IDENTIFICATION AND DELINEATION OF QRS COMPLEXES IN ELECTROCARDIOGRAM USING FUZZY C-MEANS ALGORITHM

Transcription

1 IDENTIFICATION AND DELINEATION OF QRS COMPLEXES IN ELECTROCARDIOGRAM USING FUZZY C-MEANS ALGORITHM S.S. MEHTA 1, C.R.TRIVEDI 2, N.S. LINGAYAT 3 1 Electrcal Engneerng Department, J.N.V, Unversty, Jodhpur. Rajasthan, Inda 2 Electrcal Engneerng Department, SSPC, Vsnagar, GTU, Gujarat, Inda 3 Electrcal Engneerng Department, Dr. B.A. Technologcal Unversty, Lonere, Maharasthra, Inda emal: ssmehta_58@redffmal.com, chrg.trvd@gmal.com, nslngayat@yahoo.com ABSTRACT Over the past few years, there has been an ncreased trend toward processng of the electrocardogram (ECG) usng mcrocomputer. The system based on mcrocomputer can perform the needed medcal servces n extremely effcent manner. In fact, many systems have already been mplemented to perform sgnal processng task such as 12-lead ECG analyss. All these applcatons requre an accurate detecton of QRS complex of ECG. Thus QRS complex detecton s an mportant part of many ECG sgnal processng system. Ths paper presents applcaton of Fuzzy C-Means algorthm (FCM) for detecton of QRS complex n ECG sgnal. The performance of the algorthm s valdated usng orgnal 12-lead ECG recordng from the standard ECG data base. Sgnfcant detecton rate s acheved. The onset and offset of the QRS complexes are found to be wthn tolerance lmt gven by CSE lbrary. Keywords: ECG, QRS complex, FCM, Delneaton 1. INTRODUCTION Correct detecton of QRS-complexes forms the bass of most of the algorthms used n automated processng and analyss of ECG. The other waves lke T and P waves are detected by dentfyng ther poston relatve to QRS complex. The ECG recordng may contan varous challengng problems such as segment wth hgh nose content, sudden change n QRS ampltude and morphology, or muscle and electrode artfact whch are not often detected correctly. Hence relable and correct detecton of QRS complexes, under varous backgrounds, s very mportant n any algorthm used for ECG analyss. The correct performance of these systems depends on several mportant factors such as qualty of ECG sgnal, the appled detecton rule, the learnng and testng dataset used. Fg.1 dsplays typcal ECG cycle. To facltate the analyss, the horzontal segment of ths waveform precedng the P wave s desgnated as baselne or sopotental lne. The P wave represents depolarzaton of atra musculature. The QRS complex s manly due to depolarzaton of the ventrcle. The T wave s the wave of ventrcular repolarzaton. The U wave f present s generally beleved to be the result of after potental n ventrcular muscle. Fg.1 ECG sgnal Varous methods, for QRS detecton are found n the lterature, method based on dgtal flter [6, 22], mathematcal transformaton [2, 4, 11, 19, 20], pattern recognton [9, 28, 24,], artfcal neural networks [31, 13, 25], genetc algorthm [14, 15], heurstc method [7, 23,] and statstcal methods [16, 17, 18]. Ths paper presents an applcaton of Fuzzy C-Means algorthm (FCM) [29] for the detecton of QRS complexes, usng the entropy crtera for the generaton of the feature sgnal. Ths method s sutable for the detecton of all knd of morphologes of QRS complexes. It not only detects the QRS complex but also locates ther 609

