samples were included in the 0.24 sec eventually removed from the IE and IF waveforms (see below). The procedure of applying CD to a given real signal x(t) (a sleep spindle in our case), which is assumed to be narrowband (with no spectral contribution at the origin, a necessary condition for using CD, which, due to the band-pass filtering, our sleep spindle data satisfied ), is as follows [3]: (1) The frequency spectrum of the signal is shifted to the left (towards the origin) by the demodulating frequency. In our case, this frequency was taken to be the center of gravity of the Fourier transform of the signal in the frequency band of Hz, where most of the energy of a sleep spindle lies. (2) The resulting complex signal is filtered with a low-pass filter (in our case, an FIR filter, of order 100, designed using MATLAB s FIR1-command and then implemented in a zerophase version using the filtfilt-command) having a cut-off frequency of f c Hz. This cut-off frequency is chosen such that, beyond that frequency, the frequency content of x(t) may be considered negligible. In our case, f c was taken to be 6 Hz, which was decided based on simulation studies as well as on real spindle data. (3) The frequency spectrum of the filter output is shifted to the right by the demodulating frequency. The instantaneous envelope and phase (as well as frequency) functions of x(t) are subsequently calculated from the magnitude and argument, respectively, of the complex function that results after the last step. Thus, we obtain the IE and IF waveforms. As mentioned above, for a sampling rate of 512 Hz that we were using, about 0.24 sec of data had to be deleted from the estimated waveforms (about 0.12 sec each from the beginning and from the end of the waveforms) because of the distortion introduced by the CD method (due to the low-pass filtering).

3 2.3 Curve-fitting of IE and IF Waveforms Using MP, and Model Parameter Estimation Since the estimated IE and IF waveforms may not be purely sinusoidal, we performed MP-based curve-fitting in order to estimate the six parameters that define the spindle model. In MP, the aim is to decompose a given signal S into a linear combination of N waveforms (atoms) d i chosen from a predefined dictionary D k so that: N S = w d + R (2) i= 1 i i where, R N is the decomposition residual In our case, we performed the decomposition only once, i.e., for the first d i atom chosen by the method. Accordingly, for each IE and IF waveform, one atom was chosen from the following dictionary D = cos ( 2 π f t + φ ) (3) N fit fit fit π where, f = 0.1:0.005:6 and φ = 0: :2π fit fit 10 The six model parameters were then estimated from the MPfitted sinusoids. More specifically, f a and f b were taken directly from the sinusoid dictionary created within the MP procedure. To estimate the remaining four parameters, the maximal and minimal values of the IE (and IF) waveformadjusted sinusoids were detected. A 0 corresponded to the average of the maximum and minimum value of the IE waveform-adjusted sinusoid, while f 0 corresponded to the average of these two values from the IF waveform-adjusted sinusoid. k a corresponded to the amplitude of the IE waveform-adjusted sinusoid, while k b corresponded to the amplitude of the IF waveform-adjusted sinusoid divided by f b. If the MP-fitted sinusoids were characterized by very low frequencies (f a, f b ), say, lower than 1 Hz, some of the model parameters could not be estimated, because no sufficient peaks and troughs could be present in the waveform-adjusted sinusoids. In such cases, A 0 and f 0 were defined by averaging the IE and IF waveforms, respectively. However, in those cases, no estimates of k a or k b were possible. There may be cases of sleep spindles where the IE or IF waveforms deviate considerably from a quasi-sinusoidal form. In these cases, the MP-based curve-fitting method may fail, since the sleep spindle waveform may not be able to be represented by the assumed model of Equation (1). Therefore, the possibility was provided for interactive MPfitting, under the supervision of the user. Accordingly, in cases where the particular shape of the IE or IF waveform did not relate to a quasi-sinusoidal form, the (first) MP-fitted sinusoid was subtracted from the original waveform (IE or IF) and MP-based curve-fitting was performed on the residual. Model parameters were then calculated from the residual-mpfitted sinusoids, as described above. It should be pointed out that values for A 0 and f 0 based on this procedure are meaningless. Figure 2 shows an example of residual curvefitting of an IE waveform. 2.4 Sleep Spindle Data Night sleep EEG signals from 3 healthy young adults (male, age range yrs) and 3 subjects with dementia were obtained from the Sleep Research Unit of the Department of Psychiatry at the University of Athens. Standard polysomnographic procedures were applied for the sleep EEG recording of two or three nights for each subject, utilizing a Brain Spy (Micromed) data acquisition system at 512 Hz sampling rate. Data from the second or third recording night were used in this study. The dementia subjects were drugnaïve in-patients at the Neurological Clinic of the University of Athens, diagnosed for dementia through standard neuropsychological procedures. The dementia cases had different etiologies, including progressive supranuclear palsy (female, 59 yrs), posterior cortical atrophy (female, 68 yrs) and fronto-temporal dementia, semantic type (male, 71 yrs). (a) Figure 2. Example of residual curve fitting of an IE waveform. (a) MP-based curve-fitting of original waveform, MP-based curve-fitting of residual waveform. Solid lines correspond to waveforms for which MP-fitting is performed, and dotted lines correspond to fitted curves The sleep EEG record of each subject was visually scored for sleep stages according to standard procedures [5]. Each record was divided into three parts of equal length, and visually well-defined sleep spindles from the largest sleep stage 2 of each part (3-4 spindles) were obtained for automatic analysis. 3 Results

