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PatternsofattractordimensionsofsleepEEG

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Compur. Biol. Med. Vol. 25. No. 5, pp. 455-462, 1W5 Copyright 0 1W5 Elscvicr Science Ltd

Printed in Great Britain. All rights reserved INlO-4825&i $9.50+0.00

PATTERNS OF ATTRACTOR DIMENSIONS OF SLEEP EEG

N. PRADHAN,* P.K. SADASIVAN,* S. CHATTERlIt and D. NARAYANA

DU’ITS *Dept. of Psychopharmacology, National Institute of Mental Health & Neurosciences, Bangalore-560029, India; *Dept. of Psychiatry, National Institute of Mental Health &

Neurosciences, Bangalore-560029, India; and #Dept. of Electrical Communication Engineering, Indian Institute of Science, Bangalore-560012, India

(Received 3 October 1994; in reuised form 17 March 1995)

Abstract-Low dimensional chaos is a property of many physiological oscillatory systems including the brain. Time series of sleep EEG records have been analyzed in the framework of recent developments in nonlinear dynamics. One of the characteristics of a chaotic time series is its attractor dimension. The running attractor dimension of a chaotic time series may reflect changes in states more accurately than manually scored records. In the present study the attractor dimensions of consecutive EEG segments of five sleep records were analyzed. The block of the EEG segment (window) was shifted by various lengths along the entire sleep data of each subject thus producing a running attractor dimension curve for each record. The attractor dimension values for different sleep stages were significantly different. The pattern of the running attractor dimension closely matched the scored hypnograms in these five sleep records.

EEG Sleep stages Hypnogram Nonlinear dynamics Chaos

Attractor dimension Running attractor dimension

1. INTRODUCTION

The complicated dynamical behavior of the brain activity is reflected in the recording of its electrical activity, the electroencephalogram (EEG). As an individual moves from a resting awake state to various stages of sleep, the EEG shows changes that are characteristic of the respective sleep stage. Even though the sleep EEG has been extensively studied using methods of time domain analysis and by the application of spectral methods, the nature of the underlying neuronal processes has remained unclear. Recent developments in the understanding of nonlinear dynamics and the theory of chaos may be seen as a way out of the impasse of dealing with large scale cooperative neuronal behavior [l]. Nonlinear dynamical analysis of EEG signals has been described previously [2]. This paper analyses the physical and dynamical aspects of the brain’s electrical activity during sleep from this new perspective and indicates possible future directions in the analysis of transitional activities of the brain.

Sleep is considered to be a stable process and is universal in the animal kingdom. The phylogeny of sleep has revealed an evolution whose complexity parallels the evolution- ary process of the brain [3,4]. Two basic sleep behaviors are noticed in human beings: quiet, resting, synchronized or nonrapid eye movement (NREM) sleep and an active dreaming, desynchronised, paradoxical or REM sleep. In biological systems, the tran- sition from chaotic dynamics to periodic behavior is often a marker of disease or dysfunction as seen in epilepsy and coma for example [5]. Evidence suggests that chaotic dynamics provide a mechanism for desynchronisation of potentially fatal periodic

cortical behaviors by 10~ dimensional controls. The interposition of REM within the quasiperiodic slow wave sleep may be viewed from this angle. During wakefulness, various behaviors are clearly not reflected as transitions in an EEG record. Therefore sleep EEG with its established and known transitional states is a good candidate for

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456 N. PRADHAN et al.

Table I. Characteristics of subjects

Subject Sex Age

1 M 45 2 M 20 3 F 25 4 M 17 5 F 32

exploration through the application of nonlinear methods. In this paper, the importance of the emerging trends of nonlinear dynamics and chaos to neurobiology is discussed in the context of the various states of sleep behavior.

The attractor dimension is the most widely used measure to describe the chaotic behavior of experimental time series data [6]. Several excellent reviews of the concept of an attractor dimension have appeared recently [7,8]. The attractor dimension of a system is the minimum number of dimensions of a phase-space that can contain the trajectory generated by the system. The dimension of a system may be viewed as its number of degrees of freedom [S]. The attractor dimension of periodic systems is a whole number whereas the dimensions of chaotic systems are fractions. A comparison of systems can be made by referring to this quantity. Researchers have mainly focused on the absolute value of the attractor dimension (D2). It would be better, however, to concentrate on how the value of D2 changes in response to changing states of brain activity. The concept of a running attractor dimension may be useful in this context [9]. The changing state of the brain activity, as occurs during sleep, can be monitored through the running attractor dimensions of the EEG. In this study we have analyzed the various transitional states of the brain in sleep with reference to the attractor dimension of the EEG signal.