2 onset and offset accurately, wthn the tolerance lmts specfed by the physcans n CSE lbrary. 2. OVERVIEW OF FUZZY C-MEANS Pattern recognton technques can be classfed nto two broad categores: unsupervsed technques and supervsed technques. These two types of technques are complementary. For example unsupervsed clusterng can be used to produce classfcaton nformaton needed by the supervsed pattern recognton technque. The Fuzzy C-Means algorthm s an unsupervsed fuzzy clusterng algorthm [29]. Conventonal clusterng algorthm fnds hard partton of a gven dataset based on certan crtera that evaluate the goodness of partton. By hard partton we mean that each datum belong to exactly one cluster of the partton. Whle the soft clusterng algorthm fnds soft partton of a gven dataset. In soft partton datum can partally belong to multple clusters. A soft partton s not necessarly a fuzzy partton, snce the nput space can be larger than the dataset. However, most soft clusterng algorthms do generate a soft partton that also forms fuzzy partton. A type of soft clusterng of specal nterest s one that ensures membershp degree of pont x n all clusters addng up to one,.e., μ ( x ) = 1 x X j c j (1) A soft partton that satsfes ths addtonal condton s called a constraned soft partton. The Fuzzy C-Means algorthm, whch s best known fuzzy clusterng algorthm, produces constraned soft partton. In order to produce constraned soft partton, the objectve functon J 1 of hard c-means has been extended n two ways: (1) The fuzzy membershp degree n cluster has been ncorporated n the formula. (2) An addtonal parameter m has been ntroduced as a weght exponent n fuzzy membershp. The extended objectve functon, denoted by J m, s: J P, V ) = ( μ ( x )) m ( k = 1 xk X C k m x k v (2) where P s fuzzy partton of dataset X formed by C 1, C 2,.., C k and k s number of clusters. The parameter m s weght that determnes the degree to whch partal members of cluster affect the 2 clusterng result. Lke hard c-means, fuzzy c-means also tres to fnd good partton by searchng for prototype v that mnmzes the objectve functon J m. Unlke hard c-means, however, the fuzzy c- means algorthm also needs to search for membershp functon μ C that mnmzes J m. A constraned fuzzy partton {C 1, C 2,.., C k } can be local mnmum of the objectve functon J m only f the followng condtons are satsfed: 1 μ C (x) = 1 2 m 1 k x v = 2 J 1 x v j 1 k, x X (3) v = (4) FCM (X, c, m, ε) X: unlabeled dataset c: the number of cluster to be formed. m: the parameter n objectve functon. ε: threshold for the convergence crtera. 1. Intalze the prototype V ={v 1, v 2,, v k } 2. Repeat steps 3,4 and 5 untl, x X n C = 1 x X μ ( x) C prevous v v C m μ ( x) m x ε 3. V prevous V 4. Compute the membershp functon usng equaton Update the prototype, v n V usng equaton 4. 1 k Based on ths theorem, FCM updates the prototypes and membershp functon teratvely usng equaton 3 and 4 untl a convergence crteron s reached. Here t s worth mentonng few mportant ponts regardng the FCM algorthm: (1) It guarantees converge for m > 1. (2) It fnds local mnmum of the objectve functon J m. (3) The result of applyng FCM to a gven dataset depends not only upon the choce of parameter m and c, but also on the choce of ntal prototype. 610

3 3. ALGORITHM FOR QRS DETECTION In ths secton, t s descrbed how the proposed algorthm can be appled for the detecton of QRS complex. Fg.2 dsplays the result of each step of the proposed method when appled to sngle lead ECG recordng to clearly demonstrate how the algorthm works and ts effectveness n the dentfcaton of QRS complexes. The algorthm s as follows. Step 1: A raw dgtal ECG sgnal s acqured as shown n fg. 2(a). Step 2: A raw ECG sgnal s often contamnated by dsturbances such as power lne nterference and base lne wander. The fnte mpulse response (FIR) notch flter proposed by Van Alste and Schlder [1] s used to remove base lne wander. The adaptve flter used to remove base lne wander s specal case of notch flter, wth notch at zero frequency (or dc). The bandwdth of the flter s ( μ / π ) * f s, where f s s the samplng frequency of the sgnal and μ s the convergence parameter. In ths case, the samplng frequency s 500 Hz and the value of the convergence parameter s Frequences n the range Hz are removed to reduce the base lne drft. The flter proposed by Furno and Tompknson [8] s used to remove 50 Hz power lne nterference. Fg. 2(b) dsplays the fltered ECG sgnal after removal of power lne nterference and baselne wander. Step 3: The gradent at every samplng nstant s calculated to enhance the sgnal n the regon of QRS-complex. The varous slopes obtaned at dfferent samplng nstant are dvded n to two classes namely QRS-class and non-qrs class. Now mean and standard devaton are calculated for each class and probablty of each sample belongng to QRS and non-qrs class s calculated. Step 4: The entropy s used as a sutable crteron n the desgn of optmum feature selecton. Entropy s a statstcal measure of uncertanty. Features that reduce the uncertanty of a gven stuaton are consdered more nformatve than those that have the opposte effect. After calculatng probablty, entropes for the QRS and non-qrs class are calculated usng the equaton: h (x) = -p (x) log e p (x); = 1, 2; x = 1, 2,, n (5) where n s the number of samples present n the ECG recordng. Here n=5000 for CSE database ECG recordngs of ten seconds duraton sampled at 500 Hz. The entropes are then normalzed. Fg. 2(c) and 2(d) dsplay the entropes n the non-qrs and QRS regon. Step 5: The values of QRS entropy are used to form nput vector A 1. Apply Fuzzy C-means algorthm to obtan two cluster centers C 1 and C 2. Calculate the average value of the two cluster centers C average. Cluster center whose value s greater than C average s desgnated as C 1 and other C 2. Calculate the dstance of frst element of vector A 1 from both cluster center C 1 and C 2. If t s closer to cluster center C 1 then assgn value 0 to sgn vector Y 1, otherwse assgn value 1. Repeat the above step for all elements of QRS entropy vector. Step 6: Take the values of non-qrs entropy vector n vector A 2 and repeat the procedure as n step 4. Calculate the dstance of frst element of non-qrs entropy vector from both cluster center C 1 and C 2. If t s closer to cluster center C 1 assgn value 1 to sgn vector Y 2, otherwse assgn 0 values to the sgn vector. Repeat the above procedure for all elements of non-qrs entropy vector. Step 7: The vector Y has value of 1 only where both the sgn vector Y 1 and Y 2 has value of 1. It s dsplayed n Fg. 2(e). It s observed that contnuous tran of 1 s s observed n QRS regons and 0 s n non-qrs regon. 611

