2014 International Conference on Electronics and Communication System (lCECS -2014)

Empirical mode Decomposition for frequency analysis of Heart rate variability

N aziya A. Shaik Instrumentation and Control (Biomedical), Cummins College o/Engineering /or Women,

Pune, India. noonalif@gmail.com

Abstract--The malignant ventricular tachyarrhythmia

have the great harmfulness to life, so it is very important

for prediction of ventricular arrhythmias. Sudden

cardiac death can occur due to ventricular arrhythmia.

The purpose of this work is to help physicians in early

diagnosis of ventricular arrhythmia. Applying the right

solution at the right time can help avoid the tragedy of

sudden arrhythmic death. Heart rate variability (HRV)

represents one of the most promising quantitative

markers of autonomic activity. There are various time

and frequency domain parameters related to HRV

which helps in diagnosis of various disorders. This paper

aims to take into consideration the parametric method

which gives asmoother spectral component, which can

be distinguished independently of preselected frequency

bands. The proposed method of heart rate variability

analysisin frequency domain includes decomposition of

RR interval using Empirical mode decomposition

(EMD) which is followed by Hilbert spectral analysis of

the decomposed functions. This method of analysis is so

called Hilbert-Huang transform (HHT) method which is

a novel method for analyzing non-linear and non­

stationary signals and it is applicable to nonlinear and

non-stationary processes. High frequency (HF)

component of the total power reflects parasympathetic

activity low frequency (LF) component is the result of

sympathetic and parasympathetic activity.

Keywords -Empirical mode decomposition, Hilbert

spectrum, Intrinsic Mode function (IMF), Heart rate

variability, spectral analysis, and Hilbert-Huang

transform

I. INTRODUCTION

Heart rate variability as said by McCraty and Singer is" A measure of neurocardiac function that reflects heart-brain interactions and autonomic nervous system dynamics".The autonomic nervous system plays an important role in a wide range of visceral­somatic and mental diseases. The heart is dually innervated by the autonomic nervous system such that relative increases in sympathetic activity are associated with heart rate increases and relative increases in parasympathetic activity are associated with heart rate decreases. Thus relative sympathetic increases cause the time between heart beats (the interbeat interval) to become shorter and relative parasympathetic increases cause the interbeat interval to become longer. The parasympathetic influences are pervasive over the frequency range of the heart rate

DipaliRamdasi Instrumentation and Control (Biomedical),

Cummins College of Engineering for Women, Pune, India.

dipali.ramdasi@cumminscollege.in

power spectrum whereas the sympathetic influences 'roll-off at about O. 15 Hz (Saul, 1990). Therefore high frequency HRV represents primarily parasympathetic influences with lower frequencies (below about 0.15 Hz) having a mixture of sympathetic and parasympathetic autonomic influences. The oscillatory pattern which characterizes the spectral profile of heart rate and arterial pressure short-term variability consists of two major components, at low (LF, 0.04-0. 15Hz) and high (HF, synchronous with respiratory rate) frequency, respectively, related to vasomotor and respiratory activity.

This paper describes the frequency domain analysis of HRV out of various methods used for frequency domain measurement of heart rate variability and algorithm used for detection of various cardiovascular diseases using Hilbert-Huang transform. EMD is a method used to decompose the signals into oscillatory data embedded into it.

The rest of the paper is organized as follows: Section 2describes the EMD algorithm with Hilbert spectral analysis which has been proposed for analyzing the frequency domain parameters of HRV along with the results obtained. Hilbert transform has used EMD as a filtering method to differentiate various frequencies.Hilbert spectral analysis is used to calculate instantaneous frequencies. The normalized amplitude Hilbert spectrum is used to calculate the error index associated with the instantaneous frequency [ 1 ].

II. FREQUENCY DOMAIN MEASUREMENT OF HRV

Various spectral methods for the analysis of the heart rate variability (HRV) have been applied since the late 1960s. Powerspectral density (PSD) analysis provides the basic information of how power (i.e. variance) distributes as a function of frequency. Short-term recordings: Three main spectral components are distinguished in a spectrum calculated from short term recordings of 2 to 5 min [2], very lowfrequency (VLF), low frequency (LF), and high frequency (HF) components.