2. DATA COLLECTION

Five subjects in the age group 17-45 years were recruited for the study (Table 1). These were normal volunteers without any history of neuropsychiatric illnesses or intake of any psychotropic drugs. Subjects were acclimatised to the sleep laboratory for two nights and polysomnographic data was obtained using a Nihon Kohden polysomno- graphic system for the third night. Each recording session lasted 8 h. One channel (C3- A2) of sleep EEG data along with the EOG (two channels) and EMG (one channel) were acquired by direct digitization to a micro-computer (PC-AT) through an ADC coupled to an array processor (Data Translation, DT-2841, DT-7020) at 128 samples/s/ channel. For varying sensitivities, the EEG amplifier outputs ranged between 1.2 and 6.2 V which are of a sufficient magnitude for digitization by the 12 bit ADC with adequate resolution [lo]. The data were ported to a high speed graphics workstation (HP 9000/735). The raw EEG signals were filtered through a bandpass (0.2532 Hz) 4th order Butterworth filter twice cascaded. The EOG and EMG signals were also filtered through low pass (1.0 Hz) and high pass (30.0 Hz) filters, respectively. The filtration removes many unwanted signals (artifacts) and the filtered data are suitable for sleep scoring. A computer assisted program was used to classify and score the sleep records as per the manual of Rechtschaffen and Kales [ 111. In the present study two experienced polysom- nographers scored all the records independently. They differed in their scoring of sleep stages in less than 5% of the 30 s epochs. Differences were resolved by discussion and a consensus rating assigned to the discrepantly scored epochs. The sleep pattern thus scored is called a “hypnogram”. The sleep EEG signal was further analyzed for the attractor dimension values using singular value decomposition (SVD) methods [12,13]. The entire sleep EEG data were then analyzed in blocks using the technique of running attractor dimension.

Patterns of attractor dimensions of sleep EEG

3. CALCULATION OF ATTRACTOR DIMENSION

457

Temporally the EEG is a single dimensional piece of data. Being a time series, the EEG at any given instant of time has only one phase variable. A multidimensional phase- space can be constructed from the measurement of a single variable (like the electrical potential) [14]. For a time series V(t), i=O, 1,2,3, . . . . N, the phase space vector x(t) is constructed by assigning coordinates

x,(t) = V(t) X?(f) = V(t+ T)

x,(t)=V(t+(d-l)T),

where T is a delay time and d is the embedding dimension. The lag or delay T is determined by the first zero-crossing of the corresponding autocorrelation function [15]. We have used an embedding dimension, d= 16, in our study. After construction of the multidimensional phase-space vectors from the EEG data segments, the attractor dimensions are calculated.

4. SINGULAR VALUE APPROACH FOR ESTIMATION OF ATTRACTOR DIMENSION

The dimension of the attractor is a characteristic feature of the underlying neuronal process generating the EEG signals. The dimension value of the attractor is of significance in feature detection of various brain states and in classification and differen- tiation of various types of neural activities including those occurring in a sleep cycle. The attractor dimension directly reflects the degrees of freedom of the system under study. Therefore, the nonlinear dynamics provide a model for signal generation and temporal prediction which may help in determining the nature of neuronal processes governing the state of brain activity in sleep.

The overall interpretation of a sleep record is based on a qualitative impression about the changing patterns in EEG, EMG and EOG activity. The resulting picture, the hypnogram, depicts the progressive transitional behavior of the brain during the sleep cycle. This study utilizes the singular value decomposition of subsets of phase space trajectories to evaluate the attractor dimension. The application of the SVD method to EEG and its computational efficiency in comparison to the Grassberger Procaccia Algorithm [7] has been described in detail elsewhere [12, 161. The data length require- ment of the SVD method for its application to EEG analysis has been evaluated.

