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(Circulation. 2000;101:47.)
© 2000 American Heart Association, Inc.
Clinical Investigation and Reports |
Fractal Correlation Properties of R-R Interval Dynamics and Mortality in Patients With Depressed Left Ventricular Function After an Acute Myocardial Infarction
From the Division of Cardiology, Department of Medicine, University of Oulu, Finland (H.V.H.); Department of Cardiology, Odense University Hospital, Odense, Denmark (T.H.M., U.H., M.M.); and The Margret and H.A. Rey Laboratory for Nonlinear Dynamics in Medicine and Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Mass (C.-K.P., A.L.G.).
Correspondence to Heikki V. Huikuri, MD, Division of Cardiology, Department of Medicine, University of Oulu, Kajaanintie 50, 90220 Oulu, Finland. E-mail heikki.huikuri{at}oulu.fi
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionReferences |
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Background—Preliminary data suggest that the analysis of R-R interval variability by fractal analysis methods may provide clinically useful information on patients with heart failure. The purpose of this study was to compare the prognostic power of new fractal and traditional measures of R-R interval variability as predictors of death after acute myocardial infarction.
Methods and Results—Time and frequency domain heart rate (HR)
variability measures, along with short- and long-term correlation
(fractal) properties of R-R intervals (exponents 
1 and
2) and power-law scaling of the power spectra (exponent
ß), were assessed from 24-hour Holter recordings in 446
survivors of acute myocardial infarction with a depressed left
ventricular function (ejection fraction 
35%). During a
mean±SD follow-up period of 685±360 days, 114 patients died (25.6%),
with 75 deaths classified as arrhythmic (17.0%) and 28 as
nonarrhythmic (6.3%) cardiac deaths. Several traditional and fractal
measures of R-R interval variability were significant
univariate predictors of all-cause mortality. Reduced
short-term scaling exponent 1 was the most powerful R-R
interval variability measure as a predictor of all-cause mortality
(1 <0.75, relative risk 3.0, 95% confidence interval
2.5 to 4.2, P<0.001). It remained an independent
predictor of death (P<0.001) after adjustment for other
postinfarction risk markers, such as age, ejection fraction, NYHA
class, and medication. Reduced 1 predicted both
arrhythmic death (P<0.001) and nonarrhythmic cardiac
death (P<0.001).
Conclusions—Analysis of the fractal characteristics of short-term R-R interval dynamics yields more powerful prognostic information than the traditional measures of HR variability among patients with depressed left ventricular function after an acute myocardial infarction.
Key Words: mortality • heart rate • infarction
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Analysis of time and frequency domain measures of heart rate (HR) variability from 24-hour ambulatory ECG recordings provides prognostic information on patients after an acute myocardial infarction.1 2 3 4 A number of new methods based on nonlinear system theory ("chaos theory and fractals") have been recently developed to quantify the complex HR dynamics and to complement the conventional measures of HR variability.5 6 7 8 9 10 11 12 New fractal analysis methods have already provided clinically useful information on patients with impaired left ventricular function,13 14 15 but their prognostic power has not been proved in large-scale studies.
In the present investigation, we assessed the use of various fractal analysis methods of HR variability to predict death in a population of patients with acute myocardial infarction (MI) and depressed left ventricular function. The prediction of death was evaluated in survivors of acute MI included in the Danish Investigations of Arrhythmia and Mortality on Dofetilide (DIAMOND-MI) trial. We also sought to determine whether these new fractal measures of R-R interval dynamics predict specifically either arrhythmic or nonarrhythmic cardiac death.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Population
A substudy of the DIAMOND MI trial was conducted in 37 Danish coronary care units that included patients with an acute MI and a left ventricular wall motion index of
1.2 (equal to an
ejection fraction of 0.35). A detailed study design has been
previously described.16 A substudy of the DIAMOND trial
was designed to assess the prognostic power of various measures of HR
variability in predicting death in this population. In this subset of
patients, a 24-hour Holter recording was obtained in 645
patients 5 to 10 days after MI. The patients were followed for a mean
of 685±360 days after randomization, and the Events Committee
of the DIAMOND trial classified the deaths according to the CAST
criteria,17 except that resuscitated cardiac arrest was
not counted as death.
