Model-based imaging of cardiac electrical excitation in humans

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 21, NO. 9, SEPTEMBER 2002 1031

Model-Based Imaging of Cardiac ElectricalExcitation in Humans

Bernhard Tilg, Member, IEEE, Gerald Fischer, Robert Modre, Friedrich Hanser, Bernd Messnarz, Michael Schocke,Christian Kremser, Thomas Berger, Florian Hintringer, and Franz Xaver Roithinger

Abstract—Activation time (AT) imaging from electrocardio-graphic (ECG) mapping data has been developing for severalyears. By coupling ECG mapping and three-dimensional (3-D)+ time anatomical data, the electrical excitation sequence canbe imaged completely noninvasively in the human heart. In thispaper, a bidomain theory-based surface heart model AT imagingapproach was applied to single-beat data of atrial and ventriculardepolarization in two patients with structurally normal hearts. Inboth patients, the AT map was reconstructed from sinus and pacedrhythm data. Pacing sites were the apex of the right ventricle andthe coronary sinus (CS) ostium. For CS pacing, the reconstructedAT pattern on the endocardium of the right atrium was comparedwith the CARTO map in both patients. The localization errors ofthe origins of the initial endocardial breakthroughs were deter-mined to be 6 and 12 mm. The sites of early activation and theareas with late activation were estimated with sufficient accuracy.The reconstructed sinus rhythm sequence was in good qualitativeagreement with the pattern previously published for the isolatedLangendorff-perfused human heart.

Index Terms—Activation time map, atrium, electrocardio-graphic (ECG) mapping, human heart, inverse problem, magneticresonance imaging, modeling, ventricle.

NOMENCLATURE

CS Coronary sinus.IVC Inferior vena cava.LA Left atrium.LAA Left atrial appendage.LAr Left arm.LL Left lower pulmonary vein.LLe Left leg.LU Left upper pulmonary vein.LV Left ventricle.MA Mitral annulus.RA Right atrium.

Manuscript received November 5, 2001; revised July 6, 2002. This work wassupported by the START Y144 program under the Austrian Federal Ministryof Education, Science and Culture (bm:bwk) in collaboration with the AustrianScience Fund (FWF).Asterisk indicates corresponding author.

*B. Tilg was with the Institute of Biomedical Engineering, Graz Universityof Technology. He is now with the Institute for Medical Signal Processing andImaging, University for Health Informatics and Technology Tyrol, 6020 Inns-bruck, Austria (e-mail: [email protected]).

G. Fischer, R. Modre, F. Hanser, and B. Messnarz were with the Institute ofBiomedical Engineering, Graz University of Technology. They are now withthe Institute for Medical Signal Processing and Imaging, University for HealthInformatics and Technology Tyrol, 6020 Innsbruck, Austria.

M. Schocke and C. Kremser are with Radiology Department I, UniversityHospital Innsbruck, 6020 Innsbruck, Austria.

T. Berger, F. Hintringer, and F. X. Roithinger are with the Cardiology Depart-ment, University Hospital Innsbruck, 6020 Innsbruck, Austria.

Digital Object Identifier 10.1109/TMI.2002.804438

RAA Right atrial appendage.RAr Right arm.RL Right lower pulmonary vein.RU Right upper pulmonary veinRV Right ventricle.RVOT Right ventricular outflow tract.SVC Superior vena cava.TA Tricuspid annulus.WCT Wilson Central Terminal.

I. INTRODUCTION

COMBINING acquisition of three-dimensional (3-D)time anatomical with electrocardiographic (ECG) map-

ping data from an individual patient enables the noninvasiveimaging of the electrical function in the heart. Three-dimen-sional time anatomical data from the human thorax can beobtained from magnetic resonance imaging (MRI), computedtomography, or ultrasound. ECG mapping data are obtainedby employing multichannel ECG recording systems [27],[28], [39]. In addition to the imaging of cardiac movement,perfusion, and metabolism, the reconstruction of electricalfunction should have a significant clinical impact.

The primary electrical source in the cardiac muscle is thespatiotemporal distribution of the transmembrane potential.According to thebidomainand bioelectromagnetic field theory,this impressed transmembrane potential distribution causes an(extracellular) potential distribution in the entire human thorax[8], [10], [14], [18]. The epicardial potential and the potentialon all other conductivity interfaces are related to by a Fred-holm integral equation of the second order [5]. In the so-calledelectrocardiographic inverse problem, the impressed electricalsource distribution is estimated from chest surface ECG map-ping data. For this kind of imaging, an electrical source model isneeded. Because of the generally unknown individual fiber ori-entation, electrical isotropy is assumed in ourbidomain theory-based surface heart source model formulation [5], [8], [18]. Thissource model is equivalent to the so-calleduniform dipole layerformulation [9], [14], [15]. For depolarization, the assumptionof electrical isotropy yields reasonable results—first, because ofthe small spatial extension of the excitation wavefront, which ison the order of 1 mm, and secondly, because surface ECG map-ping takes place in the far field. The forward and inverse for-mulation, therefore, can be reduced to a two-dimensional scalarpotential problem [5], [30]. In general, the boundary elementmethod (BEM)—a surface integral equation approach—is ap-plied to this kind of problem. The applied source model does

0278-0062/02$17.00 © 2002 IEEE

1032 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 21, NO. 9, SEPTEMBER 2002

not have any constraints on wavefront propagation. It still al-lows anisotropic propagation throughout the myocardium.

