(Circulation. 1996;93:2142-2151.)
© 1996 American Heart Association, Inc.
Articles |
Power Law Behavior of RR-Interval Variability in Healthy Middle-Aged Persons, Patients With Recent Acute Myocardial Infarction, and Patients With Heart Transplants
From the Division of Cardiology (J.T.B., R.C.S., L.M.R., J.L.F.), Department of Medicine, and Division of Biostatistics, School of Public Health, Columbia University, New York, NY; and the Harvard University-Massachusetts Institute of Technology Division of Health Sciences and Technology (P.A., R.J.C.), Cambridge, Mass.
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.
Methods and 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 
-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.
Key Words: Fourier analysis • myocardial infarction • transplantation
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