title: Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and heart-transplanted patients.
abstract: OBJECTIVE
  Heart rate variability (HRV) is characterised by a variety of linear, non-linear, periodical and non-periodical oscillations. The aim of the present study was mainly to investigate the role played by neural mechanisms in determining non-linear and non-periodical components.
  
  
  METHODS
  Analysis was performed in 7 recently heart transplanted patients and in 7 controls of similar age whose HRV signal was collected during 24 h. Parameters that quantify non-linear dynamic behaviour, in a time series, were calculated. We first assessed the specific non-linear nature of the time series by a test on surrogate data after Fourier phase randomization. Furthermore, the D2 correlation dimension, K2 Kolmogorov entropy, and H self-similarity exponent of the signal were estimated. From this last parameter, the dimension D = 1/H can be obtained. In order to assess whether the dynamics of the system are compatible with chaotic characteristics, the entire spectrum of Lyapunov exponents was calculated. We used return maps to graphically represent the non-linear and non-periodical behaviours in patients and controls.
  
  
  RESULTS
  Surrogate data suggest that the HRV time courses have unique non-linear characteristics. D2, K2 and 1/H parameters were significantly lower in transplanted subjects than in controls. Positivity of the first Lyapunov exponent indicates divergence of trajectories in state-space. Furthermore, the display of return maps on projections obtained after Singular Value Decomposition, especially in low-complexity data (as in transplanted patients), shows a structure which is suggestive of a strange attractor. These findings support the hypothesis that chaotic dynamics underlie HRV.
  
  
  CONCLUSIONS
  These results indicate that non-linear dynamics are likely to be present in HRV control mechanisms, giving rise to complex and qualitatively different behaviours. System complexity decreases in transplanted patients and this may be related to loss of the neural modulation of heart rate.
authors.affiliation: Centro Ricerche Cardiovascolari del CNR, Medicina Interna II, Università di Milano, Italy.
authors.forename: S
authors.initials: S
authors.lastname: Guzzetti
authors.forename: M G
authors.initials: MG
authors.lastname: Signorini
authors.forename: C
authors.initials: C
authors.lastname: Cogliati
authors.forename: S
authors.initials: S
authors.lastname: Mezzetti
authors.forename: A
authors.initials: A
authors.lastname: Porta
authors.forename: S
authors.initials: S
authors.lastname: Cerutti
authors.forename: A
authors.initials: A
authors.lastname: Malliani
mesh_terms: D000328:Adult; D000368:Aged; D001341:Autonomic Nervous System / Q000502:physiology; D015716:Electrocardiography, Ambulatory; D006339:Heart Rate / Q000502:physiology*; D016027:Heart Transplantation; D006801:Humans; D008875:Middle Aged; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted