Noninvasive Imaging of Cardiac Transmembrane Potentials Within Three-Dimensional Myocardium by Means of a Realistic Geometry Anisotropic Heart Model

Transcription

1 1190 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 Noninvasive Imaging of Cardiac Transmembrane Potentials Within Three-Dimensional Myocardium by Means of a Realistic Geometry Anisotropic Heart Model Bin He*, Senior Member, IEEE, Guanglin Li, Member, IEEE, and Xin Zhang, Student Member, IEEE Abstract We have developed a new approach for imaging cardiac transmembrane potentials (TMPs) within the three-dimensional (3-D) myocardium by means of an anisotropic heart model. The cardiac TMP distribution is estimated from body surface electrocardiograms by minimizing objective functions of the measured body surface potential maps (BSPMs) and the heart-model-generated BSPMs. Computer simulation studies have been conducted to evaluate the present 3-D TMP imaging approach using pacing protocols. Simulations of single-site pacing at 24 sites throughout the ventricles, as well as dual-site pacing at 12 pairs of sites in the vicinity of atrio-ventricular ring were performed. The present simulation results show that the correlation coefficient (CC) and relative error (RE) between the true and inversely estimated TMP distributions were and , for single-site pacing, and and for dual-site pacing, respectively, when 10 V Gaussian white noise (GWN) was added to the BSPMs. The effects of heart and torso geometry uncertainty were also evaluated by shifting the heart position by 10 mm and altering the torso size by 10%. The CC between the true and inversely estimated TMP distributions was above 0.97 when these geometry uncertainties were considered. The present simulation results demonstrate the feasibility of noninvasive estimation of TMP distribution throughout the ventricles from body surface electrocardiographic measurements, and suggest that the present method may become a useful alternative in noninvasive imaging of distributed cardiac electrophysiological processes within the 3-D myocardium. Index Terms Body surface potential map, cardiac activation, cardiac mapping, electrocardiographic imaging, electrocardiographic inverse problem, transmembrane potential imaging. I. INTRODUCTION CARDIAC electrophysiological processes are distributed over the three dimensional (3-D) myocardium. It is of importance to noninvasively image distributed cardiac electrophysiological processes throughout the 3-D space of the heart. Such knowledge may provide a better understanding Manuscript received September 6, 2002; revised March 10, This work was supported in part by the National Science Foundation (NSF) under Grant BES and CAREER Award BES , in part by the American Heart Association under Grant N, and in part by the National Institutes of Health (NIH) under Grant 1R01EB178. Asterisk indicates corresponding author. *B. He is with the University of Illinois at Chicago, SEO 218, M/C-063, 851 S. Morgan Street, Chicago, IL USA ( bhe@uic.edu). G. Li and X. Zhang are with the Department of Bioengineering, University of Illinois at Chicago, Chicago, IL USA. Digital Object Identifier /TBME of the mechanisms of cardiac pathophysiology, and may aid clinical diagnosis and management of cardiac diseases. It is known that cardiac electrophysiological and pathophysiological processes are closely associated with transmembrane potentials (TMPs) of myocardial cells. Attempts have been made to characterize cardiac electrophysiological processes from equivalent cardiac electrical sources, which reflect the properties of electrophysiological processes. Efforts have been made to estimate the cardiac electrical sources from body surface electrocardiographic measurements, by solving the so-called electrocardiogram (ECG) inverse problem. A number of scientists have attempted to solve the ECG inverse problem by estimating equivalent cardiac generators such as equivalent dipole solutions and multipoles (see [1] for review), or distributions of epicardial potential and isochrones from body surface ECGs [2] [9]. More recently, the endocardial potentials and isochrones have also been reconstructed from the balloon-surface-recorded electrograms [10], [11]. These approaches are in principle based on physical equivalent source models of cardiac electrical activity. From the reconstructed inverse solution parameters, the electrophysiological properties of cardiac electrical activity are further deduced. Efforts have also been made to directly estimate the electrophysiological characteristics from body surface ECGs. Activation time [12] [16] has been estimated over the epicardium and endocardium from body surface ECGs. The TMP has also been estimated over the heart surface from magnetocardiograms [17]. Recently, efforts have been extended from the heart surface to the 3-D myocardium. Three dimensional distributions of equivalent current dipoles have been estimated within the myocardium from body surface ECGs using weighted minimum norm algorithms [18]. We have developed a 3-D heart-modelbased electrocardiographic imaging approach to localize the site of origin of cardiac activation [19] and image the activation sequence within the 3-D ventricles [20]. Ohyu et al. has developed an approach to estimate the activation time and approximate amplitude of the TMP from magnetocardiograms using Wiener estimation technique [21]. In the present study, we aim at estimating the 3-D TMP distribution throughout the 3-D myocardium from noninvasive body surface ECG recordings, the anatomic information obtained from computed tomography (CT) or magnetic resonance imaging (MRI), and the a priori knowledge of cardiac electrophysiology. The 3-D TMP distribution is linked with body surface ECGs through a realistic geometry computer /03$ IEEE

