Fractal analysis of heart rate variability and mortality after an acute myocardial infarction.

Abstract

The recently developed fractal analysis of heart rate (HR) variability has been suggested to provide prognostic information about patients with heart failure. This prospective multicenter study was designed to assess the prognostic significance of fractal and traditional HR variability parameters in a large, consecutive series of survivors of an acute myocardial infarction (AMI). A consecutive series of 697 patients were recruited to participate 2 to 7 days after an AMI in 3 Nordic university hospitals. The conventional time-domain and spectral parameters and the newer fractal scaling indexes of HR variability were analyzed from 24-hour RR interval recordings. During the mean follow-up of 18.4 +/- 6.5 months, 49 patients (7.0%) died. Of all the risk variables, a reduced short-term fractal scaling exponent (alpha(1) <0.65), measured by detrended fluctuation analysis, was the most powerful predictor of mortality (univariate relative risk 5.05, 95% confidence intervals [CI] 2.87 to 8.89, p <0.001). A low scaling exponent alpha(1) predicted death in the patients with and without depressed left ventricular function (p <0.001 and p <0.01, respectively). Several other HR variability parameters also predicted mortality in univariate analyses, but in a multivariate analysis after adjustments for clinical variables and left ventricular ejection fraction, alpha(1) was the most significant independent HR variability index that predicted subsequent mortality (relative risk 3.90, 95% CI 2.03 to 7.49, p <0.001). Short-term fractal scaling analysis of HR variability is a powerful predictor of mortality among patients surviving an acute myocardial infarction.

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Fractal Analysis of Heart Rate Variability
and Mortality After an Acute
Myocardial Infarction
Jari M. Tapanainen, MD, Poul Erik Bloch Thomsen, MD, PhD, Lars Køber, MD, PhD,
Christian Torp-Pedersen, MD, PhD, Timo H. Ma ¨kikallio, MD, PhD, Aino-Maija Still, MD,
Kai S. Lindgren, MD, and Heikki V. Huikuri, MD, PhD
The recently developed fractal analysis of heart rate (HR)
variability has been suggested to provide prognostic
information about patients with heart failure. This pro-
spective multicenter study was designed to assess the
prognostic significance of fractal and traditional HR vari-
ability parameters in a large, consecutive series of sur-
vivors of an acute myocardial infarction (AMI). A con-
secutive series of 697 patients were recruited to
participate 2 to 7 days after an AMI in 3 Nordic univer-
sity hospitals. The conventional time-domain and spec-
tral parameters and the newer fractal scaling indexes of
HR variability were analyzed from 24-hour RR interval
recordings. During the mean follow-up of 18.4 ? 6.5
months, 49 patients (7.0%) died. Of all the risk vari-
ables, a reduced short-term fractal scaling exponent (?1
<0.65), measured by detrended fluctuation analysis,
F
mortality in various patient groups. In selected patient
populations with depressed left ventricular function
and/or heart failure, the decreased short-term fractal
scaling exponent (?1), an index of qualitative fluctu-
ation patterns of HR, has been shown to be a strong
predictor of cardiac and total mortality.1–4So far, the
value of fractal scaling analysis has not been docu-
mented in a consecutive series of post-acute myocar-
dial infarction (AMI) patients. This prospective study
was designed to assess the prognostic significance of
fractal analysis of HR variability in a large sample size
of consecutive patients who survived an AMI. The
was the most powerful predictor of mortality (univariate
relative risk 5.05, 95% confidence intervals [CI] 2.87 to
8.89, p <0.001). A low scaling exponent ?1predicted
death in the patients with and without depressed left
ventricular function (p <0.001 and p <0.01, respective-
ly). Several other HR variability parameters also pre-
dicted mortality in univariate analyses, but in a multi-
variate analysis after adjustments for clinical variables
and left ventricular ejection fraction, ?1was the most
significant independent HR variability index that pre-
dicted subsequent mortality (relative risk 3.90, 95% CI
2.03 to 7.49, p <0.001). Short-term fractal scaling anal-
ysis of HR variability is a powerful predictor of mortality
amongpatientssurviving
infarction.
?2002 by Excerpta Medica, Inc.
