Empirical Mode Decomposition (EMD) analysis of
HRV data from locally anesthetized patients
K Shafqat, S K PAL, S Kumari and P A Kyriacou Senior Member, IEEE
Abstract—Spectral analysis of Heart Rate Variability (HRV)
is used for the assessment of cardiovascular autonomic control.
In this study data driven adaptive technique Empirical Mode
Decomposition (EMD) and the associated Hilbert spectrum has
been used to evaluate the effect of local anesthesia on HRV
parameters in a group of fourteen patients undergoing brachial
plexus block (local anesthesia) using transarterial technique.
The confidence limit for the stopping criteria was establish and
the S value that gave the smallest squared deviation from the
mean was considered optimal. The normalized amplitude Hilbert
spectrum was used to calculate the error index associated with
the instantaneous frequency. The amplitude and the frequency
values were corrected in the region where the error was higher
than twice the standard deviation. The Intrinsic Mode Function
(IMF) components were assigned to the Low Frequency (LF) and
the High Frequency (HF) part of the signal by making use of the
center frequency and the standard deviation spectral extension
estimated from the marginal spectrum of the IMF components.
The analysis procedure was validated with the help of a simulated
signal which consisted of two components in the LF and the HF
region of the HRV signal with varying amplitude and frequency.
The optimal range of the stopping criterion was found to be
between 4 and 9 for the HRV data. The statistical analysis showed
that theLF/HF amplitude ratio decreased within an hour of the
application of the brachial plexus block compared to the values
at the start of the procedure. These changes were observed in
thirteen of the fourteen patients included in this study.
In the frequency domain, three frequency bands can be dis-
tinguished in the spectrum of short term (2 to 5 minutes)
HRV signals . These components are termed as High-
Frequency (HF) band (0.15 Hz to 0.4 Hz), Low-Frequency
(LF) band (0.04 Hz to 0.15 Hz) and Very Low-Frequency band
(VLF) which is the band of less than 0.04 Hz frequencies.
The HRV indices such as the ratio ofLF/HF power or the
fractional LF power have been used to describe sympathovagal
balance . The dependence on linearity and stationarity make
the parametric and non-parametric spectral methods unsuitable
HE study of interbeat variations of the Electrocardio-
graph (ECG) is known as Heart Rate Variability (HRV).
This work was supported by Chelmsford Medical Education and Research
K Shafqat is with School of Engineering and Mathematical Sciences
(SEMS), City University, London, UK
P A Kyraicou is with School of Engineering and Mathematical Sciences
(SEMS), City University, London, UK
S K PAL is with St Andrew’s Center for Plastic Surgery & Burns,
Broomfield Hospital, Chelmsford, UK.
S Kumari was with St Andrew’s Center for Plastic Surgery & Burns,
Broomfield Hospital, Chelmsford, UK.
for the analysis of the data like HRV which depends on time-
varying phenomena such as respiration.
In this study the Empirical Mode Decomposition (EMD)
and the associated Hilbert spectrum technique  has been
used to evaluate the effect of local anesthesia on HRV pa-
rameters in a group of patients undergoing local anesthesia
(brachial plexus block) using the transarterial technique. The
ability of driving a basis set directly from the data instead of
using fixed predefined basis as used by other techniques allows
EMD to provide more compact and meaningful representation
of the signals especially in the case of non-stationary and
non-linear signals . This signal analysis technique has been
used previously for analyzing HRV signals ,  and other
biological signals , .
A. Subject and Protocol
Before commencing clinical trials on ASA 1 and 2 patients
undergoing local anesthesia, research ethics committee ap-
proval was obtained. Fourteen patients (7 males and 7 females)
aged 50.6 ± 20.7 years (mean weight 67 ± 15.3 Kg, mean
height 1.6 ± 0.2 m) undergoing elective general surgery under
local anesthesia were recruited to the study. In all cases the
transarterial approach was used for the brachial plexus block.
