Download Spectral characteristics of ventricular response to atrial fibrillation

Spectral characteristics of ventricular
response to atrial fibrillation
JUNICHIRO HAYANO,1 FUMIYASU YAMASAKI,2 SEIICHIRO SAKATA,1
AKIYOSHI OKADA,1 SEIJI MUKAI,1 AND TAKAO FUJINAMI1
1Third Department of Internal Medicine, Nagoya City University Medical School, Nagoya 467,
Japan; and 2Department of Clinical Laboratory, Kochi Medical School, Nankoku 783, Japan
heart rate variability; power spectral analysis; fractal; heart
failure
has recently been used to
characterize the nonharmonic fluctuation of heart rate
variability (4, 14) as well as to quantify its harmonic
components that reflect the autonomic modulations of
sinus node activity (19, 20). Power spectra of irregular
or noisy signals observed in dynamic systems often
show a linear downsloping pattern (called power law
relationship) when plotted as log power against log
frequency, and the absolute value of the slope of the
spectrum (spectral exponent) provides an assessment
of complexity of the systems (9, 17). The power spectrum of the nonharmonic component of heart rate
variability during sinus rhythm (SR) has been reported
to show a power law relationship with a spectral
exponent of ,1 (23, 29), suggesting its origination from
complex regulatory processes.
POWER SPECTRAL ANALYSIS
During atrial fibrillation (AF), the sinus node loses
its ability to govern the ventricular response (VR) and
the R-R intervals on electrocardiogram (ECG) show
totally nonharmonic fluctuation (6). Nevertheless, the
R-R intervals during AF and SR seem to have some
physiological characteristics in common, such as shortening in the upright position (16) and during exercise
(1, 6, 16) and circadian rhythm with a nocturnal
increase (21). The changes in the R-R interval during
AF have been thought to result mainly from autonomic
neural modulations of the electrophysiological properties of the atria and atrioventricular (AV) node (25, 26).
Therefore, power spectral analysis of the R-R interval
fluctuation during AF may provide useful information
about the dynamic properties of such regulatory processes. Thus we investigated the spectral characteristics of the 24-h R-R interval fluctuation during AF and
compared them with those during SR.
METHODS
Subjects. We evaluated 24-h ambulatory ECGs in 45 patients with chronic AF [31 males, 14 females; mean age (6
SD), 66 6 12 yr, age range 42–84 yr]. Data were excluded if
the ambulatory ECG showed artifacts or noises during .5%
of the total monitoring period, frequent ventricular ectopic
beats accounting for .5% of total recorded beats, bundlebranch blocks, or atrial tachyarrhythmias other than AF. The
duration of chronic AF ranged from 10 mo to .20 yr (Table 1).
No patient had cardiomyopathy. All but 3 patients were
receiving cardiovascular medications, and 32 of them were
receiving AV node-blocking drugs (digoxin and calcium antagonists). No patients were receiving b-adrenergic blockers or
class Ia, Ic, or III antiarrhythmic drugs. Sixteen patients had
chronic heart failure (CHF) of New York Heart Association
(NYHA) class II or III, although none of them was in NYHA
class IV.
We also evaluated 24-h ambulatory ECGs in 30 healthy
age-matched subjects (25 males, 5 females; mean age 65 6 12
yr, age range 44–84 yr). None of them had a medical history of
chronic diseases or was taking any medications for 2 wk
before the study. The ambulatory ECG in all of the healthy
subjects showed normal SR during .95% of the total monitoring period.
All subjects gave their written informed consent. The
procedures of this study were performed in accordance with
the Ethical Guidelines of Nagoya City University Medical
School.
Data collection. Ambulatory ECGs were recorded with a
portable tape recorder (DMC-3253, Nihon Koden, Tokyo,
Japan) for at least 24 h during normal daily activities. In six
AF patients, another ambulatory ECG was recorded 12–82
days [mean (6SD) 37 6 25 days] after the first recording
under similar clinical conditions (functional class and medications). The data in these six patients were used to evaluate
the reproducibility of measurements.
0363-6135/97 $5.00 Copyright r 1997 the American Physiological Society
H2811
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Hayano, Junichiro, Fumiyasu Yamasaki, Seiichiro
Sakata, Akiyoshi Okada, Seiji Mukai, and Takao Fujinami. Spectral characteristics of ventricular response to
atrial fibrillation. Am. J. Physiol. 273 (Heart Circ. Physiol.