Ambulatory ECG Recordings
All of the subjects were monitored for 24 hours with an
ambulatory 2-channel ECG recorder (Tracker, Reynolds, UK) with an
R-R interval sampling frequency of 128 Hz. The data were sampled
digitally and transferred to a microcomputer for the analysis
of HR variability. The HR variability analysis techniques have
been described elsewhere.5 13 14 18 19 The methods are
briefly described here.
Nonspectral and Spectral Analyses of HR
Variability
After the transfer of the ECG data to a microcomputer, the R-R
interval series were edited both manually and
automatically.14 19 Only recordings with at least
20 hours of data and with >85% of qualified sinus beats were included
in the analysis of HR variability. The nonspectral and spectral
measures of HR variability were analyzed according to the
methods recommended by the task force.20 The SD of all
normal-to-normal R-R intervals (SDNN) and the geometric HR variability
index were computed as standard time domain measures from the entire
recording period. Spectral power was quantified through fast
Fourier transform analysis in 4 frequency bands: <0.0033 Hz
(ultralow frequency), 0.0033 to 0.04 Hz (very low frequency [VLF]),
0.04 to 0.15 Hz (low frequency), and 0.15 to 0.40 Hz (high
frequency).20 Ultralow-frequency and VLF spectral
components were computed over the entire recording
interval.20 Low- and high-frequency components were
computed from the segments of 512 R-R intervals, and the average values
of the entire recording interval were calculated for these
components.20
Poincaré Plot Analysis
The Poincaré plot is a graph in which each R-R interval is
plotted as a function of the previous R-R interval. The quantitative
2-dimensional analysis of these plots has been described in
detail previously.18 Briefly, scattergrams of successive
R-R intervals were plotted for the entire 24-hour period, and the SD of
instantaneous R-R interval variability and the SD of continuous
variability (SD2) were then analyzed
Power-Law Scaling Analysis
The power-law relation of R-R interval variability was
calculated from the frequency range of 10-4 to
10-2 Hz. The point power spectrum was
logarithmically smoothed in the frequency domain, and the power was
integrated into bins spaced 0.0167 log (Hz) apart. A robust
line-fitting algorithm of log (power) versus log (frequency) was then
applied to the power spectrum between 10-4 to
10-2 Hz, and the slope of this line was
calculated, yielding the scaling exponent (ß). The details of this
method have been described previously.19 21
Detrended Fluctuation Analysis
The detrended fluctuation analysis technique was used to
quantify the fractal scaling properties of short- and intermediate-term
R-R interval time series. The root-mean-square fluctuation of
integrated and detrended time series is measured at different
observation windows and plotted against the size of the observation
window on a log-log scale. The details of this method have been
described elsewhere.5 13 15 The HR correlations were
defined separately for short-term (<11 beats,
1) and longer-term (>11 beats,
2) R-R interval data (scaling
exponents).5 14 Both 32 1 and
2 were analyzed from segments of 8000
R-R intervals and averaged to obtain mean values for the entire
recording period. Scaling exponents were calculated both for
real R-R interval data after editing only for artifacts and for the
same preedited data that were used in traditional analyses.
Statistical Analysis
The measures of R-R interval variability and clinical data were
used as the explanatory variables in univariate
comparisons. Univariate comparisons were performed with the
2 test for categorical variables and the
2-tail 2-sample t test for continuous variables. The
Pearson correlation coefficient was used to estimate the correlations
between different variables. The frequency domain measures of HR
variability were transformed to natural logarithms, because their
distributions were skewed. A value of P<0.05 was considered
to indicate statistical significance.
x proportional hazards regression analyses were used to assess the association between different risk predictors and mortality by using the SPSS for Windows version 7.5. The continuous R-R interval variability measures were dichotomized. To find the best cut points for various variables, the dichotomization cut points that maximized the hazards ratio obtained from the Cox regression model were sought, with all-cause mortality as the end point. The dichotomization procedure was performed within the 10th to 70th percentiles in 5th-percentile steps for each variable. Kaplan-Meier estimates of the distribution of the times from the baseline to death were computed, and log-rank analysis was performed to compare the survival curves. Each measure was first tested univariately and then retested after adjustment for other post-MI risk factors in the Cox regression model. The sensitivity, specificity, and predictive accuracy values of R-R interval variability measures for all-cause mortality were also analyzed.
