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Empirical Mode Decomposition as a tool for the investigation of
short-term heart rate variability
R. BALOCCHI1, D. MENICUCCI1, G. RAIMONDI2, M. VARANINI1
1
Institute of Clinical Physiology, CNR, Pisa
2
Internal Medicine Dept. – Biomedicine Space Centre, University of Roma Tor Vergata
Istituto di Fisiologia Clinica,
Area Ricerca S. Cataldo,
via Moruzzi, 1, 56124-Pisa
ITALY
Abstract: - Beat-to-beat changes in heart rate are modulated by different mechanisms of control. A strong
influence on heart rate variability (HRV) is exerted by the competing activity of the sympathetic and
parasympathetic nervous system, the so-called sympathovagal balance. Traditionally this balance is evaluated
by power spectral analysis of the heartbeat time series (RR), in particular by computing the ratio between the
powers in the low (LF) and high (HF) frequency bands (LH=LF/HF). To overcome the limitations imposed by
the use of spectral analysis and to avoid the rigidity inherent the definition of the frequency bands, we
evaluated a new index computed on the intrinsic oscillations of the RR series. These oscillations were extracted
using Empirical Mode Decomposition, a technique able to decompose any signal into a basis of functions
(IMFs) with well defined instantaneous frequency. The ratio between the power of the two IMFs
corresponding, respectively, to the LF and HF band was proposed as the new sympathovagal balance index.
The new index was tested in twenty normal subjects at rest showing a strong relationship (r=0.90) with the
traditional LH, indicating its validity to act as a sympathovagal balance index, at least in similar experimental
conditions. We are now investigating its effectiveness in other pathophysiological contexts, to propose the use
of this index in all those circumstances for which the LH index is not applicable or insufficiently selective.
Key-Words: - Empirical Mode Decomposition (EMD), Heart Rate Variability (HRV).
1 Introduction
The heart rate variability (HRV) analysis is a
powerful, noninvasive tool for the assessment of the
cardiovascular system functioning, particularly of the
autonomic nervous system (ANS) activity.
Traditionally the series of the time interval between
consecutive heart beats (tachogram, RR time series)
is analysed in both time and frequency domain,
according to formalized guidelines [1].
For short-term HRV investigation, power spectral
analysis is a particularly suitable approach since the
values of absolute and relative powers in the low
(LF, 0.04-0.15Hz) and high frequency (HF, 0.150.4Hz) bands can give information on the activity of
the sympathetic and parasympathetic nervous
systems, which constitute the two branches of the
ANS. As a very simplified explanation we can say
that ANS regulates vasomotion (LF) and respiratory
modulation (HF), each of them mainly influenced by
sympathetic
and
parasympathetic
activity
respectively.
In most physiological conditions, the activation of
either sympathetic or parasympathetic outflow is
accompanied by the inhibition of the other. This is
the concept of the sympathovagal balance:
sympathetic
excitation
and
simultaneous
parasympathetic (vagal) inhibition, or vice versa, are
presumed to control the increase or decrease of the
heart rate [2]. Although both LF and HF components
are present simultaneously in sympathetic and vagal
activity, various experiments showed that HF and LF
can be regarded as markers of vagal and sympathetic
modulation, respectively. The LH=LF/HF power
ratio is considered the elective index to characterize
the sympathovagal balance. It's known that an
enhanced vagal tone has a salutary effect on the
ventricle to prevent the occurrence of ventricular
arrhythmias and so parameters like LH could serve
as a measure of risk stratification for cardiac hazard.
There are a few drawbacks in this approach: first,
the computation of power spectra, regardless the
technique employed, would require stationarity of
the series, which is not always ensured especially in
physiological signals; second, the rigidity of the
frequency bands separation can, in some
circumstances, induce an uncontrollable mistake. We
know, for instance, that the respiratory frequency
does not necessarily stay fixed during time, and
even though it usually ranges inside the HF band, it
can also happen that it lowers down to the LF band.
In this case, the contribution of parasympathetic
activity would be erroneously attributed to the
sympathetic branch. A displacement outside the LF
band can also occur for the vasomotor frequency. To
overcome these limitations, we propose a new
approach for the power evaluation of the oscillatory
modes embedded in the tachogram and we tested its
validity by comparing the results obtained in a group
of healthy subjects analyzed in controlled conditions
using the canonical [1] approach.
This new approach makes use of a technique
named Empirical Mode Decomposition (EMD) [3]
which allows the decomposition of signals under
very general conditions, in particular independently
on stationarity and number of sources embedded in
the data, without making any assumptions on the
physical time scales present in the data.
