2.1 .1 .01

Laplacian Electrocardiography

Department ofUniversity

sEo 1120,851 s.

Abstract: We review the recent progress in thefield of Laplacian electrocardiography. The workbeing carried out by investigators all over theworld indicates that the Laplacianelectrocardiogram promises to enhance ourcapability of imaging cardiac electrical activity,and merits further investigation.

Introduction

It is of great importance to image and localize cardiacelectrical activity from body surface electrocardiographicrecordings. Extensive efforts have been made by a numberof investigators to localize and image cardiac electricalactivity from body surface potentials Il-21.

Recently, considerable efforts have been made toinvestigate the applicability of body surface Laplacianelectrograms to localizing and imaging of important cardiacelectrical activity t3-51. It has been reported that bodysurface Laplacian electrograms play an unique role inenhancing our capability of imaging cardiac electricalactivity.

The Laplacian principle has also been pursued intheoretical and experimental studies for detection ardanalysis of myocardial electrical events from epicardialrecordings t6-81.

In this paper, we review the principles of Laplacianelectrocardiogram and recent developments of body surfaceLaplacian mapping, and forward and inverse Laplacianelectrocardiography.

Laplacian Electrocardiogram

The Laplacian electrocardiogram can be defined as thenegative surface Laplacian of the body surface potential[3,9]. Considering a local orthogonal coordinate system (x,y, z) with origin at a point on the body surface, and with zbeing the normal to the body surface, the Laplacianelectrogram can be represented as

LQ=-(#.ff, (r)

where Q represents the potential electrogram. The negativesign facilitates the comparison between the distributions ofthe potential and Laplacian electrograms.

The Laplacian electrogram is in principle inverselyproportional to the fourth power of the distance from a

dipole to the observation point, whereas the potentialelectrogram is proportional to the inverse power of that

Bin He, Ph.D.EECS and Bioengineering Programof Illinois at Chicago (M/C 154)Morgan Street, Chicago, lL 60607, USA

distance. Thus the potential electrogram to a great extentintegrates the contributions of distributed sources, whereasthe Laplacian electrogram heavily weights sources closestto the measurement point. This unique characteristic of theLaplacian electrogram constitutes the basis of its strongcapability of localizing underlying cardiac electricalactivity.

Body Surface Laplacian Mapping

The most notable application of the Laplacianelecfocardiogram has been in body surface mapping t3l.Body surface Laplacian maps (BSLMs) have been pursuedby using an array of bipolar concentric electrodes [3,9], anda set of unipolar elecffodes t101. The lead field of thebipolar concentric elecffode was analyzed and shown to beapproximately proportional to the surface Laplacian of thepotential [11]. The simplest implementation of Laplacianrecording based on unipolar electrodes is that first used byHjorth in recording scalp Laplacian electroencephalograms

Il2l. By measuring and visualizing body surfacedistributions of Laplacian electrogram, a clear mappingrelationship has been reported between the known cardiacelectrical events and activities observed in the BSLMs[3,9-10].

Recently, a new 3D mapping algorithm has beendeveloped in our laboratory at the University of Illinois, bywhich the Laplacian mapping can be performed over arealistic geometry torso model from a set of unipolarrecordings [3]. Our human experimental results show thatthe BSLMs are highly reproducible and provide a clear bodysurface manifestation of the underlying myocardialactivation process. A typical BSLM during ventricularactivation process in a healthy human subject is shown inFig. 1.

Fig. 1 A typical example of BSLM (right) and BSPM (left)during ventricular activation over the anterior chest of ahealthy human subject

Medical & Biological Engineering & Computing Vol. 34, Supplement 1, Part 2, lggoThe 1st InternationalConference on Bioelectromagnetism, June 9-13, 1996, Tampere, Finland 29

Forward Simulation of Laplacian ECG

Computer modeling and simulation studies have beenconducted to investigate the relationship between cardiacsources and BSLMs. The torso volume conductor has beenmodeled using simplified models [3,16] and realisticgeometry models [4-15,17]. Source models being used inforward simulations include simplified dipole models [3],and 2D tl5l and 3D physiologically reasonable heartmodels [16-17]. Fig.2 shows an example of BSLM (right)and BSPM (left) induced by two site pacing with a distanceof 3 cm over the anterior epicardium in a 3D heart-torsomodel [16]. Note the enhanced spatial resolution of theBSLM in localizing and imaging anterior myocardialsources as compared with the BSPM. These simulationstudies demonstrate important characteristics of theLaplacian electrocardiogram and help interpret recordedLaplacian electrocardiograms in human subjects.

Fig. 2 A 3D heart-torso modeling result of BSLM (right)and BSPM (lett) induced by two site pacing over theanterior epicardium

Inverse Laplacian Electrocardiography

It has been proposed to use Laplacian electrograms insolving electrocardiography inverse problems t181.Computer simulation studies conducted in our laboratory[9] and other laboratories [20] showed consistent resultswhich suggest the feasibility of imaging epicardialelecfrical events from the body surface Laplacian

LaplaclenPotentlal

elecfrocardiograms. Fig. 3 depicts a computer simulationresult obtained using an eccenfric sphere heart torso model,which indicates the feasibility of employing the Laplacianelectrograms in imaging epicardial electrical events t191.Because Laplacian ECG is a reference-free measurement,problems associated with variation in reference potential önot exist in solving the inverse problems using LaplacianECG.

Summary

The development of Laplacian electrocardiography hasrecently received considerable attention. Theoretical atdexperimental investigations are actively pursued byinvestigators all over the world. The promising resultsreported up to date suggest the great potential of Laplacianelectrocardiography in enhancing our capability of imagingcardiac electrical activity and in facilitating clinicaldiagnosis of cardiac functional abnormalities.

Acknowledgment

This work was supported in part by a grant from TheWhitaker Foundation and a grant from the University ofIllinois at Chicago Campus Research Board.

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Fig. 3 lnverse reconstruction errors between thesimulated and reconstructed epicardial potentials fromBSLMs (solid line) and BSPMs (dashed line)

Medical & Biological Engineering & Computing Vol. 34, Supplement 1, Part 2, 1996The 1st InternationalConference on Bioelectromagnetism, June 9-13, 1996, Tampere, Finland30