(Am J Cardiol 2002;90:347–352)
anacute myocardial
ractal analysis of heart rate (HR) variability has
been used as a new approach to evaluate the risk of
prognostic value of various indexes of HR variability
was compared with various other risk factors.
METHODS
Study population: A consecutive series of 806 pa-
tients were screened in 3 centers (Gentofte and Glostrup
Hospitals, Copenhagen, Denmark; and Oulu University
Hospital, Oulu, Finland) as part of the Nordic implant-
able cardioverter-defibrillator pilot study. This pilot
study aimed to assess the predictive power of HR vari-
ability and left ventricular function as predictors of mor-
tality. The results, including implantation of cardio-
verter-defibrillators in 33 patients, have been previously
reported.5The patients were recruited to participate in
the study during the first 7 days after an AMI. The
diagnosis of AMI was based on an elevation of myocar-
dial enzymes up to ?2 times the upper limit of normal
that could not be attributed to any other condition, and 1
or 2 of the following parameters: (1) chest pain or dys-
pnea lasting for ?30 minutes, and (2) ischemic electro-
cardiographic changes on admission or any later change
in the electrocardiogram caused by AMI. The exclusion
criteria were advanced age (?75 years), unstable angina
atrecruitment,dementia,alcoholism,drugabuse,ornon-
sinus rhythm on the electrocardiogram, or any other
condition that could impair the subject’s capacity for
informed consent. Patients who underwent coronary by-
pass surgery before measurements or were not dis-
charged alive from the hospital were not included in the
analysis. The study protocol was approved by the ethical
From the Division of Cardiology, Department of Internal Medicine,
University of Oulu and Oulu University Hospital, Oulu, Finland; De-
partment of Cardiology, Gentofte University Hospital, Copenhagen,
Denmark; and Medical Department B, Division of Cardiology, Rig-
shospitalet, University of Copenhagen, Copenhagen, Denmark. This
study was supported by grants from the Polar Electro, Co. Ltd., Oulu,
Finland; the Finnish Foundation for Cardiovascular Research; Astra-
Zeneca Oy, Finland; and Medical Council of the Finnish Academy of
Science, Helsinki, Finland. The Nordic ICD Pilot Study was supported
by grants and devices provided by Medtronic, Europe S.A.,
Tolochenaz, Switzerland and Guidant/CPI Corp., Europe NV/SA,
Diegem, Belgium. Manuscript received January 2, 2002; revised
manuscript received and accepted April 17, 2002.
Address for reprints: Heikki V. Huikuri, MD, Division of Cardiol-
ogy, Department of Internal Medicine, Oulu University Hospital,
P.O.Box 20, (Kajaanintie 50) FIN-90029 Oulu, Finland. E-mail:
Heikki.Huikuri@oulu.fi.
347
©2002 by Excerpta Medica, Inc. All rights reserved.
The American Journal of Cardiology Vol. 90 August 15, 2002
0002-9149/02/$–see front matter
PII S0002-9149(02)02488-8

Page 2

committees of the institutions, and all the patients gave
informed consent.
Risk variables: Left ventricular systolic function
was measured with 2-dimensional echocardiography 2
to 7 days after the AMI. Wall motion index, an esti-
mate of the left ventricular ejection fraction, was mea-
sured by a previously described method.6,7A 24-hour
RR interval recording was carried out with a portable
RR interval recorder (Polar Electro Co Ltd., Kempele,
Finland) with a sampling frequency of 1,000 Hz8–10
between days 5 and 14. All the RR interval ta-
chograms went through a detailed manual editing pro-
cess as previously described.11,12For fractal scaling
analysis, this was performed in 2
steps: in the first phase, only the ar-
tifacts were edited off the recording
(analysis of “unedited data”); the
second analysis was performed on
the data including only sinus beats
(“edited data”). Recordings with
?18 hours of data or ?85% of qual-
ified sinus beats were excluded. All
the HR variability analyses were per-
formed in the core laboratory, Oulu
University, which has extended ex-
perience of RR interval editing and
analysis.11–13
The time- and frequency-domain
analyses of HR variability were per-
formed according to the recommen-
dation of the task force.14The SD of
consecutive RR intervals (SDNN)
was chosen as a time-domain index
of HR variability. The power spec-
trum of HR variability was measured
using fast-Fourier transform analysis
in 4 frequency bands: ?0.0033 Hz (ultra low fre-
quency, ULF), 0.0033 to 0.04 Hz (very low frequency,
VLF), 0.04 to 0.15 Hz (low frequency, LF), and 0.15
to 0.40 Hz (high frequency, HF). ULF and VLF com-
ponents were computed over the entire recording in-
terval. LF and HF components were computed from
segments of 512 RR intervals. LF/HF ratio was cal-
culated as the ratio of LF power (in square millisec-
onds) to HF power (in square milliseconds). For long-
term fluctuations, the scaling exponent ? was com-
puted to assess the power-law relation of HR
variability as previously described.15,16
For short- and intermediate-term scaling properties
TABLE 1 Clinical Patient Characteristics
All Patients (n ? 697) Alive (n ? 648) Dead (n ? 49)
Men/women
Age (yrs, mean ? SD)
Systemic hypertension
Diabetes mellitus
Previous myocardial infarction
Non–Q-wave myocardial infarction?