A combination of 30 ml of 1% Lignocaine and 29 ml of 0.5%
Bupivacaine with 1:200000 part Adrenaline was used as anes-
thetic agent. An AS/3 Anesthesia Monitor (Datex-Engstrom,
Helsinki, Finland) was used to collect lead II ECG signals
from the patients. The monitoring started about 30 minutes
before the start of the block and continued for approximately
another 30 minutes after the surgery in the recovery ward.
The ECG signal was digitized at 1 kHz sampling frequency
using a PCMCIA 6024E 12-bit data acquisition card (National
Instruments Corporation, Austin, Texas).
B. Data preprocessing
The algorithm for the detection of the R-waves in the
recorded ECG signals was developed using the wavelet trans-
form with first derivative of Gaussian smoothing function
as the mother wavelet. The detection was carried out using
wavelet scales 2m, m=4, 8, 12, 16, 20. After the R-wave
detection the heart timing signal  was used for the HRV
signal representation and also for the correction of missing
and/or ectopic beats. The signals were resampled using cubic
spline at a sampling rate of 4 Hz as recommended for HRV
C. Empirical Mode Decomposition (EMD)
In the EMD technique the signal is first decomposed into a
set of simple functions called Intrinsic Mode Function (IMF).
Definition and further details about IMF properties and extrac-
tion can be found in the literature , . A systematic way
for extracting IMF from a complicated data set is known as
sifting. The properties of the IMF depend to a large extent on
the stopping criterion that is used in the sifting process. In this
study the criterion suggested by Huang et.al  was used and
the sifting process was stopped when the number of zero cross-
ings and extrema remains the same for S successive sifting
steps. The confidence limit for the parameter S was established
S = 2-10, 15 and 20 as proposed by Huang et.al . Using
the Hilbert spectrum obtained from the individual decom-
positions, the mean and the standard deviation values were
estimated. The S value that gave the smallest squared deviation
from the mean was considered optimal and used as the
stopping criteria for the sifting process.
D. Normalized Amplitude Hilbert spectrum and instantaneous
frequency error index
In order to validate that the estimation yields a physically
meaningful instantaneous frequency for the IMF components,
the Normalized Amplitude Hilbert spectrum (NAHS) intro-
duced by Huang and Long  was used and the error bound
was defined as shown in Eq. 1.
E(t) = [abs(Hilbert Transform(y(t))) − 1]2
The instantaneous frequency was considered to be incorrect
at positions where the error index was higher than twice the
standard deviation of the error. These values were corrected
by using a model based interpolating scheme purposed by
Paul et.al . After the correction, the marginal spectrum
(Eq. 2) of the IMF components was used to estimate the center
frequency and the standard deviation spectral extension using
Eq. 3 and Eq. 4.
E. IMF component assignment to LF and HF band
The IMF components were assigned to the LF or the HF
band of the signal if the center frequency lay within the band
limits and the center frequency ± standard deviation spectral
extension value was not more than twenty percent outside the
boundary of that band.
F. Simulated signal study
In order to validate the analysis setup described in this work
a simulated signal representing the non-stationary conditions,
with changing amplitude and frequency, usually encountered
in the HRV analysis was used. The signal was generated using
an Integral Pulse Frequency Modulation (IPFM) model for a
duration of five minutes. The threshold and the DC component
of the IPFM model were kept constant at one. Equispace
representation of the signal from the IPFM model was obtained
at 4 Hz through cubic spline interpolation.
The signal consisted of two frequency components one in
the LF region and one in the HF region of the HRV signal.
The amplitude of both the components at the start of the IPFM
simulation was set to unity and the frequencies of the LF and
the HF component were set to 0.1 Hz and 0.25 Hz respectively.
The amplitude of the LF component was dropped to half
and that of the HF component was increased to two midway
through the IPFM simulation. The frequencies of both the
components were increased to 0.12 Hz for the LF component
and to 0.3 Hz for the HF component at the same time.
