2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA December 8-10.Paper no. 400

A Review Work on Reconstruction ofECG WavefromFourier Harmonic Components

Satish Chandra BeraDepartment ofApplied Physics

University of CalcuttaKolkata, India

e-mail: scbl52@indiatimes.com

Abstract-Analysis and reconstruction of ECG wave fromsampled data is an important aspect in estimating thephysiological condition of heart as well as in transmitting theECG data to a remote location. In the present paper softwarebased off line Fourier analysis technique has been reported tofind the harmonic components of ECG wave of a normal subject.The respective Fourier harmonic data have been combined toreconstruct the ECG wave and thus to find the maximumnumber of harmonic present in a normal ECG wave. Theanalysis results are reported in the paper and it has beenobserved that complete reconstruction of ECG wave is possible ifonly fifteen Fourier harmonic data are considered. Thustransmission of ECG wave may be easier since fifteen harmonicsamplitude are only required to be transmitted along with theirrespective phase angles.

Keywords- ECG wave, Fourier analysis, Maximum harmonicnumbers, Off-line analysis, Reconstruction.

I. INTRODUCTION

The ECG signal is generally sampled at a low rate, sampleddata are transmitted over a communication link of a limitedbandwidth to a remote station where analog bioelectric signalsare reconstructed and then analyzed by a diagnostic computer.This transmission process may suffer from error if thebioelectric signal is not sampled at a proper rate depending onmaximum harmonic content of the signal. The ECG signal is aperiodic time varying signal measured and recorded by arecorder on the surface of a human body [12, 13, 14] and thenature of its wave shape is almost identical in all subjects. So itcan be easily sampled and the sampled data can be transmittedthrough a communication link to a remote location. A largenumber of ECG models [5, 8, 12, 13] have been proposed byvarious workers in order to explain the distribution of ECGsignal over the human body. The investigation on analysis ofECG waves by using Fourier transform (FT), Discrete Fouriertransform (DFT), Fast Fourier transform (FFT) etc. techniquesare still being continued by various workers in both time andfrequency planes. Data compression [5, 15], transmission andreconstruction [3, 4, 6, 7, 9, 10, 11] of ECG wave are otherimportant tools that are being used in telemedicine [5] andteletreatment of patients.

Rajan Sarkar, and Nirupama MandalAsansol Engineering College

Asansol, Indiae-mail: rajan_maa@rediffmail.com,

nirupama_cal@rediffmail.com

For accurate transmission and reconstruction of ECG wavemaximum harmonic content of the wave should be accuratelyknown. From some classical works [12,13,14] it appears thatthe maximum harmonic content of normal ECG wave tends tolie near 25Hz. But the works revealing the exact value ofmaximum harmonic content of normal ECG wave appears tobe few. So in the present work an attempt has been made tofind the exact value of maximum harmonic content of normalECG wave. In this work the sampled data of normal 12 leadECG waves available in website www. ysonetorg have beenutilized to find the Fourier harmonic components of ECGwaves by using a software program in C language. In the nextpart of the work the Fourier harmonic components thusobtained have been combined to reconstruct the ECG wave.ECG waves of 50 normal subjects in all 12 leads have beenanalyzed and reconstructed. It has been observed that themaximum harmonic content of normal ECG wave is identicalin all subjects. Results of 5 subjects have been reported in thepaper.

II. METHOD OF APPROACH

The mono-polar ECG signal measured at any electrodelocation on the surface of a normal human body with respectto the Wilson's Central Terminal (WCT) is a periodic signaland hence may be represented by the Fourier harmoniccomponents given by,

n

e(t) = CO + E An sin(nwot) + Bn cos(nwot)n=l

(1)

where e(t) = The instantaneous value ofECG potential.

C0 = Average value ofECG potential signal.

2ITcoo = Angular frequency of fundamental component=T

T = Time period ofECG potential wave.

IEEE Kharagpur Section & IEEE Sri Lanka Section

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2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA December 8-10.Paper no. 400

2 TA A=-|e(t) sin(nwot)dt

0

2TBn = Je(t)cos(nwot)dt

0

(2)

(3)

Assuming A, = C,1 cos On. and B1 = C11 sin O., the aboveequation (1) may be written as

n

e(t) = CO + E Cn sin(nwot + On)n=I

Iwhere C= [A2 +B2]2 and On = tan n_]

(4)

B, =2M2I*Y(k)cosi k

Cj =[A2+B2]2

and Oj = tan ( B)Aj

(7)

(8)

(9)

Using the equation (6), (7), (8) and (9) a software program inC language is developed by following the flowchart as shownin Fig (2)

(5)

Let a typical ECG record as shown in Fig 1 be sampled

manually by following sampling theorem.

