Automatic ECG wave extraction in long-term recordings using Gaussian mesa function models and nonlinear probability estimators

computer methods and programs in b iomed ic ine 8 8 ( 2 0 0 7 ) 217233

journa l homepage: www. int l .e lsev ierhea l th .com/ journa ls /cmpb

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Article history:

Received 15 March 2007

Received in revised form

4 September 2007

Accepted 19

Keywords:

Machine-lea

Neural netw

Orthogonal

Adaptive sig

Cardiac wav

ECG

This paper describes the automatic extraction of the P, Q, R, S and T waves of electrocardio-

graphic recordings (ECGs), through the combined use of a new machine-learning algorithm

termed generalized orthogonal forward regression (GOFR) and of a specic parameterized

function termed Gaussian mesa function (GMF). GOFR breaks up the heartbeat signal into

1. Int

Long-termrecords thato their amand oftenediting lonalthough thclinically reoped to aucardiac comtion [11,12]addition toautomaticing the card

CorresponE-mail a

0169-2607/$doi:10.1016/September 2007

rning

ork

forward regression

nal processing

e recognition

Gaussian mesa functions, in such a way that each wave is modeled by a single GMF; the

model thus generated is easily interpretable by the physician. GOFR is an essential ingredi-

ent in a global procedure that locates the R wave after some simple pre-processing, extracts

the characteristic shape of each heart beat, assigns P, Q, R, S and T labels through auto-

matic classication, discriminates normal beats (NB) fromabnormal beats (AB), and extracts

features for diagnosis. The efciency of the detection of the QRS complex, and of the dis-

crimination of NB from AB, is assessed on the MIT and AHA databases; the labeling of the P

and T wave is validated on the QTDB database.

2007 Elsevier Ireland Ltd. All rights reserved.

roduction

ECGs have many applications, especially 24ht reect the effects of daily physical activities. Duebulatory character, such ECGs tend to be very noisy,require analysis by experts [13]. Reviewing andg-term ECG data are time-consuming processes,e data stream may contain a very small amount oflevant information. Algorithms have been devel-tomatically detect, classify and analyze electricalplexes [410]: they include wavelet decomposi-

, and radial basis function (RBF) modeling [13]. Inthese methods for parameter extraction, severalclassication methods have been used for label-iac waves such as neural networks [14,15], Hidden

ding author. Tel.: +33 1 40 79 46 96; fax: +33 1 47 07 13 93.ddress: [email protected] (R. Dubois).

Markov Models [1618] or Support Vector Machines [19]. Butthe specicity and the sensitivity of such algorithms are farfrom being fully satisfactory. Even for 10-s ECGs obtained insupine conditions, there is still a need for improved solutions[20,21].

In the present paper, we describe a new algorithm, whichautomatically detects the electrical waveforms from cardiaccomplexes (P-Q-R-S-T), and further discriminates abnormalbeats (AB) from normal beats (NB) originating from the sinusnode. The core of our method is the modeling of cardiacbeats by a new class of parameterized functions (Gaussianmesa functions or GMFs) which were specially designed formodeling each cardiac waveform by a single function. Theestimation of the parameters of the GMF is performed byan original algorithm termed generalized orthogonal forward

see front matter 2007 Elsevier Ireland Ltd. All rights reserved.j.cmpb.2007.09.005atic ECG wave extraction in lGaussian mesa function modbility estimators

boisa,, Pierre Maison-Blancheb, Brigitte Que dElectronique (CNRS UMR 7084), ESPCI-Paristech, 10 rue Vauquee hospital, APHP, Paris 7 University, France

l e i n f o a b s t r a c tg-term recordingsand nonlinear

ta, Gerard Dreyfusa

005 Paris, France

218 computer methods and programs in b iomed ic ine 8 8 ( 2 0 0 7 ) 217233

regression (GOFR). Once a heartbeat is segmented into GMFs,a medical assignment (P, Q, R, S or T) for each function isperformed automatically, based on probability estimationsprovided by neural networks. The latter step is performedwith remarkable accuracy and simplicity, due to the fact thatthe GMF modeling extracts features that are very relevant forquantitative electrocardiology.

The above algorithms are embedded into a global analysisprocedure that does not require any ad-hoc adaptation for agiven ECG recording, and allows multi-lead ECG processing:manual lead selection by the cardiologist is not required.

2. Me

Fig. 1 showdescribed isecond stepprerequisitpost-proce

2.1. EC

In this studticated, but[22] and Mcomputatioiso-electricamplitude.is based onthe signal (which therelatively of the noisinto cardiadeveloped

Since thdescribed isegmentatiin this papprocedureInteresteddescriptionand 8490.

2.2. He

In the presin two steing. To modMesa Funct

machine-learning algorithm, called generalized orthogonalforward regression (GOFR), was designed for adapting thosefunctions to the cardiac signal [26,27]. The purpose of couplingGMF and GOFR is to provide a mathematical model in whicheach monophasic cardiac waveform from the body surfaceECG is modeled by a single GMF, and each biphasic waveformby two GMFs, which greatly facilitates the subsequent label-ing of the waves. The GMF function is dened in Section 2.2.1,and the GOFR algorithm in Section 2.2.2. The labeling proce-dure, which performs the labeling of each cardiac wave fromthe corresponding GMF(s) is described in Section 2.2.3.

Gaectriby tmonof uicwaositea givave ation

tionor t

xhibieteriofmve pctedF det futivesis esforveeviaion ontals mu

Mor tonal,d regas cot) algise mtions behm i

ceduthods

s pictorially an overview of the whole algorithmn this section. Although the paper focuses on the(heartbeat processing), preprocessing, which is a

e for ECG analysis, is briey described; examples ofssing are described for performance assessment.

G signal preprocessing

y, the preprocessing methods used are unsophis-they are suitable for the data present in the AHA

IT [23] databases used here. The rst step is then of the electrical baseline, in order to obtain anreference for the computation of the waveformThe algorithm that corrects for baseline variationsthe detection of the active and passive zones of

an active zone is dened as a time interval duringheart has an activity); the result of that step is aat iso-electric baseline, together with an estimatee level. The ECG signal is subsequently segmentedc complexes by an efcient and popular algorithmby Pan and Tompkins [24].e focus of this paper is the heartbeat processingn the next section, the baseline correction and theonof the rawsignal intoheartbeats arenot detaileder but are only introduced as a part of the wholefor the analysis of the MIT and AHA databases.readers may refer to [25] and [26] for a detailed; many examples are provided in [25], pages 5964

artbeat processing

ent approach, heartbeat processing is performedps, namely heartbeat modeling and wave label-el the heartbeat, a new function, called Gaussianion (GMF), was introduced; in addition, an original

2.2.1.The elsentedcan beposedbiphasof opp

Onmay horientaderivabe atmay eparamabilitywith connethe GM

Thaderivawhichrithms

Thedard ddeviathorizostraint

2.2.2.In ordeical sigforwarGOFR,pursuia precdescrip

Letalgorit

Fig. 1 Overview of the global analysis proussian mesa function (GMF)cal cardiac cycle on surface ECG is typically repre-hree waveforms: P, QRS and T. Both P and T wavesophasic or biphasic, and the QRS complex is com-p to three monophasic waveforms Q, R and S. Aveformcanbe seenas twomonophasicwaveformspolarities.en ECG lead, each monophasic cardiac waveformpositive or a negative polarity depending on theof the cardiac electrical activity with respect to theunder consideration. These individual waves mayall, narrow or wide, symmetric or asymmetric, ort a plateau. A Gaussian mesa function (GMF) is azed function that was designed to model the vari-onophasicwaveforms. It is an asymmetric functionarameters, made of two half-Gaussian functionstogether by a horizontal line (Fig. 2). The shape ofpends on its ve parameters.nction is continuous, differentiable, and all itswith respect to its parameters are continuous,

sential when applying standard optimization algo-parameter estimation.parameters are thus: (location in time), 1 (stan-tion of the rst Gaussian function), 2 (standardf the second Gaussian function), L (length of thepart), A (amplitude of the GMF). The following con-st be satised: 1, 2 > 0, L 0.

deling algorithmefciently t parameterized functions to a biolog-a new algorithm, termed generalized orthogonalression (or GOFR), was developed. The efciency ofmpared to that of the standard OFR (or projection-orithm, was investigated in [26,27] together withathematical description. We provide a generalbelow.the signal to be modeled with M GMFs. The GOFRs a four-step procedure used to select and tune the

re ECG preprocessing.

computer methods and programs in b iomed ic ine 8 8 ( 2 0 0 7 ) 217233 219

me

parametersofM functio

The fou

selectiondate GMF

tuning of orthogon

GMF, orthogon

Since ththe ve chM=6GMFsare modelemodels a nthe modelibetween inby the classSection 2.2

Fig. 3 deGMFs of th(M=1, stepeach GMF othe rst iteGMF that is

Thevethat end, thlinear optimcost functioNote that coL must beis shown on

The laslibrary and(Fig. 3D) isand is usedorthogonal

AfterM=of 6 GMFs (

Fig. 4 shbeat, (b) anan abnorming from thalgorithm,versely, eacfor exampling from thnumber 2 acontraction

Fs aal acMF hysicibtainvan): inorithhic

ude.se foses,on t

GMevioeat iep cl laers assignenetask. Th

. Labhearentito e

Fig. 5MFsnetwhe pre thabeleeat ae hig. 6).esigtureFig. 2 Denition of the Gaussian

of one GMF function. To obtain amodel composedns, the four steps of the GOFR are iteratedM times.

r steps are the following:

of the most relevant GMF from a library of candi-s,the GMF parameters in order to t the signal s,alization of the library with respect to the tuned

alization of s.

e purpose of the method is to model each ofaracteristic cardiac waveforms with a single GMF,were used in this study. Five characteristic wavesd by ve GMFs out of six, and the sixth GMF eitheron-informative part of the signal, or contributes tong of a biphasic P, R or T wave. The discriminationformative and non-informative GMFs is performedication procedure described in Section 2.2.3.1 and.3.2.scribes the GOFR algorithm. Fig. 3A shows the 67e library available at the beginning of the GOFR1). A correlation coefcient is computed betweenf the library and s1, where s1 is equal to signal s atration. The rst GMF g1 selected to model s1 is themost correlated to s1 (Fig. 3B).parameters of g1 are subsequently tuned tot s1. Toe BFGS (BroydenFletcherGoldfarbShanno) nonisation algorithm [28]minimizes the least squaresns (sum of squared differences between s1 and g1).nstrained optimization is required since 1, 2 andpositive.The GMF g1* obtained after optimisationFig. 3C.

t two steps consist of orthogonalizing both thes1 with respect to g1*. The resulting signal s2

the part of the ECG that remains to be explained,to iterate the four steps described above with the

ized library.6 iterations, the algorithmprovides amodelmade

Fig. 3, right panel).ows representative GMF models for (a) a normal

fth GMiologiceach Gthe phS, T) oThe adFig. 4(dthe algtude, wamplit

Thodatabadetails

2.2.3.The prheartbnext stologicaclassito be aeters d

Thelabeled

2.2.3.1up therst idtrainedwave (fromGneural

In tsier ato be lheartbhas thR (Figically dthe feaaberrant beat from the ventricle, (c) a beat withal ST segment, and (d) a premature beat originat-e atria. Each GMF, selected and tuned by the GOFRhas an electrophysiological background, and con-h monophasic wave is modeled by a single GMF:e, in Fig. 4(a), the rst GMF models the signal aris-e repolarization process of the ventricles, GMFsnd 6 refer to ventricle depolarization, and the atriais modeled by GMF number 3. The fourth and the

nating, theclassier.

