DERIVING THE 12-LEAD ECG FROM EASI ELECTRODES VIA NONLINEAR REGRESSION

Size: px

Start display at page:

Download "DERIVING THE 12-LEAD ECG FROM EASI ELECTRODES VIA NONLINEAR REGRESSION"

Joseph Henderson
5 years ago
Views:

DERIVING THE 1-LEAD ECG FROM EASI ELECTRODES VIA NONLINEAR REGRESSION 1 PIROON KAEWFOONGRUNGSI, DARANEE HORMDEE 1, Departmet of Computer Egieerig, Faculty of Egieerig, Kho Kae Uiversity 4, Thailad

1 DERIVING THE 1-LEAD ECG FROM EASI ELECTRODES VIA NONLINEAR REGRESSION 1 PIROON KAEWFOONGRUNGSI, DARANEE HORMDEE 1, Departmet of Computer Egieerig, Faculty of Egieerig, Kho Kae Uiversity 4, Thailad 1 kpiru@hotmail.com, darhor@gmail.com Abstract- The stadard 1-lead Electrocardiogram (ECG) is the basic cliical method of heart disease diagosis. Measurig all 1 leads is ofte cumbersome ad impractical especially o a log term moitorig. I 1988, Gordo Dower has itroduced a EASI-lead ECG System, where oly 5 electrodes are used. I order to gai all 1-lead ECG back from this EASI system, Dower s equatio was proposed the. Ever sice various attempts have bee explored to improve the sythesis accuracy, mostly via Regressio. This paper presets how Polyomial Regressio is used to fid a set of trasfer coefficiets for derivig the 1-lead ECG from EASI system. The experimets were coducted to compare the results those of Polyomial Regressio agaist those of equatio ad those of Dower s method. The experimetal results have show that the best performace amogst those methods with the highest correlatio coefficiet for all sigals with the stadard 1-lead ECG was obtaied by Polyomial degree 3, followed by degree, the Regressio ad Dower s equatio, respectively. Keywords- ECG; 1-lead System; EASI-lead ECG System; Regressio; Dower; Polyomial Regressio. I. INTRODUCTION The covetioal 1-lead Electrocardiogram (ECG) is a reliable diagostic tool, widely used i routie cliical practice for screeig, for outpatiet ad emergecy evaluatio, for evaluatig complicated cardiac arrhythmias, ad for diagosig other cardiac disorders. Typically for measurig 1-lead ECG requires 9 electrodes to be placed strategically o the body ad oe electrode to be coected to groud as show i Fig. 1[1,]. The systems with reduced umbers of leads that sythesize ito a 1-lead ECG are usually called derived 1-lead ECG systems [6]. These systems ca be divided ito two categories: systems that employ subsets of the leads from a 1-lead ECG, referred to as reduced-lead sets, ad systems that use special leads. Previously, i 1968, Dower [4] preseted a case for the first category. I 1988, Dower, agai, ad team [7] set a example for the latter category, by derivig the 1-lead ECG from four completely ew (EASI) electrodes, as show i Fig.. Fig.1. Stadard 1-lead ECG. From Fig.1, the stadard 1-lead ECG sigals are Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6 sigals. Reducig the umber of leads from the covetioal 1-lead ECG yieldig the smaller umber of measuremet electrodes ad cosequetly fewer wires, is possible by derivig the missig sigals from the actual measured electrodes. The developmet of ECG systems with reduced umber of electrodes started i the 194s [3], but the first otable work o derived 1-lead ECG system came i 1968 [4] with the itroductio of a derived 1-lead ECG sythesized from the spatial Vectorcardiography previously itroduced by Frak [5]. Fig.. Lead placemet for the EASI system. The E electrode is o Lower extreme of the sterum, while the A ad I electrodes are at the left ad right mid-auxiliary lies, same trasverse lie as E. The S electrode is at the steral maubrium. The fifth electrode is a groud ca be placed aywhere o the torso. The sythesis method implemeted i this work used paired sigals A-I, E-S, A-S derive as a weighted liear sum of these 3 base sigals as i the Equatio (1). L = a(a I) + b(e S) + c(a S) (1) Where L represets ay surface ECG lead ad a, b, ad c represet empirical coefficiets. These coefficiets, developed by Dower, are positive or egative values with accuracy up to 3 decimal poits. Proceedigs of The IRES 11 th Iteratioal Coferece, Bagkok, Thailad, 4 th October 15, ISBN:

2 After the derived 1-lead ECG system via EASI electrodes has bee preseted, various improvemets o coefficiets i Dower s equatio have bee ivestigated ever sice. I 1, Oleksy [8] proposed the Regressio method as opposed to Dower s equatio, i order to sythesize the stadard ECG sigals from EASI lead system usig E, A, S ad I sigals as iput data. This yielded to less error compared to the previous Dower method. Up till recetly, the previous works mostly focused o Regressio as the sythesis approach to derive the 1-lead ECG sigals from EASI leads. This paper attempts to preset Polyomial Regressio as the alterative method as opposed to Dower s or Regressio. II. LINEAR REGRESSION Regressio [9] is the oldest ad most widely used predictive model. The goal is to miimize the sum of the squared errors to fit a straight lie to a set of data poits. The liear regressio model fits a liear fuctio to a set of data poits. The fuctio is as follow: Y = β + β X + β X +.. +β X () Where Y is the target variable ad X, X,... X are the predictor variables ad β, β, β are the coefficiets that multiply the predictor variables ad β is costat. III. POLYNOMIAL REGRESSION Polyomial Regressio [1] used to fit oliear data ito a least squares liear regressio model. It is a form of liear regressio that allows oe to predict a sigle y variable by decomposig the x variable ito fuctio. The fuctio is as follow: Y = β + β X + β X + β X +.. +β X (3) Where Y is the target variable ad X, X,... X are the predictor variables ad β, β, β are the coefficiets that multiply the predictor variables ad β is costat. I Polyomial Regressio, differet powers of the x variable are successively added to the fuctio ad a powers of x are added to the fuctio, the best fit lie chages shape. IV. METHODOLOGY The experimets are coducted to compare various sythesis methodologies for derivig the 1-lead ECG from EASI lead system. These sythesis methods are Dower s, Regressio ad Polyomial Regressio with degree of ad 3. All dataset used i this work are obtaied from PhysioNet database [11] cosistig of 4,813 samples for each sigal to shuffle data sets i order to prevet over fittig ad usig Five-fold Cross-validatio, to fid the best parameter. These dataset are used as the traiig dataset ad the other as the testig dataset. At the traiig process; all 1 Lead sigals are used i order to derive the trasfer fuctio. The at the testig process; 4 Lead sigals (Lead E, Lead A, Lead S, Lead I) represet the measured data. By substitutig these sigals ito the derived fuctio, all missig 1 Lead sigals (Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6) are obtaied. The followig steps preset how to derive the trasfer fuctio; 1) Five-fold Cross-Validatio is utilized. All dataset from PhysioNet is divided ito 5 equal parts/folds. Each roud a sigle fold is used for testig, leavig the other 4 folds for traiig. I the th roud, Fold# is used for testig while the remaiig folds are used for traiig. For istace, i the th roud, Fold# is used for testig while Folds#1 ad Folds#3-5 are used for traiig. I total 5 rouds are processed. To fid the average errors i the regressio of each fold, the Root Mea Squared Error (RMSE) i the Equatio (4) is used. RMSE = (A F ) (4) Where At is the actual value i time t, Ft is the forecast value i time tad is sample of testig set i each fold. ) From all 5 folds, the RMSE value of the Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6 sigals are cosidered. I order to fid the trasfer fuctio of each sigal, the fold that provides the miimum RMSE value of that sigal must be idetified. The the costat ad coefficiets from that fold will be substituted ito the equatio of Regressio i Equatio (5), Polyomial Regressio Degree i Equatio (6) ad Polyomial Regressio Degree 3 i Equatio (7) to form the trasfer fuctio of that sigal. Y x x x x (5) Y x x x x x x x x x x x x x x x x x x x x Y x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x (6) (7) Proceedigs of The IRES 11 th Iteratioal Coferece, Bagkok, Thailad, 4 th October 15, ISBN:

Where Y is the trasfer fuctio of Lead sigal, is Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6, β is the costat ad β,.

3) After obtaiig the trasfer fuctio models for each sigal, the big test i order to evaluate these trasfer fuctios ca the be started.

oes from the PhysioNet dataset. V. RESULTS TABLE III.

3 Where Y is the trasfer fuctio of Lead sigal, is Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6, β is the costat ad β,..,β are coefficiets of X1,..,X4 from the fold providig the miimum RMSE of Lead sigal. X is Lead E, X is Lead A, X is Lead S, X is Lead I. 3) After obtaiig the trasfer fuctio models for each sigal, the big test i order to evaluate these trasfer fuctios ca the be started. By feedig the data set from those 4,813 data samples ito these 1 trasfer fuctios to get the calculated Lead sigal, the RMSE values of each Lead sigal ca be determied from the calculated sigals ad the oes from the PhysioNet dataset. V. RESULTS TABLE III. ROOT MEAN SQUARED ERROR WITH POLYNOMIAL DEGREE 3 REGRESSION OF 5-FOLD CROSS VALIDATED The testig results with 5-fold Cross-validatio to fid RMSE value of Regressio, Polyomial Regressio Degree ad Polyomial Regressio Degree 3 for Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6 sigals are listed i Table I-III. TABLE I. ROOT MEAN SQUARED ERROR WITH LINEAR REGRESSION OF 5-FOLD CROSS VALIDATED From Table I, Table II ad Table III, the miimum RMSE values of Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6 are highlighted of each Fold. The costat ad coefficiets of those folds with the miimum of RMSE value are used for derived ECG of 1 sigals. The plots of Lead I, Lead II, Lead III, Lead avr, Lead avl, Lead avf, Lead V1, Lead V, Lead V3, Lead V4, Lead V5 ad Lead V6 sigals measured usig stadard 1-lead ECG method, derived usig EASI method by Regressio method ad Polyomial regressio method are show i (Fig.3) TABLE II. ROOT MEAN SQUARED ERROR WITH POLYNOMIAL DEGREE REGRESSION OF 5-FOLD CROSS VALIDATED (a) Lead I Sigal. 6 4 Proceedigs of The IRES 11 th Iteratioal Coferece, Bagkok, Thailad, 4 th October 15, ISBN: (b) Lead II Sigal.