2 HE et al.: NONINVASIVE IMAGING OF CARDIAC TMPS WITHIN 3-D MYOCARDIUM 1191 Fig. 1. Schematic diagram of the 3-D cardiac TMP imaging by means of a realistic geometry anisotropic heart-model. heart-torso model, in which the a priori knowledge of cardiac electrophysiology is incorporated in an anisotropic heart-excitation-model, and the detailed anatomic information on the heart and torso is embedded in a realistic geometry inhomogeneous torso volume conductor model. We have successfully conducted the first investigation, to our knowledge, on noninvasive imaging of the 3-D distribution of cardiac TMP within the ventricles from body surface ECGs by means of a realistic geometry anisotropic heart model. In the present study, we have conducted computer simulations using single-site-pacing and dual-site-pacing protocols. Partial results have been presented at the 4th International Conference on Bioelectromagnetism on July 4, II. METHODS A. Principles of Transmembrane Potential Imaging in 3-D Myocardium The whole procedure of the present heart-model-based TMP imaging approach is illustrated in the schematic diagram in Fig. 1. A 3-D heart-model was constructed based on the knowledge of cardiac electrophysiology and geometric measurements via CT/MRI. The anisotropic nature of myocardium can be incorporated into this computer heart model and was implemented in the present computer simulation study. The relationship between the BSPM and the 3-D TMP distribution was then established by the heart-excitation-torso-volume-conductor-model (to be simplified to the heart-torso-model in the remainder of this paper for the sake of simplicity). To reduce the dimensionality of the parameter space, a preliminary diagnosis system (PDS) was employed to determine cardiac status based on the a priori knowledge of cardiac electrophysiology and the BSPM, by means of an artificial neural network (ANN) [38]. The output of the ANN based PDS provided the initial estimate of heart model parameters being used later in a nonlinear optimization system. The optimization system then minimized the objective functions that assess the dissimilarity between the measured (in the present simulation study, the measured BSPMs were simulated) and heart-torso-model-generated BSPMs. If the measured BSPM and the heart-torso-model-generated BSPM match

3 1192 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 well, the 3-D TMP distribution was determined from the heart model parameters corresponding with the resulting BSPM. If not, the heart model parameters were adjusted with the aid of the optimization algorithms and the optimization procedure proceeded until the objective functions satisfied the given convergent criteria. When the procedure converged, the TMP distribution throughout the 3-D myocardium was determined. In the ANN-based PDS, the number of neurons in the input layer was set to 200, corresponding to the number of body surface electrodes used in the present simulation study. The hidden layer had 25 neurons that were determined heuristically. Two ANNs were trained in the present simulation study. 1) Single-site pacing protocol: The output layer had 53 neurons, which corresponded to the 53 ventricular myocardial segments of the computer heart model [19]. Five myocardial cellular units were selected for each of the 53 myocardial segments in the ventricles, and each of these sites was then paced in the forward simulation using the computer heart-torso model, generating the dataset for training the ANN. Each of these 265 training sites was different with the 24 testing pacing sites in the present simulation. 2) Dual-site pacing protocol: The output layer had ten neurons, which corresponded to ten ventricular myocardial segments close to the atrio-ventricular (AV) ring. One hundred pairs of myocardial cellular units were selected in these ten myocardial segments, and then paced in the forward simulation using the computer heart-torso model, generating the dataset for training the dual-site-pacing ANN. Each of these 100 pairs of training sites was different with the 12 pairs of testing pacing sites in the present simulation. Gaussian white noise (GWN) was added to the BSPMs to simulate noise-contaminated body surface ECG measurements, with zero mean and standard deviation being equal to the simulated noise level. The BSPM maps at five time instants during 25 to 50 ms after initial activation were used as inputs to train the ANN. The heart model parameters were further optimized by minimizing the dissimilarity between the measured and model-generated BSPMs. The following objective function [19] was used to reflect the dissimilarity between the measured and model-generated BSPMs for the pacing protocols:, which was constructed with the average correlation coefficient (CC) between the measured and model-generated BSPMs during a certain time period following initiation of cardiac excitation. In addition, the following two constraints [19] were used: 1), which was constructed with the deviation of the positions of minima of the measured and model-generated BSPMs during a certain time period following the initiation of cardiac excitation. 