In the uclassiers oset, and thber of hidwhich is di

Both datical databasa function.

re not informative, and do not correspond to phys-tivity. Note that the specic number attached toas no signicance: the information presented toan is not those numbers, but the labels (P, Q, R,ed automatically as described in the next section.tage of that modeling strategy appears clearly inthat case, the GMF that is labeled as a P wave (bym described in Section 2.2.3) has negative ampli-h reects the fact that the P wave has negative

ur examples are extracted from the MIT and AHAused to validate the modeling algorithm; for morehose databases, see Section 3.

F labelingus section described the procedure whereby eachs modeled by six Gaussian mesa functions. Theonsists in assigning to each GMF an electrophysi-bel (P, Q, R, S or T). To perform that task, automaticre trained to estimate the probability for each GMFed a given label, from the values of its ve param-d in Section 2.2.1.is performed in two steps: rst, the R waves are

en the P, Q, S, and T labels are assigned to the GMFs.

eling of R waves. Among the six GMFs that buildtbeatmodel, the function thatmodels the Rwave ised. To that end, a neural network classier (NNC) isstimate the probability of each GMF to model an R), in order to discriminate GMFs thatmodel Rwavesthatmodel non-R waves. A cursory introduction toork classication is provided in Appendix A.

resent case, the features that are input to the clas-e ve parameters of the Gaussian mesa functiond: the parameters of the six GMFs that model there input in turn to the classier, and the GMF thathest probability of being a R wave is assigned labelSince the Gaussian mesa function has been specif-ned for tting a cardiac wave by a single function,s that are fed to the classier are very discrimi-

reby facilitating to a great extent the task of the

sual framework of statistical machine-learning,f increasing complexity are trained on a traininge selection of the optimal complexity (i.e. the num-den neurons) is performed on a validation set,stinct from the training set.a sets are composed of digital ECGs from ELAMed-se on which each cardiac wave has been manually


labeled by a cardiologist (P. Maison-Blanche). For R-wave label-ing, 960 GMFs that model R waves (R GMFs) and 960 GMFs thatdo not model R waves (non-R GMFs) are used for training; val-idation is performed on a different set of 960 R GMFs and 960

non-R GMFs. The results on both data sets, and the selectedcomplexity, are presented in Table 1 for the R wave classier,together with the data pertaining to the classiers of P, Q, Sand T, described in the next section.

Fig. 3 GO a GMunits, propFR algorithm for selection, tuning and orthogonalization ofortional to the amplitude in mV).F (, 1, 2 and L are in ms; A is in arbitrary


Fig. 4 Four heartbeats modeled by six Gaussian mesa functions, tted with the GOFR algorithm: (a) normal cardiac beatoriginating from the sinus, (b) abnormal beat of ventricular origin, (c) abnormal ST segment, and (d) premature atrial beat.

Fig. 5 A classier designed to estimate the probability that a GMF, whose parameters are fed to the classier, models an Rwave.

Fig. 6 Procedure for assigning label R to one GMF out of a 6-GMF representation of a heartbeat. P(R|GMFi) denotes theprobability for the ith GMF to be an R wave, hence a probability 1 P(R|GMFi) of being a non-R wave.


Table 1 Results on the training set and validation set for each classier; the choice of the decision thresholds used for P,Q, S and T classiers is explained in the next section

Number of hiddenneurons selected

Size of thetraining set

Size of thevalidation set

Mon

R NNC 4 1920 1920P NNC 3 1464 1710Q NNC 3 600 290S NNC 3 956 824T NNC 5 2238 2506

2.2.3.2. Labeling P, Q, S and T waves. Prior to the labeling ofP, Q, S and T waves of a given GMF model, a new time origint0 is chosen at the location of the R wave previously detected.Therefore the value of the parameter of each GMF, whichexpresses its location, is changed to t0 (Fig. 7); that providesa temporal description of the sequence of activity of the beat,which is important for the labeling process. For example, thenew value of for the GMF that models a P wave of a normalbeat is negative around 120 and 200ms, so that a GMF with anegative value of has a large probability of being a P wave.Conversely, a GMFwith around 300mshas a large probabilityof being a T wave.

Assigning label P: To assign label P to one or more GMF,a neural network classier (NNC) has been trained to recog-

Fig. 7 A ndetected Rheartbeat m2 and the amplitu

nize a P-GMperforman

Similarlto the GMFhighest woper heartbsic P modebe assignedchosen, anability estim

The chotradeoff beresentation[29]) is usedpositive ratshows thethe curve ithe statistichoosing awith low faresult in aa signicanspecicity.

igninthemaye of 0nd sold dr P w

igninLabebabir th11 sf thes beAssilar toGMFsA valutivity athreshthan fowave.

