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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 Empirical Mode Decomposition Analysis of Heart Rate Variability C.Santhi.M.E., Assistant Professor, Electronics and Communication Engineering, Government College of Technology, Coimbatore-641 013 N.Kumaravel Ph.D Professor, Head of the Department, Electronics and Communication Engineering, Anna University,Chennai-600 025. Abstract power in the LF and HF bands (LF/HF) provides the The analysis of heart rate variability (HRV) measure of cardiac sympathovagal balance. Empirical Mode demands specific capabilities not provided by either Decomposition (EMD) retains the intrinsic nonlinear parametric or nonparametric spectral estimation methods. nonstationary property of the signal. Any intrinsic timescale Empirical mode decomposition (EMD) has the possibility of derived from the signal is based on the local characteristics dealing with nonstationary and nonlinear embedded timescale of the signal [2-4]. EMD carries out layer upon phenomena, for a proper assessment of dynamic and layer sifting and obtains ordered array components from transient changes in amplitude and time scales of HRV smallest scale (highest frequency) to largest scale (lowest signal. In this work EMD and a non-linear curve fitting frequency) [4]. Empirical mode decomposition has the technique are used to study half an hour HRV signal and its possibility of dealing with nonstationary and nonlinear intrinsic mode function obtained from 20 healthy young embedded phenomena, and owing to its suitability for a control subjects, 20 healthy old control subjects and 20 proper assessment of the dynamic and transient changes in subjects with long term ST. The intrinsic oscillations are amplitude and in frequency of the HRV components [2& 3]. measured by means of its meanperiod and variance. Application of EMD to half an hour HRV data Significant meanperiod reduction is observed in the intrinsic yields nine intrinsic mode functions (IMFs). The first scale time scales of healthy old control subjects and subjects with represents the highest frequency or the shortest period long term ST, which is used to classify the three groups of component of the signal. The second scale represents the HRV signal with high sensitivity and specificity. The lower frequency or the longer period component of the estimated slope using the non-linear curve fitting technique signal. Similarly the last IMF represents the lowest time represents the flexibility of the cardiovascular system. The scale present in the HRV signal. The first two scales contain main advantage of this method is it does not make any prior more than 85% of total signal power. The meanperiod and assumption about the HRV signal being analyzed and no variance of IMFs are computed as time domain measures. artificial information is introduced into the filtering method. The variance of IMF decreases exponentially with respect to increasing timescales (meanperiods). Using nonlinear curve Index Terms- Empirical Mode Decomposition, Heart Rate fitting technique the IMFs variations are estimated. The Variability, Intrinsic Mode Functions, RR intervals, estimated parameter represents the flexibility of the nonlinear curve fitting. cardiovascular system.The methodology is applied to HRV signal obtained from 20 healthy young control subjects, 20 1. Introduction healthy old control subjects and 20 subjects with long term Over the last 20 years there has been widespread interest in ST. The intrinsic time scale of IMF 2 classifies the three the study of variations in the beat-to-beat interval of heart groups HRV signal with high sensitivity and specificity. known as heart rate variability (HRV) or RR interval 2. Empirical Mode Decomposition (EMD) variations. HRV has been used as a measure of mortality primarily with patients who have undergone cardiac EMD is a procedure oriented adaptive method for surgery. Clinical depression strongly associated with decomposing non-linear non-stationary signals. The mortality with such patients may be seen through a decrease components resulting from EMD are called Intrinsic Mode in HRV [1]. HRV is a non invasive measure of autonomic Functions (IMFs) [2]. The IMFs are amplitude frequency nervous system balance. Heart rate is influenced by both modulated intrinsic signals. The IMF’s represents the sympathetic and parasympathetic (vagal) activities of ANS. oscillatory modes imbedded in the signal. It should satisfies The influence of both branches of the autonomic nervous the following two conditions. 