5. RUNNING ATTRACTOR DIMENSION OF SLEEP EEG

The technique of ‘running attractor dimension’ has been used in this paper. A window is applied to the EEG data in which the attractor dimension of the contents is calculated. The window is moved along the EEG. By sliding the window it is possible to generate a curve whose points correspond not only to the time axis of the time series, but reflect the attractor dimension at any given time. In this study, we present the continuous attractor dimension of sleep EEG data with the conventional hypnogram of the sleep record to demonstrate the utility of running attractor dimension as a method for extracting information on the transitional patterns of brain activity during sleep. The effects of window length and shift have been studied to show the optimality of these two parameters in a given application.

The attractor dimension values of various sleep stages were compared using a statistical package (SYSTAT: SYSTAT Inc., Evanston, IL, U.S.A., 1988) on an IBM PC-AT. The mean and standard error of mean was calculated and comparisons between the stages were made using the one-way analysis of variance (ANOVA).

458 N. PRADHAN et al.

6. RESULTS

Running attractor dimension curves with varying lengths of data windows (512, 1024, 2048, 4096, 8192, 16,384 and 20,480 points) were obtained (Fig. 1 a-g) while the data window shifted by a fixed length (64, 128, 256, 512 and 1024 points) along the whole of the EEG record. The attractor dimension measurements with different lengths of data windows produced different values for the same data. The running attractor dimension curves with small data windows were grossly different from those with large data windows even though the information content of the actual pattern lay embedded within these (Fig. la-g) and was obtained from the same sleep EEG record of one subject. The attractor dimension values ranged from 1 .O to 19.98 for a data window of 512 points and 2.08 to 8.44 for a data window of 20,480 points. For a window length of 4096 points, attractor values were within 1.84 to 11.94. Thus there is no meaning in comparing attractor values, unless the window size is kept constant. Therefore, the number of data points or the window length of the data may be considered as one of the important factors that accounts for discrepancies in the values of attractor dimension reported by different researchers. The running attractor dimension curves for the entire sleep EEG record show constancy in the pattern of sleep behavior. The transitions in sleep processes are encountered as the sleep progresses with time. The values of the attractor dimension were significantly lower in slow wave sleep as compared to stage 1 or stage 2 sleep. The attractor dimension values for REM sleep were significantly higher as compared to the slow wave sleep and comparable to the awake stage (Table 2). The F-Ratio (F (5,24) =801.588, p<O.OOO) implies a significant difference in the values of attractor dimension for different sleep states. The phase-space plots show discerning patterns for alpha and beta activities (in a wakeful state) and that of delta activity (in stage 4 sleep) (Fig. 2 a-c). The phase-space plots of alpha and delta activity are strongly indicative of limit cycle behavior of low dimensional attractors. This may reflect synchronization of activities in neuronal ensembles. In contrast the phase-space plot of beta activity is more

Shift 64 128 256 512 1024

Fig. 1. Running attractor dimension for a single night sleep record of 8 h with different window lengths and shifts. The data length or the window sizes are (a) 5 12 (4 s) (b) 1024 (8 s) (c) 2048 (16 s) (d) 4096 (32 s) (e) 8192 (64 s) (f) 16,384 (128 s) and (g) 20,480 (160 s) data points. The shifts

are given by 64, 128, 256, 512 and 1024 data points.

Patterns of attractor dimensions of sleep EEG

Tabte 2. Attractor dimen- sion of different sleep stages (Mean f SEM,

N=5)

459

Awake 8.70 (0.14)@ Stage 1 7.26 (0.21)@ Stage 2 6.88 (0.32)@ Stage 3 5.36 (0.22)@ Stage 4 4.45 (0.12)@ REM 9.20(0.16)@

SEM-Standard Error of sample Mean, Cp (p<0.ooo).

suggestive of high dimension chaotic behavior which appears like random activity. The dimension values are higher in wakefulness and light sleep. It also increases to the level of wakefulness during REM. The hypnogram scored by the visual analysis of the sleep record is matched closely by the changes in the running attractor dimension (Fig. 3). Independently, the running attractor dimension curve may be seen as an objective measure of the transitional states in sleep.