The electrocardiographic inverse problem determines eitherparameters describing features of or the epicardial (moreprecisely the pericardial) potential distributions. Further, thereconstruction of endocardial potential distributions from bal-loon-catheter data and the application of a heart-model-basedelectrocardiographic imaging approach are alternatives, inorder to get an image of electrical activity [22], [25]. Themost established inverse formulations are composed of theimaging of theactivation time(AT) map on the entire surfaceof the ventricle or the atrium (employing the bidomain theoryor uniform dipole layer formulation) and the imaging of theepicardial potential pattern (by solving the so-calledepicardialpotential problem) [3], [12], [13], [20], [21], [29], [30], [31],[33], [34]. The epicardial potential problem aims at estimatingthe (extracellular) potential on the pericardium. When usedin a straightforward manner, however, this formulation doesnot allow the imaging of the potential on the endocardium.In contrast, thebidomain theory-based surface heart modelapproach permits the imaging of electrical excitation on theentire atrial or ventricular surface, i.e., on the endocardiumand epicardium as well [18], [29], [30]. This is especiallyimportant from a clinical point of view because most of thecatheter procedures (e.g., radio-frequency catheter ablation)are performed on the endocardium [1], [23], [36], [37].

In clinical electrocardiology, arrhythmias—in particular,within the human atrium—and their therapeutic treatmentplay a significant role [24], [36], [37]. In clinical practice,the localization of the origins of arrhythmias is currentlyachieved by traditional catheter techniques and by recentlyintroduced catheter mapping techniques, e.g., CARTO. A moredetailed description of the CARTO technology can be found in,e.g., [1] and [2]. These mapping techniques show significantlimitations when it comes to acquiring single-beat activationmaps. Also, they are mostly applied to single target chambersonly. Another important point is the fact that it is impossibleto obtain information from the epicardium under clinicalconditions. The proposed single-beat AT imaging approachovercomes these limitations and provides in a noninvasive wayinformation about electrical excitation. This information isavailable immediately after the ECG recording.

From a clinical point of view, this might have several benefits.The AT imaging method permits the reconstruction of singlefocal, multiple focal, and more distributed activation patterns. Italso can distinguish between areas with early and late activation.Potentially promising clinical applications of the ECG inverseproblem are the noninvasive imaging of atrial and ventricularectopic beats as well as preexcited activation.

In this paper, we investigate the applicability and the perfor-mance of the AT imaging method in two patients who underwentan electrophysiological (EP) study in the catheter laboratory. Wefocused on atrial and ventricular sinus and paced activation se-quences. This paper advances our previous work in three impor-tant aspects [29], [30]: the AT imaging approach is 1) appliedto atrial data, 2) applied to single-beat data, and 3) is clinicallyvalidated by means of CARTO data.

II. M ETHODS

A male (A) and a female (B) patient, 65 and 36 years old,respectively, were considered for this clinical inverse study.Patient A suffered from an atrial flutter, and patient B wastreated because of a Wolff–Parkinson–White syndrome. Bothhad structurally normal hearts, with normal findings from theechocardiographic study. Informed consent was obtained fromboth patients before any diagnostic and therapeutic procedure.The study was approved by the local ethics committee.

A. Measurement Protocol

Prior to the treatment in the catheter laboratory, individualanatomical data were obtained by MRI using a MagnetomVision Plus 1.5 Tesla scanner. Atrial and ventricular geometrywas recorded in CINE-mode during breath-hold (expiration,21 7 oblique short-axis scans, 4- and 6-mm spacing). Thelungs and the torso shape were recorded in T1-FLASH-modeduring breath-hold (expiration, 40 axial scans, 10-mm spacing).Eleven markers (vitamin E capsules, seven anatomical land-marks on the anterior and lateral chest wall, four electrodepositions on the patient’s back) were used to couple theelectrode positions and the reference points to the MRI frame.Based on this MRI data set, a BEM volume conductor modelwas formulated [5], [6].

The patients were then moved to the catheter laboratory.ECG mapping data were recorded during and after the EPstudy. ECG mapping data were acquired in 62 channels by theMark-8 system (Biosemi V.O.F.) [27], [28], [36]. The WCTdefined the reference potential [7], [11]. The sampling ratewas 2048 Hz. Signals were bandpass filtered with a lowerand upper edge frequency of 0.3 and 400 Hz, respectively.The AC-resolution of the system is 500 nV/bit (16 bits perchannel). Radiotransparent carbon electrodes were used inorder to allow simultaneous X-ray examination. The positionsof the electrodes on the anterior and lateral chest wall weredigitized by the Fastrak system (Polhemus Inc.). Additionally,the positions of the seven anterior and lateral landmarks weredigitized in order to allow coordinate transformation to theMRI frame. Four posterior electrode positions were obtainedfrom the sites of the vitamin E capsules.

The ECG mapping raw data were preprocessed by baselinecorrection, but no additional filtering was applied.

B. Inverse Modeling

The transfer function, relating to the surface ECG map-ping data, was calculated by applying the BEM with linear tri-angular elements, defining WCT as the reference potential. Themathematical basis for the implemented BEM is given by aFredholm integral equation of the second order [5], [6], [30].For the transfer matrix calculation, the following conductivitieswere assumed for the different torso compartments: chest (0.20Sm ), lungs (0.08 Sm ), blood mass (0.60 Sm), ventric-ular and atrial myocardium (0.20 Sm), and intracellular ef-fective conductivity (0.10 Sm ).

The segmentation of the MRI data and the triangular meshingof the surfaces were done with recently developed software,running under AmiraDev 2.3 (TGS Template Graphics Soft-

TILG et al.: MODEL-BASED IMAGING OF CARDIAC ELECTRICAL EXCITATION IN HUMANS 1033

Fig. 1. BEM thorax model for patient A from an anterior–posterior view.RAr, LAr, and LLe define the WCT that was used as reference for the ECGrecording and for the inverse modeling. The spheres represent the 55 ECGelectrode positions.

ware, Inc.). The meshing procedure is summarized as follows:based on a generalized marching cube algorithm, a triangularsurface mesh representation of each individual surface is com-puted. Afterwards, the initial surface mesh is optimized withregard to the shape, i.e., the angles and the distribution of thetriangles. The density of the triangles can be adapted with re-gard to the local surface curvature. Fig. 1 shows the BEM thoraxmodel for patient A with the 55 electrode positions from an an-terior–posterior view. The entire model consisted of 6794 trian-gles. The ventricular and atrial surface consisted of 1462 and1600 triangles and of 731 and 790 nodal points, respectively.The chest and the lung surfaces were reconstructed from axialMRI scans. The ventricular and atrial surface model was con-structed from CINE-mode short-axis scans with 6- and 4-mmslice thicknesses, respectively. Static models for the ventriclesand for the atria were constructed from this CINE MRI data thatfitted to the time during the QRS-wave and the P-wave, respec-tively. For modeling during the end-diastolic phase, trigger de-lays were 0 ms (QRS-interval) and 600 ms (TP-interval) afterthe R-peak. In patient A, only 55 of the 62 electrodes were con-sidered. Forty-one electrodes were located on the anterior, tenon the left and right lateral chest, and four electrodes on the pos-terior chest. Seven electrodes from the posterior chest were notused for inverse modeling because of missing localizations inthe MRI frame. The configuration of the applied electrode gridis already in use for paced mapping [36]–[38]. Fig. 2 depicts theECG-gated ventricular and atrial surface model from patient Ain an anterior–oblique view. The shaded surfaces in the red color

Fig. 2. Ventricular and atrial surface model of patient A from an anterior–oblique view.

Fig. 3. Atrial surface model from patient A in a caudal–oblique view.

are the modeled blood masses. The transparent surfaces repre-sent the entire ventricular and atrial surface, both the endo- andthe epicardium.

The thorax model for patient B consisted of 5676 triangles.In this patient, only 49 of the 62 electrodes were considered.Forty-one electrodes were located on the anterior, four on theleft and right lateral chest, and four on the posterior chest. Thir-teen electrodes were not used for inverse modeling. The staticventricular (QRS-wave) and the atrial (P-wave) surface modelconsisted of 1210 and 1438 triangles, respectively. In the inverseproblem, 607 and 709 unknown activation times, respectively,had to be determined.

Specific attention has to be paid to the modeling of the sur-face of the ventricle and of the atrium. Because of the complex


anatomy of RA and LA, there are several aspects in the evalu-ation of a “good” atrial surface model [23], [24]. Specific carehas to be taken on the MRI protocol in order to obtain scans witha high gray-value contrast. The segmentation of the epicardiumcould not be done from these MRI scans. We therefore assumeda uniform wall thickness of 4 mm for the left and right atrialfree wall in order to model the epicardium. Specific attentionhas to be paid to the identification of the pulmonary veins, ofSVC and IVC, and of TA and MA. The modeling of these struc-tures is important for this kind of inverse formulation. To makeit more clearly, the source-containing surface of the atrium andof the ventricle in combination with the spatiotemporal distribu-tion produces surface ECG signal, as can be seen from theFredholm integral equation of the second order [5], [30]. Be-cause of the sophisticated curvature and the narrowness of theindividual endo- and epicardial surfaces, the proper meshing isof outmost importance in order to obtain a high-quality transfermatrix. Fig. 3 depicts the atrial surface model from patient A in acaudal–oblique view. The endocardium and the epicardium areshown as a red shaded and as a triangular surface, respectively.

After triangualization of the conductivity interfaces and of theatrial and ventricular surfaces, the BEM approach results in alinear equation, relating to the surface ECG mapping data

[5].Considering the time course of during depolarization, the

relation between the activation timeand the surface ECG databecomes nonlinear. Indeed, for imaging the AT map on the

surface of the ventricle and atrium, we have to solve a nonlinearill-posed inverse problem. The cost function, which has to beminimized, can be formulated as [12], [20], [29], [30]

(1)

which is composed of an integral over the residual norm plusa regularization term. The transfer matrixdescribes the re-lation between the transmembrane potential on the endo-and epicardium and the body surface ECG data. is a denserectangular matrix, with, for instance, 55 rows and 790 columns(patient A, atrial source imaging). is linear at fixed and

; becomes nonlinear with respect to. The timeinterval 0 corresponds to the duration of the ECG targetwave considered for AT imaging. A second-order Tikhonov reg-ularization approach with an approximation of the Laplacianoperator is employed to stabilize the inverse solution in termsof measurement noise and errors in modeling the patient’s ge-ometry [19], [32]. The regularization parameterspecifies theweight between the residual norm and theregularizing smoothing norm . The determination of isbased on the L-curve method [16], [17], [29], [30].