1. In the whole data set the system (ANS) is known as sympathovagal balance reflected number of extrema’s and the number of zero crossings must in the RR interval changes. A low frequency (LF) be either equal or differ by at most one. 2. At any point the component provides a measure of sympathetic effects on the mean value of the envelope defined by the local minima and heart and generally occurs in a band between 0.04 Hz and the envelope defined by the local maxima is zero. 0.15 Hz. A measurement of the influence of the vagus nerve in modulating the sinoatrial node can be made in the high frequency band (HF) loosely defined between 0.15 and 0.4 Hz known as respiratory sinus arrhythmia (RSA), and is a measure of cardiac parasympathetic activity. The ratio of 255 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 1.8 Heart rate variability 0.2 0 -0.2 0 200 400 Intrinsic mode functions 600 800 1000 1200 1400 Step 5: Check h(t) for the conditions of an Intrinsic Mode Functions. [2] 1.7 0.2 0 -0.2 0 200 400 600 800 1000 1200 1400 1.6 0.2 0 -0.2 0 200 400 600 800 1000 1200 1400 0.2 If h(t) is an IMF compute residue r(t)=x(t)-h(t) and again 1.5 0 -0.2 0 200 400 600 800 1000 1200 1400 0.2 1.4 0 rr intervals -0.2 the process is repeated to extract the next IMF. If h(t) is not 0 200 400 600 800 1000 1200 1400 0.1 1.3 0 -0.1 0 200 400 600 800 1000 1200 1400 0.1 0 an IMF x(t) is replaced with h(t) and the procedure is 1.2 -0.1 0 200 400 600 800 1000 1200 1400 0.05 0 1.1 -0.05 0 200 400 600 800 1000 1200 1400 0.01 repeated from step 1. Fig.6 shows all IMFs of the signal 0 1 -0.01 0 200 400 600 800 1000 1200 1400 1.4 1.3 0.9 x(t). 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400 beat number Fig.1.RR interval signal Fig.2. Intrinsic Mode Functions The process ends when the range of residue is below a 0.3 Detrended HRV signal predetermined level or the residue has a monotonic trend. In order to guarantee that the IMF components retains enough Reconstructed signal 1.8 0.2 1.7 1.6 0.1 physical sense in both amplitude and frequency modulations, the sifting process is stopped by limiting the 1.5 0 1.4 rr intervals -0.1 1.3 -0.2 size of standard deviation(SD) which is computed from two consecutive sifting results. 1.2 -0.3 1.1 -0.4 1 T SD = ∑ [ h1( k −1) (t ) − h1k (t ) / h 21( k −1) (t )] (1) 0.9 0 200 400 600 800 1000 1200 1400 -0.5 0 200 400 600 800 1000 1200 1400 2 beat number Fig.3.Reconstructed signal Fig.4.Detrended signal t =0 where k represents number of siftings. Figs 1-4 explain the efficiency of EMD for RR interval signal. The ECG data has been collected from the The process of finding an intrinsic mode function biomedical website [7] http://www.physionet.org. The RR requires number of iterations and the process to find all the intervals are derived from half an hour ECG signal by IMFs requires further more iterations. As a result of this identifying the QRS complexes. The signal is manually iterative procedure finally yields many IMFs and a residue. edited and only noise free ectopic free segments are used for By summing up all the IMF functions and the residue, the the analysis. A real time RR interval signal and its EMD original signal is reconstructed, given by the mathematical decomposed IMFs are shown in Fig.1&2. Application of formulae EMD to real time RR interval signal identifies eight to nine n IMFs. The IMFs are zero mean amplitude frequency X (t ) = ∑ hi (t ) + r (n) (2) modulated signal. The decomposition is adaptive and i =1 lossless. The original RR interval signal is reconstructed using decomposed IMFs (Fig.3). The nonstationary trend is Where each hi represents an intrinsic mode function and r(n) removed when the residue or monotonic trend (last IMF) is either a mean trend or a constant. omitted while reconstructing the signal (Fig.4). For each IMF the meanperiod and variance are From the RR intervals the HRV signal or ∆RR computed. The meanperiod is the ratio of distance between signal (Ri+1-Ri) is obtained by computing successive the first and last zero-crossings to number of zero-crossings difference between consecutive RR intervals. The obtained of IMF. HRV signal and its IMFs are shown in Fig.5 and Fig.6. Matlab 7.1 tools are used for the analysis. The obtained RR interval signal using ECG represents the response of the cardiovascular system to ANS 3. Methodology activities not the ANS activities themselves. The SIFTING ALGORITHM: characteristics of cardiovascular system determine how the system responds to ANS activity and can alter significantly Intinsic mode functions of HRV signal Heart rate variability signal 0.5 0.6 0 -0.5 0 200 400 600 800 1000 1200 1400 0.5 0.2 0 the characteristics of the HRV signal. The response -0.2 0 200 400 600 800 1000 1200 1400 0.4 0.1 0 -0.1 0 200 400 600 800 1000 1200 1400 0.3 0.05 characteristics are often nonlinear in nature. The IMFs 0 -0.05 0 200 400 600 800 1000 1200 1400 0.2 0.05 0 -0.05 0 200 400 600 800 1000 1200 1400 capture the all the variations present in the HRV signal. 