A HEART CELL GROUP MODEL FOR THE IDENTIFICATION OF MYOCARDIAL ISCHEMIA

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1 A HEART CELL GROUP MODEL FOR THE IDENTIFICATION OF MYOCARDIAL ISCHEMIA Mohamed A. Mneimneh, Miheal T. Johnson and Rihard J. Povinelli Eletrial and Computer Engineering, Marquette University, 55 Wisonsin ave, Milwaukee, Wisonsin,USA Keywords: Abstrat: Inverse problem, Ishemia, Deision Tree. Due to the inreasing pries of medial are, and espeially due to ardiovasular injury; sientists are looking for inexpensive and less invasive ways to diagnose myoardial ishemia. Many studies have shown that the variations of the ST-segment in the ECG signal are an indiator for ishemia. For this purpose, this work proposes an approah based on a heart ell group model and priniple omponent analysis, using a deision tree lassifier to differentiate between the ishemi and healthy beats. The ardia based model is based on a physiologial model of the eletrial yle of depolarization and repolarization of the atria and ventriles. The model parameters are estimated by minimizing the squared error between the generated signal and the reorded ECG. The approah is applied to beats from the Long-Term ST database, whih onsists of 86 subjets and more than, beats in whih 8% of the beats are ishemi and % are healthy. A -fold ross validation test is performed over the dataset. The auray of this approah is 9.6%, with sensitivity of 95.9% and speifiity of 75.66%. INTRODUCTION Ishemi heart disease is the leading ause of death in the world with almost 4% of all deaths (AHA 5) Moreover, the average number of individuals who undergo a heart attak as a result of myoardial ishemia in the United States is approximately.5 million ases, of whih 5, are fatal (AHA 5). Myoardial ishemia is defined as the deprivation of oxygen in some portions of the ardia tissue due to a blokage in the oronary artery. If the deprivation ontinues for an extended period, the effeted ardia tissue will die; thus, leading to a heart attak. Tissue that has died is no longer funtional and diminishes the mehanial pumping funtion of the heart (Pardee 9). Early detetion of ishemia is ruial beause, in most ases, the effets of myoardial ishemia are reversible if deteted early enough (Long 98). General sreening of patients is vital to preventing myoardial infartion, sine ishemia an be present without exhibiting symptoms. This work proposes a ardia based model, Priniple Component Analysis (PCA) and a C4.5 deision tree lassifier for the detetion of myoardial ishemia. The ardia model is based on a physiologial model of the eletrial yle of depolarization and repolarization of the atria and ventriles. The Sinoatrial (SA) node, the Atrioventriular (AV) node, bundle branhes, Purkinje fibers, and left and right ventriles are modelled as signal generators. The ECG is generated by the differene in signal amplitudes arriving at the positive and negative terminals of an ECG lead. The model parameters are estimated through the minimization of the squared error between the generated signal and the reorded ECG. In addition to the obtained model parameters, 5 of the omponents from applying PCA to the signal are used in the diagnosis. A C4.5 deision tree is then used as a lassifier to determine if a beat is healthy or ishemi. The purpose of using eletroardiogram signals for the diagnoses of myoardial ishemia is beause it is one of the least expensive tehniques available to physiians. Figure shows a labelled ECG signal showing the P, Q, R, S, T waves, the ST segment and the J point. The use of the ST level in the detetion of myoardial ishemia was hypothesized in 9 (Pardee 9). Examples of low ost methods are ST event alerts ($5 ost) and easy to administer) with sensitivity of 46% and speifiity of 9% and exerise stress testing ($-$3 ost) with 68% auray of 68% (R. Gianrossi 989). 5

