1 INTRODUCTION 2 HEART-BEAT CYCLE DETECTION

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1 Abstract: Ths artcle ntrouces a metho for constructng a heart-beat sgnal from a long recor of phonocarogram (PCG). The metho comprses a seres of algorthms that ecompose a long ata recor of heart soun to ts heart-beat cycles usng the smultaneously recore electrocarogram (ECG). Frst the carac cycles are entfe usng the synchronze ECG sgnal. The corresponng heart-beat cycles are then extracte from the PCG sgnal an use to construct a template sgnal. Usng the correlaton of the heart-beat sgnals wth the template sgnal, the heart-beats corrupte by nose are entfe an scare. The remanng heart-beats are then use to construct a heart-beat sgnal whch s free of artefacts an can be use for varous heart soun analyss purposes. INTRODUCTION A phonocarogram (PCG) s a recorng of an acoustc wave prouce by perocal contractons an relaxaton of the heart muscles along wth acceleraton an eceleraton of bloo wthn the carac structure. The sequence of events occurrng urng such actvtes s calle the carac cycle. Each carac cycle s categorze nto four basc groups: frst, secon, thr, an forth heart souns []. Phonocarograms have been stue for agnostc purposes for varous heart seases [2]-[5]; an also for better unerstanng of heart souns [6]-[8]. The PCG sgnals are oscllatory n nature; although t may not be exactly peroc n strct mathematcal sense. Observaton of the evoluton of these sgnals reveals that there are smlar events or peros, but they may not exactly reprouce themselves. Furthermore, phonocarograms are quas-statonary sgnals; consequently, ther characterstcs o not change rastcally wthn few mnutes of recorngs. However, analyzng long ata recors of PCG sgnals usng some sgnal processng technques such as tmefrequency or wavelet methos mposes a huge computatonal buren. The heart-beat sgnal extracton technque presente heren can be use to obtan a sngle heart-beat sgnal encapsulatng the characterstcs of the PCG sgnal. The extracte heart-beat sgnal can then be use for analyss or agnostc purposes. The propose heart-beat sgnal extracton technque s explane n the succeeng two sectons. Frst the electrocarogram beat cycle etecton algorthm s ntrouce n Secton 2. In Secton 3, the segmentaton of the PCG sgnal an the reconstructon of a sngle heart-beat sgnal are explane. Then n Secton 4 expermental results are presente, followe by a conclung remarks n Secton 5. 2 HEART-BEAT CYCLE DETECTION The central ea of the propose heart-beat separaton scheme s the ecomposton of phonocarograms nto heart-beat sgnals through the etecton of the heart-beat cycles of the synchronze electrocarograms; beat cycle etecton s easer usng ECG sgnals. In orer to accomplsh ths, frst the QRS peaks of the ECG sgnal are etecte, an then the corresponng beat cycles are entfe. 2. QRS Peak Detecton QRS etecton s one of the mportant tasks n ECG analyss; a great eal of research effort has been evote to ths task [2]. Most of the QRS etectors escrbe n the lterature are ame for analyss of the ECG sgnal tself. Our am, however, s to fn the temporal locaton of the peaks of the QRS complexes an use them to separate the heart-beat cycles from the PCG sgnal. Our QRS etecton scheme s ve nto two sub-systems: the preprocessor an the ecson rule system, as shown n Fgure. The man concern n the QRS etector s to avo etecton of false peaks, f any. xn ( ) Low- Pass Ampltue rmalzaton Decson Rule yn ( ) Processor Fgure QRS peak etector. Fgure 2 shows the QRS etecton algorthm. The nput sgnal, S ecg (t), s ntally normalze n ampltue. Ths s essental snce a thresholng scheme s employe for etecton of peaks of the QRS complexes. There are usually some fluctuatons n the QRS ampltues, hence the threshol level s set to a value V th gven n Eq. ().