AssandS.est prois large

Fig.GMF osied aew time origin t0 is dened at the bottom of thewave. The value of of each GMF of theodel shown in Fig. 3 is changed by t0 (, 1,

are in ms; A is in arbitrary units, proportional tode in mV).

label X: suheartbeat d

2.2.4. MuThe heartbing) descriHence, theconsists inmaking a dfor each misclassication ratethe training set (%)

Misclassication rate onthe validation set (%)

4 2.70.3 0.52.8 22 1.50.5 0.8

F from its parameters. The architecture and theces of the selected NNC are indicated in Table 1.y to the assignment of label R, assigning P labelamong the six GMFs for which the probability isuld result in assigning label P once and only onceeat; that procedure would not account for bipha-led by two GMFs to which the same label shouldtwice. Therefore, a probability threshold must be

d label P is assigned to all GMFs for which the prob-ated by the NNC is above this threshold (Fig. 8).

ice of the threshold must result in a satisfactorytween sensitivity and specicity. A graphical rep-(ROC Receiver Operating Characteristics curve: the true positive rate is plotted against the falsee for the different values of the thresholds. Fig. 9ROC curve for the P wave NNC. The area unders larger than 0.9, which provides an estimate ofcal accuracy of the classier [29]. For this classier,threshold value of 0.8 guarantees high sensitivitylse positive rate. Increasing the threshold wouldslight improvement of sensitivity while incurringt increase in false negative rate, i.e. a decrease in

g label T: The procedure for assigning label T is sim-procedure used for P wave labeling. Since severalmodel a T wave, a threshold must also be chosen..3 results in a satisfactory tradeoff between sensi-pecicity for T wave NNC (Fig. 10). The fact that theerived from the ROC curves for T waves is smalleraves is due to the variability of the shape of the T

g labels Q and S: Similarly, two NNCs assign labels QlQ (resp. S) is assigned to theGMF that has thehigh-lity to be a Q wave (resp. S wave) if this probabilityan 0.8.ummarizes the P, Q, S and T labeling process: eachmodel is tested for each label. A GMF that is clas-ing neither R, nor P, nor Q, nor S, nor T, is assigned

ch a GMF is considered as non-signicant for theescription.

ltilead processingeat processing (GMF decomposition and GMF label-bed above was designed for single lead analysis.simplest processing strategy for multilead ECGprocessing each lead separately and subsequentlyecision as to which is the most signicant leadedical label (Fig. 12). One of the advantages of the


Fig. 8 Procedure for assigning labe; P to one or more GMFs. P(P|GMFi) denwave, hence a probability 1 P(P|GMFi) of being a non-P wave. The label P iP wave is higher than 0.8.

GMF labeling is that the process estimates a probability foreach label; these probabilities are used in the decision step toselect themost signicant lead for eachmedical label (Fig. 13).For example, when processing a two-lead cardiac beat, the Pwave on the rst lead is modeled by one GMF out of six towhich the label P is assigned with probability P(P-GMF, lead 1).

Similarly, the P wave is modeled on the second lead byanother GMF out of six, which is labeled P with the probabil-

Fig. 9 ROThe area u

Fig. 10 ROThe area u

ity P(P-GMFmodel of tbeing a P wlead 1) >P(Pchosen (Fig

2.3. Pos

The characeachbeat. Tily derived

2.3.1. WaAuseful feaacteristic wbeginning aters of thesingleGMFsis of theMprovide inf

centht Gtre ito i

fsetnctistan

rly, foC curve of the P wave neural network classier.nder the curve is 0.95.

of theand rigthe cenextendand ofsian fuat twoSimilaC curve of the T wave neural network classier.nder the curve is 0.91.

is dened athat the are97% of theto exhibit thother autho

When aGMFs, threother: it wters of the

1 In the camonophasicas being theings, at leawave).otes the probability for the ith GMF to be a Ps assigned to all GMFs whose probability to be a

, lead 2). The GMF selected as the most signicanthe P wave is the GMF with largest probability ofave1: the GMF from lead 1 is chosen if P(P-GMF,-GMF, lead 2); otherwise, the GMF from lead 2 is. 13).

t-processing

teristic waves of the ECG have been localized forheir shape and thedistance between themare eas-from the parameters of the corresponding GMFs.

ve boundary identicationture for diagnosis is the distance between the char-aves, which is obtained from the position of thend the end of each wave, provided by the parame-corresponding GMF: when a wave is modeled by a(which is by far themost frequent case in the analy-IT andAHAdatabases), the parameters of that GMFormation on the morphology of the wave: locationre, length of the linear part, half-widths of the leftaussians, and amplitude (Fig. 14a). The position ofs taken equal to . Since Gaussian mesa functionsnnity on either side of the maximum, the onsetcursors cannot be computed exactly. For a Gaus-on, the beginning and the end are usually locateddard deviations on either side of the maximum.r Gaussian mesa functions, the onset of the wave

s 21 L/2 and the offset as +22 + L/2, soa of the GMF enclosed by the two cursors exceedstotal area; methods based on area of the T wavese T wave offset have been shown to be efcient byrs [30,31].biphasic P or a T wave is modeled by two

e cases may arise: (i) one GMF is wider than theas found empirically that choosing the parame-wider GMF for segmentation provided satisfactory

se of a biphasic wave on one of the available leads, themodel of the wave, found on the other lead, is chosenmost signicant (in standard multilead ECG record-

st one of the derivations will exhibit a monophasic


Fig. 11 Global procedure for labeling the P, Q, S and T waves. The decision is made according to the label probabilityestimated by each NNC. GMF 5 is assigned the label X, since it is classied as being neither P, nor Q, nor R, nor S, nor T.

ltilea

results; sindatabases,(ii) the twois taken equi denotesto max (1

center is taoverlap: theeation.

The perreported in

2.3.2. AmThe rst inwhether th

ECGina

us beFig. 12 Global procedure for mu

ce such cases arise very infrequently in the presentthis point will be further investigated in the future;GMFs overlap as illustrated on Fig. 14b: the onset

ing andiscrimprevioal tomin (1 211 1L/2, 2 221 2L/2), wherethe center of GMFi; the offset is taken equal

+ 211 + 1L/2, 2 + 221 + 2L/2); the position of theken equal to (1 +2)/2; (iii) the two GMFs do notGMFwith larger probability is used forwave delin-

formance of the wave boundary identication isSection 3.

plitude, polarity and shape of the wavesformation derived from the shape of the R wave ise heartbeat is normal or aberrant. When analyz-

axis, etc. Smesa functneighborinadvantageto build a d

A timetional usefFig. 15 sho24-h ECG:beat onwacult fromRR interv

Fig. 13 Example of two-lead processing: preprocessing, md analysis.