2 HEALTHINF 8 - International Conferene on Health Informatis DATA SET AND PRE-PROCESSING Various ECG and intraardia datasets are available for the use of modelling and deteting myoardial ishemia. The data sets preserve the privay of the subjets as there are no diret or indiret identifiers linking bak to them.. Long Term ST Database Figure : Labelled (ECG) signal.(moody ). Signifiant researh has been undertaken to develop a more aurate, less invasive, and less expensive method for deteting myoardial ishemia. Muh of this researh fouses on the use of ECG signals. These methods build models or use thresholds of the ST deviation to determine if a patient s ECG signal might indiate ishemia. Previous tehniques that dealt with ishemia lassifiation and detetion when monitoring ECG signals started with low auray that inreased signifiantly over time. These tehniques are based on the hypothesis that myoardial ishemia an be deteted by monitoring the ST variations. Maglaveras et al. (N. Maglaveras 994) have investigated a method for ishemia detetion that uses supervised neural networks. The auray of this approah is of sensitivity of 73.% and positive preditive auray of 69.5%. RV Andreao et al. (R.V. Andreao 4) employed a Hidden Markov Model for beat segmentation with the appliation of ishemia detetion. The auray of this model is of sensitivity of 83.% and positive preditive auray of 85%. Additionally, T. Stamkopoulos et al. proposed an approah using nonlinear Priniple Component Analysis (PCA) and neural networks in the identifiation of ishemi beats. The auray of this approah was 8% for healthy and 9% for ishemi beats when applied to the European ST-T Database (Stamkopoulos 998). Similarly, Vitor-Emil Neagoe applied a Gaussian Neuro-Fuzzy Approah and PCA toward the lassifiation of myoardial ishemia. The auray shown in the paper was % for 5 features. However, Neagoe dealt with only identifying ishemi and normal patients. Moreover, the number of training and testing data were 4 patients, half used for training and half for testing (Vitor-Emil Neagoe 3). The Long-Term ST Database from PhysioNet ontains 86 Holter ECG reordings from 8 independent patients. Holter reordings are ECG reordings reorded using portable reording devies, generally taken over a long period. These reordings were seleted from the Holter libraries at Beth Israel Deaoness Medial Center in Boston, Physiolab (Laboratory of Biosignal Proessing) of the Institute of Clinial Physiology in Pisa, Brigham and Womens Hospital in Boston, and the Zymed ompany. The reordings vary in length from to 4 hours. Eah reord ontains either two or three ECG leads. The reords are digitized at 5 Hz with bit resolution (Moody ). Complete annotations have been provided for the database. These annotations label the signifiant ST shifts and episodes, the beginning (3-point) of most ST segments has been annotated along with R wave annotations using a 6 seond averaging window. The beats were deteted using WQRS funtion as part of the WFDB pakage supplied by the Physionet (Moody ). To aid in the development of an ishemia lassifiation algorithm, omplete ST level annotations have also been provided. These annotations give the ST level, ST referene funtion, and the alulated ST deviation. The ST referene is expertly labelled moving average of the important ST shifts. The ST deviation is alulated by subtrating the ST level from the ST referene funtion shown in Figure (Jager, Taddei & Moody 3). Figure : Example of ST deviation alulation. The data onsists of 43 free reords from 4 patients and 43 fee reords from 38 patients. The total number of beats used in this work is,58 for 5

3 A HEART CELL GROUP MODEL FOR THE IDENTIFICATION OF MYOCARDIAL ISCHEMIA both healthy and ishemi. The number of ishemi beats is 6,794, while that of the healthy beats is In order to evaluate the proposed lassifier, a ten fold ross validation is applied to the dataset. The ten fold ross validation is desribed as follows:. Divide data into set of size n/. Train on 9 sets and test on set 3. Repeat the proess times and take the mean of the auray.. Signal Pre-proessing As mentioned in the previous setion, the beats are obtained automatially from the reords using the WQRS funtion provided by the Physionet Toolkit. Eah beat is then anhored suh that the isoeletri line prior to the P wave is set to zero. A wavelet deomposition approah is used to denoise the signal from high frequeny noise (GD. Clifford 5). 