4 (c) Lead III Sigal (h) Lead V Sigal (d) Lead avr Sigal (e) Lead avl Sigal (i) Lead V3 Sigal (j) Lead V4 Sigal (f) Lead avf Sigal. -1 (g) Lead V1 Sigal (k) Lead V5 Sigal. - (l) Lead V6 Sigal. Fig. 3. Derived vs origial values of Lead I, II, III, avr, avl, avf, V1, V, V3, V4, V5 ad V6 sigals. Proceedigs of The IRES 11 th Iteratioal Coferece, Bagkok, Thailad, 4 th October 15, ISBN:

Lastly, RMSE errors ad correlatio coefficiet values obtaied from all methods are show ad compared i Table IV ad Table V. TABLE IV. ROOT MEAN SQUARED ERROR (MV) degree 3 provided less RMSE values.

As for correlatio coefficiets, the highest values were also obtaied from Polyomial degree 3, followed by Polyomial degree, the Equatio ad lastly Dower s Equatio.

5 Lastly, RMSE errors ad correlatio coefficiet values obtaied from all methods are show ad compared i Table IV ad Table V. TABLE IV. ROOT MEAN SQUARED ERROR (MV) degree 3 provided less RMSE values. Secod best model was obtaied from the Regressio method while Dower s method came last i the series. As for correlatio coefficiets, the highest values were also obtaied from Polyomial degree 3, followed by Polyomial degree, the Equatio ad lastly Dower s Equatio. Therefore, it is obvious to coclude that Noliear Regressio is worth chose for derivig the 1-lead ECG from EASI system. As for future works, other regressio ad machie learig techiques to improve the performace of derivig the 1-lead ECG sigals from EASI system should be ivestigated further. REFERENCES TABLE V. CONCLUSIONS CORELATION COEEFICIENT This paper has preseted Polyomial Regressio for derivig the stadard 1-lead ECG from EASI system. The experimetal results showed that the best performace i this work, was obtaied from the Polyomial Regressio method, whereas Polyomial [1] Ed. Joseph D. Brozio. Priciples of Electrocardio Graphy, The Biomedical Egieerig Hadbook:Secod Editio.,. [] Bioelectromagetism [Web page]. [3] I. Tomasic, R. Trobec, Electrocardiographic Systems With Reduced Numbers of Leads Sythesis of the 1-Lead ECG, Biomedical Egieerig, IEEE Reviews i Biomedical Egieerig, vol.7, pp.16-14, 14. [4] G. E. Dower, A lead sythesizer for the Frak system to simulate the stadard 1-lead electrocardiogram, J. Electrocardiol., vol. 1, o. 1, pp , [5] E. Frak, A accurate, cliically practical system for spatial vectorcardiography, Circulatio, vol. 13, o. 5, pp , May [6] P. W. Macfarlae, et al, Derived 1-Lead ECG Systems, Comprehesive Electrocardiology, pp , Lodo: Spriger-Verlag, 11. [7] G. E. Dower, et al, Derivig the 1-lead electrocardiogram from four (EASI) electrodes, Joural of Electrocardiology, Vol.1, Supplemet, pp.s18-s187, [8] W. Oleksy, E. Tkacz, ad Z. Budziaowski, Improvig EASI ECG Method Usig Various Machie Learig ad Regressio Techiques to Obtai New EASI ECG Model, Iteratioal Joural of Computer ad Commuicatio Egieerig, vol. 1, o. 3, pp , 1. [9] Regressio. [Web page] [1] Polyomial Regressio. [Web page] [11] PhysioNet database. [Web page] Proceedigs of The IRES 11 th Iteratioal Coferece, Bagkok, Thailad, 4 th October 15, ISBN:

Improving EASI Model via Machine Learning and Regression Techniques

Improving EASI Model via Machine Learning and Regression Techniques P. Kaewfoongrungsi, D.Hormdee Embedded System R&D Group, Computer Engineering, Faculty of Engineering, Khon Kaen University, 42, Thailand.