Non-stationary time series (i.e., time series with statistical properties that vary over time) arise in many areas of neuroscience research and clinical practice. For example, the spectral properties of electroencephalograms (EEGs) vary with brain state, and frequently this variation is of central clinical or scientific importance. Existing methods of spectral analysis assume that a time series is a realization of a stationary random process. These methods can be extended to non-stationary processes using windowed Fourier transforms, but the number and size of the windows must be chosen subjectively. We propose to develop improved, automatic statistical methods for analysis of non-stationary multivariate time series. We will evaluate the methods in applications to realistic simulated data and to real multi-channel EEG data acquired from patients with brain disorders. We will compare results from our automatic methods with the clinical judgments.
Our specific aims are to develop, evaluate, apply, implement, and distribute the following statistical methods: (1) an estimator of the time-varying power spectrum of a univariate random process; (2) estimators of the time-varying spectral density matrix, coherences, and phase spectra of a multivariate random process; (3) time-frequency principal component analysis; (4) time-frequency filters; (5) cycle-spinning to reduce bias due to the dyadic structure of our estimators; and (6) improved color time-frequency plots for displaying the results. Our proposed statistical methods are based on the Smooth Localized complex Exponential (SLEX) transform, which provides a rich selection of orthogonal transforms. The structure of the SLEX transform allows us to use the simple and computationally efficient Best Basis algorithm of Coifman and Wickerhauser to automatically select a particular transform, which represents a segmentation of a non-stationary time series into approximately stationary intervals. SLEX coefficients, unlike wavelet, wavelet packet, and cosine packet coefficients, contain phase information, facilitating the estimation of time-varying phase relationships in multivariate time series. The SLEX transform can be made arbitrarily close to a tapered Fourier transform, so that our proposed methods for spectral analysis of nonstationary processes using the SLEX transform will parallel existing methods for spectral analysis of stationary processes.

Agency
National Institute of Health (NIH)
Institute
National Institute of Mental Health (NIMH)
Type
Research Project (R01)
Project #
1R01MH062298-01
Application #
6044082
Study Section
Special Emphasis Panel (ZRG1-SNEM-5 (01))
Program Officer
Glanzman, Dennis L
Project Start
2000-02-01
Project End
2001-01-31
Budget Start
2000-02-01
Budget End
2001-01-31
Support Year
1
Fiscal Year
2000
Total Cost
$167,424
Indirect Cost
Name
University of Pennsylvania
Department
Biostatistics & Other Math Sci
Type
Schools of Medicine
DUNS #
042250712
City
Philadelphia
State
PA
Country
United States
Zip Code
19104
Parish, L M; Worrell, G A; Cranstoun, S D et al. (2004) Long-range temporal correlations in epileptogenic and non-epileptogenic human hippocampus. Neuroscience 125:1069-76
Ratcliffe, Sarah J; Guo, Wensheng; Ten Have, Thomas R (2004) Joint modeling of longitudinal and survival data via a common frailty. Biometrics 60:892-9
Worrell, Greg A; Parish, Landi; Cranstoun, Stephen D et al. (2004) High-frequency oscillations and seizure generation in neocortical epilepsy. Brain 127:1496-506
Germain, Anne; Buysse, Daniel J; Ombao, Hernando et al. (2003) Psychophysiological reactivity and coping styles influence the effects of acute stress exposure on rapid eye movement sleep. Psychosom Med 65:857-64
D'Alessandro, Maryann; Esteller, Rosana; Vachtsevanos, George et al. (2003) Epileptic seizure prediction using hybrid feature selection over multiple intracranial EEG electrode contacts: a report of four patients. IEEE Trans Biomed Eng 50:603-15
Nofzinger, Eric A; Buysse, Daniel J; Miewald, Jean M et al. (2002) Human regional cerebral glucose metabolism during non-rapid eye movement sleep in relation to waking. Brain 125:1105-15
Litt, Brian; Lehnertz, Klaus (2002) Seizure prediction and the preseizure period. Curr Opin Neurol 15:173-7
Worrell, Gregory A; Cranstoun, Stephen D; Echauz, Javier et al. (2002) Evidence for self-organized criticality in human epileptic hippocampus. Neuroreport 13:2017-21
Moul, Douglas E; Ombao, Hernando; Monk, Timothy H et al. (2002) Masking effects of posture and sleep onset on core body temperature have distinct circadian rhythms: results from a 90-min/day protocol. J Biol Rhythms 17:447-62
Cranstoun, Stephen D; Ombao, Hernando C; von Sachs, Rainer et al. (2002) Time-frequency spectral estimation of multichannel EEG using the Auto-SLEX method. IEEE Trans Biomed Eng 49:988-96

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