Anterior wall myocardial infarction¶
Thrombolytic therapy or primary coronary angioplasty
Left ventricular systolic function
Wall motion index (mean ? SD)
Ejection fraction (%) (mean ? SD)#
NYHA class at discharge**
I–II
III–IV
? blockers
ACE inhibitors or angiotensinogen II
receptor antagonists
521/176 (75%/25%)
61.2 ? 10.1
300 (44%)
135 (20%)
139 (20%)
297 (44%)
301 (45%)
329 (50%)
486/162 (75%/25%)§
60.8 ? 10.1‡
272/367 (43%)*
119/518 (19%)*
122/520 (19%)†
267/340 (44%)†
271/290 (48%)†
317/312 (50%)‡
35/14 (71%/29%)
67.4 ? 7.9
28/21 (58%)
16/33 (33%)
17/32 (35%)
30/17 (64%)
30/11 (73%)
12/37 (25%)
1.53 ? 0.33
45.9 ? 9.9
1.55 ? 0.32‡
46.5 ? 9.6
1.33 ? 0.34
39.9 ? 10.2
534 (89%)
67 (11%)
559 (84%)
506 (91%)‡
52 (9%)
522 (85%)§
28 (65%)
13 (35%)
37 (79%)
272 (41%)
8 (1%)
246 (40%)*
7 (1%)§
26 (55%)
1 (2%) Amiodarone
*p ?0.05;†p ?0.01;‡p ?0.001;§p ? NS.
?Number of infarctions of indeterminate site (67).
¶Number of infarctions of indeterminate type (21).
#Ejection fraction calculated from wall motion index by multiplying with 30.
**New York Heart Association (NYHA) class was not assessed in all patients in 1 of the participating hospitals (data on 96 patients are therefore missing).
ACE ? angiotensin-converting enzyme.
TABLE 2 Various Heart Rate (HR) Variability Parameters in the Patient Groups
Divided by Survival
All Patients
(n ? 697)
Alive
(n ? 648)
Dead
(n ? 49)
Nonspectral HR variability measures
Mean RR interval
SDNN
Spectral measures
ULF ln (ms2)
VLF ln (ms2)
LF ln (ms2)
HF ln (ms2)
LF/HF ratio
Fractal measures
?1
?1(edited)
?2
?2(edited)
?
898 ? 143
94.5 ? 32.0
901 ? 144*
95.6 ? 32.1‡
859 ? 123
79.4 ? 25.7
8.6 ? 0.7
6.5 ? 0.9
5.4 ? 1.2
4.7 ? 1.1
2.7 ? 2.1
8.6 ? 0.7*
6.5 ? 0.9‡
5.5 ? 1.2‡
4.7 ? 1.1§
2.7 ? 2.1*
8.4 ? 0.7
5.8 ? 1.0
4.6 ? 1.2
4.4 ? 1.2
1.9 ? 2.1
1.00 ? 0.31
1.25 ? 0.24
1.08 ? 0.14
1.15 ? 0.11
?1.28 ? 0.55 ?1.27 ? 0.56‡?1.44 ? 0.24
1.02 ? 0.30‡
1.26 ? 0.23‡
1.08 ? 0.13‡
1.14 ? 0.10§
0.76 ? 0.33
1.10 ? 0.32
1.01 ? 0.21
1.16 ? 0.14
*p ?0.05;†p ? 0.01;‡p ?0.001;§p ? NS.