For a successful imaging of the single-beat AT map, one of themost important aspects is the application of physiologically rel-evant, spatiotemporal regularization [12]. In (1), this is given bythe following aspects: First, is restricted to the surface of theatrium or ventricle only. This is given due to the assumption ofelectrical isotropy, resulting in thebidomain theory-based sur-face heart model approach. Secondly, in the inverse algorithm,an a priori template function is considered for , with only the

activation time as unknown. Thirdly, a surface Laplacian op-erator is applied to for further spatial smoothing, avoidingseveral unphysiological breakthroughs.

In the inverse formulation, the transmembrane potentialisdescribed at each source point of the ventricular or atrial surfaceby the analytical formula

(2)

with the resting membrane potential mV, the actionpotential amplitude , and the rise time .This template function describes the onset of the transmembranepotential (phase 0) for a given[14].

There are different methods available for solving (1). Awell-known algorithm in the inverse problem literature is theGauss–Newton approach [12], [29]. To our experience, underclinical conditions, the determination of the properbecomesvery difficult in applying this type of algorithm [29], [30].Hence, we further developed a novel approach, which decom-poses the nonlinear problem into a sequence of linear problemformulations [29], [30], [40]. In particular, for the applicationto clinical data, we found that this method is superior to theGauss–Newton approach. In short, this novel approach can bemathematically described by

(3)

where is a nonlinear operator that maps the activation timeonto the body surface ECG dataat time instant . Assuming

to be a series of approximations of the true solutionand linearizing (3) in the point yields

(4)

where is an abbreviation for representing theFrechet derivative of the operator at point .

Equation (3) can be written in a technically more useful form

(5)

with . Equation (5) is, in general, againill-posed. To find a regularized approximation for, a regular-ization method for linear ill-posed problems can be employed.Applying second-order Tikhonov regularization with the Lapla-cian operator and the regularization parameter yields thefollowing regularized approximation:

(6)

where the asterisk marks the adjoint operator. By repeating thisprocess, an iteration method is obtained

(7)

with the incremental activation time

(8)


Fig. 4. ECG data (Wilson lead V1, channel no. 12) for patient A for sinusrhythm (upper panel), RV pacing (middle panel), and CS ostium (CS 7–8)pacing (lower panel) with WCT as reference. The bold line segments indicatethe interval [0; T ] for the ECG target wave, considered for the imaging of theunderlying AT sequence.

As the index increases, the iteration process in (7) convergesto a regularized approximation of the AT pattern[40]. In bothpatients, the number of iterations was in between 15 and 25. Ateach iteration step, again, the determination ofis based on theL-curve method [16], [17]. This iteration process is equivalentto the Gauss–Newton method for minimizing the cost function

. The limit of the iteration represents a solution of the corre-sponding Euler equation of the cost function (1) [40]. It is thuspossible to extend regularization methods from linear to non-linear inverse ill-posed problems [29], [30], [40].

The initial guess for the AT map can be calculated by applyingthe critical point theorem [14], [21]. In the case of “good dataquality,” this theorem enables the estimation of a high-qualitystarting vector. The actual inverse solution was compared withthe CARTO map.

III. RESULTS

We reconstructed the AT maps from single-beat ECG map-ping data. Fig. 4 depicts the Wilson lead V1 ECG data (channelno. 12) for patient A for the normal sinus rhythm (upper panel),for pacing the apex of RV (middle panel), and for pacing the CSostium at the catheter electrode position no. 7–8 (lower panel).The ECG target wave, considered for the imaging of the under-lying atrial or ventricular surface AT map, is indicated by ver-tical lines. In (1), the interval [0,] describes this ECG targetwave. For inverse calculation, in each channel individual base-line correction was performed at the onset of the ECG targetwave. The isochrones in Figs. 5–11 and in Fig. 13 are shownin steps of 5 ms. For patient A, the reconstructed sinus rhythmsequence on the endocardium of RV and LV is shown in Fig. 5,from an anterior left-lateral view. The anterior epicardium is notshown. Early endocardial activation in RV occurred at 19 ms. Asecond endocardial breakthrough at 35 ms is on the endocardialleft-lateral free wall of LV. As can be seen from Fig. 6, the firstepicardial breakthrough is on the anterior epicardium of RV at

Fig. 5. Sinus rhythm AT map for RV and LV for patient A from an anteriorleft-lateral view. The anterior epicardium is not shown.

Fig. 6. Sinus rhythm AT map for RV and LV for patient A from an anterior–posterior view.

27 ms. The ventricle of patient A is shown in an anterior–poste-rior view. The interval for the entire ventricular depolarizationwas determined with 90 ms.

The left and the right heart base are electrically activated at80 and at 88 ms, respectively. These findings for normal ven-tricular depolarization are in good qualitative agreement withthe previously published sinus rhythm pattern from the isolatedLangendorff-perfused human heart [4].