2 Start S ecg (t) V th.5 Threshol Set threshol V th Set scannng wnow W m S w () t S ecg ()W t m ( t m) S w () t > V th +.5 τ τ 2 (a) One ECG cycle β ----S t w () t zerocrossng n β PK() t max ( sw () t ) Is S ecg (t) scanne all? En.8 V th Fgure 2 QRS peak etecton algorthm. () W m ( t km) complex above threshol. The slope of the wnowe ECG sgnal above threshol level s β () t W m ( t ( k+ )m) mllsecons wnow (b) Peak of QRS Complex. Fgure 3 The process of thersholng an wnowng the ECG sgnal [ S t ecg ()W t m ( t m) ] W m ( t ( k+ 2 )m ) (2) The zero crossng n β () t represents a local maxmum n the ECG sgnal,.e., a potental QRS peak. The nput ata s scanne wth a rectangular wnow the wth of whch s much less than a heart-beat pero, whose length coul vary from about half a secon to more than one secon epenng on the person. A small wnow sze reuces the possblty of mssng any QRS peaks urng the scannng process. Wthn each wnow the parts of the ata that are above threshol are selecte an ther maxmum value s foun. The thresholng scheme ensures that only regons of the sgnal that are n the vcnty of the peak of the QRS complex are consere for peak etecton. In Fgure 3 shows one cycle of an ECG sgnal wth threshol level V th an a scannng wnow W m of length m. 2.2 True QRS Interval Detecton The prmary objectve of the true QRS nterval etecton s to ensure that the peaks etecte wth the algorthm of Fgure 2 are real QRS peaks; that s, we want to entfy any false etectons an remove them. There are two stuatons n whch a false etecton may occur: a presence of an artefact whose heght s hgher than the threshol level, or the presence of small fluctuatons (ue to nose) near the QRS peak. The mean nterspke (.e., QRS peak-to-peak) nterval s calculate as In orer to stngush an locate the poston of the actual QRS peak, the slope of the sgnal above threshol s calculate wthn each wnow. Let W m ( t m) be the th wnow an S ecg (t) be the porton of the QRS M T M PK ( j + ) PK() j j (3)

3 where M s the number of etecte QRS peaks, an PK s a vector contanng the locatons of the QRS peaks. We efne the mnmum an the maxmum acceptable tme nterval between two consecutve QRS peaks as: T mn T.T T mx T +.T (4) (5) The average nterval between the th peak an ts nearest neghbours s calculate as follows: t δt + t (6) where t an t + are the tme ntervals between the th peak an ts preceng an succeeng peaks, respectvely; that s, t PK() PK( ) t + PK( + ) PK() (7) (8) The nterval, δt, for every etecte peak s compare wth T mx an T mn. If t s wthn the nterval [ T mn, T mx ], t s accepte as a true QRS peak, otherwse t s consere to be a false peak, an hence rejecte. That s, for a true QRS peak, Eq. (9) must be satsfe. t δt + t Φ() PK() q M β Φ t Start QRS Peak Locatons, PK Mean Interspke Interval, T T mn δt T mx β() PK( q) [ ] En Fgure 4 QRS nterval etecton algorthm. T mn δt T mx (9) When a false QRS peak occurs at poston, the value of ts average nterval δt, an possbly those of ajacent peaks, wll not satsfy Eq. (9). In partcular, there wll be a local valley centre on n the values of the vector δt, the vector whose elements are the ntervals δt. In orer to fn the locaton of the false QRS peak, t s necessary to fn the poston of the bottom of the valley. Ths s accomplshe by calculatng the ervatve of the vecotr δt an fnng the poston at whch the ervatve becomes zero. The propose QRS nterval etecton algorthm s shown n Fgure ECG Beat Cycle Detecton In orer to etect the beat cycles, the begnnng of each carac cycle wth respect to QRS peaks must be entfe. The P-wave s chosen as the begnnng of the carac cycle. If the tme nterval between two consecutve QRS peaks s ve nto three sectons, the P-wave occurs n the thr secton. The onset of the thr secton of the th QRS peak s gven by Eq. (). tr PK() -- [ PK() PK( ) ] 3 () where ts offset tme s the th entry n the vector PK. Ths s llustrate n Fgure () P-Wave (2) (3) τ f τ t onset an offset Fgure 5 Two consecutve cycles of ECG sgnal for P-wave recognton.

