Understanding dynamics of the system using Hilbert phases: an application to study neonatal and fetal brain signals.

The Hilbert phase phi(t) of a signal x(t) exhibits slips when the magnitude of their successive phase difference |phi(t(i+1))-phi(t(i))| exceeds pi. By applying this approach to periodic, uncorrelated, and long-range correlated data, we show that the standard deviation of the time difference between the successive phase slips Deltatau normalized by the percentage of slips in the data is characteristic of the correlation in the data. We consider a 50x50 square lattice and model each lattice point by a second-order autoregressive (AR2) process. Further, we model a subregion of the lattice using a different set of AR2 parameters compared to the rest. By applying the proposed approach to the lattice model, we show that the two distinct parameter regions introduced in the lattice are clearly distinguishable. Finally, we demonstrate the application of this approach to spatiotemporal neonatal and fetal magnetoencephalography signals recorded using 151 superconducting quantum interference device sensors to identify the sensors containing the neonatal and fetal brain signals and discuss the improved performance of this approach over the traditionally used spectral approach.

[1]  M. Scher,et al.  Postnatal adaptation of brain function in full-term neonates as assessed by EEG sleep analyses. , 1995, Sleep.

[2]  B. Kedem,et al.  Spectral analysis and discrimination by zero-crossings , 1986, Proceedings of the IEEE.

[3]  Hui Zhao,et al.  Simultaneity of foetal heart rate acceleration and foetal trunk movement determined by foetal magnetocardiogram actocardiography. , 2002, Physics in medicine and biology.

[4]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[5]  Shlomo Havlin,et al.  Return intervals of rare events in records with long-term persistence , 2004 .

[6]  Jens Timmer,et al.  Cross-spectral analysis of physiological tremor and muscle activity , 1998, Biological Cybernetics.

[7]  C. Peng,et al.  Long-range correlations in nucleotide sequences , 1992, Nature.

[8]  Hui Zhao,et al.  Simultaneous Fetal Magnetocardiography and Ultrasound/Doppler Imaging , 2007, IEEE Transactions on Biomedical Engineering.

[9]  R. Dahl,et al.  Comparison of EEG sleep measures in healthy full-term and preterm infants at matched conceptional ages. , 1992, Sleep.

[10]  A M Amjad,et al.  A framework for the analysis of mixed time series/point process data--theory and application to the study of physiological tremor, single motor unit discharges and electromyograms. , 1995, Progress in biophysics and molecular biology.

[11]  S. Havlin,et al.  Indication of a Universal Persistence Law Governing Atmospheric Variability , 1998 .

[12]  A G Balanov,et al.  Phase synchronization between several interacting processes from univariate data. , 2001, Physical review letters.

[13]  Milan Palus,et al.  Direction of coupling from phases of interacting oscillators: an information-theoretic approach. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  G. Pfurtscheller.  Handbook of electroencephalography and clinical neurophysiology , 1978 .

[15]  Jürgen Kurths,et al.  Alternating Locking Ratios in Imperfect Phase Synchronization , 1999 .

[16]  Hubert Preissl,et al.  Human fetal brain imaging by magnetoencephalography: verification of fetal brain signals by comparison with fetal brain models , 2004, NeuroImage.

[17]  Hubert Preissl,et al.  Development of auditory evoked fields in human fetuses and newborns: A longitudinal MEG study , 2005, Clinical Neurophysiology.

[18]  Hubert Preissl,et al.  Functional development of the visual system in human fetus using magnetoencephalography , 2004, Experimental Neurology.

[19]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[20]  J Kurths,et al.  Phase synchronization in the forced Lorenz system. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  A G Balanov,et al.  Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  J. Timmer,et al.  On generating power law noise. , 1995 .

[23]  Reinhold Kliegl,et al.  Twin surrogates to test for complex synchronisation , 2006 .

[24]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[25]  Hubert Preissl,et al.  Magnetoencephalography in healthy neonates , 2006, Clinical Neurophysiology.

[26]  L. Zetterberg.  Estimation of parameters for a linear difference equation with application to EEG analysis , 1969 .

[27]  Hubert Preissl,et al.  Sound frequency change detection in fetuses and newborns, a magnetoencephalographic study , 2005, NeuroImage.

[28]  Hubert Preissl,et al.  Non-invasive detection and identification of brain activity patterns in the developing fetus , 2007, Clinical Neurophysiology.

[29]  Hubert Preissl,et al.  First magnetomyographic recordings of uterine activity with spatial-temporal information with a 151-channel sensor array. , 2002, American journal of obstetrics and gynecology.

[30]  S. Havlin,et al.  Phase synchronization in temperature and precipitation records , 2002, physics/0211092.

[31]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[32]  J. Timmer,et al.  Tempting long-memory - on the interpretation of DFA results , 2004 .

[33]  Hubert Preissl,et al.  Fetal MEG redistribution by projection operators , 2004, IEEE Transactions on Biomedical Engineering.

[34]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[35]  H Eugene Stanley,et al.  Spurious detection of phase synchronization in coupled nonlinear oscillators. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  H. Freund,et al.  Cortico‐muscular synchronization during isometric muscle contraction in humans as revealed by magnetoencephalography , 2000, The Journal of physiology.