In patient A, after sinus rhythm recording, a pacing catheterwas then moved to the posterior-septal site of the apex of RV.Pacing was performed during the end-diastolic interval. Fig. 7depicts the reconstructed AT pattern from a posterior–obliqueview. The pacing site is indicated with “RV PAC.” The estimatedtime interval for depolarizing RV and LV was 110 ms. Earliestactivation at 35 ms was localized at the posterior–septal site ofRV. No additional breakthroughs—as appeared during the sinusrhythm—could be found. The earliest activation of LV is onthe septal site at 70 ms. Afterwards, the apex and the base of


Fig. 7. AT map on the endocardium of RV and LV for the RV pacing protocolfor patient A from a posterior–oblique view. The pacing site is indicated withRV PAC.

Fig. 8. AT map on the endocardium of RA and LA for the CS pacing protocolfor patient A from a posterior left-lateral view. Pacing was performed at CS 7–8.

LV are activated, reaching the basal area of LV at 100 ms. Thereconstructed pacing site (i.e., the earliest endocardial activationin RV) could only be compared qualitatively with the pacingcatheter position. Using the posterior–septal site in RV as ananatomical marker, the localization error was determined to besmaller than 15 mm.

For the imaging of the electrical excitation in RA and LA,sinus and paced rhythm data were available for patient A. Pacingwas performed at the CS ostium site, at catheter electrode posi-tion no. 7–8. This electrode position anatomically correspondedto the posterior–septal area, in between RA and LA. In Fig. 8,the estimated AT map on the endocardium of RA and LA for CS7–8 pacing is depicted from a posterior left-lateral view. Ear-liest activation is determined on the posterior–septal site of LA

Fig. 9. AT map as in Fig. 8, but in a caudal-oblique view.

Fig. 10. AT map on the epicardium of RA and LA for the CS 7–8 pacingprotocol for patient B from a posterior–anterior view.

at 2 ms. The LL and RL areas are activated at 60 ms. The an-terior–septal area of LA is depolarized at 90 ms. Earliest acti-vation of RA is at 13 ms, i.e., 9 ms after the first breakthroughin LA. In RA, the excitation wave spreads continuously towardRAA and SVC. The SVC area is activated at 70 ms.

Fig. 9 depicts the same AT map from a caudal–oblique view.For CS 7–8 pacing, a CARTO map for RA was available.This electroanatomical catheter map was coupled to the 3-D

time anatomical model of RA, using the seven externalreference marker positions. After acquiring the catheter map,these reference points were digitized in the CARTO devicecoordinate system. This information was then used to transformthe catheter map to the MRI and BEM modeling coordinatesystem. To obtain a quantitative localization criteria, the firstendocardial breakthroughs determined in the eletroanatomicalcatheter map and in the reconstructed AT map of RA werecompared. The mean geometrical error between the modeledRA and the points of the catheter map was determined with


Fig. 11. AT map on the endocardium of RA and LA for the CS 7–8 pacing forpatient B from an anterior right-lateral view. Spheres show 92 CARTO pointsfor RA coupled to the ECG-gated MRI and BEM model coordinate system. Theelectroanatomical map covers the basal area of RA as well as the posterior walland the RAA.

Fig. 12. CARTO map for RA of patient B from a posterior–anterior viewfor the CS 7–8 pacing protocol. The red color indicates very early electricalexcitation.

6.4 mm. The localization error for the first endocardial break-through was 6 mm. The global AT pattern was found to be ingood qualitative agreement with the electroanatomical map.

For patient B, sinus and paced ECG mapping data were ac-quired. Pacing was done at CS 7–8, as indicated by “CS 7–8PAC” in Figs. 10 and 11. In Fig. 10, the epicardial AT map forCS 7–8 pacing is shown from a posterior–anterior view. Earliestactivation is on the septal site of RA at 9 ms. The first break-through on the posterior basal site of LA is at 24 ms. LAA andRAA are activated at 55 and 85 ms, respectively. From patientB, a CARTO map for the endocardium of RA for this pacedrhythm was available. This electroanatomical catheter map isdepicted in Fig. 12 from a posterior–anterior view. Red indi-cates very early activation. During the CS 7–8 pacing protocol,92 points, nonuniformly distributed over the RA target surface,

Fig. 13. AT map on the endocardium of RA and LA for the sinus rhythm forpatient B from a superior–oblique view.

were acquired. From this electroanatomical map, the depolar-ization interval for the endocardium of RA was determined with82 ms. From the reconstructed AT map in RA, the entire intervalwas determined with 85 ms. The 92 points of the catheter mapare visualized in Fig. 11 as spheres and are overlaid onto theECG-gated BEM model of RA. RA and LA are shown in ananterior right-lateral view. The mean geometrical error betweenthe model of RA and the CARTO map was determined with5.3 mm. The localization error for the first endocardial break-through in RA was 12 mm.

For patient B, also the sinus rhythm sequence in RA and LAwas imaged. In Fig. 13, the sinus rhythm AT map is shown froma superior–oblique view. Early activation occurred at 22 ms onthe right-lateral site of SVC. This might correspond to the sinusnode area. The first endocardial breakthrough in LA is on theanterior–superior site at 35 ms. The basal area of RA is activatedat 85 ms. The depolarization interval for the entire atrium wasdetermined with 98 ms. As expected, the sinus rhythm AT maphas nearly the opposite propagation direction throughout RA,compared with the CS 7–8 pattern.