Edited indicates analysis after editing for premature beats.
? ? slope of the power-law regression line.
348
THE AMERICAN JOURNAL OF CARDIOLOGY?
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of HR variability, the detrended fluctuation analysis
(DFA) technique was used. This method detects the
presence or absence of fractal-like scaling properties
and has been validated for time series data. The details
of this method have been previously described.17–19
The correlation properties were measured both for
short-term (?11 beats, ?1) and intermediate-term
(?11 beats, ?2) fluctuations of RR interval data.17–19
Follow-up and end points: The pa-
tients were followed for up to 2 years
after the AMI, and they were rou-
tinely contacted via telephone at 6,
12, and 24 months after the AMI.
The end point was all-cause mortal-
ity.
Statistical analysis: Data were an-
alyzed using SPSS software (SPSS
10.0.1, SPSS Inc., Chicago, Illinois).
Univariate comparisons of the base-
line characteristics between the sub-
jects who died and the survivors
were performed with the chi-square
test for categorical variables and
with the 2-sample t test for continu-
ous variables. The cut-off points for
all predictive variables were deter-
mined by searching the value that
maximized the statistically most sig-
nificant hazard ratio obtained from
the Cox regression analysis. The
analysis was performed in fifth per-
centile steps below the median for
each variable. Relative risk and 95%
confidence intervals were calculated
for each categorical variable as a pre-
dictor of all-cause mortality in the
Cox regression model. To estimate
the independent power of the vari-
ables in predicting mortality, the test
results that had a univariate associa-
tion with all-cause mortality (p ?0.05) were included
in the Cox proportional hazards regression analyses
after adjusting for clinical variables and wall motion
index. Kaplan-Meier estimates of the distribution of
times from baseline to death were computed, and
log-rank analysis was performed to compare the sur-
vival curves between the groups. A p value ?0.05 was
considered significant. In addition, receiver-operating
characteristic curves showing sensitivity as a function
of the complement of specificity were generated to
compare the predictive power of various prognostic
variables.
RESULTS
Of the screened population of 806, 697 patients
with analyzable HR variability measurements were
eligible for the study. The most common reason for a
missing HR variability result was a technically unsuc-
cessful recording (with artifacts or ectopy). Patient
characteristics are listed in Table 1. By the mean
follow-up of 18.4 ? 6.5 months (4 to 24), 49 patients
(7.0%) had died and 648 (93%) were still alive.
Univariateandmultivariatepredictorsofmortality:Table
1 lists the prevalence of clinical features and Table 2
lists the various HR variability parameters in the sur-
vivors and those who died. The relative univariate risk
of the clinical variables and the test results as predic-
tors of all-cause mortality are listed in Table 3. Con-
ventional clinical risk factors were associated with an
unfavorable prognosis during the follow-up. Most of
TABLE 3 Predictors of All-cause Mortality in Univariate and Multivariate Analysis
Relative Risk95% CIp Value
Univariate analysis
Age ?70 yrs
Diabetes mellitus
Previous myocardial infarction
No reperfusion therapy
Anterior wall myocardial infarction
Non–Q-wave myocardial infarction
NYHA class III-IV
Wall motion index ?1.5
Mean RR interval ?815 ms
SDNN ?65
ULF (ln) ?8.45
VLF (ln) ?5.30
LF (ln) ?3.85
LF/HF ratio ?1.45
?1?0.65
?1(edited) ?1.00
?2?1.05
? ??1.55
Multivariate analysis
Age ?70 yrs
NYHA class III-IV
Wall motion index ?1.5
ULF (ln) ?8.45
VLF (ln) ?5.30
LF (ln) ?3.85
LF/HF ratio ?1.45
?1?0.65
?1(edited) ?1.00
? ??1.55
3.16
1.96
2.08
3.08
2.86
2.25
4.69
3.69
2.14
2.37
2.37
3.70
3.50
3.75
5.05
4.09
2.70
3.09
1.80–5.53
1.08–3.54
1.16–3.73
1.61–5.88
1.44–5.69
1.24–4.06
2.51–8.78
2.00–6.79
1.22–3.76
1.32–4.28
1.34–4.18
1.99–6.87
1.85–6.59
2.11–6.67
2.87–8.89
2.31–7.23
1.54–4.74
1.66–5.74
0.000
0.027
0.014
0.001
0.003
0.007
0.000
0.000
0.008
0.004
0.003
0.000
0.000
0.000
0.000
0.000
0.001
0.000
2.47
3.66
2.46
2.05
2.51
2.20
3.49
3.90
2.89
2.21
1.31–4.64
1.88–7.13
1.30–4.65
1.06–3.98
1.23–5.13
1.08–4.48
1.76–6.90
2.03–7.49
1.49–5.63
1.11–4.44
0.005
0.000
0.006
0.033
0.012
0.029
0.000
0.000
0.002
0.025
CI ? Confidence interval; other abbreviations as in Table 1.