7. DISCUSSION

The analysis of EEG in the past several decades has been attempted by the phenomenological approach in which the EEG is seen to be a band-limited signal produced by some black-box with unknown or white Gaussian noise input [17]. In this paper, the more recent model-based approach, incorporating concepts developed in the area of nonlinear dynamics and chaos theory have been used. The model-based approach to EEG interpretation has the advantage that computer analysis will produce infor- mation not easily derived from visual inspection of the EEG traces. Therefore, this method may provide information which was hitherto not extractable from EEG. The attractor dimension curves presented in this study may be a potential means of understanding the transitional process of the chaotic dynamics involving large scale neuronal behavior of the brain during sleep. We have presented a hypnogram and the attractor dimension time record of the sleep EEG. The transitions in the sleep behavior can be clearly discerned in the attractor dimension record which corresponds to the changes seen in the hypnogram. The attractor dimensions with different shifts of 64, 128, 256,512 and 1024 points along the data file with a fixed window length of 4096 points did not affect the pattern of the attractor curves. Moving the data window by small steps resulted in a greater number of attractor dimension values, and an increase in the data points of the shift resulted in fewer attractor dimension values without any change in the shape of the attractor curve. The attractor dimension analysis for all the different window lengths with different shifts showed consistency in the pattern of the attractor dimension curves. The complexity and transitions of sleep behavior are maintained in all the running attractor dimension curves of the sleep EEG data recorded for the five subjects in this study. It may be mentioned that a sleep EEG record may contain 3.6 mega samples and is about 32 megabytes of floating voltage values. The analysis of such

(a) Alpha activity (b) Beta activity (c) Delta activity

Fig. 2. The phase space plots of different EEG activities: (a) alpha activity. (b) beta activity. and

(c) delta activity.

460 N. PRADHAN et al.

Hypnogram 8 I I 1 I I 1 I

REM I

Stage4 6

Stage 3

Stage 2 -

Stage 1 u

r

Awake

Movement 1

Not scored 0 4 1 I , I I 1 I

0 1 2 3 4 5 6 I 8 9

12

10

8

s 6

4

2

0

Time in hours

Running attractor dimension

I I I I I I , I

c , I I I I 1 2 3 4 5 6 I 8 9

Time in hours

Fig. 3. Hypnogram and running attractor dimension for a typical sleep record

voluminous data for understanding the patterns of brain activity poses considerable problems. A scorer has to visually score the sleep data and at times it may be subjective [ 111. The running attractor dimension method has been applied to sleep EEG in this data set of five nights of sleep data. This method may also find possible applications in other EEG monitoring situations such as anesthesia, coma, epilepsy and other neurological emergencies.

The chaotic model of EEG generation, i.e. the notion that simple, nonlinear systems can produce complex and almost random looking output, is very appealing [ 181. The fact that the EEG appears unpredictable, yet is bounded to a limited frequency and amplitude range with a few basic rhythms and waveforms points to chaotic aspect of the brain’s electrical activity [19]. There are a number of transitions from one stage of activity to another. The degree of chaoticity varies in different stages. The present study of the analysis of sleep EEG has been made here keeping in mind the nonlinear deterministic nature of EEG [20].

The attractor dimension has been used to study different sleep stages. The estimated attractor dimension of slow wave sleep of stage 2 (D2 = 5.03) and stage 4 (D2 = 4.0-4.4) was first reported by Babloyantz et al. demonstrating the presence of a low dimensional chaos in EEG [l]. It has been followed by a number of reports of attractor values in various stages of sleep in human beings and other experimental animals [21]. The slow wave sleep (D2 = 4.25) is well differentiated from the REM sleep (D2 = 6). The sleep results are the most stable results and are reproducible whereas there is a wide variation in the reported waking state D2 values (2.4-11.0). There have been no attempts to see whether the D2 patterns of the entire sleep data have any similarity to a hypnogram. Even though a certain amount of training and subjectivity is encountered in evaluating the sleep by sleep staging and scoring, it is probably the only method known in sleep

Patterns of attractor dimensions of sleep EEG 461

physiology. In this paper we have studied the running attractor dimension values of sleep records. We have presented the attractor dimension values in different stages of sleep (Table 2) and the pattern of the changes in the attractor dimension has clearly delineated the transitional states in sleep. During slow wave sleep, there is a loss of complexity in large neuronal assemblies which is reflected in a low attractor dimension value (D2 = 4.2-4.8 for stage 4 NREM) implying a transitional state with loss of degrees of freedom. It may be ascribed to a loss of positive feedback processes in the brainstem reticular structures. It is hoped that nonlinear dimensional and trajectory analysis may become another tool for discriminating various normal and pathological states as the spectral methods. The nonlinear dynamics, being a model driven approach, give a more direct way of causal links between psychological processes and the neuronal substrate than does the simple representation of EEG in the frequency domain [22].