2), which was constructed with the relative error (RE) of the number of body surface recording leads, at which the potentials are less than a certain negative threshold, in the measured and model-generated BSPMs during a certain time period following the initiation of cardiac excitation. The mathematical model of the nonlinear optimization can be represented as the following minimization problem: (1) (a) (b) (c) Fig. 2. Illustration of computer heart-torso modeling and pacing simulation. (a) Heart model and a pacing site at middle anterior ventricular epicardium. (b) Anterior view of torso-heart model. (c) Anterior view of simulated epicardial isochrone (up), and an example of the BSPM over the anterior chest following pacing (bottom). where is the probable value region of the parameters in the computer heart model. is a parameter vector of the initial sites of activation in the heart model for the pacing protocol. is the optimal value of the objective function. and are the allowable errors of the constraints and, respectively. The selection of the or will affect the recognition accuracy and convergence rate of the optimization system. The smaller the or, the higher the recognition accuracy and the slower the convergence. In the present study, the Simplex Method [19], [31] was used to solve (1). B. Computer Heart Model A previously developed computer heart model [22] was modified by incorporating the anisotropic properties of propagation of excitation and equivalent cardiac source density in the ventricular myocardium for more accurate simulation of the body surface ECG and myocardial activation sequence [24] [29]. The geometry model of the heart and torso was constructed using CT images of a human subject. The torso surface, lung surface, endocardial surface and epicardial surface were divided into 412, 297, 154, and 158 nodes, and 820, 586, 296, and 308 triangles connecting these nodes, respectively. The different conductivities of the intraventricular blood masses and lungs were taken into consideration in the computation. The ventricle model contains about myocardial cellular units. Each cellular unit is a cubic myocardial block with a side length of 1.5 mm. The spatial location of each unit was denoted by a set of three integers (,, and ). From the base to the apex, the ventricles are divided into 53 myocardial segments. Every segment is comprised of approximately the same number of myocardial cellular units. The ventricles consisted of 50 vertical sections (from Section 30 to Section 79). Section 30 corresponds to the base and Section 79 the apex. Each myocardial segment corresponds to a 3-D ventricular myocardial block that includes seven-sections of myocardial cellular units. The action potential of each of myocardial cellular units was predetermined according to the experimental findings on cardiac action potentials [Fig. 2(a)]. From the epicardium to the endocardium, the refractory period

4 HE et al.: NONINVASIVE IMAGING OF CARDIAC TMPS WITHIN 3-D MYOCARDIUM 1193 of the action potential of myocardial cellular units gradually increased for T-wave simulation. Ventricular myocardium was divided into different layers with thickness of 1.5 mm from epicardium to endorcardium, and the myocardial fiber orientations rotated counterclockwise over 120 from the outermost layer (epicardium, ) to the innermost layer (endocardium, ) [30] with identical increment between the consecutive layers. All units on a myocardial layer of ventricles from epicardial layer to endocardial layer had identical fiber orientation or fiber angle (for example, all units on the epicardial layer have a fiber angle of ). The fiber angle of a myocardial unit is the angle [30] between its fiber orientation or fiber direction and the horizontal direction that is orthogonal to the ventricular axis direction (from base to apex). In order to incorporate the myocardial anisotropy characteristics into the heart model, the fiber direction of each of all myocardial units has to be determined from its fiber angle. For each myocardial unit, its fiber direction was represented by a spatial vector the fiber direction vector that has a starting point at the current unit (,, and ) and is along the fiber direction. When a second point on the fiber direction vector is determined, this vector will be uniquely determined by the two points. The second point on the fiber direction vector can be determined by the fiber angle of a myocardial unit, while assuming that the fiber direction vector of the myocardial unit is located on its local tangential plane that is parallel with the ventricular axis direction. The fiber directions of all myocardial units of ventricles were determined, and put in the realistically shaped torso [Fig. 2(b)] for calculating the body surface ECG. Excitation conduction velocity (ECV) of myocardial units was set