42): H2811–H2816, 1997.—To investigate the spectral characteristics of the fluctuation in ventricular response during
atrial fibrillation (AF), R-R interval time series obtained from
ambulatory electrocardiograms were analyzed in 45 patients
with chronic AF and in 30 age-matched healthy subjects with
normal sinus rhythm (SR). Although the 24-h R-R interval
spectrum during SR showed a 1/f noise-like downsloping
linear pattern when plotted as log power against log frequency, the spectrum during AF showed an angular shape
with a breakpoint at a frequency of 0.005 6 0.002 Hz, by
which the spectrum was separated into long-term and shortterm components with different spectral characteristics. The
short-term component showed a white noise-like flat spectrum with a spectral exponent (absolute value of the regression slope) of 0.05 6 0.08 and an intercept at 1022 Hz of 4.9 6
0.3 log(ms2/Hz). The long-term component had a 1/f noise-like
spectrum with a spectral exponent of 1.26 6 0.40 and an
intercept at 1024 Hz of 7.0 6 0.3 log(ms2/Hz), which did not
differ significantly from those for the spectrum during SR in
the same frequency range [spectral exponent, 1.36 6 0.06;
intercept at 1024 Hz, 7.1 6 0.3 log(ms2/Hz)]. The R-R intervals
during AF may be a sequence of uncorrelated values over the
short term (within several minutes). Over the longer term,
however, the R-R interval fluctuation shows the long-range
negative correlation suggestive of underlying regulatory processes, and spectral characteristics indistinguishable from
those for SR suggest that the long-term fluctuations during
AF and SR may originate from similar dynamics of the
cardiovascular regulatory systems.
H2812
1/F NATURE OF ATRIAL FIBRILLATION
Table 1. Characteristics of patients with chronic
atrial fibrillation
6.2 6 4.4
16 (36)
9 (20)
3 (7)
6 (13)
25 (56)
2 (4)
3 (7)
30 (67)
9 (20)
0 (0)
10 (22)
16 (36)
7 (16)
6 (36)
2 (4)
896 6 1923
23.2 6 2.7
4.5 6 0.6
55 6 18
133 6 20
74 6 9
Values are means 6 SD or number of patients with characteristic
(no. in parenthesis 5 percentage); n 5 45 patients. AF, atrial fibrillation; NYHA, New York Heart Association; ACE, angiotensinconverting enzyme; VE, ventricular ectopic beat. * Durations longer
than 20 yr were counted as 20 yr.
The tapes were played back with a Holter ECG scanner
(DMC-4100, Nihon Koden) at a rate 240 times faster than
real time and digitized to 12-bit data at a sampling frequency
of 128 Hz. QRS complexes were detected and labeled automatically. The results of the automatic analysis were reviewed,
and any errors in R wave detection and QRS labeling were
edited manually. The labels of each QRS complex and the
preceding R-R interval were transferred to a computer workstation (HP750, Hewlett-Packard, Tokyo).
Time series analysis. The R-R interval time series was
defined as the 24-h sequence of the intervals between two
successive R waves with a normal QRS complex. For the data
during SR, to avoid the adverse effects of remaining errors in
the detection of supraventricular ectopic beats on the analysis of R-R interval fluctuation, all abrupt large changes in R-R
interval (.20% of moving average of R-R intervals) were
reviewed interactively until all errors were corrected. The
R-R interval sequences for both AF and SR data were
interpolated by a linear step function, i.e., the value of the
function between two successive R waves was assumed to be
constant at a value equal to the R-R interval, and the value
during a gap resulting from artifacts, noises, or exclusions of
ventricular or supraventricular beats (only for SR) was
considered equal to the R-R interval subsequent to the gap.
The interpolated R-R interval functions were resampled
equidistantly so that 218 regularly spaced points were sampled
(sampling interval was 329 ms). After filtering the data with a
Hanning window, we performed fast Fourier transformation.
The obtained power spectral density (PSD) was corrected for
the attenuating effects of the sampling and filtering.