4 Fg.2 Results obtan at each step of algorthm Step 8: A contnuous tran of 1 s s pcked and usng ther duraton, average pulse duraton of all the trans of 1 s s evaluated. The tran of 1 s whose duraton turns out to be more than average pulse duraton s dentfed as QRS complex and other ones are dscarded. Ths crteron s known as average pulse wdth crteron. The locaton of QRS complexes, after applyng average pulse wdth crtera s shown n Fg. 2(f). Step 9: The above steps are repeated for all the twelve leads. 4. PERFORMANCE EVALUATION AND DISCUSSION The valdaton of the proposed algorthm for the QRS complex detecton s done usng 125 orgnal, 12 lead ECG record of data set 3 of CSE ECG data base [30]. The data base 3 covers wde varety of the pathologcal case. Every record pcked from CSE ECG data base s of 10 s duraton sampled at 500 samples per second thus gvng 5000 samples. Detecton s sad to be true postve (TP) f the algorthm correctly detects the QRS complex, t s sad to be false postve (FP) f component other than our nterest s detected and t s sad to be false negatve (FN) f the algorthm fals to detect the component of our nterest. The result usng the proposed FCM algorthm on CSE database for 12-lead s gven n Table 1. Fg.3 dsplays performance of the algorthm for the record M01_47. Here, the lead avl of the record has been selected to clearly demonstrate the effectveness of the algorthm. As depcted n fg. 3(a), the preprocessor removes power lne nterference and base lne wander. The QRS (non QRS) entropy s mnmum (maxmum) n the regon where QRS complex (non-qrs) s present as shown n Fg. 3(b) and 3(c). The FCM algorthm correctly detects all the sxteen QRS complexes present n the record. Smlarly, Fg. 4 shows lead avr of record MO1_117 where the algorthm has correctly dentfed nne QRScomplexes out of twelve. The ampltude and hence the slope of the thrd, seventh and eleventh QRS complexes s qute low n comparson wth the other ones. Hence the algorthm has faled to detect these three QRS-complexes marked False Negatves (FN) n the fgure. 612

5 Lead Total QRS Journal of Theoretcal and Appled Informaton Technology QRS Detected FP FN %QRS Detected L L L AVF AVL AVR V V V V V V Table 1 Lead wse test results 5. DELINEATION Delneaton determnes characterstc pont (onset and offset) of QRS complexes n ECG sgnal. The procedure begns by applyng sngle lead QRS detector to recognze beat actvty n each lead, after that wave s onset and offset are searched n each lead. The method performance has been evaluated wth referee s annotaton and combne program medan provded n CSE multlead measurement database. The tme dfference of QRS onset and offset between automatc (proposed FCM algorthm) and referee cardologst annotaton/combne program medan s calculated, whch s known as error. The mean (m) s calculated as average of error. Standard devaton S n ms s calculated. In order to assess the agreement between automatc (proposed FCM algorthm) and referee cardologst annotaton/combne program medan for QRS onset and offset Bland-Altman analyss [3] s done. Fg. 5-6 dsplays Bland-Altman plot of QRS onset and offset respectvely, for comparng the performance of FCM wth combne program medan gven by CSE. In case of QRS onset the standard devaton s ± ms and n case of QRS offset the standard devaton s ± ms, whch s wthn the acceptable lmts. Thus FCM based algorthm not only detects the QRS complexes of ECG, but also delneate them accurately. 6. CONCLUSION Ths paper represents new method for the QRS complex detecton n ECG sgnal usng Fuzzy C-Means algorthm. The method has been comprehensvely tested usng the CSE ECG database coverng wde varety of QRS complexes. A consderable detecton rate s obtaned. The delneaton results show that the standard devatons of the error are wthn the tolerance lmt. 613