3 METHOD The lassifiation approah utilizes a heart ell group model fitted to the patient s ECG signal along with the priniple omponent analysis of the signal. The method is desribed in the blok diagram shown in Figure 3. A heart ell group model is used to generate a template ECG signal. Then, using a nonlinear onstrained optimization tehnique, the model parameters are updated until reahing a ertain error with the patient s signal beat. The estimated model fitting the ECG signal are then used with the PCA omponents as features in the C4.5 deision tree lassifier. Figure 3: Blok diagram of the Ishemia diagnosing method. 3. Heart Cell Group Model Eletroardiograms indiate the eletri ativity of the heart over the body surfae. In general, two types of model have been developed to haraterize the ECG signal. The first type is a model used for interpolating experimental data and an be fitted to ECG signals without having a referene to the physial system. The seond type is a model that an haraterize the ECG signal and an be related bak to the heart ativity. The objetive of this work is the latter modelling approah, fousing on development of a model that an estimate the ativation sequenes of the heart ells from real patient ECG signals. This objetive is alled the inverse problem. The diffiulty of this problem is that unless it is stated in a partiular manner, the solution will not be uniquely defined. Several tehniques have been employed for generating models to solve the forward and inverse problem. These tehniques overome the uniqueness problem by modelling the heart as a small number of moving dipoles. Some of these tehniques apply the solution of Green s theorem (Method of Moments) or Multi-Pole tehnique to determine the sattering of the eletri waves over the heart. These methods are onsidered aurate. However, the main drawbak of these tehniques is the omputational omplexity (Gulrajani 998). MSharry et al. presented a dynami ECG model that inorporates the ECG features as a ombination of Gaussian funtions. Although this model is easy to build, it annot be related to the heart ell ativity (GD. Clifford 5). 3.. Proposed Cell Group Model A Heart Cell Model (HCM) is proposed in this work based on the reonstrution of the ECG signal using a ell group model. This model aounts for the wave propagation of the SA node, the AV node, the bundle branhes, Purkinje fibers, and left and right ventriles. We hypothesize that the eletri ativity of a heart ell group an be represented by a differene of two sigmoid funtions. The eletri ativity of the myoardial ells is aused by the variation of the positively and negatively harged ions of the ells. As presented by researhers (Andrew J. Pullan 5), the eletri ativity of the ell is given in Figure 4 and it an be approximated by a differene of two sigmoid funtions as shown in Figure 5. 53

4 HEALTHINF 8 - International Conferene on Health Informatis i [ SA, AV, Bb, Pf, LV, RV] + ( i i ) fˆ = f f ECG, () Figure 4: Condution ativity of the heart. Figure 5: Proposed heart ell ativity. The ell group ativity is modelled as the differene between two sigmoid funtions: f ( t, a,, a,, k ) = k a a ( t ) t, () + e + e where k represents the magnitude of the wave, a and a ontrol the rising slope, and and ontrol the translation in the diretion of the time axis. We hypothesize that the umulative ECG signal is generated from the atrial and ventriular ondution ativity. In this work, the P wave is assumed to be generated from the SA node ativity; the PR interval from the AV node ativity, and the QRS omplex and T wave are generated from the ativation of the bundle branhes, the Purkinje fibers and, the right and left ventriles. 