2 Materials and Methods
This study was aimed at introducing a new approach
to the analysis of short-term HRV. To this aim we
followed a well controlled experimental protocol by
recording the Electrocardiographic (ECG) signal of
twenty healthy subjects in resting condition, when
the HRV is known to be mainly influenced by the
parasympathetic activity and the RR series
component associated to breathing has a dominant
peak in the HF band. We wanted to demonstrate that
the modes extracted from the RR series by EMD can
be associated to the physiological mechanisms of
HRV generation and that the spectral power
associated to each mode can be used for a correct
evaluation of the sympathovagal balance. To verify
the above hypotheses the results obtained were
compared to the ones obtained following the
classical approach.
2.1 Experimental setup
The ECG signals of twenty healthy subjects have
been
recorded for twenty minutes in resting
condition. A well tested derivative method was used
to detect the R-wave peak (ventricular contraction);
the series of times between successive R events (RR
series) were processed to remove possible artifacts.
The unevenly-sampled RR series were then
interpolated at 1Hz in order to allow a spectral
estimation in hertz.
2.2 Empirical Mode Decomposition
To identify the oscillatory modes embedded in the
RR series we applied the Empirical Mode
Decomposition (EMD), a recently developed
technique to decompose any time series into a finite
number of functions, named Intrinsic Mode Function
(IMFs), which exhibit some interesting properties:
they are almost orthogonal and do not overlap in
frequency. The extracted components have well
behaved Hilbert transform from which the
instantaneous frequencies can be calculated. This
decomposition method is adaptive and therefore it
may track the amplitude and frequency variations of
the embedded oscillations, so as an IMF can be
amplitude and/or frequency modulated and can even
be nonstationary. Applications of EMD have been
successfully performed
in several fields: in
climatology, to decompose ocean wave data and
altimeter data from the equatorial ocean [4]; in
geophysics, on the earthquake data [3], and in
biology on blood pressure [5], electrogastrogram [6]
and heart rate data [7]. In all the above applications
the extracted modes have been recognized to be
associated to specific physical processes and the
purity of the extracted modes has been emphasized
in contrast to classical approaches like Fourier or
wavelet analysis.
The essence of the EMD is to identify the intrinsic
oscillatory modes of a data set X(t) using its
characteristic time scales identified as the interval
between successive alternations of local maxima and
minima. The extraction of each IMF (sifting process)
begins with the construction of two envelopes, the
upper across all the local maxima and the lower
across the local minima separately. The envelopes
are constructed using cubic splines interpolation.
In the sifting process, both upper and lower
envelopes cover all the data length and their pointby-point mean is subtracted from the original data to
obtain a new series. This new series should be a
zero-mean signal (mean of its envelopes identical to
the zero function) but, due to the envelope
procedure, this is not attainable in one step and
therefore the mean-envelope subtraction procedure is
repeated over the new series until the resulting series
has a zero mean function: in this case the final series
is characterized by a well defined instantaneous
frequency, and it is retained as an IMF (first IMF =
IMF1). The sifting process is repeated over the new
data
r1  X (t )  IMF1
(1)
and iteratively, the n-th IMF (IMFn) component is
obtained by sifting the residue signal
n 1
rn  X (t )   IMFi
(2)
i 1
The sifting process is stopped when rn becomes
monotonic (no others IMFs can be extracted) or his
amplitude becomes smaller than a predetermined
value. At the end of the EMD procedure X(t) has
been decomposed in a number M of IMFs, generated
in decreasing order of mean frequency and such that
M
X (t )   IMFi  rM
(3)
i 1
2.3 RR modes characterization
As for the other applications in literature, the IMF
functions obtained by RR series decomposition are
expected to be the expression of specific control
systems. For this particular framework of HRV
analysis, each IMF was characterized by its mean
frequency FIMF and power PIMF: FIMF was computed
by averaging the instantaneous frequencies detected
by the IMF Hilbert transform while PIMF was
evaluated directly as the IMF variance normalized
with respect to the cumulative variance of the IMFs
(total power).
2.4 Power spectral analysis
For comparison purposes the RR series were also
analyzed in the frequency domain via Fast Fourier
Transform (FFT) to compute the spectral power in
LF and HF bands and the LH index.
2.5 Correlation matrix
To characterize the interrelationships among the
IMFs, the correlation matrix C of PIMF was evaluated
as follows. Let’s indicate by
pi j = (PIMFi)J - <PIMF>J
(4)
the zero-mean power of the i-th IMF of subject j and
by P the matrix whose elements are pij (i=1,.., M; j =
1,…N), where M is the number of IMFs and N is the
number of subjects. The correlation matrix is then
C = (P PT) /N
(5)
To test whether the elements cij of the matrix C
were significantly different from zero, we analyzed
the distributions of one thousand correlation
coefficients computed after permutations of the
elements of each row of matrix P to obtain randomly
ordered sequences and therefore destroy any true
correlation. The element cij was considered null
when its value fell inside the 95% probability
interval.