G. Statistical test
An unpaired t-test and a Mann–Whitney rank sum test
were used to compare the parameters values estimated from
the data obtained from the locally anesthetized patients. The
parameters from each patient were tested individually to check
for differences before and after the block. The statistical
analysis was carried out using SigmaStat 2.03 (Systat Software
Inc., USA). The significance level was set at P < 0.05 in all
A. Simulated signals results
The S value of eight gave the minimum squared deviation
from the mean and was considered optimal. The results
obtained for the simulated signal are shown in Fig. 1. The
changes in the amplitude and the frequency can be clearly
seen in the first two IMF components shown in Fig. 1. The
ratio values calculated using these two IMF components are
close to the theoretical value of one in the first half of the data,
while it changes to one fourth in the second half reflecting the
changes in the amplitude of the two signal components. In
this case the dotted line in the ratio plot, second last plot
in the right column of Fig.1, shows the values calculated
before the correction of instantaneous frequency and amplitude
as described in section II-D. The uncorrected ratio values
show a large fluctuation in the middle of the data where
the parameters of the signal components were changed and
the error index was considered high. After the correction
the fluctuations have been reduced quite considerably. Due
to the smoothness caused by the correction procedure the
transition in the corrected ratio values is slower than it was in
the uncorrected ratio values and care should be taken while
defining the threshold for the error index as too low threshold
would result in the loss of meaningful information present in
Fig. 2: Part (a) and (b) of this figure shows marginal spectrum of first six IMF components (labeled (i) to (vi) in each subfigure)
for two different five minute data segments from locally anesthetized patients. In each plot the solid black line represents the
marginal spectrum and the dash dotted black lines represent the traditional LF and HF rigid a priori frequency bands. The
diamond mark represents the center frequency and the solid horizontal (gray) line indicates the center frequency ± standard
deviation spectral extension.
0 0.1 0.25 0.5
0 0.1 0.250.5
0 0.1 0.25 0.5
0 0.1 0.25 0.5
0 100 200300
Tim e (s)
Tim e (s)
Fig. 1: Results from the simulated signal. The left column
represents the signal and the first three IMF components.
The marginal spectrum of the first four IMF components
are shown in the right top corner. In each plot the diamond
marker indicates the center frequency while the horizontal
line indicates center frequency ± standard deviation spectral
extension. The graphs at the bottom right corner indicates the
ratio between the first two IMF components and the Hilbert
spectrum obtained with these two components
B. HRV data from locally anesthetized patients
The minimum value of squared deviation has occurred be-
tween S values of 4 to 9. Each data set was decomposed using
the optimal S value. After obtaining the IMF components the
amplitude and frequency values where corrected as mentioned
in section II-D. After the correction the IMF components were
assigned as the LF or the HF part of the signal by making use
of the marginal spectrum and calculating the center frequency
and the standard deviation spectral extension through Eq. 3 and
Eq. 4 respectively (see section II-E). The marginal spectrum of
the first six IMF components from two different five minutes
data sets are presented in Fig. 2(a) and Fig. 2(b). The spectrum
in Fig. 2(a) indicates that the first two IMF components belong
to the HF band and the next three belongs to the LF band.
The situation is different in case of Fig. 2(b) where the first
component belongs to the HF band and the second and third
component make up the signal in the LF region.
0 500100015002000250030003500 400045005000
0 50010001500 20002500 3000 3500
Amplitude ratio (LF/HF)
500 1000 15002000 25003000 3500 40004500
0 5001000 150020002500 3020
Fig. 3:LF/HF amplitude ratio obtained from four locally
anesthetized patient data. In each case the values with circle
marks represent the ratio values before the block, diamond
marked values represents ratio during the block while values
with plus mark represent the ratio after the application of the
After the assignment of the IMF components into the HF
and the LF bands their amplitude ratio was calculated. Apart
from the ratio the total amplitude and the amplitude of the
LF and HF components were also estimated in the normalized
units. These values were averaged over a period of one minute.