3.. ECG Generation As presented above, the ECG signal an be generated from the ativation sequenes of the heart ell groups. The same steps are used to generate the ECG from the modelled ativation sequenes. The model divides the heart into groups or nodes. Eah node onsists of a ombination of ells at the SA node, the AV node, the bundle branhes, the Purkinje fibers and, the right and left ventriles. Eah node ativation and deativation sequene is represented as the differene between two sigmoid funtions. The variables in the sigmoid funtions onsist of the magnitude, infletion (ativation) point and the inlination slope. By summing the potential differene of the node signals at the positive and negative terminals of eah lead, the ECG signal is generated: where: SA and AV represent the ativity of the SA and the AV node respetively. Bb and Pf represent the ativity of the bundle branhes and Purkinje fibers respetively LV and RV represent the ativity of the Left and right ventriles respetively f + and f are the differene between two sigmoid funtions as presented in () for eah of the nodes at the positive and negative probes respetively The following setions presents how the ECG wave features are generated. The features are the P wave, the PR segment, the Q wave, the R wave, and the S wave (QRS omplex), ST segment, and T wave P Wave Generation The P wave is generated from the potential differene between the eletri ondution ativity measured at the atrial ells at the positive and negative probes. In this approah, the atrial ondution ativity at a single probe is estimated by equation (). Moreover, it is hypothesized that the P wave an be generated from the ondution ativity of the SA node: + P = f f, (3) wave SA SA The generation of the P wave using the differene of sigmoid estimation is shown in Figure 6. SA ativity 5 5 SA P Wave Figure 6: P wave generation using the differential sigmoid model. SA - 54

5 A HEART CELL GROUP MODEL FOR THE IDENTIFICATION OF MYOCARDIAL ISCHEMIA 3..4 PR Segment Generation The PR segment ours as the impulse travels from the AV node through the onduting tissue (bundle branhes, and Purkinje fibers) towards the ventriles. Most of the delay in the PR segment ours in the AV node. The PR segment is generally at the baseline; however, variations might our due to ertain heart diseases. Thus, by modelling the eletri ativity of the AV node as proposed in (), and similar to the proedure shown in (3), we are able to generate the variations in the PR segment as shown in Figure 7. AV ativity PR interval 3 AV Figure 7: PR interval generation using the differential sigmoid model QRS Complex and T Wave Generation The QRS omplex and the T wave denote the interval for the beginning and end of the ventriular ativation. When generating the QRS omplex, the ativity of the ell groups of the bundle branhes, Purkinje fibers, and left and right ventriles are modelled during the ventriular yle. The representation of the model for the QRS omplex and T wave in an ECG signal is dependent on the differene between the positive and negative eletrodes at the modelled ell groups. Figure 8 through Figure show how eah wave of the QRS omplex and the T wave are generated using the differential sigmoid model. AV ativity PR interval AV - AV Figure 8: R wave and T wave generation. AV - RV ativity R wave ; T wave LV ativity ST segment LV ativity ST segment Figure 9: R wave and T wave generation LV + LV + RV + RV Figure : S wave and T wave generation Figure : ST segment generation Parameter Estimation and Signal Fitting This setion disusses how to determine the parameters of the ativation sequenes in order to generate a real patient ECG signal. In order to ahieve this task, a parameter estimation of the proposed model () and () is performed using the minimization of the least squares with the real ECG LV + LV + 55

6 HEALTHINF 8 - International Conferene on Health Informatis signal. This proess was performed with the help of the fminon funtion, in Matlab, whih finds a onstrained minimum of a funtion for several variables. The funtion being minimized is given: signal ( ˆECG ) Error = ECG f, (4) The onstraints applied to the funtion are that the atrial ativity ours prior to that of the ventriles. Moreover, the ativation of the ell ativity is onstrained to our prior to that of the deativation. Additionally, the slopes of the ativation are higher than those of the deativation urves. A template initial ondition with known parameters for f ˆECG is used to set the initial ondition for the optimization proess. Additionally, a dynami template is generated for eah beat. This hoie of the template depends on the sign of the R peak. This allows more auray during the nonlinear optimization proess. The highest rossorrelation point between the initial template the patient signal is then hosen. Figure shows the real and estimated ECG signal. It an be seen that the fitted signal generated from the model mathes the original patient signal. The model parameters used to generate the fitted signal are used as features in the lassifiation proess. ECG Real Signal Estimated Signal Figure : Estimated signal and original ECG signal. 