4 After band-pass filtering, IE and IF waveforms were obtained for each sleep spindle, utilizing CD methodology. The IE and IF waveforms for each spindle were examined visually, and spindles exhibiting well-defined, quasi-sinusoidal IE and IF waveforms, that is waveforms with visually obvious modulation patterns, were chosen for further analysis and parameter estimation. In particular, the IF waveforms had to have most of their duration within the spindle frequency band (11-15 Hz). As a result of the above analysis, 11 spindles from controls and 11 spindles from dementia subjects were chosen for parameter estimation. This number may appear small. However, since the objective of this work was to present preliminary results of a promising application of the described methodology, the above number of spindles analyzed was deemed sufficient. In general, spindles from dementia subjects were less welldefined visually and appeared shorter than spindles from controls. However, any detail as to modulation patterns in instantaneous envelope and instantaneous frequency was not easily discernible visually. Figure 3 shows two spindle examples, each one from a different control subject, while Figure 4 shows two spindle examples, each one from a different dementia subject. Observe that the spindles from the dementia subjects are shorter and somehow less well-formed than the spindles from the controls. In addition, observe that the spindles from the dementia subjects exhibit faster oscillations in the sinusoids fitted to the IF waveforms (related to f b ) than the spindles from the controls. Incidentally, the fitted sinusoids in all cases are the ones chosen as first in the MP curve-fitting procedure. Table 1 shows average values for model parameters and spindle duration across all spindles analyzed in this work (11 from control and 11 from dementia subjects). As expected from Figs. 3 and 4, the dementia subjects differed significantly from controls as far as f b and spindle duration was concerned. 4 Discussion and Conclusions The results presented in this work indicate that the proposed parameterization based on the spindle model of Equation (1) may quantify subtle differences in the time-varying microstructure of sleep spindles which are not that obvious visually. These differences may have clinical significance as shown in the dementia example of this work. Accordingly, sleep spindles from dementia subjects were found to exhibit faster instantaneous frequency dynamics, quantified by parameter f b, than spindles from control subjects. This finding, along with the shorter spindle duration, may relate to the visually obtained impression that sleep spindles in dementia exhibit a deteriorated morphology, when compared to spindles from control subjects. Therefore, the utilization of the proposed spindle model parameters as potential EEG-based biomarkers in dementia appears promising. However, additional studies, involving larger data sets, are needed to explore this promise further, as well as possible differences among types of dementia. The physiological significance of the observed difference in f b may relate to the possibility that the IF waveform reflects dynamics at the thalamic site(s) responsible for sleep spindle generation [1, 6, 7], which may be compromised as a result of brain pathology in dementia. Given the small sample of data analyzed in this work, such a conjecture is very tentative. Nevertheless, quantifiable results such as the ones presented in this work, aside from possible clinical applications, may lead to further exploration of the underlying neurophysiological mechanisms of sleep spindle generation in pathological conditions. Acknowledgement This work was supported in part by the EU NoE BIOPATTERN project (project no ). References [1] L. De Gennaro and M. Ferrara, Sleep spindles: an overview, Sleep Medicine Reviews, 7, pp , (2003). [2] L. Hu and P. Ktonas, Automated study of sleep spindle morphology utilizing envelope and instantaneous frequency parameters, Proceedings of the 17 th Congress of the European Sleep Research Society, Prague, October (2004). [3] P. Y. Ktonas and N. Papp. Instantaneous envelope and phase extraction from real signals: theory, implementation, and an application to EEG analysis, Signal Processing, 2, pp , (1980). [4] D. Petit, J. F. Gagnon, M. L. Fantini, L. Ferini-Strambi and J. Montplaisir, Sleep and quantitative EEG in neurodegenerative disorders, Journal of Psychosomatic Research, 56, pp , (2004). [5] A. Rechtschaffen and A. Kales, editors, A Manual of Standardised Terminology, Techniques and Scoring System for Sleep Stages of Human Subjects, Washington, DC: Public Health Service, U.S. Government Printing Office, (1968). [6] M. Steriade and F. Amzica, Coalescence of sleep rhythms and their chronology in corticothalamic networks, Sleep Research Online, 1, pp. 1-10, (1998). [7] M. Steriade, D. A. McCormick and T. J. Sejnowski, Thalamocortical oscillations in the sleeping brain, Science, 262, pp , (1993). [8] P. Xanthopoulos, S. Golemati, V. Sakkalis, P. Y. Ktonas, M. Zervakis, and C. R. Soldatos, Modeling the time-varying microstructure of simulated sleep EEG spindles using timefrequency analysis methods, Proceedings of the 28 th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, New York, USA, August, (2006). [9] P. Xanthopoulos, S. Golemati, V. Sakkalis, P. Y. Ktonas, M. D. Ortigueira, M. Zervakis, T. Paparrigopoulos, H. Tsekou and C. R. 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5 (a) (c) (d) Figure 3. Two examples of sleep spindles and related IE and IF waveforms and MP-fitted curves in control subjects. (a), spindles, IE waveforms and MP-fitted curves. (c), (d) IF waveforms and MP-fitted curves. Solid lines correspond to CD-estimated IE and IF waveforms and dotted lines correspond to MP-fitted curves. (a) (c) (d) Figure 4. Two examples of sleep spindles and related IE and IF waveforms and MP-fitted curves in dementia subjects. (a), spindles, IE waveforms and MP-fitted curves. (c), (d) IF waveforms and MP-fitted curves. Solid lines correspond to CD-estimated IE and IF waveforms and dotted lines correspond to MP-fitted curves.

6 A 0 (microvolts) f a (Hz) k a (microvolts) f 0 (Hz) f b (Hz) k b (rads) Duration (sec) Controls (n=11) 8.50± ± ± ± ± ± ±0.73 Dementia (n=11) 7.62± ± ± ± ±1.40* 0.82± ±0.27* Table 1. Average (±std) values of model parameters and spindle duration for control and dementia subjects. * indicates statistically significant difference (Student s t-test, p<0.05).