3 Results
For all the subjects we retained only the first five
IMFs (IMF1,.., IMF5) disregarding possible higher
EMD decomposition
1000
800
100
0
-100
100
0
-100
50
0
-50
20
0
-20
40
20
0
-20
50
100
150
200
250
300
350
400
Fig.1. An example of EMD decomposition. From top to
bottom: the original RR series and its first five modes
IMF1,.., IMF5.
order IMFs, because their FIMF was unstable and too
close to the lower limit of the very low frequency
(VLF, <0.04) band,
supposed to be mainly
representative of artifacts. In Fig.1 is reported an
example of EMD decomposition of a RR series, on
top, with its first five IMFs, in decreasing order of
frequency.
A clear correspondence among IMFs of the same
order was found across all subjects. Fig.2 shows the
FIMF values of the five IMFs for each subject: as it
can be seen the frequency is restricted to a very
narrow range (indicated by the standard deviation
bars) and therefore we can hypothesize that each
IMF is the expression of the same feedback control.
For each IMF the frequency averaged over all the
subjects is reported in Table 1.
The first IMF belongs to the HF band and, as
demonstrated in a previous work [8] corresponds to
the respiratory activity; IMF2 and IMF3 fall into the
LF band and IMF4 and IMF5 into the VLF band .
IMF mean frequencies
-1
10
Hz
-2
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Fig.2. FIMF values of IMF1,…IMF5 for each subject in
decreasing order of mean frequency from top to bottom.
Table 1. Frequencies of the first five IMFs
averaged over the subjects.
mean
sd
mean-2*sd
FIMF1
0.2596
1.298
0.1576
FIMF2
0.1186
0.0593
0.085
FIMF3
0.0603
0.03015
0.0425
FIMF4
0.0276
0.0138
0.0173
FIMF5
0.0131
0.00655
0.0084
Indexes correlation
4
3.5
3
2.5
P3/12
1.5
An example of the power spectral density (PSD) of
the RR series and its IMF components is shown in
Fig.3.
RR series
25
30
2
3
4
Fig.4. Relationship between the two indexes LH (abscissa)
and P3/1 (ordinate).
20
25
1
LH
30
35
0.5
0
0
IMF1
35
40
1
15
20
0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
IMF2
0.3
0.4
0.5
IMF3
30
20
20
10
0
0
-10
-20
0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
0.4
0.5
IMF5
IMF4
20
20
0
0
-20
-20
-40
0
0.1
0.2
0.3
0.4
0.5
0
frequency (Hz)
0.1
0.2
0.3
frequency (Hz)
Fig.3. PSD of one RR series and its IMF components.
The matrix C of correlations between pairs of PIMF
was
1
-0.53
C= -0.64
-0.78
-0.63
-0.53
1
-
-0.64
1
0.48
-
-0.78
0.48
1
-
-0.63
1
As expected, there was a high anticorrelation
between PIMF in the HF band and PIMF in the LF band,
especially in the couple PIMF1 and PIMF3 and therefore
we selected the ratio P3/1= PIMF3 / PIMF1 to be
compared with the LH index. The strong relationship
between P3/1 and LH (r = 0.90) is shown in Fig.4.
4 Discussion and conclusions
It has been largely reported that heart rate undergoes
spontaneous fluctuations over time, modulated by
different processes. Periodic oscillations are significantly
modulated by the sympathetic and parasympathetic
activity of the autonomic nervous
system whose balance is commonly evaluated with
the LH index. However, some problems affect the
HRV study making unreliable or scarcely significant
the power spectrum evaluation of the RR interval
data and therefore the LH index: this is especially
true when dealing with nonstationary series and in all
those circumstances that escape from the rigidity of
the frequency band limits. We tested a new approach
for the sympathovagal balance evaluation which
makes use of the EMD technique of RR
decomposition and selected the P3/1= PIMF3 / PIMF1
ratio as the new index of balance. We then compared
this ratio with the LH index measured in a well
controlled experiment to ensure their equivalence in
that context. The results obtained with the approach
proposed are perfectly superimposable to the ones
obtained with the canonical approach. Besides this
final result, some interesting considerations can be
derived from this experiment. First, the
decomposition of the tachograms shows the same
structure in all the subjects, allowing to make an
unambiguous identification of the correspondent
modes among subjects, while maintaining individual
specificity such as the intrinsic variability of the
mode and the range of fluctuation. Second, we can
reasonably hypothesize that the modes extracted
from the tachograms have a physiological meaning.
Third, the modes can be selectively associated to the
ANS activity. The above considerations lead us to go
ahead with a new experiment, where the
sympathovagal
balance shows a sympathetic
prevalence, that is a condition opposite to the one
examined here. The preliminary results of this new
study seem to confirm the effectiveness of P3/1 as an
index of sympathovagal balance. The challenge is,
now, to show the effectiveness of P3/1 in all those
pathophysiological conditions for which the LH
index is not applicable or insufficiently selective.
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