, the physician relies on expert knowledge for thistion: width of the R wave, RR time interval fromat, RR time interval to next beat, depolarization

ince each R wave is modeled by a single (or two)ion(s), its width, its inception time, the distance tog R waves, etc., are readily available. Therefore, fullcan be taken of expert knowledge [3234] in orderecision tree.change in the cardiac wave shapes is an addi-ul feature for the experts to perform a diagnosis.ws an episode of abnormal atrial activity on athe P waves are upside down from the sixthrd. The detection of such activity is very dif-rhythm analysis, because of the stability of theals. Our methodology localizes the P waves for

odeling, labeling, and decision.


Fig. 14 Wparameterssegmentattwo GMFsmade fromtheir shape

each beat,of the P wthis patholmodeled th

Fig. 15 ECsixth beatis still veryanomaly; tanalysis.

Fig. 16 Ti(mV). The ris displayeabnormal arepresenta

(Fig. 16): thbeats. Notediologist onbut has nevanalysis.

17 shbeleP anresuFig.119), laof theTheseave segmentation is derived from theof the GMFs. (a) In the case of a single GMF, the

ion is derived directly from the parameters; (b) ifare required to model the wave, a decision isthe parameters of the two GMFs, depending ons.

and models it with a GMF, so that the amplitudeave for each beat is known. In order to detectogy automatically, the amplitude of the GMF thate P wave can be plotted as a function of time

G with an abnormal atrial activity. From theonward, the P wave is upside down. The rhythmstable during the occurrence of this conductionherefore, it is very hard to detect from rhythm

The abnormtion step deother featushows the ethe upside-clearly on ttwo consecGMF labeliof the abnabnormalit

2.4. Im

The procedronment. Tincrease spand label 1eling of threquire mobecause thtime-consucellation anlong-termfew minutebeats wereprocedurethe heartbenext beat, QThat step rheartbeats,

2 C progra2.8Ghz.me evolution of the amplitude of the P waveectangle contains the part of the recording thatd on Fig. 15. Each cross is a heartbeat. Thetrial activity appears clearly in thistion.

e GMF amplitude is negative for these ectopicthat the latter curve is already available to car-short-term ECG for patients in supine position,er been presented on long-term ambulatory ECG

ows a two-lead ECG from theMIT database (recorddbyour algorithm. In this gure, only the beginningd the end of the T waves are labeled for each beat.lts are obtained without any expert annotation.al beats have been detected by the discrimina-

scribed above. But the abnormality appears also onres extracted by the algorithm. For example, Fig. 18volution in time of the Twave amplitude on leadA;down repolarisation of the abnormal beats appearshis graph. Fig. 19 shows the GMF decomposition ofutive beats (one normal and one abnormal). Theng process did not assign label P to any waveormal beat; this absence can also be a ag fory.

plementation and computation time

ure has been developed under the Matlab envi-he optimisation step with GOFR is in C-code toeed. At present, 36ms are required to model00 heartbeats2; therefore, brute-force GMF mod-e 180,000 heartbeats of a 24-h recording would

re than 1min. For routine use, this is too longe global analysis procedure requires additionalming steps such as QRS detection, baseline can-d wave labeling, while an automatic analysis of

ECG (Holter record) must be performed within as. To shorten the modeling step, similar heart-grouped together by an unsupervised clustering(see [26] for details) based on several features ofat (RR interval from previous beat, RR interval toRS principal axis direction, shape of the QRS loop).esulted in less than 200 clusters for the 180,000which reduces the expected computation time

m running under Windows XP on a Pentium IV-m,


Fig. 17 Automatic annotation of ECG with the present algorithm. The GMF decomposition of the cardiac beats marked byan asterisk is shown in Fig. 19.

Fig. 18 EvFig. 17. The

for the glorecording.

In its mented in tuse.

Fig. 19 GMthe secondolution in time of the T wave amplitude. The rectangle containsvariation of repolarisation direction is a ag of abnormality.

bal analysis procedure to about 2min for a 24-h

nal version, the whole procedure will be imple-he ELAMedical Holter analysis software for clinical

3. Re

This sectio(Fig. 1). The

F decomposition and labeling of two consecutive beats markeddecomposition is a ag for abnormality.the part of the recording that is displayed in

sults

n describes the results of the global procedureresults pertaining to heartbeat recognition (NB vs.

by asterisks on Fig. 17. The absence of label P in


Table 2 Results for R wave assignment and heartbeat labeling on MIT3 and AHA4 databases

MIT Database

Normal beats Abno

Present algorithm Number of analyzed beats 86,071Sensitivity S (%) 99.80Positive predictivity P+ (%) 99.47

Coast et al.

Martinez e

Pan and To

aValues tha natio

AB) are rstpresented iwere obtainneither for

3.1. Ca

The performabnormal band the AHabnormal bBeats labelture beat, nare consideas ventriculabeled asfrom ventritaken into

The senreported in

S = TP(TP + F

where TP i(resp. FP) is

These rrecognitionple, reectsQRS locatioare betterby state-of-they providby commer[26].