TARTfx71

0 0i2 04 0.6 8A

Titme ec

Fig - 1

Let Y (k) be the magnitude of k0 sample at tt instant, thetime period of ECG wave be T and the total number of samplesbe M.

Therefore sample interval

AT =TM

Forksample, t=k*At=k*T/MHence from equation number (2) Aj is given by

2M 2zITkTA j= Y(k)sin(j* * )AT

Tk ~ T M

2 .2*ff*l*k T

or, Aj =- Y(k) sin( )

Similarly from equation number (3), Bj is given by

(6)Fig 2: Flowchart of the software program

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2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA December 8-10.Paper no. 400

III. ANALYSIS

Using the above software program, off-line Fourier analysisof normal ECG records of 50 subjects was made in order tofind out the maximum harmonic content of normal ECGrecords. The harmonic components (C0, An, and B11) wereutilised to reconstruct the ECG wave by the equation (1).Starting from 50 harmonics, resultant ECG wave wasdetermined and then number of harmonics in equation (1) isdecreased one by one until the original ECG wave wasobtained. It has been observed that the total number ofharmonics required to reconstruct the ECG wave is almostidentical in all the normal subjects. The original waves and theresultant waves after adding 13, 14, 15, 16 and 17 harmonicsalong with the original wave for 3 normal subjects (out of 50subjects analyzed in the present work) are shown in Fig. 3, Fig.4, and Fig.5. In each of these figures, first, second, third, fourth,fifth and sixth columns from left denote the original wave andreconstructed waves for 13, 14, 15, 16 and 17 harmonicsrespectively where instantaneous ECG value is plotted againsttime. The rows from 1 to 12 from top denote the ECG waves of12 leads, i, ii, iii, avr, avl, avf, vl, v2, v3, v4, v5 and v6respectively.

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Fig. 3: Original ECG wave and Reconstructed ECG wave byadding 13,14,15,16 and 17 harmonics for 12 leads of subject 1.

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Fig. 4: Original ECG wave and Reconstructed ECG wave byadding 13,14,15,16 and 17 harmonics for 12 leads of subject 2.

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Fig. 5: Original ECG wave and Reconstructed ECG wave byadding 13,14,15,16 and 17 harmonics for 12 leads of subject 3.

In the next part of the present work, the ECG samples of theoriginal wave and those of the reconstructed wave arecompared. The percentage deviation curves for 3 subjects areshown in Fig. 6, Fig. 7 and Fig.8. In each of these figures, first,second, third, fourth and fifth columns denote the percentagedeviation of the ECG samples of reconstructed wave obtainedby adding 13, 14, 15, 16 and 17 harmonics. Respectively wherethe percentage deviation of a sample of reconstructed at anyinstant of time from its respective sample of the original waveis plotted against time. The rows from 1 to 12 from top denotethe ECG waves of 12 leads, i, ii, iii, avr, avl, avf, vl, v2, v3, v4,v5 and v6 respectively.

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2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA December 8-10.Paper no. 400

the Fig 3 to Fig 8. Hence it may be concluded that normalECG wave may consist of only fifteen harmonics. Soduring the transmission of ECG signal, only fifteenharmonic components may be required to be transmitted toa remote station where the original wave may be easilyreconstructed. Thus instead of transmitting huge amount oftemporal data, only 31 data (namely average value cz, and(an,bn) values for fifteen harmonics) obtained from ECGanalysis may be needed to be transmitted so that at thereceiving end ECG wave may be easily reconstructed fromthese data.

ACKNOWLEDGMENT

The authors are thankful to the Department of AppliedPhysics, University of Calcutta, Kolkata, and AsansolEngineering College, Asansol, for providing the facilities inthe present investigation and to carry out this work.

