title: Nonlinear dynamical analysis of the neonatal EEG time series: the relationship between sleep state and complexity.
abstract: OBJECTIVE
  The complexity of the EEG time series during stages of neonatal sleep states is investigated. The relationship between these sleep states, birth status (i.e. preterm and full-term), and the complexity of the EEG is assessed.
  
  
  METHODS
  Dimensional complexity, an estimate of the correlation dimension (D(2)) of the EEG time series, is used as a novel index for quantifying the complexity of the EEG time series during different neonatal sleep states. The dimensional complexity is estimated by using both the Grassberger-Procaccia algorithm and Theiler's modified algorithm. Also, the hypothesis that the neonatal EEG time series contains nonlinear features is investigated and verified in certain sleep states using surrogate data testing.
  
  
  RESULTS
  Dimensional complexity of the neonatal EEG time series during active (REM) sleep tends to be higher than during quiet (NREM) sleep; while dimensional complexity of the neonatal EEG time series during indeterminate sleep is virtually at the midpoint of the dimensional complexity range between the active and quiet sleep states. Consequently, there are statistically significant differences between the neonatal EEG time series during different sleep states as measured by dimensional complexity. Also, the birth status (preterm or full-term) of the neonate has an influence on dimensional complexity of the neonatal EEG time series. Further, the surrogate data testing null hypothesis for dimensional complexity cannot be rejected during active sleep.
  
  
  CONCLUSIONS
  The neonatal EEG time series tends to have statistically different complexities corresponding to different sleep states. Given that the neonatal EEG time series during active sleep is more complex than during quiet sleep, one can suggest that there is greater activity among cortical circuit elements during active as compared to quiet sleep. Further, active sleep neuronal dynamics are best modeled by a linear stochastic process, while in quiet sleep a nonlinear deterministic model may be more appropriate.
  
  
  CONCLUSIONS
  There has been considerable controversy associated with measures of complexity, such as dimensional analysis, as applied to neonatal EEG data. This paper confirms that there are statistically significant differences in dimensional complexity associated with different states of sleep and that the origin of this complexity shifts from linear stochastic to nonlinear deterministic with transitions from active to quiet sleep, and is further influenced by maturation. This may provide important insight into the organization and structure of neuronal networks during sleep and with brain maturation in the neonatal period.
authors.affiliation: Ubon Ratchathani University, Department of Electrical and Electronic Engineering, Warinchamrab, Ubon Ratchathani 34190, Thailand; Case Western Reserve University, Department of Electrical Engineering and Computer Science, Cleveland, OH 44106, USA. Electronic address: suparerk.janjarasjitt@case.edu.
authors.forename: S
authors.initials: S
authors.lastname: Janjarasjitt
authors.affiliation: Case Western Reserve University, Department of Pediatrics, Cleveland, OH 44106, USA. Electronic address: mark.scher@case.edu.
authors.forename: M S
authors.initials: MS
authors.lastname: Scher
authors.affiliation: Case Western Reserve University, Department of Electrical Engineering and Computer Science, Cleveland, OH 44106, USA. Electronic address: kenneth.loparo@case.edu.
authors.forename: K A
authors.initials: KA
authors.lastname: Loparo
mesh_terms: D000465:Algorithms; D004569:Electroencephalography; D005260:Female; D005333:Fetus / Q000502:physiology; D006801:Humans; D007231:Infant, Newborn; D007233:Infant, Postmature / Q000502:physiology*; D007234:Infant, Premature / Q000502:physiology; D008297:Male; D008954:Models, Biological; D017711:Nonlinear Dynamics; D017286:Polysomnography; D012815:Signal Processing, Computer-Assisted; D012894:Sleep Stages / Q000502:physiology*; D013997:Time Factors; D014851:Wakefulness / Q000502:physiology