4 Snce we are gong to use the QRS peak etector to fn the peaks of the P-waves, t s essental to remove the porton of the QRS complex that falls wthn secton three. Ths s the part of the sgnal between τ f an τ t n Fgure 5. Ths s accomplshe by calculatng the slope of the sgnal from tr to PK as: mp ----S t ecg () t for tr t PK() () The sgnal mp s scanne n a bottom-up fashon; that s, scannng starts from the en an procees towars the begnnng. When the frst zero crossng s encountere, the scannng s stoppe. Ths pont correspons to the frst mnmum n the sgnal just before the QRS complex. The part of the sgnal to the rght of the zero crossng s scare. In orer to etect the peak of the P-wave, the algorthms of Fgure 2 an 4 are apple to the remanng part of the sgnal. Ths process s repeate for all etecte QRS ntervals. The fnal outcome s a vector the same sze as the ECG sgnal S ecg () t, the elements of whch are all zeros except at the locatons of the P-wave peaks, where a value of one s recore. The flow chart of ths algorthm s shown n Fgure 6. mp Mx Start QRS Peak Locatons, PK Intalze v(t) to zero r PK ( PK PK ) 3 Λ() t S ecg () t for ---- ( Λ() t ) t µ t mp S ecg () t for r t PK r t µ Peak Detector of Fg. 2 wth V th. + 3 SEGMENTATION OF PCG SIGNAL The prme purpose for evelopng the QRS etecton algorthm was to evse a scheme whch woul enable us to ecompose the PCG sgnal nto ts beat cycles wth mnmum error of mss-etecton. As was mentone earler, the ECG an PCG sgnals must be recore smultaneously. Therefore, the ecomposton process of the PCG sgnal nto ts consttuent beat cycles can be accomplshe by smply algnng t wth the sgnal obtane by the algorthm of Fgure 6, v ecg () t, whch s a tran of mpulses locate at the starts of the carac cycles. 3. Ientfcaton of Artefact-Free Beat Cycles Among the separate heart-beat cycles, t s necessary to entfy an scar those cycles that contan artefacts. Let each PCG heart-beat sgnal be enote by S pcg () t, where s the orer of the beat cycle wthn the PCG sgnal. A correlaton scheme s evse to stngush the artefact-free heart-beat cycles wthn the PCG sgnal. A template sgnal s constructe for ths purpose, an every beat cycle s compare wth t. The template sgnal, S tmp () t s constructe by takng the ensemble average of all the beat cycles. ν() t t peaks of P-wave M En The egree of smlarty between the beat cycle waveforms an ths template sgnal s measure by calculatng the correlaton coeffcent of the template sgnal wth each of the beat cycles. The correlaton coeffcent between the template sgnal an a gven beat cycle s efne as (3) where C tmp, btc s the cross-covarance between the template sgnal an the beat cycles, C tmp an C btc are, respectvely, the covarances of the template sgnal an the beat cycle. Fgure 6 ECG beat cycle etecton. ρ C tmp, btc C tmp C btc S tmp () t M ---- S M pcg () t where M s the total number of heart-beat cycles. (2) In orer to obtan the maxmum correlaton coeffcent possble, the beat cycle s shfte wth respect to the template sgnal. In other wors, the correlaton coeffcent s compute at the smallest tme-lag whch yels maxmum cross-correlaton between the two sgnals.

5 The cross-correlaton of the template sgnal wth the beat cycle s efne as N X( τ) S tmp ( n)s btc ( n τ) n (4) where N s the length the template sgnal, whch s equalt to the length of the beat cycle. In orer to entfy the beat cycles corrupte wth artefacts, a threshol level for the correlaton coeffcents s set to.9; that s, those beat cycles that have ther correlaton coeffcent below 9% of the maxmum correlaton coeffcent are rejecte. 3.2 The Heart-beat sgnal The fnal heart-beat sgnal s reconstructe usng only the artefact free beat cycles. The mean sgnal of the beat cycles s compute n the frequency oman. Frequency oman averagng s use to avo errors that may occur ue to small mss-algnments of the beat cycles n the tme oman. To obtan the tme oman sgnal, the average frequency oman sgnal s converte back to the tme oman usng the nverse screte Fourer transform (IDFT). The heart-beat cycle reconstructon algorthm s presente n Fgure 7. 4 RESULTS Start S pcg (); t β P ecg (); t ecompose PCG to ts beat cycles; S tmp () t M ---- S M btc () t S pcg m () t In ths secton we present the results of applyng the algorthms presente n ths artcle to real sgnals recore from patents suspecte wth coronary artery sease. Thrty secons of synchronously recore PCG an ECG sgnals are shown n Fgure 8 below; clearly the PCG sgnal contans some artefacts. N X( τ) S tmp ( n)s btc ( n τ) n K τ m t max( X( τ) ) τ m M Sbtc () t S btc ( t τ m ) ρβ ( ) C tmp, btc C tmp ma x( ρβ ( )).max( ρβ ( )) α ρα ( ) K C btc Y α () t Sbtc α () t α M en β β + α α + Fgure 8 Synchronously recore PCG (a) an ECG (b) sgnals. The ECG sgnal was scanne wth a mllsecon long rectangular wnow. A threshol level of.8 was selecte, an the QRS etecton algorthm was apple. The etecte QRS peaks were examne wth the algorthm of Fgure 4 for false etectons. Then the startng ponts of the carac cycles were etecte usng the ECG beat-cycle etecton algorthm (Fgure 6). The output of the ECG cycle etecton algorthm, the sgnal ν ecg () t, s shown n Fgure Fgure 7 Heart-beat constructon algorthm. Fgure 9 The sgnal ν ecg () t obtane from the ECG beatcycle etecton algorthm.