0.1 0.02 0 -0.02 0 200 400 600 800 1000 1200 1400 0 0.02 0 -0.02 Plotting the variance of all IMFs against its meanperiods -0.1 0 200 400 600 800 1000 1200 1400 -3 x 10 2 0 -2 -0.2 0 200 400 600 800 1000 1200 1400 -3 x 10 5 gives a nonlinear function. The variance of IMF decreases 0 -5 -0.3 0 200 400 600 800 1000 1200 1400 0.01 0 -0.4 -0.01 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400 with increasing meanperiod and this behavior is Fig.5.HRV signal Fig.6. Intrinsic Mode Functions approximated using a geometric function Step 1: All the minima and maxima of the HRV Signal x (t), Y= aXb (3) are located. where Y represents vector of IMF’s variance,. X represents Step 2: Spline Interpolate the minima and maxima points to vector of meanperiods of IMFs, a is constant and b is the obtain lower and upper envelopes of the signal. exponential decrease of the function. The IMFs meanperiod and variance of healthy young control subjects, healthy old Step 3: Compute mean envelope control subjects and long term ST subjects vary m (t)=(maxima’s+minima’s)/2. significantly. The variations in the IMF are quantified by Step 4: Subtract local mean from the original Signal to the parameter b. The parameter b represents the flexibility obtain local details h(t)=x(t)- m(t). of cardiovascular system to ANS activities. The parameter b is estimated using nonlinear curve fitting technique explained below. 256 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 0.15Hz; 3. Very low frequency band from 0.01Hz to Taking logarithm of equation (3), gives 0.04Hz.. ln Y = ln a + b ln X (4) Relative powers of IMF 1 and IMF 2 * * * putting Y =ln Y , X =ln X , A = ln a then the above 0.9 0.8 0.7 nonlinear equation becomes Y* = A* + bX* which is a linear 0.6 0.5 Relative power 0.4 Relative powers of IMF 1 0.3 Relative powers of IMF 2 equation in X. The corresponding normal equations are 0.2 0.1 0 ∑Y = NA* + b∑ X * 1 3 5 7 9 11 13 15 17 19 * (5) Healthy young control records Fig 8: Relative powers of IMF 1 and IMF 2 ∑X * Y =A * * ∑X * + b∑ X *2 (6) 0.01 0.005 IMF1 4 3 2 x 10 -3 IMF2 1 Nonlinear response of IMFs 0.9 0 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 -3 -4 0.8 x 10 IMF3 x 10 IMF4 2 8 0.7 1.5 6 1 4 0.6 0.5 2 0 0 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 -4 IMF5 -4 IMF6 x 10 x 10 0.4 8 8 6 6 0.3 4 4 0.2 2 2 0 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.1 0 0 20 40 60 80 100 120 140 160 180 Fig.7. Curve fitting Fig 9: Welch periodogram of IMFs N represents number of IMFs. Solving the normal equations IMFs Peak Peak power in using least mean square method the variables ‘a’ and ‘b’ are estimated [5]. The simulated response function using the frequency in ms2 estimated parameter is shown in Fig.7. Hz 4. Results and Discussion IMF1 0.2891 0.01 EMD and curve fitting techniques are applied to half an hour HRV signal of 20 healthy young control subjects, 20 IMF2 0.13 0.003 healthy old control subjects and 20 subjects with long term IMF3 0.068 0.002 ST. Empirical mode decomposition adaptively decomposes the half an hour HRV signal into number of Intrinsic mode IMF4 0.03 0.00069 functions (Fig.6). The analysis is done with ∆RR intervals. IMF5 0.021 0.0007 ∆RR (Ri+1-Ri) represents the difference between successive beat intervals. The IMFs are measured by their absolute IMF6 0.01 0.00062 variance, relative variance and meanperiods. The Table-1 Spectral values of IMFs meanperiod is the ratio of distance between the first and last zero-crossings to the number of zero-crossings of IMF. First The meanperiod of IMF2 of healthy young controls subjects 3 IMFs contains more than 92% of total variance. The IMF1 are significantly higher compared to healthy old controls represents the highest frequency or the shortest period subjects and subjects with long term ST. Considering component of the signal. The IMF2 contains the lower meanperiod of IMF2 (2.9724 secs) as threshold value, we frequency or the longer period component of the signal. classified the healthy young control subjects and subjects Since the 1st and 2nd IMF contains more than 85% of total with long term ST with 95% sensitivity and 90% specificity. power they are very significant. The classification is shown in Fig. (10). A threshold value Relative powers are computed with respect to total power of 2.8 secs classifies the healthy old controls subjects and considering all IMFs except the residue with zero subjects with long term ST with 90% sensitivity and 70% meanperiod. In healthy young subjects an increase in specificity shown in Fig .