IV. DISCUSSION

We presented a method for the imaging of the AT map onthe surface of the atrium and ventricle from ECG mapping data.The individual thorax models of the patients were constructedfrom 3-D time MRI data. ECG and MRI data were coupledin time and space. Results were presented for sinus rhythms, aswell as for RV and CS 7–8 paced rhythms. Electroanatomicalcatheter mapping data were available in part for validation. TheCARTO mapping solution was considered the “gold standard”for the endocardial propagation pattern.

Thebidomain theory-based surface heart model AT imagingapproach constitutes an excellent basis for the electrocardio-graphic inverse problem formulation. As long as we are dealingwith cardiac excitation, it not only allows one to image theisochrones on the endo- and epicardium but also enables the


incorporation of a mathematical model for the relationship be-tween the AT map and the surface ECG data. This is not thecase in the epicardial potential formulation, when it comes todetermining the (epicardial) AT map. In the epicardial poten-tial problem, the epicardial AT map is often determined fromthe negative maximum of the first time derivative of the recon-structed epicardial potential. Under clinical conditions, how-ever, this empirical approach is often unstable [31], [33], [34].

Having applied the Gauss–Newton approach to clinical data,we frequently experienced the problem of an unstable regular-ization procedure (i.e., the determination of the “optimal”).In order words, it was difficult to determineuniquely becausethe L-curve did not show its typical L-shape. In addition, theinverse solutions between neighborings were discontinuousreferring to the AT pattern. The choice of the finalwas there-fore rather difficult. These “nonlinear” effects were heavily pro-nounced when the modeling error became higher. In a “theoret-ical” environment (e.g., using a heart or phantom model), theseeffects are almost meaningless.

An alternative method has been developed in order to makethis AT imaging approach more stable. This linearized approachdecomposes the nonlinear formulation (1) into a sequence oflinear problem formulations. The regularization parametercan now be uniquely determined at each step of iteration. Thisstabilizes the global regularization procedure, especially in thepresence of measurement noise and modeling errors. Detailedinformation on this novel approach can be found elsewhere [29],[30].

One of the advantages of the presented AT imaging approachis its stability with regard to (relatively small) changes in the am-plitudes of the surface ECG data, e.g., due to drift or because ofnot knowing the correct conductivities. For this reason, the ab-solute values of the a priori conductivities of the different com-partments in the patient’s thorax, therefore, do not play that im-portant role in the modeling process. This circumstance dramat-ically improves the stability of the AT imaging approach withrespect to modeling errors belonging to chances in the ampli-tudes. On the contrary, we found that errors related to the tem-poral information of the data are of significant importance forthe stability of the AT imaging approach. The consideration ofan accurate source-containing surface model for the atrium orthe ventricle, and their coupling in time and space to the ECGmapping data, is one of the critical aspects. This surface mod-eling, together with the coupling of the data, influences the tem-poral information and the associated numerical stability. In thestudy reported in this paper, we tried to perform this heart sur-face modeling and data coupling as accurately as possible.

Baseline correction at the beginning of the target ECG wavewas of particular importance for the reconstruction of the ATmaps. Under clinical conditions, the drift in the ECGs arisingfrom various sources in the catheter laboratory and from theelectrode and amplifier setup itself cannot be neglected. Theemployed baseline alignment is based on the assumption thatprior to the electrical excitation, the surface resting membranepotential distribution gives zero potential in all channels. Theappliedbidomain theory-based surface heart model AT imagingapproach displays exactly this source-field behavior. Togetherwith the employed inverse approach, this signal preprocessing

technique was of outmost importance in order to reproduce sub-sequent single-beat AT maps of the same cardiac rhythm in asatisfying way.

Imaging methods of the human ventricular fiber orientationhave been presented recently [26], [35]. Diffusion tensor MRIpromises to play a prominent role for providing structuralinformation about the individual fiber orientation. This mighthave a substantial impact in the near future for imagingelectrical function during repolarization. During that phase,electrical anisotropy will be the crucial point for an appropriateelectrical source model description because of the large spatialextension of the gradient of , which is on the order of severalcentimeters [6], [8].

V. SUMMARY

This paper suggests the feasibility of AT imaging within thehuman atrium and ventricle from paced and sinus rhythm ECGmapping data in a clinical setting. Of course, the imaging ofspontaneous rhythms, like the onset of flutter or spontaneousfoci from the pulmonary veins, will be another importantmilestone in the development and clinical establishment of thisnovel diagnostic imaging technique. To the extent to whichthis method may be applicable at the present developmentstage and to our experience attained up to now, there aresome important aspects for a successful imaging of the targetactivation pattern. First, not surprisingly, an accurate modelof the target source-containing surface coupled as exactly aspossible in time and space with the ECG data is of outmostimportance. Secondly, the target ECG wave for which imaginghas to be performed should uniquely represent the underlyingactivation process. In clinical situations, this often is not thecase, and therefore signal-subtraction techniques will havea huge methodical impact [38]. Thirdly, the applied inverseapproach must show a good numerical performance to extracta unique and stable inverse solution in the presence of a noisyenvironment.

In summary, the obtained results achieved on atrial and ven-tricular AT imaging are very promising and give hope that fur-ther research will bring this new diagnostic tool closer to clinicalapplications.

ACKNOWLEDGMENT

The authors would like to thank M. Abou-Harb for her tech-nical assistance in the catheter laboratory.