Analysis of spectral characteristics. The spectral exponent
of the R-R interval power spectrum was evaluated by plotting
log PSD against log frequency. The spectral exponent was
defined as the value that satisfied the following equation
P 5 C · (1/f b)
log P 5 log C 2 b · log f
which shows that b can be estimated by linear regression of
log PSD on log frequency. We used the method of Saul et al.
(23) to avoid the effects of uneven density of spectral data
points along the log frequency axis. Briefly, the log frequency
axis was divided into 60 equally spaced bins/decade, i.e., 307
bins 0.0167 log(Hz) wide. Log PSD was averaged for each bin;
the values for bins without data points in the lower frequency
range were obtained by interpolation. Linear regression
analysis was performed for the averaged log PSD and log
frequency data of the bins within the frequency bands of
interest.
The properties of dynamic systems, when their fluctuations
show a power law spectrum, can be analyzed by comparing
the spectral exponents with those of various types of noise
seen in known dynamic systems (9, 11, 17). White noise shows
a flat power spectrum with a spectral exponent of 0. White
noise is a sequence of independent, random values uncorrelated with each other, indicating that the process is not
regulated. Brownian noise shows a steep downsloping power
law spectrum with a spectral exponent of 2. Brownian noise is
known as a random walk, in which the value at any given
instance is the result of a random shift from the previous
value and, hence, the successive differences are uncorrelated.
Brownian noise is another form of noise generated by nonregulated processes. Another type of noise, called 1/f noise, shows
a downsloping power law spectrum with a spectral exponent
of ,1. This type of noise shows long-range negative correlations in the successive differences, which cannot be generated
as an additive process of uncorrelated noise and, hence, is
generally regarded as being regulated.
Statistical analysis. The Statistical Analysis System (SAS)
program package (SAS Institute, Cary, NC) was used for
analysis. Differences in mean values were evaluated by
Student’s t-test. The relationships between spectral characteristics and clinical features of AF were evaluated by multipleregression analysis by the SAS Regression procedure with the
Stepwise selection option. Categorical variables were processed as binary data (yes 5 1 and no 5 0) and a P value
,0.15 was used as the criteria for entering and retaining
independent variables in the regression models.
The reproducibility of the parameters of spectral characteristics was evaluated by the intraclass correlation coefficient
for one-way random-effects analysis of variance defining
subjects as the random factor (24) and by the coefficient of
repeatability of Bland and Altman (5), which estimates the
limit for a true change distinguishable from random errors
between repeated measurements.
Data are presented as means 6 SD. P values ,0.05 were
considered statistically significant.
RESULTS
Power spectrum of R-R interval fluctuation during
AF and SR. Compared with the trendgrams of R-R
interval in the healthy subjects with SR, the trendgrams
in the AF patients showed a greater variability, although both groups showed circadian variation with a
nocturnal lengthening in R-R interval (Fig. 1). The
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Duration of AF, yr*
NYHA class II or more
Associated disease
None
Coronary artery disease
Systemic hypertension
Valvular disease
Hyperthyroidism
Medications
No medication
Digoxin
Calcium antagonist
b-Adrenergic blocker
ACE inhibitor
Diuretics
Vasodilator
Warfarin
Mexiletine
Holter VE, beat/day
Body mass index, kg/m2
Left atrial diameter, cm
Left ventricular ejection fraction, %
Systolic blood pressure, mmHg
Diastolic blood pressure, mmHg
where P is the PSD, f is the frequency, b is the spectral
exponent, and C is a proportionality constant (23). When the
logarithms of both sides of the equation are derived, this
equation can be rewritten as
1/F NATURE OF ATRIAL FIBRILLATION
H2813
Fig. 1. Trendgrams (top) of 24-h fluctuation of R-R interval in a representative patient with chronic atrial fibrillation (AF; A) and in a healthy man with
normal sinus rhythm (SR; B) and their
power spectra (bottom) plotted in linear scales for power spectral density
(PSD) and frequency.
long-term and short-term components, log PSD was
regressed against log frequency between 1024 and 1023
Hz and between 1022 and 1021 Hz, respectively. The
breakpoint frequency was determined as the frequency
at which the regression lines for the two components
crossed. To compare between AF and SR, the same
frequency bands of the power spectra, which were also
referred to as the long-term and short-term components, were examined in the same way.