3 We discdatabase as

4 We discaventricularwell dened

P a

presELAd, wipresour knnottabaleng

are mhe CncesB feell-se, annotwav

reoveiththeore,relev[36] Number of analyzed beats N/SSensitivity S (%) N/SPositive predictivity P+ (%) N/S

t al. [12]a Number of analyzed beats 109,428Sensitivity S (%) 99.80Positive predictivity P+(%) 99.86

mpkins [24]a Number of analyzed beats 109,809Sensitivity S (%) 99.75Positive predictivity P+ (%) 99.54

t refer to QRS detection only without normal/abnormal beats discrimi

described; results for P and Twave localization aren the second subsection. All results reported belowed on test sets, i.e. on heartbeats that were usedtraining nor for optimizing the NNC classiers.

rdiac beat recognition: NB vs. AB

ance of the discrimination of normal beats fromeats was estimated on the MIT database3 [23],A database4 [22]. In this paper, we considered aseats, beats which did not come from AV node.ed in the MIT database as normal, atrial prema-odal premature escape beat, or bumble branch beatred as normal beat in this study, and beats labeledlar contraction are considered as abnormal. Beatsfusion beats that correspond to a depolarizationcular and from AV node merged together were notaccount for performance estimation.sitivity (S) and the positive predictivity (P+) areTable 2:

N)and P+ = TP

(TP + FP)

3.2.

In theon theappliewavesbest ofually aCSE da(signalrates)than tdiffere

QTDfrom wdataba3622 a(3194 P

Moratio, wtion ofTherefthat iss the number of true positive detections, and FNthenumber of false negatives (resp. false positives).esults involve both heartbeat localization and. Thus, the value of S for normal beats, for exam-the efciency of the algorithm for detecting then and labeling it as a normal beat. These resultsthan, or in the same range as, results obtainedthe-art published methods (e.g. [11,12,35,36]), ande a substantial improvement over results obtainedcially available programs on the same databases

ard records #102, #104, #107, and #217 in the MITthey correspond to pacemaker records.rd series 800x in the AHA database. These records arebrillation, so that the ventricle depolarization is notin such cases.

recordings.

3.2.1. SinThe rst twlead 2 wheshows theleads that alatter meth

To estimthe sensitivmean magn

E = 1N

i=1...N

where N ismiann the pAHA Database

rmal beats Normal beats Abnormal beats

4,771 131,949 11,40791.72 99.68 87.7795.46 98.95 95.93

N/S 14,350 799N/S 99.82 97.25N/S 98.90 85.67

N/S N/SN/S N/SN/S N/S

N/S N/SN/S N/SN/S N/S

n.

nd T labeling on QTDB database

ent section, the neural network classiers trainedmedical database (as described in Section 2) werethout further processing, to the labeling of P and Tent in the records of the QTDB database [35]. To thenowledge, only twopublic databases containman-ated P, R and T waves: the QTDB database, and these [37]. The characteristics of the QTDB databaseth, number and position of the leads, samplinguch closer to those available with Holter records

SE database. Table 3 (from [38]) summarizes thebetween the QTDB and CSE databases.atures a signicant number of records, sampledknown databases such as MIT database or AHAnd manually annotated by an expert. It includesated beats, with a variety of ECG morphologieses and 3542 T waves).r, QTDB is known tohave a verypoor signal tonoiseseveral pathologies that make an accurate detec-waves over the whole database a challenging task.at present, QTDB is the only annotated databaseant for testing ourmethod for analyzing long-termgle lead processingo rows of Table 4 contain the results for lead 1 andn each lead is processed separately. The third rowresults obtained when the marker from the twogreed most with the annotation was selected. Theodology was described in [12].ate the performance, three values are shown: rst,ity of the algorithm for each marker; second, theitude of the error E over all annotated beats:

miann mialg (1)

the number of detected markers of a given type,osition in time of the ith annotators marker, and


Table 3 Comparison of QTDB and CSE databases (from Table 1 of [38])

Property CSE Multilead

Signal leng About 10 sSample rat 500HzNumber of 15 (12 standard leads and 3 orthogonal leads)Number of

markers25

Number ofsignal

1

Total numb 25 (QRSonset), 25 (T offset)Location of

within sie signal First beat only

Number of perts 5

Table 4 lead processing. P waves are described by Pon,Ppeak and d

Ppeak Pend Tpeak Tend

3194 3194 3542 3542

Present alg 80.9 80.9 82.1 82.115.5 21.1 29.2 45.012.2 22.3 17.9 38.6

Present alg 76.2 76.2 81.6 81.618.1 27.2 25.4 42.816.3 31.2 17.4 40.3

Present alg 91.2 91.2 93.6 93.611.1 17.6 19.9 34.8

Ref1 vs. Re

mialg the pomarkers froas the mar

Some puvalue of thtors markethan the abthe resultsdiscrepancwith thosethe value ocan be direpublication

For 11 rfor T waveannotatorbetween thas a referebetween thues can becan expectcannot be o

The diswave is shomarker, thrange as thTable 3). TQTDB (PhysioNet)

th About 15mine 250Hzchannels 2signals containingfor QRS onset et T offset

103

annotated beats per 3080

er of annotated events 3623 (QRS onset), 3542 (T offset)experts annotationsgnal

About 10min after the beginning of th

experts One, except for 11 signals with two ex

Results for P and T labeling on the QTDB database for singlePend markers; for T waves, Tpeak and Tend only are annotate

Markers Pon

#of annotations 3194

orithm Lead 1 S (%) 80.9E (ms) 22.6 (ms) 22.6

orithm Lead 2 S (%) 76.2E (ms) 24.7 (ms) 25.7

orithm Best lead S (%) 91.2E (ms) 17.3

(ms) 17.7 8.9 18.6 12.0 30.3

f2 Eref (ms) 17.5 24.5

sition found by our method. Therefore, E=0 if allm the algorithm are exactly at the same positions

kers of the annotator.blications [12,35] dene the error as the algebraic

e discrepancy between the position of the annota-r and the position of the computed marker, rathersolute value of that discrepancy. In those papers,are given in terms of mean value of this algebraicy and its standarddeviation. To compare our resultspublications, the third value given in Table 4 isf the error () such that Pr(E< ) = 0.67. This valuectly compared to the standard deviation (Std) ofs that use algebraic values of the error.ecords of the QTDB database, a second references is available from a second cardiologist (second); the last row of the table provides the differencee two annotations (the rst annotation was usednce; Eref is the mean magnitude of the differencee two annotations, for each marker): these val-viewed as the maximum performance that onefrom automatic detection, assuming that humansutperformed for annotation.tribution of the magnitude of the error for the Pwn on Fig. 20. For the onset marker and the offsete results obtained for that wave are in the sameose published previously (for a review see [12],

he marker that labels the peak of the P wave isFig. 20 Distribution of the magnitude of the error for Pwave markers.