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Results are reported on 446 patients who fulfilled the criteria for meaningful R-R interval variability analysis. Patients were excluded because the ECG data could not be analyzed due to signal artifacts (n= 55), long or frequent episodes of atrial tachyarrhythmias (n= 45), or unsuccessful signal collection (n= 49) or due to frequent premature beats on the ECG recordings (<85% qualified sinus beats) (n=50).
Univariate Predictors of Death
During the follow-up period of 685±360 days, 114 (25.6%)
patients died. Seventy-five deaths (17.0%) were classified as
arrhythmic, and 28 (6.3%) were classified as nonarrhythmic cardiac
deaths. The baseline characteristics of the patients who survived and
those who died during the follow-up period are shown in Table 1
. The results of R-R interval
variability analyses for the total study group and separately
for the patients randomized to receive placebo (n=216) or dofetilide
(n=217) are shown in Table 2. The mean
R-R interval, SDNN, HR variability index, and SD2 differed
significantly between the survivors and nonsurvivors. All power
spectral components, except the HF component, also differed between the
groups. The fractal analysis indices obtained through the
detrended fluctuation method and the power-law scaling method were also
different between survivors and nonsurvivors (Table 2). The
differences in the measures of HR variability between the survivors and
those who died were the same as those between the patients randomized
to receive either placebo or dofetilide.
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Table 3 shows the sensitivity,
specificity, and predictive accuracy values of various measures of R-R
interval variability as predictors of all-cause mortality. Among the
R-R interval variability measures, the reduced short-term scaling
exponent 1 had the best overall accuracy
(Table 3). Scaling exponent 1
analyzed from the real R-R interval data performed slightly
better than that analyzed from the data edited for premature
beats as a predictor of death. Figure 1
shows examples of Kaplan-Meier survival curves and mortality rates.
Among the R-R interval variability measures, the reduced short-term
scaling exponent (<0.75) was the dichotomized variable that most
powerfully predicted the differences in survival curves.
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0.75 and <0.75, respectively (top
left); patients with SDNN of
Multivariate Predictors of Death
Table 4 shows the
univariate and multivariate relative risks
adjusted for other risk variables for dichotomized R-R interval
variability measures as predictors of all-cause, arrhythmic, and
nonarrhythmic cardiac death. The short-term scaling exponent was also
the most powerful independent predictor of all-cause mortality after
adjustment for other variables. It independently predicted
arrhythmic death, which was not predicted by the other measures of HR
variability after adjustment for clinical risk factors.
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Characteristics of R-R Interval Data With Reduced Short-Term
Scaling Exponent
The characteristics of R-R interval dynamics with a low
1 value were evaluated by printing out the R-R
interval tachograms, portions of ECG recordings, power spectra,
and Poincaré plots for all cases with an
1 value of <0.75. Figure 2 shows the typical R-R interval data
obtained from the patients with a low 1
value.
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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The main finding of this study was that a short-term fractal-like scaling exponent of R-R interval time series is a better predictor of death than the traditional measures of HR variability among patients with acute MI and depressed left ventricular function. These data confirm and generalize the preliminary observations, which have suggested the clinical applicability of fractal analysis methods in the risk stratification of patients with left ventricular dysfunction.13 14 15 A measure of R-R interval dynamics, which reflects the correlation properties (or randomness) of short-term HR behavior, provided prognostic information on all-cause, arrhythmic and nonarrhythmic cardiac deaths independent of the clinical variables and the degree of left ventricular dysfunction.
Nonspectral and Spectral Analyses of R-R Interval
Variability and Death
The independent prognostic power of the traditional indices of HR
variability was generally not as strong as that reported in prior
studies,1 2 3 4 and none of the time or frequency domain
measures provided independent prognostic information on the risk of
arrhythmic death. A recent study of patients with heart failure also
showed that analysis of SDNN from 24-hour ECG
recordings does not provide independent information on the risk
of sudden death.22 The previous studies have mostly
included post-MI patients with relatively well preserved left
ventricular function1 2 3 4 or patients with
heart failure due to various causes.22 The mechanisms of
death may be different in post-MI patients with preserved and impaired
left ventricular function. In the former category, death
after acute MI is commonly related to a reinfarction or recurrent acute
ischemic events, whereas in the latter category, a primary
arrhythmic event and progressive heart failure are the most probable
mechanisms of death.23
Fractal Analysis of R-R Interval Dynamics and
Death
Analysis methods derived from nonlinear dynamics, based on
chaos theory and fractal mathematics, have opened a new approach for
the study and understanding of the characteristics of dynamic
phenomena.24 HR time series in healthy subjects are
fractal-like, because they display self-similar (scale-invariant)
fluctuations over a wide range of time scales.9 25 In the
detrended fluctuation analysis method used here, the
fractal-like correlation properties of R-R interval dynamics are
quantified in short and intermediate time scales (ie, from seconds to
minutes) over a 24-hour period.5 13 14 This
analysis method differs from the traditional measures of HR
variability, because it does not measure the magnitude of variability
but rather the distribution of spectral characteristics at various
frequencies and other features in HR behavior that cannot be detected
through methods based on moment statistics.
