title: Power law behavior of RR-interval variability in healthy middle-aged persons, patients with recent acute myocardial infarction, and patients with heart transplants.
abstract: BACKGROUND
  The purposes of the present study were (1) to establish normal values for the regression of log(power) on log(frequency) for, RR-interval fluctuations in healthy middle-aged persons, (2) to determine the effects of myocardial infarction on the regression of log(power) on log(frequency), (3) to determine the effect of cardiac denervation on the regression of log(power) on log(frequency), and (4) to assess the ability of power law regression parameters to predict death after myocardial infarction.
  
  
  RESULTS
  We studied three groups: (1) 715 patients with recent myocardial infarction; (2) 274 healthy persons age and sex matched to the infarct sample; and (3) 19 patients with heart transplants. Twenty-four-hour RR-interval power spectra were computed using fast Fourier transforms and log(power) was regressed on log(frequency) between 10(-4) and 10(-2) Hz. There was a power law relation between log(power) and log(frequency). That is, the function described a descending straight line that had a slope of approximately -1 in healthy subjects. For the myocardial infarction group, the regression line for log(power) on log(frequency) was shifted downward and had a steeper negative slope (-1.15). The transplant (denervated) group showed a larger downward shift in the regression line and a much steeper negative slope (-2.08). The correlation between traditional power spectral bands and slope was weak, and that with log(power) at 10(-4) Hz was only moderate. Slope and log(power) at 10(-4) Hz were used to predict mortality and were compared with the predictive value of traditional power spectral bands. Slope and log(power) at 10(-4) Hz were excellent predictors of all-cause mortality or arrhythmic death. To optimize the prediction of death, we calculated a log(power) intercept that was uncorrelated with the slope of the power law regression line. We found that the combination of slope and zero-correlation log(power) was an outstanding predictor, with a relative risk of > 10, and was better than any combination of the traditional power spectral bands. The combination of slope and log(power) at 10(-4) Hz also was an excellent predictor of death after myocardial infarction.
  
  
  CONCLUSIONS
  Myocardial infarction or denervation of the heart causes a steeper slope and decreased height of the power law regression relation between log(power) and log(frequency) of RR-interval fluctuations. Individually and, especially, combined, the power law regression parameters are excellent predictors of death of any cause or arrhythmic death and predict these outcomes better than the traditional power spectral bands.
authors.affiliation: Department of Medicine, School of Public Health, Columbia University, New York, NY 10032, USA.
authors.forename: J T
authors.initials: JT
authors.lastname: Bigger
authors.forename: R C
authors.initials: RC
authors.lastname: Steinman
authors.forename: L M
authors.initials: LM
authors.lastname: Rolnitzky
authors.forename: J L
authors.initials: JL
authors.lastname: Fleiss
authors.forename: P
authors.initials: P
authors.lastname: Albrecht
authors.forename: R J
authors.initials: RJ
authors.lastname: Cohen
mesh_terms: D000328:Adult; D015716:Electrocardiography, Ambulatory; D016027:Heart Transplantation / Q000502:physiology*; D006801:Humans; D008875:Middle Aged; D009203:Myocardial Infarction / Q000503:physiopathology*; D011184:Postoperative Period; D012016:Reference Values; D012044:Regression Analysis