6 Fg. 3 Detecton of QRS complexes n lead avl of record M01_47 Fg. 4 Detecton of QRS complexes n lead avr of record M01_

7 Fg. 5 Bland-Altman plot for QRS onset Fg. 6 Bland-Altman plot for QRS offset 615

8 REFERENCES [1] Alste Van J. A., and Schlder T. S., Removal of base-lne wander and power lne nterference from the ECG by an effcent FIR flter wth a reduced number of taps, IEEE Trans. Bomed. Eng., vol. 32, pp , [2] Bentez D., Gaydeck P. A., Zad A., and Ftzpatrck A. P., The use of Hlbert transform n ECG sgnal analyss, Comp. n Bo. and Med., vol. 31, pp , [3] Bland J. M., Altman D. G., Statstcal Methods for assessng agreement between two methods of clncal Measurement, Lancet, pp , [4] Chen S. W., Chen H. C. and Chan H. L., A real tme QRS detecton method based on movng-averagng ncorporatng wth wavelet denosng, Comp. Methods and Progs. n Bomed., vol. 82, pp , [5] Chouhan V. S. and Mehta S.S., Detecton of QRS-complexes n 12-lead ECG usng adaptve quantzed threshold, Internatonal Journal of Computer Scence and Network Securty, vol. 8, no.1, pp , [6] Engelse W. A. H. and Zeelenberg C., A sngle scan algorothm for QRS detecton and feature extracton, Computer n Cardology, IEEE compu. Soc., pp , [7] Fraden J. and Neurman M. R., QRS wave detecton, Med. & Bo comp., vol. 18, pp , [8] Furno G. S., and Tompkns W. J., A learnng flter for removng nose nterference, IEEE Trans. Bomed. Eng., vol. 30, pp , [9] Grtzal F., Towards a generalzed scheme for QRS Detecton n ECG Waveforms, Sgnal Processng, vol. 15, pp , [10] Kohler B. U., Hennng C. and Orglmester R., The prncples of software QRS detecton, IEEE Eng. n Med. and Bo, pp , 2002 [11] Kyrkos A., Gakoumaks E. A. and Carayanns G., "QRS detecton through tme recursve predcton technque", Sgnal Processng, vol. 15, pp , 1988 [12] Mehta S.S., Sexana S.C. and Verma H.K, Computer-aded nterpretaton of ECG for dagnostcs, Internatonal Journal of System Scence, vol. 27, pp , [13] Mehta S.S., Dave V., Vyas S.D. and Chouhan V.S., Detecton of QRS-complexes n 12-lead ECG usng Error Back Propogaton neural network, Int.Cong. on Bo. and Med. Engg., Sngapore, [14] Mehta S. S, Bansal S. K., Lngayat N. S., Applcaton of Genetc Algorthm for ECG Pattern Recognton, UGC Natonal Conference on Advances n Computer Integrated Manufacturng (NCACIM), Jodhpur, Inda, [15] Mehta S. S, Bansal S. K., Lngayat N. S., Detecton of QRS complexes n Prcordal Leads of ECG usng Genetc Algorthm, Natonal Conference on Informaton Technology Engneerng Perspectve and Practces, Tapar Insttute of Technology, Patala, Inda, [16] Mehta S. S. and Lngayat N. S., Development of Entropy based algorthm for cardac beat detecton n 12-lead electrocardogram, Sg. Proc., vol. 87, pp , [17] Mehta S. S. and Lngayat N. S., Combned Entropy based method for detecton of QRS complexes n 12-lead electrocardogram usng SVM, Comp. n Bol. And Med, vol. 38, pp , [18] Mehta S.S. and Lngayat N. S., ECG Pattern Classfcaton usng Support Vector machne 12-lead Combned Entropy, The Sxth Internatonal Conference on Advances n Pattern recognton, Indan Statstcal Insttute, Kolkota, Inda, [19] Mehta S. S., Lngayat N. S., Development of SVM based classfcaton technques for the Delneaton of wave components n 12-lead electrocardogram, Bomedcal Sgnal Processng and Control, 2008 (Artcle n Press). [20] Murthy I. S. N. and Prasad G. S. S. D., Analyss ECG from pole zero models, IEEE Trans. Bomed. Eng., vol. BME-39, no.7, pp , [21] Murthy I. S. N. and Nranjan U. C., Component wave delneaton of ECG by flterng n the fourer doman, Med.& Bo. Eng. and Compu., vol.30, pp , March [22] Okada M., A dgtal flter for the QRS complex detecton, IEEE Trans. Bomed. Eng., vol. BME-26, no.12, pp , Dec [23] Pan J. and Tompkns W. J., A real tme QRS detecton algorthm, IEEE Trans. Bomed. Eng., vol. 32, pp , [24] Sornmo L., Pahlm O. and NyGards M., Adaptve QRS detecton: A study performance, IEEE Trans. Bomed. Eng., vol. BME-32, no. 6, pp , [25] Suzuk Y., Self organzng QRS wave Recognton n ECG usng Neural networks, 616