3. Priniple Component Analysis Priniple Component Analysis (PCA) is a linear transform where the basis funtions are taken from the statistis of the signal, and an thus be adaptive. It is optimal in the sense of energy ompation, i.e it plaes as muh energy as possible in as few oeffiients as possible. The PCA is typially implemented using Singular Value Deomposition. The transform is generally not separable, and thus the full matrix multipliation must be performed: T X = U x, x = UX, (5) where the U is the basis for the transform. U is i k : estimated from a number of x i where [ ] T UΣ V = [ x x x k ] = A T U = eigve( AA ) 3.3 C4.5 or J48 Deision Tree. (6) Deision trees represent a supervised approah to lassifiation. A deision tree is a simple struture where non-terminal nodes represent tests on one or more attributes and terminal nodes reflet deision outomes. Generally, a deision tree algorithm hooses the attributes that best differentiates the output attribute values. The Weka lassifier pakage (Eibe Frank 7) has its own version of C4.5 known as J48. Weka s J48 is used in this work to solve the lassifiation problem. 4 RESULTS The HCM-PCA/C4.5 lassifier is applied to the Long Term ST-Database. The proposed approah is ompared to the tehnique proposed in (Stamkopoulos 998). As mentioned before, the beat is deteted using an automati tool wqrs provided by Physionet. The high frequeny noise in the signal is removed using wavelet deomposition (Clifford 6). The model is fitted to the model by minimizing the sum squared error using a onstrained optimization proess. The onstraints are used to maintain the order of the heart s ativation sequenes. That is, the atrial ativation ours prior to that of the ventriles and the depolarization event ours prior to the repolarization. The model parameters are used in the lassifiation proess, i.e. as features to determine whether a beat is ishemi or healthy. A C4.5 deision tree is used in the lassifiation proess. As mentioned above, a fold ross validation is performed. The lassifiation method is applied with and without using the PCA omponents as features. Using the model parameters without the PCA features, the auray is 87.83% with sensitivity and speifiity of 9.6% and 65.69%, respetively. Using the PCA features without the model parameters leads to an auray of 87.83% with sensitivity and speifiity of 93.8% and 7.7%. However, when using the PCA features in addition to the model parameters, the auray inreases to 56

7 A HEART CELL GROUP MODEL FOR THE IDENTIFICATION OF MYOCARDIAL ISCHEMIA 9.6% with sensitivity of 94.89% and sensitivity of 75.66%. Sensitivity and speifiity are defined as the auray of deteting the ishemi beat and the auray of deteting the non ishemi beat respetively. The onfusion matries for the proposed approahes are given in Table, Table, and Table 3 respetively. Confusion matrix is a visualization tool that presents the instanes lassified as ishemi or healthy in its olumns and the atual lassifiation in its rows. Table : Confusion Matrix for HCM /C4.5 approah. Classified as Ishemi Healthy Ishemi Healthy 43 4 Table : Confusion Matrix for PCA/C4.5 approah. Classified as Ishemi Healthy Ishemi Healthy 44 6 Table 3: Confusion Matrix for HCM-PCA/C4.5 approah. Classified as Ishemi Healthy Ishemi Healthy It an be seen from Table and Table that the sensitivity of the proposed approah inreases by % when using the PCA omponents in addition to the model parameters as features in the C4.5 deision tree lassifier. As mentioned above, the proposed approah is ompared to the tehniques of (Stamkopoulos 998) as applied to the LT-ST database. Table 4: Comparison between the proposed approah and previous methods. Approah Auray Sensitivity Speifiity HCM-PCA/C % 94.89% 75.66% Stamkopoulos 86.76% 9.73% 63.86% It an be appreiated from Table 4 that the proposed HCM-PCA/C4.5 approah performs better than the previous methods by (Stamkopoulos 998) for the LT-ST database. However, we have not been able to repliate the results of (Vitor-Emil Neagoe 3). The importane in the proposed model, HCM, is that it an be related bak to the heart s physial and eletrial ativity. It an be seen that the parameters of the HCM an be used in the detetion of ishemi and healthy heart beats. This is due to the fat that the model parameters aptured the information regarding the ECG waves and segments, suh as slope, interval duration, magnitude and segment s variation. 