(11). relative power of IMF1 decreases the relative power of IMF2 (Fig.8). IMF 1 and IMF 2 are in phase opposition IMF 2 meanperiod of healthy young and subjects with long term st representing different components of the HRV signal. The original signal is interpolated to 2 Hz for a meaningful 4 3.5 frequency measure. The Welch periodogram (with window 3 2.5 width 1024 and window overlap of 512 samples) of IMFs of 2 Healthy young Sub. With long term st a healthy young control subject are shown in Fig.(9). Table- 1.5 1 1 gives the peak frequency(Hz) and absolute spectralpower 0.5 (ms2-miliseconds square) of IMFs The figure shows the 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 frequency spectrum of the IMFs falls in the recognized Fig.10. Meanperiod comparison of healthy young subjects spectral bands of HRV signal: 1.High frequency band from and subjects with longterm ST. 0.15Hz to 0.5Hz; 2. Low frequency band from 0.04Hz to 257 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 IMF 2 meanperiod of healthy old and sub.with long term st rate variability analysis”, Med.Bio.Eng.Comput., 2001, 39, 4.5 471-479. 4 [3]E.P.Souza Neto, M.A.Custaud, J.C.Cejka,P.Abry, 3.5 3 J.Frutoso, C.Gharib, P.Flandrin, “Assessment of 2.5 2 Healthy old controls sub.with long term st Cardiovascular Autonomic Control by the Empirical Mode 1.5 Decomposition”, Methods Inf Med 2004;43:60-5. 1 0.5 [4] N.E.Huang, Z.Shen, S.R.Long, M.C.Wu, H.H.Shih, 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 etal.1998. “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series Fig.11. Meanperiod comparison of healthy old subjects and analysis” Proc.R.Soc.A, vol 454, pp.903-995. subjects with longterm ST. [5] B.V.Ramana, “Higher Engineering Mathematics”, Tata McGraw-Hill Publishing Company Limited,New Delhi. The parameter b of IMFs of the three groups HRV signal [6] HRV Analysis Software 1.1, developed by The are estimated, average plots are shown in Fig. (12). The Biomedical Signal Analysis Group, Department of Applied estimated parameter b of healthy young control subjects, Physics, University of Kuopio, Finland. healthy old control subjects and long term ST subjects are - http://venda.uku.fi/research/biosignal 1.49, -1.43 and -1.39 (average values only). The more [7] www.physionet.org. negative value represents the flexibility of the system. The [8] Jan W.Kantelhard, Stephan A, Armin Bunde, 2002, healthy young control subject’s cardiovascular system is Multifractal Detrended Fluctuation Analysis of more flexible than healthy old subjects and longterm ST Nonstationary Time Series, Physica A 316, 87-114. subjects. The flexibility of the system decreases in healthy old control subjects and longterm ST subjects. The absolute powers of healthy young control subjects are significantly higher compared to healthy old subjects and long term ST subjects as shown in Fig.(13) (average values only). The higher values of absolute power represent more fluctuating power in the signal. The results show the HRV of healthy young control subjects contains higher power, longer time scales and more adaptive to ANS activities compared to healthy old control subjects and subjects with long term ST. Meanperiod vs relative powers of IMFs 0.7 Absol ut e powe r s I M F1& I M F2 0.6 * healthy young controls o healthy old controls 0.5 + longterm st subjects 0.004 0.003 ers 0.4 Absol ut e elative pow 0.002 power s Absolute power of IMF1 0.3 0.001 R Absolute power of IMF2 0.2 0 1 2 3 0.1 1. Y oung 2. Ol d 3. Long t er m ST 0 0 50 100 150 200 250 300 350 Meanperiod Fig.12 Correlation graphs Fig.13. Absolute powers 5. Conclusion In order to cope up nonlinearity and nonstationarity issue of HRV signal EMD and nonlinear curve fitting techniques are used in this work. The IMFs of HRV signal are negatively correlated. The frequency spectrum of first two IMFs falls in the recognized HF and LF spectral bands of HRV signal. The meanperiod of IMF2 classifies half an hour HRV signal of healthy young control subjects, healthy old control subjects and subjects with long term ST with high sensitivity and specificity. The nonlinear curve fitting technique estimates the flexibility of cardiovascular system. The method is simple, adaptive and no artificial information is introduced in the analysis. 6. References [1] R. M. Carney, J. A. Blumenthal, P. K. Stein, L. Watkins, D. Catellier, L. F. Berkman, S. M. Czajkowski, C. O'Connor, P. H. Stone, K. E.Freedland, “Depression, Heart Rate Variability, and Acute Myocardial Infarction,” Circulation, vol. 104, no. 17, pp. 2024 – 2028, 2001. [2] J.C.Echeverria, J.A.Crowe, M.S.Woolfson, B.R.Hayes- Gill, “Application of empirical mode decomposition to heart 258 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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