The ratio changes in data from four locally anesthetized
patients are presented in Fig. 3. By looking at the ratio values
presented in Fig 3 it can be seen that after the application
of the brachial plexus block the ratio shows a peak and then
decreases to a minimum value. The increase in theLF/HF
ratio values could be due to the presence of small amount
of adrenaline in the anesthetic drug mixture. The decrease in
theLF/HF ratio values and the less variability shown by the
values were accepted due to the anesthetic drug. The timing
of the drop in the ratio value differs from patient to patient,
but in each case the drop occurs within an hour of the start of
C. Statistical analysis
Statistical tests were also carried out on the parameters
estimated using the EMD analysis technique. Depending on
Table I: Summary of the statistical test results obtained Download full-text
from the EMD analysis of the data from locally anesthetized
patients.LFamp/HFamp ratio cell indicates the total number of
cases showing significant changes after the block. For all
other parameters the first value indicates the number of cases
where the parameter values have shown significant changes
while the second value indicates the cases where the parameter
values have shown significant changes simultaneously with the
LFamp/HFamp ratio changes
13, 1312, 12
the normality test results, data was analyzed either by us-
ing Unpaired t-test or Mann–Whitney rank sum test. The
parameters related to the amplitude of the of the signal (i.e
LFamp/HFamp ratio, total amplitude (Amptotal), amplitude related
to the HF band of the signal (HFamp), the LF band amplitude
(LFamp) and the HF and LF normalized amplitude amplitudes
(HFN_amp,LFN_amp)) were compared in order to see if their
values differ significantly after the introduction of the anes-
thetic drug into the patient system. The statistical results are
summarized in table I. From the results presented in table I
it can be seen that the EMD analysis has been able to detect
significant changes in the ratio values after the application
of the anesthetic drug in thirteen out of the fourteen patients
included in this study.
In this study the EMD decomposition technique along with
the Hilbert transform was used to obtain the time-frequency
distribution of the data obtained from the locally anesthetized
patients. The decomposition into the IMF components was
carried out by establishing the confidence limit for the stopping
criteria S and then using the optimal value. The normalized
amplitude Hilbert spectrum was used to estimate the error
index associated with the instantaneous frequencies of the
IMF components. The instantaneous amplitude and frequency
values were corrected (see section II-D) in the region where the
error index values were more than twice the standard deviation.
After the correction, the IMF components were assigned to the
LF and the HF part of the signal by using the center frequency
and standard deviation spectral extension calculated from the
marginal spectrum of the IMF components.
The analysis approach described in the study and the
amplitude and/or frequency tracking capabilities of the EMD
technique was validated with the help of a simulated signal.
The error correction method has reduced the error in the
frequency and amplitude values hence reducing the larger
fluctuations in the ratio values (see Fig. 1). However, such
correction technique should be applied with care as it might
cause undesirable smoothing.
After the validation with the simulated signal the same
approach was used to analyze the data obtained from fourteen
patients undergoing local anesthesia, using a combination of
30 ml Lignocaine and 29 ml of 0.5% Bupivacaine as the
anesthetic agent. TheLF/HF amplitude ratio calculated from
these data sets showed a change after the application of the
anesthetic drug (see Fig. 3). The ratio values showed a sharp
peak almost right after the application of the block followed
by a significant decreases when compared to the values
approximately fifteen minutes before the block. Apart from
the amplitude ratio between the LF and the HF components
the total amplitude and the normalized amplitude of the two
components were also calculated. The statistical test summary
presented in table I showed that thirteen out of fourteen
patients showed significant changes in ratio values after the
application of the block. Normalized amplitude of the two
components also showed changes in the same number of
These results suggest that during brachial plexus block
using a mixture of Lignocaine and Bupivacaine there is a
noticeable and almost consistent change in the sympathovagal
balance which can be detected through HRV analysis. Such
encouraging results suggest further and more rigorous clinical
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