Fig. 21 Record (sele0116, 0:10:17.5): the P wave has a low signal-to-noise ratio; the differences between the annotatorsmarker and the computed marker for the rst beat are 156ms, 185ms, 140ms for the on, peak and off markers respectively;such values give large contributions to the overall error.

Fig. 22 Distribution of the magnitude of the error for Twave markers.

Fig. 23 In this record (sel14172, 10:17:20) the T wave isbid. For both heartbeats, the GMF decomposition modelsthe T wave with 2 GMFs and the neural network classierdetects the more accurate T-GMFs on lead II.


Table 5 Result of P and T labeling on the QTDB database for multilead processing. P waves are described by Pon, Ppeakand Pend markers; for T waves, Tpeak and Tend only are annotated

Parameters Pon

#of annotations 3194

Presented algorithm Multilead processing E (ms) 19.6.0

Ref1 vs. Re

more accursensitivity

Some auancy withheavily to

5 The disobtained whis selected. (ms) 20

f2 Eref (ms)Fig. 24 Distribution of each marker for the P wave

ate with the methodology described here, but theis slightly lower5.tomatically detectedmarkers have a large discrep-the annotators markers, so that they contributethe overall error. One example of such cases is

tributions displayed on Figs. 20 and 22 are thoseen the marker that best agrees with the annotation

shown on Fwhich mak

The resuobtained foter than thas those pslightly lowof the T wresults to tthe two errPpeak Pend Tpeak Tend

3194 3194 3542 3542

14.3 20.6 26.9 42.812.2 21.4 18.4 38.5

17.5 24.5

(a) and for the T wave (b).

ig. 21: the P wave has the same amplitude as noise,es its automatic detection very difcult.lts for Twave location are less accurate than thoser the P wave. Nevertheless, these results are bet-ose published in [8]. They are in the same rangeublished in [10,12] for the peak of the wave, ander for the end of the wave. However, the quality

ave markers appears clearly when comparing thehe annotators error Eref: the difference betweenors (Eref and E) on both T wave peak marker and T


wave offset marker is less than two sampling periods (8ms,since QTDB is sampled at 250Hz).

Distribuin Fig. 22. Juvalues of soresults. OnFig. 23: in thinclude onlalgorithmmof the wavein Sectionsuch heartb

3.2.2. MuAs indicate(onset, pea(peak and omultilead pinformation

Table 5single leadmeasured bannotator m

The resuthose obtaiis selectedobtained frThe magnitimately 5 sand smallemarkers haprocessing,all error: di

The peasampling pHowever, 6sampling p

These rlished inprocessing,to computelead decisiframework

4. Co

The preseautomaticadescribed aa combina(GMFs) indiscussedautomaticathe model.

Heartbedure that pany pre-prremoves thon the MIT

on QTDB for P and T wave detection. The results are verysatisfactory, especially for multilead processing. At present,

elineimplrovemarsinghichon Ge frosultsationn inal ceartb40,41t (ore thdditve propechanpertrm E

ally,ethod oumen, anearl

owle

thordierting

ndix

an ures)rameior p

bel).featnctioear futpun) oeight(2).

|X ) =

PNNaturetions of the error on the Twavemarkers are shownst as for the P wavemarker histograms, a few largeme errors have large adverse effects on the averagee example of record with large errors is shown inis case, theTwave is bid. Theannotatorsmarkersy the rst part of the T wave whereas the presentarkers include the twoparts of thewave. The peakis between the two parts of the wave as described2.3.1. Thus, the comparison between markers oneats produces large discrepancies.

ltilead processingd in Section 2.2.4, three markers for the P wavesk and offset) and two markers for the T waveffset) are provided for each cardiac beat from therocessing; these markers take into account thefrom all available leads.

shows the results obtained on QTDB. Similarly toprocessing, the performances of the algorithm arey the magnitude of the discrepancy between eacharker and the corresponding computed marker.lts for multilead processing are less accurate thanned for single lead processing when the best leadfor each marker, but are much better than thoseom a single lead when only one lead is processed.ude of the error on the P wave detection is approx-ampling periods for the onset and end markers,r than 4 sampling periods for its peak; 67% of theve an error in those ranges. Similar to single leada fewmarkers give a large contribution to the over-stributions are shown for each marker on Fig. 24.k of the T wave is detected with an error below 6eriods, and below 9 sampling periods for its end.7% of the markers have an error smaller than 5eriods for the peak of the wave.esults are slightly less accurate than those pub-[8,12], but these studies refer to single leadand the bestmarker from available leads is chosenthe error. Here, the processing includes multi-

on, which is a more realistic conguration in theof automatic processing.