2014 International Conference on Electronics and Communication System (lCECS -2014)

TABLEI FREQUENCY DOMAIN HRVPARAMETERS[2]

Frequency Description Range Component

Absolute Measures

Approximately <

Total Power Variance of all RR = 0.4 Hz intervals

Power in ultra-low < -0.003 Hz

ULF frequencyrange

Power in very low 0.003 Hz -0.04 frequency Hz

VLF Range

Power in low 0.04 Hz -0.ISHz

LF frequency Range

Power in High O.ISHz -O.4 Hz

HF frequency Range

Relative Measures

Normalized low LF I (Total power

LF Norm frequency -VLF) X 100 Power

Normalized high HF I (Total power

HF Norm frequency -VLF) X 100

Power

Ratio of low and high ---

LF IHF Frequency

Measurement of VLF, LF and HF power components is usually made in absolute values of power (ms\ but LF and HF may also be measured in normalized units (n.u.) which represent the relative value of each power component in proportion to the total power minus the VLF component. The representation of LF and HF in n.u. emphasizes the controlled and balanced behavior of the two branches of the autonomic nervous system. Moreover, normalization tends to minimize the effect on the values of LF and HF components of the changes in total power.Nevertheless, n.u. should always be quoted with absolute values of LF and HF power in order to describe in total the distribution of power in spectral components.

III. HEART RATE VARIABILITY ANALYSIS

In this section, the method used for analysis of HRV in this paper has been elaborated. Figure I shows the flow graph of proposed

work.

Extra cti on of Empirical M ode Hil b e rt

RR inte rval ----'l Dec om position � Spectral

{ I nterpolationl Analysis

i 1 Amplifi ·cation

and Filtration Discussion on of ECG Frequency

domain HRV r ECG

R ecording

Figurel.Flow graph of proposed work for HRV analysis

A. ECG Signal Pre-processing

The experimental data used is of patient with ventricular arrhythmia recorded with Philips Page writer TC30 provided by Sahasrabuddhe Hospital, New Bombay.The signal is sampled at I KHz. The raw ECG data is prone to noise that occurs mainly dueto power line interference, high frequency and movementartifacts. TheECG signal is de-noised using soft thresholding at level 5 of wavelet analysis. Figure 2 shows the de-noised ECG signal.

1000,-----_-----_--------,

800

600

400

200

-200

-400

-6000L...L------OS=00=0-----1O=00=0-------="15000

Figure2. De-noised ECG signal

B. Extraction of R-wavefrom ECG signal

The electrocardiograms (ECG) give cardiac functional details and helps in analyzingheart abnormalities. Corresponding to every heart beat in the ECG signal, a quasi-periodic sequence of P, QRS and T- wave can be observed [3]. The QRS complex in thissequence has the highest amplitude and once detected helps in calculating the intervalsbetween two consecutive RR peaks. The variation in these RR intervals is referred toas the Heart Rate Variability (HRV). ECG signal is susceptible to artifacts due topower-line interference, electrode motion, baseline wander, high frequency contentsand myoelectric interference. Most of the frequencies in the QRS complex are around20 Hz. Thus a band pass filter in the 10 to 40 Hz range is used to remove low frequencychanges such as baseline wander and high frequency changes such as movement artifact.QRS detection algorithm using differentiation method has been proposed for detectingR-wave in this project. For creation of a set of RR intervals from selectedECG it is necessary to

2014 International Conference on Electronics and Communication System (lCECS -2014) perform detection of R oscillations.Fordetection of R oscillations we used the Matlab functionfindpeaks whose output values are local maxima of thesignal and their temporal location. Then the identified R oscillations are verified visually in order to avoid any incorrect labeling of artifacts or other possible effects. High slopes arefound using differentiation, which distinguish the QRS complexes from other ECGwaves. Then a nonlinear transformation that involves squaring of the signal samplesis done to make the entire data positive before integration. It also highlights thehigher frequencies in the signal obtained from the differentiation process. These higherfrequencies denote the QRS complex. Then the squared waveform is passed througha moving window integrator and a decision is taken based on threshold detection.

C. Algorithm

After detection of RR interval, the decomposition of the signal obtained from the above process is carried on. The idea behind decomposition of the signal is to separate the oscillatory components embedded in the signal. The decomposition method used is called as empirical mode decomposition (EM D), which is an adaptive method of decomposition [4][5]. In this algorithm, envelope construction of local maxima and local minima is carried out using cubic spline interpolation.

Construction of Local rn axi rna by I nterp oIClion

N

Residue extraction

Figure 3 .Flow chart of Empirical Mode Decomposition method

1) Empirical Mode Decomposition

Using Empirical mode decomposition method, the obtained decomposed functions of the signal are called as intrinsic mode functions (IMF). The process of finding IMFs is known as sifting process. An intrinsic mode function should satisfy the following two conditions: I )In the whole data set the number of extrema and the number of zero crossings differby at most one.

