A new measure of acceleration of heart rate: dependence on age and comparison with
time domain conventional heart rate variability measures
Giuseppe Germanò, M.D., Gianfranco Piccirillo, M.D., *Camillo Cammarota, PhD , Giuseppe
Guarini, M.D., *Enrico Rogora, Ph.D., Mauro Cacciafesta, M.D.
Dipartimeno di Scienze dell’invecchiamento, *Dipartimento di Matematica, Università “La
Sapienza”, Rome, Italy
Abstract
We introduce a new index, Acceleration Ratio (AR), in order to investigate the dependence of
Heart Rate Variability (HRV) on age. AR measures the persistence of acceleration and
deceleration over short sequences of consecutive regular RR intervals. We study the dependence
of AR on age by analyzing separately the diurnal and nocturnal segment of the 24 hours Holter
recordings of 55 healthy subjects divided into three groups of age. We have found that the value
of AR for the diurnal segment is greater than that for the nocturnal one for young subjects while
this relation is inverted for elderly. We have also studied the dependence on age of a suitable
defined index related to AR, denoted DlogAR, and we have found that it has better directional
properties with respect to age than the other indexes in time domain.
Introduction
The heart rate variability (HRV) results from a variety of factors that are not purely stochastic
(uncorrelated) but are characterized by strong and long range correlations. Moreover the heart
rate time series is highly non stationary (for example there is a sharp difference between night
and day). In order to quantify its properties, a variety of indexes have been used (1-5) and a
rich literature already exists about their dependence on age (6-8). In particular in (8) it has been
investigated the distribution of several indexes over different groups of age: some of them show
significant differences among the groups, but none of them shows a significant directional trend
with respect to age. In this paper we propose a new index and show that it has the last property.
The motivations for the introduction of our index are the followings. The spectral components
related to sympathetic modulation of heart rate seem to decrease earlier than those related to
vagal modulation (9). Hence an indicator of the relative efficiency of these two systems should
correlate well with age. Since the autonomic nervous system controls the accelerations and
decelerations of heart rate, we introduce the Acceleration Ratio (AR) index, which measures
the persistence of acceleration and deceleration over short sequences of consecutive regular RR
intervals. This index is a minor adaptation of the one defined in (10) and further studied in (15).
More recently an index related to the accelerations of heart rate has been introduced and
analyzed in (16). Since AR measures the frequency of occurrence of rare events, it seems
appropriate to treat it as a concentration and consider its (base 10) logarithm, logAR. In order to
study the difference of behavior of logAR during day (logARDay) and night (logARNight), we
introduce DlogAR = logARDay - logARNight, which is the main object of investigation of this
work.
Methods
Subjects
We have analyzed the 24 hours Holter recordings of 55 healthy subjects whose ages have been
divided into three groups: group A: 16 subjects with age greater or equal to 20 years and less
than 40 (10 females, mean age 24.9; 6 males, mean age 26.5 ); group B: 12 subjects with age
greater or equal to 40 years and less than 60 (8 females, mean age 52; 4 males, mean age 50.5)
group C: 27 subjects with age greater than 60 years (16 females, mean age 74.7; 11 males, mean
age 72.5).
Data recording
The heartbeat series is defined as the sequence of the durations of the cardiac cycle measured as
the time interval between two consecutive R peaks in the ECG recording (RR series). The series
we have analyzed are obtained from Holter equipments (Rozinn Electronics, Glendale, USA)
with sampling frequency of 180 Hz.
Data preprocessing
We have first marked from each RR series a subset of data which from now on we call regular.
These are the qualified RR intervals whose duration is between 400 ms and 2000 ms. In all
subsequent data analysis, we have only made use of those data segments in which the number of
regular data were at least 70%. Statistical indexes have been computed using only the regular
data in the segment.
Definitions of new indexes in time domain
The RR series of each subject X1 , ... , XN, which consists of N elements, is shortly denoted by
X. We shall also use the series of differences D defined as Di = Xi+1 -Xi.
Since the series X gives a measure of the heart rate (heart beat velocity), the series D gives a
measures of the heart rate acceleration. Furthermore the series D has the advantage of being
more stationary than X (4).