to 0.6 m/s and 0.2 m/s along the longitudinal and transverse fiber direction, respectively. To determine the ECV from an excited unit to its neighboring unit, an angle between the fiber direction vector of the excited unit and a spatial vector that has the starting point at the excited unit and the end point at the neighboring unit was calculated. Then the ECV was lineally obtained by the angle. For example, when the angle is zero, which means that the neighboring unit is located at the fiber direction of the excited unit, the m/s; and when the angle is 90, which means that the neighboring unit is located at the direction orthogonal to the fiber direction of the excited unit, the m/s. Electrical conductivity (EC) of myocardial units was set to be 1.5 ms/cm along the longitudinal fiber direction and 0.5 ms/cm along the transverse fiber direction [24]. Similarly, the angle between the fiber direction vector of an excited unit and a vector from the excited unit to its neighboring unit was used to linearly determine the EC from the excited unit to the neighboring unit. For example, when the angle is zero, EC ms cm, and when the angle is 90, EC ms cm. In addition to the anisotropic propagation, the equivalent current-dipole density of each of myocardial units was determined as the product of the myocardial conductivity tensor and the gradient of TMP [39]. The current-dipole layer so-obtained is oblique to the wavefront. The strength of this dipole layer is not uniform, varying in both magnitude and orientation from one myocardial unit to another along the wavefront due to the variation in the myocardial conductivity tensor. Using the equivalent current-dipole density as sources, the extracellular potential on the torso surface was computed by means of the boundary element method [23]. Fig. 2 shows the realistic geometry inhomogeneous heart-torso model [Fig. 2(b)], an example of simulated BSPM on the anterior chest [Fig. 2(c)-bottom panel] at 30 ms following pacing on the anterior wall of the ventricle [Fig. 2(a)], and the ventricular excitation sequence over the epicardium corresponding to the pacing site [Fig. 2(c)-top panel]. The torso surface model was divided into the triangle grids with 412 nodes and 820 triangles. The torso surface model has a layered structure from neck to waist. The inter-grid distance is about 2.4 cm along the vertical direction (from neck to waist), and about 2.0 cm along the horizontal direction (around the torso). The ECGs on the 412 surface nodes were simulated by means of the boundary element method [23]. The body surface ECGs at 200 nodes, selected from the 412 surface nodes that covered anterior and posterior chest, were used to reconstruct the 200-lead BSPM (10 model is 3 ms. C. Simulation Protocols 20). The time resolution of the heart In the present study, pacing protocols were used to simulate controlled initiation and propagation of cardiac activation. By setting pacing sites in different myocardial regions of the heart excitation model, sequential pace maps were obtained by solving the forward problem. Two pacing protocols, single-site pacing, and dual-site pacing, were used to evaluate the performance of the present approach in TMP imaging over the ventricles. According to the anatomic structure of the ventricles, the ventricles were divided in the following way. The ventricular longitudinal section was divided into five regions: Anterior, Left Wall, Posterior, Right Wall, and Septum. The whole ventricle from base to apex was divided into three regions: Basal, Middle, and Apical. For example, BA in Table I means that the pacing site is located in the basal-anterior, while MLW indicates the pacing site is in the middle left wall. In total, 24 ventricular sites were paced in the single-site pacing protocol (BA: basal-anterior; BRW: basal-right-wall; BP: basal-posterior; BLW: basal-left-wall; BS: basal-septum; MA: middle-anterior; MP: middle-posterior; MLW: middle-left-wall; MS: middle-septum; AA: apical-anterior; AP: apical-posterior; AS: apical-septum). For the dual-site pacing, 12 pairs of myocardial cellular units in a seven-section myocardial region adjacent to the AV ring were randomly selected to simulate two wavefronts. For each paced activation sequence, the BSPMs within a cardiac cycle were calculated using the boundary element method. GWN of 10 V was added to the BSPMs at each time instant after the onset of pacing, to simulate the noise-contaminated body surface potential measurements. The optimal heart model parameters were estimated when the objective functions, that assess the dissimilarity between the measured and model-generated BSPMs, were minimized with the primary criterion being the temporally-averaged CC between the BSPMs,. In the pacing protocol, this represents the locations of initial activation. The TMP distribution is