6 The PCG carac cycles were separate by algnng the PCG sgnal (Fgure 8(a)) wth the sgnal ν ecg () t of Fgure 9. These extracte PCG carac cycles, shown n Fgure (a), were then use to reconstruct the PCG template sgnal presente n Fgure (b) (a) Orer of Beat Cycles as they appear n PCG sgnal Fgure Correlaton coeffcents for sgnals of Fg. (a) wth the template sgnal of Fg. (b). (b) (a) Fgure (a) Beat cycles of PCG sgnal of Fgure 8 (a). (b) PCG template sgnal. The correlaton coeffcents of the template sgnal of Fgure (b) wth each beat cycle of Fgure (a) were calculate; the compute correlaton coeffcents are tabulate below (TABLE ) an plotte n Fgure. In Table, four correlaton coeffcents fall below.9, but one of them s equal to.8946), very close to.9. If the threshol level s set at.88, as shown n Fgure, only tree beat cycles that have ther correlaton coeffcents below the threshol level, an hence are rejecte. Fgure 2 llustrates the accepte an rejecte PCG beat cycles. The fnal heart-beat cycle s constructe usng only the artefact free beat cycles as escrbe n Secton 3.2. The fnal PCG beat sgnal s presente n Fgure 3. It s an artefact free sgnal, whch represents the typcal heart-beat cycle of the person from who the sgnal was recore. TABLE Correlaton coeffcents of PCG template sgnal wth nvual beat cycles Fgure 2 (a) Accepte beat cycles, an (b) rejecte beat cycles for PCG sgnal of Fgure 8 (a)..5.5 Fgure 3 Fnal PCG heart-beat sgnal. (b)

7 5 Conclusons In ths artcle a metho was escrbe whch ecomposes the PCG sgnal nto ts consttuent heart-beat cycles usng the ECG sgnal. Fve algorthms have been evse to carry out ths task. These algorthms are summarze n TABLE 2. TABLE 2 Algorthms use to ecompose the PCG sgnal an reconstructon of an artefact-free heart-beat sgnal. ) QRS peak etector. 2) QRS nterval etector. 3) ECG beat cycle etector. 4) PCG beat cycle etector. 5) Heart-beat sgnal reconstructon algorthm. Frst the QRS peaks are etecte n the ECG sgnal, then the false peaks are entfe an remove usng the true QRS nterval etector. The thr algorthm s use to solate the carac cycles from the ECG sgnal. Ths s one by etectng the peak of the P-wave as the begnnng of the carac cycle. The startng ponts of the carac cycles are then use to ecompose the PCG sgnal nto beat-cycles. A template sgnal s forme from the PCG beat cycles. The correlaton coeffcents of the template sgnal wth the nvual beat cycles are use to entfy the artefact free heart-beat cycles. Usng frequency oman averagng, the mean of the heart-beat cycles s foun an converte back to the tme oman as the fnal heart-beat sgnal. These algorthms were successfully apple to real sgnals recore from patents suspecte wth coronary artery sease. REFERENCES [] Rushmer, R. F., 97, Carovascular ynamcs, W. B. Saners Company, Phlaelpha, PA. [2] Akay, M., Welkowtz, W., Semmlow, J. L., et al., 99, Me & Bol. Eng. & Computng, 29, [3] Tnat, M. A., Bouzeroum, A, Mazumar, J., an Mahar, L., 997, Tme-Frequency analyss of heart souns before an after angoplasty, Proc. IEEE Int. Conf. on Dgtal Sgnal Processng (DSP 97), 75-79, July, 997, Santor Greece. [4] Tnat, M. A., Bouzeroum, A, Mazumar, J., an Mahar, L., 998, Short tme Fourer analyss of phonocarograms before an after angoplasty, Proc. of Thr Bennal Eng. Math. an Applcaton Conf., (EMAC 98), , July 998, Aelae Australa. [5] Benetley, P. M., Grant, P. M., an McDonnell, J. T. E., 998, IEEE Trans. Bome. Eng., 45, [6] Frensen, G. M., Jannett, T. C., Jaallah, M. A., et. al., 99, IEEE Trans. Bome. Eng., 37, pp [7] Woo, J. C., an Barry, D. T., 994, Me. Bol. Eng. Comput., 32, S7-S78. [8] Zhang, X., Duran, L.-G., et. al, 998, IEEE Trans. Bome. Eng., 45,