AR Index
This index is computed over short segments of consecutive elements of the series. The length of
the segments has been chosen in order to analyze the effect of the nervous system control over
the heart rate. In our analysis we have chosen segments of 5 consecutive elements, after having
checked that other choices are less significant. Note that the segments we consider are not
disjoint. Given a segment, the next one is obtained by shifting the starting point one step ahead
and therefore two subsequent segments have 4 elements in common. The index AR is defined
with respect to a threshold parameter d, whose value represents the minimum amplitude of a
"meaningful" acceleration in the RR series. We have chosen d = 15 ms since accelerations
significantly smaller than 15 ms are comparable with the accuracy of the recording instrument.
We consider a new series, known as symbolic dynamics and denoted by Z, defined as follows.
Zi = + if Di >15 ms
Zi = - if Di < -15 ms
Zi = 0 if -15 ms ≤ Di ≤ 15 ms
We then define "+segment" any segment of length 5 such that each of the 4 symbols associated
to consecutive differences is a +, and analogously for "-segment". For an example see Table 1.
831
862
832
794
821
837
862
889
880
31
-30
-38
27
16
25
27
-9
+
-
-
+
+
+
+
0
818
-62
-
821
845
3
24
0
+
Table 1
In the first row appears a typical segment of an RR series, X; in the second row the series of differences, D; in the last row the
symbolic dynamics series, Z. There is one +segment and no -segments.
We define AR (acceleration ratio) as the ratio between the total number of +segments and
-segments and the number of regular segments of length 5. Essentially AR measures the fraction
of time in which the heartbeat repeatedly accelerates or decelerates. We use logAR to denote the
(base 10) logarithm of AR. The use of logAR seems more appropriate than AR for at least two
reasons: it gives the order of magnitude of AR and its distribution is more gaussian like.
Day-night dependence of logAR
We have selected from each tachogram a segment consisting of 10000 elements corresponding to
a "quiet sleep" portion of the nocturnal recording. Nocturnal recording has been identified as a
marked shift upward in the tachogram. The "quiet sleep" segment has been chosen in the
nocturnal recording by visually selecting the one which seems to have the best qualitative
stationary properties.
DlogAR Index
We define ARday as the AR index computed in the whole 24 hours Holter recording except the
"quiet sleep" segment and ARnight as the AR index computed in the "quiet sleep" segment.
DlogAR index is defined as the difference between logARday and logARnight.
The reasons why we introduce DlogAR index are the following. Beat to beat fluctuations of heart
rate is controlled by an important regulatory system which depends on two distinct mechanism:
sympathetic and vagal stimulation. The relative influence of the vagal stimulation with respect to
the sympathetic one is greater during sleep than during day time activity. We conjecture that the
efficiency of vagal stimulation can be assumed to decrease more slowly than the efficiency of the
sympathetic one with respect to age. Furthermore we conjecture that logAR is a reliable measure
of the global efficiency of the control system. Consequently we aspect that the DlogAR index,
i.e. the difference between logAR index in the period where the vagal control is relatively lower,
with logAR index in the period where vagal control is relatively higher, decreases with age.
Figure 1
Box Plots of indexes with respect to age groups
Statistical analysis of the data
The distributions of logAR and DlogAR are summarized in table 2 and in figure 1.
Variables/Groups
Number of Patients
logARday (mean ±sd)
logARnight (mean ±sd)
DlogAR (mean ±sd)
A
16
-1.94+-0.34
-2.20 ±0.38
0.26 ±0.25
B
12
-2.31+-0.49
-2.26 ±0. 32
-0.05 ±0.35
C
27
-2.74 ±0.52
-2.42 ±0.53
-0.32±0.30
Table 2
Mean ± standard deviation for groups A, B, C and variables logARday, relative to index logAR computed over the "diurnal"
segment, logARnight, relative to index logAR computed over the "quiet sleep" segment and DlogAR .