FIGURE 1. Kaplan-Meier survival curves for various HR variabil-
ity parameters. (A) SDNN. (B) LF/HF ratio spectral power (loga-
rithmic conversion). (C) ?1. (D) ? ? 1/f power-law slope.
CORONARY ARTERY DISEASE/FRACTAL ANALYSIS OF HR VARIABILITY AFTER AMI
349

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the HR variability parameters tested were associated
with increased all-cause mortality, the reduced short-
term scaling exponent ?1was the most powerful uni-
variate predictor. Its predictive value was higher when
measured from unedited HR variability data instead of
fully edited data. The survival curves obtained from
the different HR variability analyses are shown in
Figure 1. Of the several HR variability parameters
independently predicting all-cause mortality in multi-
variate analysis, the reduced short-term fractal scaling
exponent ?1measured from unedited data remained
the most powerful risk marker, followed by a de-
creased LF/HF ratio (Table 3).
Accuracy of HR variability parameters as predictors
of mortality: The sensitivity, specificity, and predictive
accuracy of various risk indicators as predictors of
all-cause mortality are listed in Table 4. Among the
different HR variability measures, a reduced short-
term scaling exponent ?1had the highest positive
predictive accuracy. The patients were divided into 2
groups based on their left ventricular systolic function,
and the predictive power of the short-term scaling
exponent was analyzed in each group. Reduced values
of ?1predicted a significantly increased risk of mor-
tality in both groups (Figure 2).
DISCUSSION
The main finding of this prospective multicenter
study was that fractal analysis of HR variability pro-
vides prognostic information beyond that attainable
from the clinical variables and the degree of left
ventricular dysfunction in a consecutive series of post-
AMI patients. The predictive power of the short-term
fractal scaling exponent surpassed the traditional time-
and frequency-domain indexes of HR variability in
risk stratification. It was of particular note that the
reduced short-term scaling exponent also predicted
mortality in patients without significant impairment of
left ventricular function.
Traditional HR variability parameters as predictors of
mortality: Numerous previous studies assessing the
prognostic power of HR variability indexes, such as
SDNN and various spectral components of HR vari-
ability, have shown that these parameters predict mor-
tality when measured in the convalescent phase after
an AMI.20–26Concurrent with these results, most of
the conventional HR variability parameters used here
were also able to predict mortality in the univariate
analysis, but after adjustment for the clinical variables
and left ventricular function, their predictive power
was somewhat lower than that reported in previous
studies.
There are some salient differences between the
present and previous observational studies that may
partly explain the substantially lower independent pre-
dictive power of the traditional HR variability indexes
in this study. The original studies showing the asso-
ciation between the reduced HR variability and mor-
tality rates are from the prethrombolytic era.20,21
Since the early 1980s, both the medical and invasive
treatments of post-AMI patients have significantly
changed, because ? blockers, angiotensin-converting
enzyme inhibitors, and revascularization are now used
more frequently, resulting in much lower mortality
figures. More recent studies, such as the Automatic
Tone and Reflexes After Myocardial Infarction
(ATRAMI) study and the study assessing postectopic
turbulence, may also suffer from obvious selection
bias, because they did usually include consecutive
post-AMI patient populations.24–27
FIGURE 2. Kaplan-Meier survival curves of patients divided into
different subgroups according to ?1and wall motion index
(WMI).