2) The local mean is zero. Specifically, the average of the upper envelope (defined by the local maxima) and the lower envelope (defined by the local minima) is point wise equal to zero.

Let x (t) be the signal, then steps in Empirical Mode decomposition is as follows:

i) Identify all the maxima and minima of x(t). ii) Generate its upper and lower envelopes, xup(t)

and x/ow(t)respectively, with cubic spline interpolation. As the cubic spline interpolation can guarantee the crossover points being smooth up to the second derivative, its betterto go for cubic spline to process.

iii) Calculate the point-by-point mean from the upper and lower envelopes,

m(t) = (xup(t) + Xlow(t)) /2. iv) Extract the detai I, d(t) = x(t) - m(t). v)Check the properties of d(t): • If d(t) meets the above-defined two conditions, an IMF is derived. Replace x(t) with the residual r(t) = x(t) - d(t); • If d(t) is not an IMF, replace x(t) with d(t). vi) Repeat Steps 1-5 until one obtains a monotonic residual, or a single maximum or minimum­residual satisfying some stopping criterion. At the end of this process, the signal x (t) can be

expressed as follows:

( 1)

wheren is the number of IMFs, and rn(t) denotes the final residue, which can be interpreted as the DC component of the signal. cit) are the IMFs and are orthogonal to each other and all have zero means.

i.::: LI '._I._.�l...III_I •• _II_I0.L�._�I_III_�I�.L._I I_.I_.�.L'_I_II_.�...LI! �_._._"...l.'�_'_._'...J.�_'_"I_"t • ...J1 o 0.5 1 1.5 2 2.5 3 3.5

5 X 10 i:::� '____�'___�\II_��'___ •• _.'___��_�'___�.,_�'___�_�I'___�_'�,___I_.

o 0.5 1 1.5 2 2.5 3 3.5 Time

Figure 4. IMFs obtained after EMD.

5 X 10

2014 International Conference on Electronics and Communication System (lCECS -2014)

, x 10 i 10:���

_100 L-----'- -----' --L---'---- -...l.--L. ------'-----'

"-LL �

o o.s 1 1.S 2 2.S 3 3.S

SO:E -soo 0 0.5 1.S 2.5 3.5

, x 10

, x 10

; 1: : : : : : J o O.S 1 1.5 2 2.5 3 3.5

Time

Figure 5. IMF 5, IMF 6, IMF 7, IMF 8 after EMD.

, x 10

The results obtained after implementation of the EMD algorithm discussed above on the RR interval data_ Figure4 show the first four IMFs in consecutive panes. Figure 5 shows IMFs 5- IMF8.

2) Hilbert Spectral Analysis

After the empirical mode decomposition, the Hilbert transform is applied to each IMF component, and compute the instantaneous frequency according to Equations (3) to (7). Consequently, the original data can be expressed as the real part in the following form:

x W = R L f= l a( (t) .6' [ J <u , ( t) (2) The Hilbert transform is the easiest way to compute instantaneous frequency [6], through which the complex conjugate y (t) of any real value function x(t)of Lp classcan be determined by:

1 J + ""' �M y(t) = H[x(t) ] = - _;Q - d.,: IT t - T

and the constructed analytic signal is defined as:

Where, ,a(t) = J x2 + y2

9(t) = tan - 1 � �

(6)

(3)

(4)

(5)

art) is the instantaneous amplitude, and 9(t) is the phase function, and the instantaneous frequency is simply: diE! ,w = a t (7)

There are two reasons that the residue should be left out. First, the energy involved in the residual trend representing a mean offset could be overpowering. Second, we are more interested in obtaining the information contained in the other low-energy but

clearly oscillatory components rather than the uncertainty of the longer trend. To accommodate non­linear and non-stationary data, with a variable amplitude and frequency form, can be expressed in the form called as 'Hilbert amplitude spectrum' or 'Hilbert spectrum'. Figure 6 and Figure 7 shows Hilbert spectrum of IMF 4 and IMF 5 respectively. With the Hilbert Spectrum defmed, we can also defme the marginal spectrum H (w) as

H(w)=l: H(.w , t)dt (8)

Time

Figure 6. Hilbert Spectrum of IMF 4

The marginal spectrum offers a measure of the total energy distribution from each frequency. The combination of the empirical mode decomposition and the Hilbert spectral analysis is known as the Hilbert-Huang transform. Different from the traditional analyses, the Hilbert-Huang transform is developed for non-linear and non-stationary data. After performing Hilbert transform on each IMF obtained, the instantaneous frequency is obtained.