8. SUMMARY

Chaotic dynamical analysis is a fundamentally different approach to the analysis of EEG. Deterministic mathematical models of neuronai systems can give rise to complex chaotic dynamics in the absence of stochastic fluctuations in the variables of brain potentials. Chaotic dynamics are expected in nonlinear feedback systems possessing time delays such as those that are expected to occur in recurrent inhibition and from the periodic forcing of neural oscillators. The implications of chaotic dynamics and mathe- matical modeling of EEG generation in transitional states may throw new light on our understanding of brain and behavioral states. Sleep is a naturally occurring behavioral state that has inherent transitions. It is one of the most stable of animal behaviors. The phylogenetic evolution of complexity of the transitional states of sleep parallels the emergence of complex networks in brain development. Therefore, the complexity of the dynamics of brain activity in sleep has been the subject of investigation in this paper. We have presented the extraction of features of sleep behavior using the concept of an attractor dimension. Evaluation of the nonlinear parameter through running attractor dimension reveals a pattern which may be viewed as an objective measure of brain’s transitional states in sleep behavior. The pattern matches to conventional visual scoring - the “hypnogram”. Our interpretations may help in the analysis and modeling of neuronal systems in the future. These attractor dimension values may have a physiologi- cal meaning with reference to neuronal activities. The methodology is also of importance in analyzing other oscillatory and transitional states of brain activity seen in epilepsy, task loaded attentional states, cognitive task performance and in various states of consciousness. In short, this paper presents the physical and dynamical aspects of the brain’s electrical activity in sleep from the new perspective of nonlinear dynamics. The importance of the emerging trends of nonlinear science to neurobiology has been highlighted with reference to the concept of the attractor dimension.

Acknowledgemenr-The work has been supported by a grant from Department of Biotechnology (BT/R&D/ 09/48/92). Government of India.

REFERENCES 1. A. Babloyantz and A. Desstxhe, Strange attractors in the human cortex. In Temporal Disorders in Human

Oscilfafory Systems L. Rensing, U. Van der Heiden and M.C. Mackey, Eds. Springer Series in Synergetics. Vol 36, pp. 48-56, Springer, Berlin (1987).

2. N. Pradhan and D. Narayana Dutt, A nonlinear perspective in understanding the neurodynamics of EEG. Compt. Biol. Med. 23, 425-442 (1993).

3. A. Culebras, The neurology of sleep, Neurology 42, 6-8 (1992). 4. M. Steriade, Basic mechanisms of sleep generation, Neurology 42, 9-18 (1992). 5. R. Pool, Is it healthy to be chaotic? Science 243, 604-607 (1989). 6. A. I. Mees. P. E. Rapp and L. S. Jenning. Singular value decomposition and embedding dimension,

Physiol. Rev. 36, 340-346 (1987). 7. P. Grassberger and I. Procacia, Measuring the strangeness of strange attractors, Physica 9D. 189208

(1983). 8. S. Elmer, Estimating attractor dimensions from limited data: a new method, with error estimates. Phys.

Lett. A 133, 128-133 (198X). 9. N. Pradhan and D. Narayana Dutt, Use of running fractal dimension for the analysis of changing patterns

in electroencephalogram, Comput. Biol. Med 23. 381-388 (1993).

462 N.PKADHAN etal.

10. A.S. Gevins, Overview of computer analysis, In Handbook of Electroencephalography and Clinical Neurophysiology, A. S. Gevins and A. Remond, Eds, Vol. (I), pp. 31-84. Elsevier, Amsterdam (1987).

11. A. Rechtschaffen and A. Kales, A manual of standardized terminology, technique and scoring for sleep stages of human subjects. Public Health Services, US Government Printing Office, Washington, DC (1968).