5 CONCLUSIONS A HCA-PCA/C4.5 approah is presented in this work to diagnose ishemi and healthy beats. The proposed approah is applied to the LT-ST database provided by Physionet. The approah showed exellent results when diagnosing ishemi and healthy beats. The proposed modelling approah provides a method to identify the features of ECG signals and an estimate to the ellular eleti ativity useful for ishemia detetion. Finally, the proposed lassifiation approah an be extended to detet different ardia diseases. REFERENCES AHA 5, Heart Disease and Stroke Statistis, Dallas, Texas: Amerian Heart Assoiation. Andrew J. Pullan, M.L.B., Leo K. Cheng 5, Mathematially Modeling the Eletrial Ativity of the Heart from Cell to Body Surfae and Bak Again, World Sientifi, New Jersey. Clifford, G. 6, 'ECG Bag', < Eibe Frank, M.H., Geoff Holmes, Mike Mayo, Bernhard Pfahringer, Tony Smith, Ian Witten 7, WEKA, The University of Waikato. GD. Clifford, P.M. 5, 'Method to Filter ECGs and Evaluate Clinial Parameter Distortion Using Realisti ECG model Parameter Fitting', Computers in Cardiology. Gulrajani, R.M. 998, 'The forward and inverse problems of eletroardiography', vol. IEEE Engineering in Mediine and Biology Magazine, pp Jager, F., Taddei, A. & Moody, G. 3, 'Long-term ST database: A referene for the development and evaluation of automated ishaemia detetors and for the study of the dynamis of myoardial ishaemia.' Medial and Biologial Engineering and Computing, vol. 4, pp Long, C. 98, Prevention and rehabilitation in ishemi heart disease, Baltimore: Williams & Wilkins. Moody, J.M., Preventive ardiology : strategies for the prevention and treatment of oronary artery disease, Humana Press, Totowa, N.J. N. Maglaveras, T.S., C. Pappas, and M. Strintzis 994, 'Use of neural networks in detetion of ishemi 57

8 HEALTHINF 8 - International Conferene on Health Informatis episodes from ECG leads', Neural Networks for Signal Proessing, pp Pardee, H. 9, 'An eletroardiographi sign of oronary artery obstrution', Arh Int Med, vol. 6, pp R. Gianrossi, R.D., D. Mulvihill, K. Lehmann, P. Dubah, A. Colombo, D. MArthur, and V. Froeliher 989, 'Exerise- indued ST depression in the diagnosis of oronary artery disease. A meta-analysis', Cirulation, vol. 8, pp R.V. Andreao, B.D., J. Boudy, J.C.M. Mota 4, 'STsegment analysis using hidden Markov Model beat segmentation: appliation to ishemia detetion', Computers in Cardiology, pp Stamkopoulos, T.D., K. Maglaveras, N. Strintzis, M. 998, 'ECG analysis using nonlinear PCA neural networks for ishemia detetion', IEEE Transations on Signal Proessing, vol. 46, no.. Vitor-Emil Neagoe, I.-F.I., Sorin Grunwald 3, 'A Neuro-Fuzzy Approah to Classifiation of ECG Signals for Ishemi Heart Disease Diagnosis', AMIA Annu Symp Pro, p APPENDIX The ost funtion for the onstrained optimization funtion is obtained by replaing () into (): ECG k g ( t a ), (7) i i i i= SA, AV, Bb, Pf, LV, RV min,, x g ( t, ai, i) = d( t, ai,, i,, ai,, i, ) d( t, ai,3, i,3, ai,4, i,4 ) (,,,, ) (,, ) (,, ), (8) d t a a = s t a s t a, (9) s( t, a, ) =, () at + e Subjet to the onstraints: () i < () i,4, < SA ( AV ), < ( SA) ( Rvep) ( AV ),4 ( Rven),, ( SA) ( AV ) <, < AV,4 ( Rvep),,4 <, < AV ( Lvep) ( Rven),4 ( Lvep),4 <, < Rven ( Rvep) ( Lvep),4 ( Rvep),4,4 <,,, ( AV ) ( Lven),4 <,,, ( Rvep) ( Lvep) <, < Rvep ( Lven), < Lven,4 ( Rvep),,4 < <, ( Lvep) ( Lven).5.,, ( Lven) ( Lvep) < SA 4 ( SA) <, SA 4 ( SA).5.,4,4.5 < <. < AV 4 ( AV ) <, Rvep 3 ( Rvep).5..5 < <.8, < Rvep 4 ( Rvep) <, Rven 4 ( Rven) < <.3, < Lvep 3 ( Lvep) <, Lvep 4 ( Lvep).5 < <.. ( Lvep) 3 ( Lvep) 4.5 < <., 58