nclusion and discussion

nt paper described an algorithm for labelinglly the characteristic waves of an ECG. We rstmethodology for representing the heartbeat as

tion of special-purpose parameterized functionsorder to extract discriminant features. We alsothe design of nonlinear classiers for assigninglly a medical label (P, Q, R, S and T) to each GMF of

at modeling and labeling is a part of a global proce-rocesses raw data from multilead records, withoutocessing by the cardiologist: it detects R waves,e baseline and labels the waves. It was testedand AHA databases for R wave localization, and

wave dvery sbe impof theprocesfrom w(basedis madthe reinformbe takeprincipeach h[26,39,ponenimprov

In avide This pshapethe exlong-te

Finthe mapplietwo-diformedfor the

Ackn

The auFaisansuppor

Appe

Given(featuis a paposterpattern(Fig. 25

Thetary funonlinThe ofunctioThe wmodel

PNNC(C

wherethe feation is performed from the GMF parameters withe rules; that part of the algorithm can probablyd in order to decrease the magnitude of the errorker. Moreover, in the present method, multileadis performed by choosing, for each beat, the leadwave delineation is statistically most probable

MF probability), so that the nal wave delineationm a single lead. Two strategies emerge to improve: rst, in order to take advantage of all available, all GMFs that are assigned the same label could

to account, e.g. for wave delineation; alternatively,omponent analysis (PCA) could be performed oneat in order to nd the most informative direction]. GMFmodeling and labeling of the principal com-possibly of the two principal components) shoulde robustness of the computation.ion to their use for wave delineation, GMFs pro-arameters that describe the shape of each wave.rty is a powerful tool for temporal detection ofges in specic characteristic waves, and provideswith new diagnosis tools on the whole ambulatoryCG.it should be noted that a signicant part ofdology described here is generic, and can betside the eld of cardiology. An extension tosional signals (timefrequencymaps) has been per-d applied to the analysis of neurophysiological, e.g.y detection of Alzheimers disease [42,43].

dgements

s are grateful to S. Christophle-Boulard and Dr Y.for discussions; they wish to thank A. Rippart forthis work.

A

nknown pattern described by a vector of numbers, a single-output neural network classier (NNC)terized function that provides an estimate of the

robability of the classes, i.e. the probability that theongs to one of two classes (posterior probability)

ures are fed to an appropriate number of elemen-ns (hidden neurons) each of which computes aunction (tanh) of a weighted sum of the features.t neuron computes a nonlinear function (logisticf the quantities computed by the hidden neurons.s of the weighted sums are the parameters of the

f

(i=1...Nhn

outi t(

j=1...Niinij xj + ini0

)+ out0

)

(2)

C is the output of the NNC, X = [x1 x2 . . . xNi ]T isvector, and Nhn is the number of hidden neu-


rons. f is thare:

{outi

}i=1..

Nhn hidd {in

ij}j=1...N

tures (j= {in

i0 }i=1...Nstant inp

out0 , pertoutput n

These pprocess (tto be classtion J. In thminimized

J() = 1Np

where Np iXk belongs

For clasbe used suc[44,45].

The comber of hiddneuron is aability is aneurons, thexamples tis too comof the traiwith freshenough, itset (the so-selection is[44,45].

Alternatmachines [given the snumber ofate for the

are not well suited to probability estimation, which is of cen-tral importance in our procedure.

r en

S. Waectroilade.H. CJ. Fer. StordneC/Aecuteric

sk foideli0 (19. Kowbul

003) 3Lagualyse KarternaSoriaerreplicae limg 45Sun,tectirdioGritze P a91.. Vilarnancom

000) 7Sterries,LaguundatabaLi, Cing w28.Fig. 25 Neural network classier.

e logistic function. The parameters of the network

Nhn, pertaining to the connections between the

en neurons (i=1Nhn) and the output neuron;

i

, pertaining to the connections between theNi fea-

1Ni) and hidden neuron i,

hn, pertaining to the connections between the con-

ut (equal to 1, called bias) and hidden neuron iaining to the connection between the bias and theeuron.

arameters are estimated through an algorithmicraining), from a set of examples of the patternsied (training set), by minimizing a cost func-e present case, the least squares cost function was:

k=1...Np(L(k) PNNC(C| |Xk ))2 (3)

s the size of the training set, L(k) = 1 if input vectorto class C and L(k) = 0 otherwise.sication problems, alternative cost functions canh as cross entropy; interested readers can refer to

plexity of the classier is determined by the num-en neurons; a neural network with zero hiddenlinear separator: the locus of points of equal prob-

r e f e

[1] G.ElPh

[2] MK.P.HGaACexAmtagu10

[3] P.RAm(2

[4] P.Anthal

[5] E.GuApthEn

[6] Y.deCa

[7] F.th83

[8] J.AFeTU(2

[9] K.se

[10] P.boda

[11] C.us21straight line. The larger the number of hiddene more complex the separation between classes ofhat is performed by the classier. If the networkplex, the classier is too sensitive to the detailsning set and gives poor results when presenteddata; conversely, if the classier is not complexis unable to classify the examples of the trainingcalled bias-variance dilemma). Therefore, modelan important part of the model design process

ive statistical classiers, such as support vector46], could be used in the same context. However,mall dimensionality of input space, and the largeavailable examples, neural networks are appropri-present task. In addition, support vector machines

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Automatic ECG wave extraction in long-term recordings using Gaussian mesa function models and nonlinear probability estimatorsIntroductionMethodsECG signal preprocessingHeartbeat processingGaussian mesa function (GMF)Modeling algorithmGMF labelingLabeling of R wavesLabeling P, Q, S and T waves

Multilead processing

Post-processingWave boundary identificationAmplitude, polarity and shape of the waves

Implementation and computation time

ResultsCardiac beat recognition: NB vs. ABP and T labeling on QTDB databaseSingle lead processingMultilead processing

Conclusion and discussionAcknowledgementsAppendix AReferences

Documents

Automatic ECG wave extraction in long-term recordings using Gaussian mesa function models and nonlinear probability estimators