title: Nonlinear measures of respiration: respiratory irregularity and increased chaos of respiration in patients with panic disorder.
abstract: BACKGROUND
  Respiratory irregularity has been previously reported in patients with panic disorder using time domain measures. However, the respiratory signal is not entirely linear and a few previous studies used approximate entropy (APEN), a measure of regularity of time series. We have been studying APEN and other nonlinear measures including a measure of chaos, the largest Lyapunov exponent (LLE) of heart rate time series, in some detail. In this study, we used these measures of respiration to compare normal controls (n = 18) and patients with panic disorder (n = 22) in addition to the traditional time domain measures of respiratory rate and tidal volume.
  
  
  METHODS
  Respiratory signal was obtained by the Respitrace system using a thoracic and an abdominal belt, which was digitized at 500 Hz. Later, the time series were constructed at 4 Hz, as the highest frequency in this signal is limited to 0.5 Hz. We used 256 s of data (1024 points) during supine and standing postures under normal breathing and controlled breathing at 12 breaths/min.
  
  
  RESULTS
  APEN was significantly higher in patients in standing posture during normal as well as controlled breathing (p = 0.002 and 0.02, respectively). LLE was also significantly higher in standing posture during normal breathing (p = 0.009). Similarly, the time domain measures of standard deviations and the coefficient of variation (COV) of tidal volume (TV) were significantly higher in the patient group (p = 0.02 and 0.004, respectively). The frequency of sighs was also higher in the patient group in standing posture (p = 0.02). In standing posture, LLE (p < 0.05) as well as APEN (p < 0.01) contributed significantly toward the separation of the two groups over and beyond the linear measure, i.e. the COV of TV.
  
  
  CONCLUSIONS
  These findings support the previously described respiratory irregularity in patients with panic disorder and also illustrate the utility of nonlinear measures such as APEN and LLE as additional measures toward a better understanding of the abnormalities of respiratory physiology in similar patient populations as the correlation between LLE, APEN and some of the time domain measures only explained up to 50-60% of the variation.
authors.affiliation: Department of Psychiatry, Wayne State University School of Medicine, Detroit, Mich, USA. vikramyershr@yahoo.com
authors.forename: Vikram Kumar
authors.initials: VK
authors.lastname: Yeragani
authors.forename: Rao K A
authors.initials: RK
authors.lastname: Radhakrishna
authors.forename: Manuel
authors.initials: M
authors.lastname: Tancer
authors.forename: Thomas
authors.initials: T
authors.lastname: Uhde
mesh_terms: D000328:Adult; D001007:Anxiety / Q000503:physiopathology; D016002:Discriminant Analysis; D005260:Female; D006339:Heart Rate / Q000502:physiology; D006801:Humans; D016014:Linear Models; D008297:Male; D017711:Nonlinear Dynamics; D016584:Panic Disorder / Q000503:physiopathology*; D011187:Posture / Q000502:physiology; D012016:Reference Values; D012119:Respiration; D013990:Tidal Volume / Q000502:physiology*; D013997:Time Factors