TABLE 4 Sensitivity, Specificity, and Predictive Accuracy of Abnormal Values of Various Risk Variables
Variable
Below Cut-off Point
n, %Sensitivity Specificity PPANPA
Area Under
ROC Curve
Wall motion index ?1.5
RR interval ?815 ms
SDNN ?65
ULF (ln) ?8.45
VLF (ln) ?5.30
LF (ln) ?3.85
LF/HF ratio ?1.45
?1?0.65
?1(edited) ?1.00
?2?1.05
? ??1.55
256 (37%)
205 (30%)
132 (19%)
271 (39%)
69 (10%)
69 (10%)
207 (30%)
93 (14%)
99 (14%)
209 (30%)
80 (12%)
68%
45%
35%
59%
29%
27%
61%
43%
41%
53%
29%
65%
72%
82%
62%
91%
91%
73%
89%
88%
71%
90%
13%
11%
13%
11%
20%
19%
15%
23%
20%
12%
18%
97%
94%
94%
95%
94%
94%
96%
95%
95%
95%
94%
0.695‡
0.588*
0.649†
0.619†
0.698‡
0.700‡
0.678‡
0.716‡
0.644†
0.629†
0.657‡
*p ?0.05;†p ?0.01;‡p ?0.001.
NPA ? negative predictive accuracy; PPA ? positive predictive accuracy; ROC ? receiver-operating curve.
350
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Fractal analysis of HR variability and mortality: The
reduced short-term fractal scaling exponent was initial-
ly observed in patients with congestive heart failure.17,27
In subsequent studies, the reduced scaling exponent
was found to provide prognostic information among
patients with depressed left ventricular function.1–4The
presentfindingsbroadentheapplicationoftheshort-term
scaling exponent as a risk stratifier of mortality beyond
the patients with impaired left ventricular function to
more general post-AMI populations. Further work will
show if postectopic turbulence analysis of HR variability
will yield even more powerful prognostic information in
addition to fractal analysis techniques.Scaling expo-
nents obtained by detrended fluctuation analysis quan-
tify the relations of HR fluctuations at different scales.
Low exponent values correspond to dynamics where
the magnitude of beat-to-beat HR variability is close
to the magnitude of longer term variability. In con-
trast, high exponent values correspond to dynamics
where the magnitude of long-term variability is sub-
stantially higher than beat-to-beat variability. Expo-
nent values correlate with normalized spectral mea-
sures in controlled situations, and the LF/HF spectral
ratio is closely related to the short-term fractal scaling
exponent in controlled external contexts with a fixed
respiratory rate.29However, the correlation is weaker
in “free-running” ambulatory conditions, because
fractal analysis provides precise information on the
scaling properties of HR fluctuations over highly seg-
mented time windows, whereas conventionally com-
puted spectral measures only vaguely represent HR
fluctuations in predetermined time windows.30An ad-
vantage of fractal analysis over the traditional analysis
techniques is that scaling exponents can also be ana-
lyzed without removing or replacing the RR intervals
caused by ectopic beats.
The physiologic background of abnormal fractal cor-
relation properties associated with an increased risk of
dying has not been fully established. However, there is
increasing evidence to support the role of sympathetic
activation behind this impairment. High norepinephrine
levels, indicative of sympathoexcitation, have been ob-
served to be related to random RR interval dynamics in
patients with heart failure.31Furthermore, intravenous
infusion of norepinephrine has been shown to lead to the
reduced short-term fractal scaling exponent.31These ob-
servations suggest that an increase in the randomness of
short-term HR behavior may be a specific marker of
neurohumoral and sympathetic activation and therefore
is also associated with an increased risk for adverse
cardiovascular events.
Acknowledgment: The investigators wish to ex-
press their sincere gratitude to Marja Hietaniemi, RN,
Pirkko Huikuri, RN, Pa ¨ivi Karjalainen, RN, Anne
Lehtinen, and Mirja Salo, BSc.
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