The breakpoint frequency of the AF spectra ranged
from 0.002 to 0.008 Hz (mean 0.005 6 0.002 Hz). The
regression analysis for the long-term component revealed that the spectral characteristics (spectral exponent and intercept at 1024 Hz) for AF were comparable
to those for SR (Fig. 3), except for the explained
variance of the regression that was smaller for AF than
SR (0.83 6 0.06 vs. 0.94 6 0.02, P , 0.001). In contrast,
the analysis for the short-term component revealed
marked differences between AF and SR (Fig. 3); although the spectral exponent for SR was comparable to
the value for its long-term component, the spectral
Fig. 2. Log PSD vs. log frequency plots
of power spectra of 24-h R-R fluctuation in representative patients with AF
(A) and a healthy man with SR (B).
Vertical and horizontal axes are in logarithmic scale. Solid lines, linear regression lines of log PSD on log frequency
between 1024 and 1023 Hz and between
1022 and 1021 Hz. Vertical dashed line
in A represents estimated breakpoint
frequency separating long-term (LT)
and short-term (ST) components.
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power spectra plotted in linear scales revealed that the
R-R interval fluctuation during AF showed a flat pattern at frequencies ,0.25 Hz with no peaks such as
that observed for the power spectrum during SR. The
spectra for both AF and SR, however, showed a large
power at the lowest end of the frequency axis.
When plotted as log PSD against log frequency,
striking differences in the power spectrum between AF
and SR were observed more clearly (Fig. 2). In contrast
to the spectrum during SR, which showed a monotonous linear downsloping pattern ,1021 Hz, the spectrum during AF showed an angular shape with a
breakpoint by which the spectrum was separated into
two different structures, i.e., a linear downsloping
structure below the breakpoint and a flat horizontal
structure above the breakpoint. These two parts of the
spectrum during AF were referred to as the long-term
and short-term components, respectively.
This feature of the power spectrum was common to
all AF patients studied, and visual inspection identified
the breakpoint between 1023 and 1022 Hz in all patients. To examine the spectral characteristics of the
H2814
1/F NATURE OF ATRIAL FIBRILLATION
Fig. 3. Spectral characteristics of LT (A) and
ST (B) components of R-R interval fluctuation
in patients with chronic AF (n 5 45) and
healthy subjects with SR (n 5 30). s, Data for
individual patients or subjects; j with error
bars, means 6 SD for each group. * P , 0.05
vs. healthy subjects with SR.
Table 2. Regression analysis of spectral characteristics
of R-R interval fluctuation in AF patients by
clinical features
Dependent
Variable
Independent
Variable
LT spectral expo- Regression model
nent
Age
Body mass index
LT intercept at
Regression model
1024 Hz
Heart failure*
Valvular heart disease*
ST intercept at
Regression model
1022 Hz
Medication of
diuretics*
Heart failure*
Regression
Coefficient
0.012
0.057
20.38
0.19
R2
0.23
0.09
0.09
0.29
0.19
0.06
F
6.11
7.39
4.20
5.55
9.33
4.12
P
0.005
0.009
0.050
0.002
0.004
0.049
0.33
0.34 10.38 0.001
0.15 16.30 0.001
20.33
0.19 11.43 0.001
LT, long-term component; ST, short-term component. * Variable
processed as binary data (yes 5 1, no 5 0).
(Table 3). The intraclass correlation coefficients and
coefficients of repeatability showed excellent agreement between repeated measurements.
DISCUSSION
Major findings. We found that the power spectrum of
the 24-h fluctuation of R-R intervals during AF showed
a unique shape with a breakpoint at 0.005 6 0.002 Hz,
by which the spectrum was divided into short-term and
long-term components with different spectral characteristics. The short-term component showed a white noiselike flat spectrum, and the long-term component showed
a 1/f noise-like power law spectrum. These features
were in marked contrast to those for the power spectrum during SR, which showed a monotonous, downsloping power law relationship with no breakpoint. Interestingly, however, quantitative analysis revealed that the
spectral characteristics of the long-term component
Table 3. Reproducibility of spectral characteristics of
ventricular response fluctuation in AF patients who
underwent repeated measurements
Time 1
Time 2
Breakpoint
frequency,
Hz
0.0039 6 0.0017 0.0039 6 0.0008
LT spectral
exponent
1.41 6 0.16
1.44 6 0.09
LT intercept
24
at 10 Hz,
log(ms2/Hz)
7.2 6 0.3
7.2 6 0.3
ST spectral
exponent
20.01 6 0.04
20.00 6 0.05
ST intercept
at 1022 Hz,
log(ms2/Hz)
4.9 6 0.2
4.9 6 0.2
ICC
P*
CR
0.999 0.001 0.0021
0.762 0.015 0.19
0.986 0.001 0.1
0.999 0.001 0.06
0.954 0.001 0.2
Time 1, time 2 values are means 6 SD. ICC, intraclass correlation
coefficient; CR, coefficient of repeatability; LT, long-term component;
ST, short-term component. * Significance of intraclass correlation
coefficient (n 5 6 patients).