12. N. Pradhan, D. Narayana Dutt, P. K. Sadasivan and R. G. Ramesh, Estimation of attractor dimension of EEG using singular value decomposition. In Recent Advances in Signal Processing and Communication: Proceedings SPCOM ‘95. V. U. Reddy and A. Makur (Eds), pp. 81-89. Tata-McGraw-Hill, New Delhi (1995).

13. A. Passamante, T. Hediger and M. Gollub, Fractal dimension and local intrinsic dimension, Phys. Reu. A 39, 3640-3645 (1989).

14. F. Takens, Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence. Lecture Notes in Mathematics, D. A. Rand and L. S. Young (Eds), Vol. 898, pp. 366-381. Springer, Berlin (1981).

15. W. Liebert and H. G. Schuster, Proper choice of time delay for the analysis of chaotic time series, Phys. Letr. A 142, 107-l 11 (1989).

16. D. S. Broomhead and G. P. King, Extracting qualitative dynamics from experimental data, Physica D 20, 217-226 (1986).

17. A. C. K. Snoog and I. J. M. Stuart, Evidence of chaotic dynamics underlying the human alpha-rhythm electroencephalogram, Biol. Cybern. 62, 5S62 (1988).

lg. T. M. McKenna, T. A. McMullen and M. F. Shlesinger, The brain as a dynamic physical system, Neuroscience 60, 587405 ( 1994).

19. E. Basar (Ed.), Chaos in Brain Function. Springer, Berlin (1990). 20. I. Dvorak and A. V. Holden (Eds), Mathematical Approaches to Brain Functioning Diagnostics,

Manchester University Press, Manchester (1991). 21. J. Roschke and E. Basar, The EEG is not a simple noise: Strange attractors in intracranial structures, In

Chaos in Brain Function, E. Basar (Ed.), pp. 4962. Springer Verlag, Berlin (1990). 22. R.A.M. Gregson, L.A. Britton, E.A. Campbell and G.R. Gates, Comparison of the nonlinear dynamics

of electroencephalogram under various tasks loading conditions: a preliminary report, Biol. Psychology 31, 17>191 (1990).

About the Author-N. PRADHAN obtained his M.D. degree in Psychological Medicine from the National Institute of Mental Health and Neurosciences (NIMHANS), Bangalore, India in 1977. He continued in the same Institute as resident doctor and became a faculty member in 1979. He held positions as Lecturer, Assistant Professor and Associate Professor in Psychiatry. Currently he is an Additional Professor and heads the Department of Psychopharmacology. His research interest is in biological psychiatry. Currently he is involved in the research in applications of nonlinear dynamics and theory of chaos to neurodynamics and cognitive psychology. He is the principal investigator for the research project “A nonlinear dynamical study of transitional processes of brain activity using sleep data”, which has been awarded to him by the Department of Biotechnology, Government of India. The present work is an outcome of the project.

About the Author-P. K. SADASIVAN obtained his B.Tech and M.Tech from the University of Calicut, Kerala, India in 1986 and 1989 respectively. He received his Ph.D degree from the Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India in 1995. Currently, he is working as a Research Associate in the project, “A nonlinear dynamical study of transitional processes of brain activity using sleep data” at NIMHANS. His research interests are in biomedical signal processing, nonlinear dynamics and chaos, neural networks, etc.

About the Author-SOMNATH CHATTERJI obtained his M.D. degree in Psychological Medicine from the National Institute of Mental Health and Neurosciences (NIMHANS), Bangalore, India in 1982. He continued in the Department of Psychiatry as an Assistant Professor and as an Associate Professor. Currently, he is an Additional Professor in the same Department. His research interest is in biological psychiatry. He has been collaborating with Dr N. Pradhan in various research projects.

About the Author-D. NARAYANA Durr obtained his B.E. degree from the Bangalore University and M.E and Ph.D from the Indian Institute of Science, Bangalore, India. He is presently working in the same institute in the Department of Electrical Communication Engineering as an Associate Professor. He had earlier worked in the areas of acoustics and speech signal processing. At present, he is working in the area of applications of digital signal processing to the analysis of biomedical signals; in particular, brain signals. He is the principal co- investigator for the project “A nonlinear dynamical study of transitional processes of brain activity using sleep data” with Dr N. Pradhan.