REFERENCES

[1] E. Andrea, J. Atie, W. Maciel, N. Araujo, E. Saad, L. E. Camanho,H. Affonso, L. Siqueira, and L. G. Belo, “Mapping of supraventriculartachycardias by using a new tridimensional technology—The CARTOsystem,”J. Electrocardiol., vol. 34, no. 4, pp. 334–334, 2001.

[2] S. A. Ben Haim, D. Osadchy, I. Schuster, L. Gepstein, G. Hayam, and M.E. Josephson, “Nonfluoroscopic,in vivo navigation and mapping tech-nology,” Nat. Med., vol. 2, no. 12, pp. 1393–1395, 1996.

[3] J. E. Burnes, B. Taccardi, and Y. Rudy, “A noninvasive imaging modalityfor cardiac arrhythmias,”Circulation, vol. 102, no. 17, pp. 2152–2158,2000.

[4] D. Durrer, R. T. van Dam, G. E. Freud, M. J. Janse, F. L. Meijler, and P. C.Arzbaecher, “Total excitation of the isolated human heart,”Circulation,vol. 41, no. 6, pp. 899–912, 1970.


[5] G. Fischer, B. Tilg, P. Wach, R. Modre, U. Leder, and H. Nowak, “Appli-cation of high-order boundary elements to the electrocardiographic in-verse problem,”Comp. Meth. Prog. Biomed., vol. 58, no. 2, pp. 119–131,1999.

[6] G. Fischer, B. Tilg, R. Modre, G. J. Huiskamp, J. Fetzer, W. Rucker, andP. Wach, “A bidomain model based BEM-FEM coupling formulationfor anisotropic cardiac tissue,”Ann. Biomed. Eng., vol. 28, no. 10, pp.1229–1243, 2000.

[7] G. Fischer, B. Tilg, R. Modre, F. Hanser, B. Messnarz, and P. Wach,“On modeling the Wilson terminal in the boundary and finite elementmethod,”IEEE Trans. Biomed. Eng., vol. 49, pp. 217–224, Mar. 2002.

[8] D. B. Geselowitz and W. T. Miller, “A bidomain model for anisotropiccardiac muscle,”Ann. Biomed. Eng, vol. 11, no. 3-4, pp. 191–206, 1983.

[9] D. B. Geselowitz, H. D. Simms Jr., and S. M. Smith, “Comments onsome imaging parameters of the oblique dipole layer cardiac generatorderivable from body surface electrical potentials,”IEEE Trans. Biomed.Eng., vol. 39, pp. 874–875, Aug. 1992.

[10] D. B. Geselowitz, “Description of cardiac sources in anisotropic cardiacmuscle. Application of bidomain model,”J. Electrocardiol., vol. 25, pp.65–67, 1992.

[11] , “The zero of potential,”IEEE Eng. Med. Biol. Mag., vol. 17, no.1, pp. 128–132, 1998.

[12] F. Greensite, G. Huiskamp, and A. van Osterom, “New quantitative andqualitative approaches to the inverse problem of electrocardiology: Theirtheoretical relationship and experimental consistency,”Med. Phys., vol.17, no. 3, pp. 369–379, 1990.

[13] F. Greensite and G. Huiskamp, “An improved method for estimatingepicardial potentials from the body surface,”IEEE Trans. Biomed. Eng.,vol. 45, pp. 98–104, Jan. 1998.

[14] F. Greensite, “The mathematical basis for imaging cardiac electricalfunction,” Crit. Rev. Biomed. Eng., vol. 22, no. 5-6, pp. 347–399, 1994.

[15] , “Some imaging parameters of the oblique dipole layer cardiacgenerator derivable from body surface electrical potentials,”IEEETrans. Biomed. Eng., vol. 39, pp. 159–164, Feb. 1992.

[16] Hansen and P. C. Hansen,Rank-Deficient and Discrete Ill-Posed Prob-lems. Philadelphia, PA: SIAM, 1997.

[17] , “The L-curve and its use in the numerical treatment of inverseproblems,” inComputational Inverse Problems in Electrocardiology, P.Johnston, Ed. Southampton, U.K.: WIT Press, 2001, pp. 119–142.

[18] C. S. Henriquez, “Simulating the electrical behavior of cardiac tissueusing the bidomain model,”Crit. Rev. Biomed. Eng., vol. 21, no. 1, pp.1–77, 1993.

[19] G. Huiskamp, “Difference formulas for the surface Laplacian on a tri-angulated surface,”J. Comput. Phys., vol. 95, pp. 477–496, 1991.

[20] G. Huiskamp and A. van Oosterom, “The depolarization sequence of thehuman heart surface computed from measured body surface potentials,”IEEE Trans. Biomed. Eng., vol. 35, no. 12, pp. 1047–1058, 1988.

[21] G. Huiskamp and F. Greensite, “A new method for myocardial activationimaging,” IEEE Trans. Biomed. Eng., vol. 44, pp. 433–446, June 1997.

[22] D. S. Khoury, K. L. Berrier, S. M. Badruddin, and W. A. Zoghbi,“Three-dimensional electrophysiological mapping of the intact canineleft ventricle using a noncontact multielectrode cavitary probe: Studyof sinus, paced, and spontaneous premature beats,”Circulation, vol.97, pp. 399–409, 1998.