9 IEEE Trans. Bomed. Eng, vol. 6, pp , [26] Trahanas P. and Skordalaks E., Syntactc pattern recognton of the ECG, IEEE Trans. on Pattern Analyss and Machne Intell.,vol.PAMI-12, no.7, pp , [27] Trahanas, P. E., An approach to QRS complex detecton usng mathematcal morphology, IEEE Trans. Bomed. Eng., vol. 40, pp , [28] Trahanas, P. E., and Skordalalks, E., "Bottom up approach to the ECG pattern-recognton problem", Med. Bo. Eng. and Compu, 27, [29] V. Deelport and D lesch Fuzzy C-means algorthm for code book desgn n vector quantzaton, Electronc letter 1994, vol. 30, no.13. [30] Wllems J.L., Arnaud P., Bemmel J. H. V., Bourdllon P. J., Degam R., Dens B., Graham I., Harms M.A., Mcfarlane P.W., Mazzacca G., Meyer J. and Zywetz C., Establshment of a reference lbrary for evaluatng computer ECG programs, Computers n Bomedcal Research vol. 18, pp , [31] Xue Q., Hu Y.M. and Tompkns W.J., Neural network based adaptve matched flterng for QRS detecton, IEEE Trans. Bomed. Eng., vol.-39, pp , BIOGRAPHIES Chrag R. Trved receved the B. E. degree n Electrcal Engneerng from North Gujarat Unversty, Patan, Inda n He s Lecturer n Electrcal Engneerng at Swam Sachchdanand Polytechnc, Vsnagar, Gujarat, Inda. He had submtted hs dssertaton for award of M.E degree n Electrcal Engneerng Department, MBM Engneerng College, J. N. Vyas Unversty, Jodhpur. He s workng n the area of ECG sgnal processng. Ntn S. Lngayat receved the B.E. degree n Electrcal Engneerng from the Unversty of Poona, Pune, Inda n 1992 and the M.Tech. degree from Indan Insttute of Technology Bombay, Mumba n He receved Ph.D degree n Electrcal Engneerng from MBM Engneerng College, J. N. Vyas Unversty, Jodhpur n He s Head, Electrcal Engneerng Department, Insttute of Petrochemcal Engneerng of Dr. B.A. Technologcal Unversty, Lonere, Maharashtra, Inda. He s workng n the area of bomedcal sgnal processng. Sarabjeet S. Mehta receved the B.E. degree n Electrcal Engneerng and M.E. degree n Control System from J. N. Vyas Unversty, Jodhpur, Inda n 1980 and 1987 respectvely. He receved Ph.D. degree n Electrcal Engneerng from Indan Insttute of Technology, Roorkee, Inda n Presently he s Professor n Electrcal Engneerng Department, J. N. Vyas Unversty, Jodhpur, Inda. Hs research nterests nclude pattern recognton, artfcal neural networks, bomedcal engneerng and soft computng. 617