By inspection of Table 2 we notice that the value of logARday is greater than logARnight for
young subjects (hence DlogAR is positive in group A) while this relation is inverted for elderly
(hence DlogAR is negative in group C). In order to quantify the significance of this statement we
have performed, in each group separately, a t-test for the mean. In each test the null hypothesis is
that the mean of DlogAR is zero; the alternative is that the mean is positive for group A, non zero
for group B and negative for group C. The results are summarized in table 3.
t-test DlogAR A
B
C
4.8e-04 0.62 4.2e-06
p-values
Table 3
P-values of t-tests of comparison of mean of DlogAR with zero.
The change of sign of DlogAR in young and older is the basis of our conjecture that DlogAR
index is more basic than logAR index. In fact the decreasing of logARDay may simply be
explained by the fact that young people are more active than older, while the change of sign in
DlogAR is related, in our opinion, to a differential aging of the two nervous control mechanism
of the heart rate.
Moreover, we have decided to measure the significance of the (expected and observed)
decreasing trend of DlogAR with age by means of a multiple comparison test. For this we have
performed unpaired t-tests for measuring the significance of the difference of the means in
groups A-B and B-C. The null hypothesis is equality of means and the alternative one is that the
mean decreases with age. The results are summarized in table 4.
t-test DlogAR A-B B-C
p-values
0.009 0.016
Table 4
P-values of t-tests of comparison of means for groups A-B and B-C.
We notice that each p-value is well below the threshold of 0.025 which is necessary to guarantee
an overall p-value below 0.05. (see [14]). Therefore this multiple comparison suggests, at a
confidence level of at least 95% that DlogAR is decreasing with age in our groups. This is what
we mean by saying that the index DlogAR shows a significant directional trend with respect to
age.
We have also noticed that the mean value of logARnight is almost constant in our groups. This
has been tested with an ANOVA test: the resulting p-level for the multiple comparison of the
means in the three groups was 0.285, which is highly consistent with the null hypothesis of
constancy of the mean.
Comparison with other indexes
Time domain indexes (1) can be divided into two categories. Those whose definition can be
given in term of the series of the differences (RMSSD, PNN50 and our new indexes) and those
which do not (Mean, SDNN, SDNNIndex, SDANN). Moreover RMSSD and PNN50 do not
change if one shuffles the series of the differences, while our indexes depend on shuffling. This
is because our index is sensitive to the time ordering in which the differences appear in
recording. By looking at figure 2 and 3 one notices that there is not a directional (increasing or
decreasing) dependence on age of the indexes RMSSD, PNN50, SDNN, SDNNIndex, SDANN.
For the mean we have a significant difference between group A and group C . As it is generally
believed, we have found an higher mean in the group of elderly, but the trend of this index fades
if we look at group B. We conclude that none of the above indexes shows a significant
directional trend with respect to age for the subjects under study.
Figure 2
In the box plots Standard deviation, SDNNIndex and SDANN
do not show a definite directional trend with respect to age
(compare with the box plot for DlogAR in Figure1)
Figure 3
In the box plots, RMSSD and PNN50 do not show a definite directional trend with respect to age
Mean show a weakly increasing trend (Compare with the box plot for DlogAR in figure 1)
Conclusions
It was described an age-related change of the autonomic nervous system control. Both autonomic
components tend to decrease with aging, although differently. In particular sympathetic nervous
system is less able to increase the heart rate as adjustment of the cardiac output to the different
metabolic demands because of the reduction of beta-receptors activity (11). In fact although in
old subjects epinephrine and norepinephrine increase more than younger subjects in response to
different stresses, in this class there is a less beta-receptor activity(12,13). This trend has an
equivalent behaviour from a spectral point of view: power spectral analysis markers of
sympathetic modulation of heart rate suffer a reduction with aging (2). The DlogAR age-related
reduction could have the same meaning. Moreover this index could help to measure the different
aging of the sympathetic and vagal modulations.
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