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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.

I. INTRODUCTION

T

In the frequency domain, three frequency bands can be dis-

tinguished in the spectrum of short term (2 to 5 minutes)

HRV signals [12]. 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 [5]. 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

Trust (CMERT).

K Shafqat is with School of Engineering and Mathematical Sciences

(SEMS), City University, London, UK

Email: k.shafqat@city.ac.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 [7] 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 [7]. This signal analysis technique has been

used previously for analyzing HRV signals [3], [11] and other

biological signals [1], [2].

II. METHODS

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 [10] 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

studies [12].

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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 [7], [8]. 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 [9] 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 [8]. 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 [6] was used and the error bound

was defined as shown in Eq. 1.

E(t) = [abs(Hilbert Transform(y(t))) − 1]2

(1)

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 [4]. 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.

h(ω) =

T

ˆ

0

H((ω, t)dt

(2)

¯fp =

´∞

´∞

−∞f h(ω)df

−∞h(ω)df

(3)

∆fp =

?´∞

−∞(f −¯fp)2h(ω)df

´∞

−∞h(ω)df

?1/2

(4)

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

the tests.

III. RESULTS

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

the signal.

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00.5

(iv)

1

0

0.2

0.4

(i)

00.5

(v)

1

0

0.75

1.5

(ii)

00.5

(vi)

1

0

0.8

1.6

(iii)

00.25 0.5

0

0.5

1

Frequency (Hz)

(a)

Marginal spectrum

00.250.5

0

1.5

3

00.250.5

0

0.75

1.5

00.5

(iv)

1

0

0.11

0.22

(i)

00.5

(v)

1

0

0.15

0.3

(ii)

00.5

(vi)

1

0

0.17

0.34

(iii)

00.25 0.5

0

0.07

0.14

Frequency (Hz)

(b)

Marginal spectrum

00.250.5

0

0.04

0.08

00.250.5

0

0.1

0.2

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 0.250.5

0

175

350

0 0.1 0.250.5

0

50

100

0 0.1 0.25 0.5

0

0.01

0.03

Frequency (Hz)

2

(imf2/imf1)

Marginal spectrum

0 0.1 0.250.5

0

0.1

0.2

-3

0

3

signal

-3

0

3

imf 1

-3

0

3

imf 2

0100200300

-3

0

3

imf 3

Tim e (s)

0

0.25

1

Ratio

Frequency (Hz)

Tim e (s)

0 100200300

0

0.1

0.25

0.5

imf 1

imf 2

imf 3

imf 4

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 500100015002000250030003500400045005000

0

2.5

5

0500100015002000250030003500

0

5.25

10.5

Time (s)

Amplitude ratio (LF/HF)

50010001500200025003000350040004500

0

2.25

4.5

050010001500200025003020

0

6

12

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

block

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

the block.

C. Statistical analysis

Statistical tests were also carried out on the parameters

estimated using the EMD analysis technique. Depending on

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Table I: Summary of the statistical test results obtained

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

LFamp/HFamp

Amptotal

8, 8

HFamp

139, 9

LFamp

HFN_amp

13, 13

LFN_amp

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.

IV. CONCLUSION

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

patients.

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

studies.

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