Time

Figure 7. Hilbert Spectrum of IMF 5

Signal's Hilbert-Huang spectrum, is shown inFigure 8,from which the R-R interval signal's frequency mutation moment point can be obtained, and colors in the figure express signal amplitude

2014 International Conference on Electronics and Communication System (lCECS -2014) distribution.

0.9

O.B

� � 0.7

g- 0.6 u:

] 0.5

� 0.4 z

0.3

0.2

0.1

Time Sample

·200 -150 -100 -50 0 50 100

Figure 8. Hilbert-Huang spectrum of RR data

150

0.1 ,-----,---,---,--,------,----,---.--,----,----,

§ 0.08 U � 0.06 (f) ! 0.04

� 002

E � 0.15

Jj- 0.1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 frequency

W 0.05 2

o l o 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

frequency

Figure 9. Power spectrum of IMF 4, IMF 5

0.45 0.5

Figure 9 shows power spectrum of IMF 4 and IMF 5, shown in Figure 4 above. Figure 10 shows power spectrum of IMF 6 and IMF 7, shown in Figure 5 above.

§ 0.15 1: Of 0.1 � � 0.05 '"

005 01 0 15 02 025 03 035 04 045 0 5 frequency

0.25 ,-----,-,------,---,--,-------,-,------,---,-----,

§ 0.2

� 0.15 (f) � 0.1 .'" � 0.05

°0-��0.� 05�0�.1�0� .1�5 �0 .�2�0.�25�0� .3�0� .35��0.4��0.4�5 �0. 5

frequency

FigurelO. Power spectrum of IMF 6 and 7

Spectral power can then be calculated from the IMF's using Equation (9), where a IS the instantaneousamplitude of the IMF,

(9)

Spectral power of the low and high frequency IMF's were computed by adding the power values of the individual IMF's. Considering the first P IMF's to contain high frequency oscillations [7], the high frequency, low frequency and total power IS

calculated using Equations (10) through (12) as,

P01lllfNHI!' = Lf�iPl POU-TfNLI!' = I�p + i p[ P01lllfNT I1t = Lf�iPl

(10) ( I I ) (12)

Table II shows the results obtained from the mean calculated using Equation (8); hence the components are assigned to low and high frequency bands respectively.

Table IIRESULTS OBTAINED

LF HF Total Frequency

Mean 0.225 0.4668 0.692+ 0.04

Power 48.73% 4.70% 53 .43 %

IV. DISCUSSION

The work discussed in this paper illustrates that empirical mode decomposition does not require a priori knowledge of the signal to be analyzed, as compared to other transforms like Fourier and wavelet transforms which requires basis functions to be described. EMD can be used for non-stationary signals. Therefore, the algorithm can be used to identify the low-frequency and high-frequency bands of HRV more sharply and effectively through Hilbert spectrum than using the Fourierspectrum, which may help physicians make decisions on individual therapy or intervention on time.

V. CONCLUSION

Empirical mode decomposition was used to decompose the signal into its intrinsic functions. Spectral analysis can be done using Hilbert spectral analysis. Results from Table II shows that there is higher activity of vagal nerve due to ventricular arrhythmia. After EMD decomposition, IMF component simultaneously has characteristics like adaptability, locality, and integrity, etc. Its obvious advantage is, IMF decomposed from Hilbert-Huang spectrum can both provide signal's useful information. Hence, usingthe proposed algorithm, valuable information onmechanisms of certain cardiac arrhythmia can be derived and thus can prove to be of importance for early diagnosis.

VI. FUTURE WORK The future work includes the implementation of the above proposed method on RR interval of various cardiovascular diseases to analyse the HRV parameters and calculate LF IHF ratio for evaluation of sympathetic or parasympathetic activity.

2014 International Conference on Electronics and Communication System (lCECS -2014)

ACKNOWLEDGMENT

The authorswould like to take this great opportunity to express a deep sense of gratitude to The Principal, Prof. Dr. Madhuri Khambete, Cummins College of Engineering for Women, Karvenagar, Pune. The authorswould also like to thank Prof. A. D. Gaikwad, Head of the Department of Instrumentation and Control, Cummins College of Engineering for Women, Pune, for their support.

REFERENCES

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Oscillations Using Improved Hilbert-Huang Transform," 2010 International Conference on Power System Technology. [7] Jerritta S, M Murugappan, Khairunizam Wan, S Yaacob," Emotion Recognition from Electrocardiogram Signals using Hilbert Huang Transform",IEEE conference on Sustainable utilization and Development in Engineering and Technology,20l2.