The short-term fractal scaling exponent 1
proved to be the most powerful predictor of death compared with the
other HR variability measures, and it clearly added to the prognostic
value of both nonspectral and spectral measures in the present
population. Of note, short-term scaling exponent analyzed from
the real R-R interval data without exclusion of the premature beats
performed even better as a predictor than that analyzed after
editing for premature beats. A reduction in the short-term scaling
exponent reflects a loss of the short-term correlation properties of
R-R intervals. From a dynamic point of view, this observation supports
the previous speculations on the meaning and significance of
fractal-like R-R interval behavior for the maintenance of
normal cardiovascular function.24
A specific abnormality in cardiovascular neural regulation may explain an increase in the randomness of HR behavior and its association with a risk of dying. Sympathoexcitation is one of the potential mechanisms responsible for this abnormality. Recent observations have shown that norepinephrine infusion may cause similar alterations in HR behavior26 as that observed here in association with a reduced short-term scaling exponent. Complex R-R interval dynamics have also been shown to be associated with high levels of norepinephrine in patients with heart failure.27 Traditional analysis methods are able to reveal reduction in overall variability but not the other abnormalities of HR behavior caused by sympathoexcitation.
Study Limitations
The purpose of the present study was to examine the prognostic
value of various HR variability measures of 24-hour recordings
during normal "free-running" conditions, with recognition of the
potential confounding effects of nonstationarities due to
irregularities in breathing patterns, physical activity, and other
factors. Because standardized conditions were not used, in this study
we were not able to compare the prognostic power of fractal and
spectral measures of HR variability analyzed in strictly
controlled conditions. Uncontrolled conditions may underestimate the
predictive power of spectral measures of HR variability, which are
highly sensitive to irregularities in breathing patterns and other
nonstationarities.
Conclusions
The results show that the analysis of short-term fractal
correlation properties of HR dynamics has significant prognostic value
independent of the clinical risk factors and that it significantly adds
to the prognostic value of traditional HR variability analysis.
Short-term scaling exponent can be easily analyzed from
ambulatory ECG recordings without time-consuming preprocessing
and editing of the real R-R interval data, which may have practical
implications for risk stratification. Prospective studies in other
post-MI populations may be necessary to confirm these findings, and
experimental studies are necessary to confirm the mechanisms behind the
increase in the randomness of short-term R-R interval dynamics.
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Acknowledgments |
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The DIAMOND study was sponsored by Pfizer Pharmaceutical. This work was also supported by grants from the Finnish Foundation for Cardiovascular Research under a contract with the Finnish Life and Pension Insurance Companies, Helsinki, Finland; the National Aeronautics and Space Administration (Washington, DC); and the G. Harold and Leyla Y. Matters Charitable Foundation (Mt Kisco, NY).
Received June 11, 1999; revision received August 9, 1999; accepted August 16, 1999.
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A. J. Hautala, T. H. Makikallio, A. Kiviniemi, R. T. Laukkanen, S. Nissila, H. V. Huikuri, and M. P. Tulppo Cardiovascular autonomic function correlates with the response to aerobic training in healthy sedentary subjects Am J Physiol Heart Circ Physiol, October 1, 2003; 285(4): H1747 - H1752. [Abstract] [Full Text] [PDF]
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P. A. Lanfranchi and V. K Somers Arterial baroreflex function and cardiovascular variability: interactions and implications Am J Physiol Regulatory Integrative Comp Physiol, October 1, 2002; 283(4): R815 - R826. [Abstract] [Full Text] [PDF]
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