5 1194 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 TABLE I SIMULATION RESULTS OF TMP IMAGING FOR SINGLE-SITE VENTRICULAR PACING. GWN (10 V)WAS ADDED INTO THE FORWARD SIMULATED BSPM. RE, CC, AND AAD BETWEEN THE FORWARD SIMULATED AND INVERSELY ESTIMATED TMP DISTRIBUTIONS THROUGHOUT THE VENTRICLES ARE SHOWN then reconstructed by determining the TMP at each myocardial cellular unit within the ventricles, based on the optimal heart model parameters. In order to assess the clinical applicability of the present technique in imaging the TMP distribution, the effects of the following two factors on the estimation accuracy were evaluated in addition to measurement noise: torso geometry uncertainty and heart position uncertainty. To study the effect of torso geometry uncertainty, two modified torso models, obtained by respectively enlarging and reducing the standard torso model (STM) by 10%, were used to replace the STM in the forward computation of the BSPMs. The heart position uncertainty was simulated by shifting the heart position within the torso model. The heart was shifted from the right to the left or from the left to the right by 10 mm: the right/left shift along -direction (RSX/LSX). In addition, GWN of 10 mm was added to the body surface electrode positions to simulate the electrode position uncertainty in this phase of the simulation study. In the present study, CC, RE, and another measure of error, the averaged amplitude difference (AAD), were used to quantitatively assess the performance of the TMP imaging approach. The CC and RE between the forward ( true ) TMP distribution and the inverse (estimated) TMP distribution, are defined as the temporal average over time points during ventricular activation as follows: CC (2) RE (3) where and are the vectors of the forward ( true ) and inverse (estimated) TMP amplitude at time, respectively, and is the Euclidean norm. AAD is defined as AAD (4) where and are the true and estimated TMP amplitude of the myocardial cellular unit at instant in the ventricular model, respectively, and is the number of myocardial cellular units in the ventricular model, that is used to evaluate the difference between the true and estimated TMP distributions. is the time from the onset of ventricular excitation to that considered in the study, and was set to 60 ms in the present simulation. From the definition of the AAD (4), it has identical physical unit with transmembrane potential, mv. III. RESULTS A. TMP Imaging of Ventricular Activation Induced by Single-Site Pacing The performance of TMP imaging was tested by single-site pacing in 24 different sites throughout the ventricles. The 200-lead BSPMs at ten time instants (from ms to

6 HE et al.: NONINVASIVE IMAGING OF CARDIAC TMPS WITHIN 3-D MYOCARDIUM 1195 Fig. 3. A typical example of TMP imaging results during single-site ventricular pacing. (a) and (b) illustrate the forward and inverse solution of the TMP distributions in five longitudinal sections within the ventricles, during ventricular depolarization following a single-site pacing at the intramural of the left ventricular wall. The TMP distribution in each longitudinal section at eight typical instances (from 6 ms to 48 ms with a time step of 6 ms) after the onset of pacing is shown in one row. The five longitudinal sections within the ventricles are illustrated in (c) by five horizontal black lines in the transverse section of the ventricles from top to bottom indicating their positions. The gray regions in the longitudinal sections indicate the resting cellular units. The max and min of color bars correspond to the maximum and minimum values of the TMP amplitude during the first 60 ms from the onset of activation. ms after the onset of pacing, with time step of 3 ms) were used to inversely estimate the TMP distribution of ventricular activation following pacing. Figs. 3 and 4 show two typical simulation examples. In these cases, 10- V GWN was added to the BSPMs and 10-mm GWN was added to the body surface electrode positions to simulate noise-contaminated body surface ECG recordings. In Figs. 3 and 4, panels (a) and (b) show the simulated true and estimated inverse TMP distributions, respectively. Fig. 3 illustrates the TMP amplitude distributions [Fig. 3(a)-(b)] of ventricular depolarization following a single-site pacing at the intramural of the left ventricular

7 1196 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 Fig. 4. Another typical example of TMP imaging results during single-site ventricular pacing at the intramural of the right ventricular. The format of display is the same as that of Fig. 3. wall in five longitudinal sections within the ventricles. The TMP distribution in each longitudinal section at eight typical instances (from 6 ms to 48 ms with a time step of 6 ms) after the onset of pacing is shown in one row. The five longitudinal sections within the ventricles are illustrated in Fig. 3(c) by five horizontal black lines in the transverse section of the ventricles from top to bottom indicating their positions. The gray regions in the longitudinal sections indicate the resting cellular units. The and of color bars correspond to the maximum and minimum values of the TMP amplitude during the first 60 ms from the onset of activation. It is seen from Fig. 3 that the TMP distribution provides spatio-temporal distribution of the cardiac activation following a single site pacing in the intramural of the left ventricular wall. The inverse TMP distribution captures well the overall spatio-temporal patterns of the forward TMP distribution, but with a slight shift of the area of initial activation toward the apex (as observed in Layer 15 in the inverse TMP distribution).