[23] M. D. Lesh, J. M. Kalman, J. E. Olgin, and W. S. Ellis, “The role ofatrial anatomy in clinical atrial arrhythmias,”J. Electrocardiol., vol. 29,no. Suppl., pp. 101–113, 1996.

[24] M. D. Lesh and F. X. Roithinger, “Atrial tachycardia,” inClinical Ap-proaches to Tacharrhythmias, A. J. Camm, Ed. Armonk, NY: Futura,2000, vol. 11.

[25] G. Li and B. He, “Localization of the site of origin of cardiac activa-tion by means of heart-model-based electrocardiographic imaging ap-proach,”IEEE Trans. Biomed. Eng., vol. 48, pp. 660–669, June 2001.

[26] E. McVeigh, O. Faris, D. Ennis, P. Helm, and F. Evans, “Measurement ofventricular wall motion, epicardial electrical mapping, and myocardialfiber angels in the same heart,” inFunctional Imaging and Modelingof the Heart, T. Katila, I. E. Magnin, P. Clarysee, J. Montagnat, andJ. Nenonen, Eds. New York: Springer-Verlag, 2001, Lecture Notes inComputer Science, pp. 76–82.

[27] R. A. C. van Rijn, A. Peper, and C. A. Grimbergen, “High qualityrecording of bioelectric events. Part 1. Interference reduction, theoryand practice,”Med. Biol. Eng. Comput., vol. 28, no. 5, pp. 389–397,1990.

[28] , “High-quality recording of bioelectric events. Part 2. Low-noise,low-power multichannel amplifier design,”Med. Biol. Eng. Comput.,vol. 29, no. 4, pp. 433–440, 1991.

[29] R. Modre, B. Tilg, G. Fischer, and P. Wach, “An iterative algorithm formyocardial activation time imaging,”Comp. Meth. Prog. Biomed., vol.64, no. 1, pp. 1–7, 2001.

[30] , “Noninvasive myocardial activation time imaging: A novel inversealgorithm applied to clinical ECG mapping data,”IEEE Trans. Biomed.Eng., vol. 49, pp. 1153–1161, Oct. 2002.

[31] T. F. Oostendorp and A. van Oosterom, “Source parameter estimationin inhomogeneous volume conductors of arbitrary shape,”IEEE Trans.Biomed. Eng., vol. 36, pp. 382–391, Mar. 1989.

[32] , “The surface Laplacian of the potential: Theory and application,”IEEE Trans. Biomed. Eng., vol. 43, pp. 394–405, Apr. 1996.

[33] H. S. Oster, B. Taccardi, R. L. Lux, P. R. Ershler, and Y. Rudy, “Noninva-sive electrocardiographic imaging: Reconstruction of epicardial poten-tials, electrograms, and isochrones and localization of single and mul-tiple electrocardiac events,”Circulation, vol. 96, no. 3, pp. 1012–1024,1997.

[34] Y. Rudy and B. Taccardi, “Noninvasive imaging and catheter imaging ofpotentials, electrograms, and isochrones on the ventricular surfaces,”J.Electrocardiol., vol. 30, no. Suppl, pp. 19–23, 1998.

[35] D. F. Scollan, A. Holmes, J. Zhang, and R. L. Winslow, “Reconstructionof cardiac ventricular geometry and fiber orientation using magnetic res-onance imaging,”Ann. Biomed. Eng., vol. 28, no. 8, pp. 934–944, 2000.

[36] A. Sippens-Groenewegen, F. X. Roithinger, H. A. Peeters, A. C. Linnen-bank, N. M. van Hemel, P. R. Steiner, and M. D. Lesh, “Body surfacemapping of atrial arrhythmias: Atlas of paced P wave integral maps tolocalize the focal origin of right atrial tachycardia,”J. Electrocardiol.,vol. 31, pp. 85–91, 1998.

[37] A. Sippens-Groenewegen, M. D. Lesh, F. X. Roithinger, W. S. Ellis,P. R. Steiner, L. A. Saxon, R. J. Lee, and M. M. Scheinman, “Bodysurface mapping of counterclockwise and clockwise typical atrial flutter:A comparative analysis with endocardial activation sequence mapping,”J. Amer. Coll. Cardiol., vol. 35, no. 5, pp. 1276–1287, 2000.

[38] A. Sippens-Groenewegen, M. D. Mlynash, F. X. Roithinger, Y. Goseki,and M. D. Lesh, “Electrocardiographic analysis of ectopic atrial activityobscured by ventricular repolarization: P wave isolation using an au-tomatic 62-lead QRST subtraction algorithm,”J. Cardiovasc. Electro-physiol., vol. 12, no. 7, pp. 780–790, 2001.

[39] B. Taccardi, B. B. Punske, R. L. Lux, R. S. MacLeod, P. R. Ershler,T. J. Dustman, and Y. Vyhmeister, “Useful lessons from body surfacemapping,”J. Cardiovasc. Electrophysiol., vol. 9, no. 7, pp. 773–786,1998.

[40] U. Tautenhahn, “On a general regularization scheme for nonlinear ill-posed problems: II. Regularization in hilbert scales,”Inverse Prob., vol.14, pp. 1607–1616, 1998.

Documents

Model-based imaging of cardiac electrical excitation in humans