REFERENCES

[1] Laszl6 Szilagyi, Sandor M. Szilagyi, Gergely Fords, Zoltan Beny6,"Quick ECG Analysis for On-Line Holter Monitoring Systems"Proceedings of the 28th IEEE EMBS Annual InternationalConference New York City, USA, Aug 30-Sept 3, 2006

[2] S Yamamoto, S Hamada2, M Miyamoto, J Masumoto, M Komizu,G.Iinuma and N Moriyama, "A new approach towards volumetricassessment of left ventricular function with MSCT", BiomedicalImaging and Intervention Journal, e 50,2006, pp 1-6

[3] Stefan P. Nelwan, Jan A. Kors, Simon H. Meij, Jan H. van Bemmeland Maarten L. Simoons , "Reconstruction of the 12-leadelectrocardiogram from reduced lead sets", Journal ofElectrocardiology, Volume 37, Issue 1, January 2004, Pages 11-18

[4] Fernando Cruz-Rold'an, Manuel Blanco-Velasco and J. IgnacioGodino-Llorente, "Nearly-Perfect Reconstruction Cosine-ModulatedFilter Bank Applied To ECG Signal Coding", XII. European SignalProcessing Conference, September 6-10, 2004, Vienna, Austria, pp2187-2190

[5] D. Narayana Dutt, S. M. Krishnan and N. Srinivasan, "A dynamicnonlinear time domain model for reconstruction and compression ofcardiovascular signals with application to telemedicine",Source:Computers in Biology Publisher: Elsevier and Medicine, Volume33, Number 1, January 2003 , pp. 45-63(19)

[6] Cesmeli; Erdogan, "EKG-less cardiac image reconstruction" USpatent 6434215, August 13, 2002

[7] Cesmeli,Erdogan , "EKG driven CT image reconstruction for cardiacimaging", United States Patent 6438196 , 2002

[8] A.Cimponeriu, C.F.Starmer, and A.Bezerianos, ".Modeling ofventricular tissue and ECG reconstruction in acute and chronicischemia",IEEE conference on Computers in Cardiology 1999 Volume,Issue, 1999, pp 503- 506

[9] P. I. Saparin, M. A. Zaks, J. Kurths, A. Voss, and V. S. Anishchenko,"Reconstruction and structure of electrocardiogram phase portraits",Journal of the American Physical Society, Phys. Rev. E 54, Issue 1 -July 1996, pp 737 - 742

[10] S. Yoshiko, "Analysis of ECG by Means of Reconstruction MethodEffect of the Heart Position on ECG", The Nippon journal of angio-cardiology, Vol.22, No.8(19581120) 1958, pp 563-578

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Fig. 7: Percentage deviation of the sample data of reconstructedwave by adding 13,14,15,16 and 17 harmonics from those oforiginal ECG wave for 12 leads of subject 2.

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due pA-toero in oflin samln of the orgia EGG wave.The sae reDsultshv been obtaie for 47§ oth*er norasllsbjectDfs1rinadd ]it1ion ofp the rslts of 3 sujcs asshoni

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IV.CONCLUSI-OV

FromFig3 to Fi 5 it i observd that he recostructe

Fig. 8percentage deviation of the ECsamplesdtofrcntuthedwavntrebyadin 13ave1,1anfihrmncromthose ofoiiaC aeas

From Fithin tolerable liitis. oberedslihat thcreconstructed

due to error in off-line sampling of the original ECG wave.The same results have been obtained for 47 other normalsubjects in addition of the results of 3 subjects as shown in

978-1-4244-2806-9/08/$25.00C 2008 IEEE 4

2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA December 8-10.Paper no. 400

[11] H. Kato, "Analysis of ECG and VCG by Means of ReconstructionMethod Effect of the Heart Position on ECG and VCG in BundleBranch Block Complicated by Myocardial Infarction",The Nipponjournal of angio-cardiology, Vol.22, No.8(19581120) 1958, pp 551-562

[12] L.A.GEDDES and L.E.Baker, "Principles of Applied BiomedicalInstrumentation" John wiley & sons, Inc. N.Y., 1968.

[13] L. Cromwell, F.J.Wwibell, E.A.Pfeiffer, "Biomedical Instrumentationand Measurements", PHI Pvt.Ltd., 1996.

[14] J.G.Webster, "Medical Instrumentation, Application and Design", 2ndEd.N.Y., John Wiley,1995.

[15] Istepanian and R.S.H. Petrosian, A.A., "Optimal zonal wavelet-basedECG data compression for a mobile-telecardiology system", In, IEEETransactions on information Technology in Biomedicine, Volume:4, Issue: 3, Sep 2000, pp 200-211.

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