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exponent for AF was almost zero, indicating that the
PSD was frequency independent. The explained variance for the short-term component during AF was
markedly smaller than that during SR (0.13 6 0.10 and
0.75 6 0.08, respectively; P , 0.001).
Relationships to clinical features of AF. In the AF
patients, the spectral characteristics, except the spectral exponent of the short-term component, showed
considerable interindividual variations (Fig. 3). To examine whether these variations are explained by differences in clinical features, multiple-regression analysis
was performed (Table 2). The regression models showed
that the spectral exponent of the long-term component
was associated with age and body mass index, whereas
its intercept was associated with heart failure and
valvular heart disease. The intercept of the short-term
component was associated with medication with diuretics and heart failure.
Reproducibility of measures. There was no significant
difference in the mean values of the spectral characteristics measured at different times in the six AF patients
1/F NATURE OF ATRIAL FIBRILLATION
of VR fluctuation in the earlier studies. The white
noise-like feature of the short-term component indicates that R-R intervals during AF are uncorrelated in
this frequency range (.0.005 6 0.002 Hz) and that the
mechanisms for VR irregularity, which may include
irregular atrial activity and resultant concealed conduction in the AV node, have no frequency dependency at
least within this frequency range. The power law
spectrum with a spectral exponent of 1.26 6 0.40
observed for the long-term component indicates that
R-R intervals during AF show long-range negative
correlation and suggests that the fluctuation may be
generated by regulatory processes (9, 11, 17). The
power law relationship that stretched close to the
lowest end of frequency (a cycle length of nearly 1 day)
suggests that the long-term component may include the
diurnal variations in R-R interval, such as those related to the circadian rhythm of body temperature,
sleep-wake cycle, and physical and mental activities.
One might speculate that the breakpoint frequency
may represent the upper frequency limit of the regulation of R-R interval during AF. This is unlikely, however, because Nagayoshi et al. (16) reported that the
average R-R interval during AF showed rapid postural
changes, with the shortest R-R interval occurring 15–
20 s after active standing, and it also showed shortening during Valsalva strain and immediately after the
beginning of handgrip. Thus it is more likely that above
the breakpoint frequency, the irregularity in VR fluctuation dominates over its regulatory changes.
Relationships to R-R interval fluctuation during SR.
Although the spectral characteristics for the short-term
component differed strikingly between AF and SR,
those for the long-term component were quite similar.
This observation suggests that despite the different
peripheral mechanisms determining R-R intervals between AF and SR, the dynamics of the regulatory
process underlying the long-term component may be
common. In an experiment with anesthetized dogs,
O’Toole et al. (18) observed parallel chronotropic and
dromotropic responses in the sinoatrial rate and anterograde AV conduction during the baroreflex modulations
of the cardiac vagal outflow. They also observed that the
dromotropic response of the AV conduction was independently regulated by the vagus when the chronotropic
response was prevented with atrial pacing. The longterm VR fluctuation during AF is likely to be mediated
through the modulations of electrophysiological properties in the atrium and the AV node by the autonomic
nervous (16) and endocrine (3) systems; however, it
may be speculated that the dynamics observed in the
long-term component during both AF and SR may
originate from the dynamics of the central nervous
controls of these regulatory systems.
Relationships to clinical features. The regression
models for the spectral characteristics also seem to
provide insights into the underlying mechanisms. In
the regression model for the intercept of the short-term
component, medication with diuretics and heart failure
showed positive and negative contributions, respectively. These might be attributable to shortening in
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during AF were indistinguishable from those during SR
in the same frequency range. These observations indicate that the dynamics of the processes generating the
R-R interval fluctuation during AF differ between the
short-term and long-term components and that, as to
the long-term component, the fluctuations in R-R interval during AF and SR may originate from similar
dynamics of cardiovascular regulation.
Earlier studies on VR fluctuation during AF. Since
the beginning of this century, absolute ventricular
arrhythmia has been recognized as an important characteristic of AF (22), and the mechanism for the irregularity in VR to AF has been a focus of electrophysiological studies (13, 15, 28). In 1970, Bootsma et al. (6) found
that the autocorrelogram calculated from 2,000 consecutive R-R intervals showed a flat shape and concluded
that the VR to AF is random. On the other hand,
long-term observations have reported different features of VR to AF. An increase in mean VR rate has been
observed during exercise and in the upright posture (1,
6, 16). Raeder (21) reported a significant circadian
rhythm in the diurnal variations of average R-R interval during AF, and he also reported that the circadian
rhythm parameters (amplitude and phase) and the
two-harmonic regression coefficients were comparable
to those in subjects with SR. These earlier observations
seem to be in line with our present findings and are
supportive for the differential properties between shortterm and long-term fluctuations of VR to AF.
Earlier studies also reported different mechanisms
for the irregularity of VR and the variations in mean
VR rate. VR irregularity is believed to originate from
irregularity in the atrial activity during AF (6). Although some controversy remains concerning the
mechanisms for the transmission of the irregular atrial
activity to VR (12, 27), much electrophysiological evidence supports the role of concealed conduction within
the AV node (8, 13, 15, 28), i.e., an interaction between
rapid and random inputs to the AV node from the
adjacent atrial tissue leads to summation and cancellation of wave fronts, thereby creating a high level of
disorganization of the penetrating impulses. The determinants of mean VR rate during AF have been a focus
of clinical studies. Such studies reported an important
role of AV nodal conductivity and refractoriness (1, 25)
and/or atrial refractoriness, which reduces the atrial f
wave frequency, thereby decreasing the degree of concealed conduction within the AV node (26).
Although the VR irregularity and the variations in
mean VR rate were investigated separately in these
earlier studies, the distinction between these two aspects of VR fluctuation seems unclear. Consequently,
the ranges of components or frequencies of VR fluctuation that correspond to the reported properties and
mechanisms have been undetermined.
Spectral characteristics of VR fluctuation during AF.
Using 24-h power spectral analysis, we demonstrated
that the R-R interval fluctuation during AF can be
separated into short-term and long-term components
with different spectral characteristics that seem to
correspond to the properties of the two different aspects
H2815
H2816
1/F NATURE OF ATRIAL FIBRILLATION
Address for reprint requests: J. Hayano, Third Dept. of Internal
Medicine, Nagoya City Univ. Medical School, 1 Kawasumi, Mizuhocho Mizuho-ku, Nagoya 467, Japan.
Received 12 May 1997; accepted in final form 2 September 1997.
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atrial refractory period by decreased serum potassium
level with diuretics and to its lengthening by reduced
vagal activity in heart failure (2, 10), because the
shortening in atrial refractoriness increases fibrillatory
activity, thereby increasing the irregularity of VR interval (2, 8, 12). Age of the patients seemed contributory to
increase in the spectral exponent of the long-term
component. This seems consistent with the finding of
Lipsitz et al. (14), who reported an age-related increase
in the spectral exponent of R-R interval fluctuation
during SR, which may be attributable to the agerelated loss of complexity in the cardiovascular regulatory systems (9, 17). Heart failure also contributed
negatively to the intercept of the long-term component.
This effect seems attributable to the decreased diurnal
variations in neurohumoral activities in patients with
heart failure (7, 30) as well as to their restricted daily
activities.
Limitations. The patient population of this study was
heterogeneous, and patients continued to receive medication. Thus the findings concerning the relationships
between the spectral characteristics and clinical features are preliminary and need to be confirmed by more
specifically designed studies. On the other hand, despite this heterogeneous population, the unique shape
of the VR interval spectrum was commonly observed in
all AF patients studied, suggesting that the spectral
characteristics we observed may be fundamental features of chronic AF.