8 HE et al.: NONINVASIVE IMAGING OF CARDIAC TMPS WITHIN 3-D MYOCARDIUM 1197 Fig. 4 illustrates the TMP amplitude distributions [Fig. 4(a)-(b)] of ventricular depolarization following a single-site pacing at the intramural of the right ventricular wall in five longitudinal sections within the ventricles [Fig. 4(c)]. All the displays are in the same format as Fig. 3. It is seen from Fig. 4 that the inverse TMP distribution captures well the overall spatio-temporal patterns of the forward TMP distribution following a single site pacing at the right ventricular wall. In order to quantitatively evaluate the proposed TMP imaging, the CC, RE and AAD between the vector of true and estimated TMP distributions [as defined in (2) (4)] were calculated for each of the 24 pacing sites. Table I shows the results when 10 V GWN was added to the BSPMs. Averaged over all 24 sites, the RE and CC between the true and estimated TMP distributions are and, respectively. The AAD between the true and estimated TMP distributions is. Table I indicates that the present TMP imaging approach can reconstruct well the TMP distributions within the ventricles corresponding to a single propagating wavefront initiated by a single site pacing. Fig. 5 illustrates the CC values between the true and estimated TMP distributions in 3-D space at each time point. Fig. 5(a) and (b) correspond to the data in Figs. 3 and 4, respectively. Fig. 5 indicates that the estimation error increased when the wavefront spreads out. However, the CC calculated over the space domain also indicated good estimation of the TMP distribution. Similar trends were observed for both RE and AAD and are not shown here. B. TMP Imaging of Ventricular Activation Induced by Dual-Site Pacing The performance of the present TMP imaging approach was also evaluated by the dual-site pacing protocol. Fig. 6 shows a typical simulation example, with the same format of display as in Fig. 3. Both pacing sites were located at the left ventricular intramural wall (one close to the epicardium and another close to the endocardium), and 10 V GWN was added to the BSPMs and 10 mm GWN was added to the body surface electrode positions to simulate noise-contaminated body surface ECG recordings. On Layer 9, the wavefront close to the endocardium appears weak in the inverse TMP distribution, whereas both wavefronts are clearly observed in the forward TMP distribution. However, the overall spatio-temporal distribution of the TMP remains similar in the inverse TMP distribution as compared with the forward TMP distribution. Twelve pairs of myocardial cellular units in a seven-section myocardial region adjacent to the AV-ring were randomly selected to further test the performance of the proposed method during dual-site pacing. Table II shows the simulation results, when 10 V GWN was added to the BSPMs to simulate noisecontaminated body surface ECG recordings. Averaged over all 12 pairs, the RE and CC between the true and estimated TMP distributions are and, respectively. The AAD between the true and estimated TMP distributions is. Comparing with the single-site pacing simulation, only about 2% increase in RE and about 0.12 mv increase in AAD are observed, suggesting the feasibility (a) (b) Fig. 5. CC values between the true and estimated TMP distributions over the space at each time point following pacing. Note the CC drops when the propagation spreads out. of the present TMP imaging in imaging cardiac electrical activity consisting of dual excitation wavefronts. Table II suggests that the present TMP imaging approach can reconstruct well the TMP distributions within the ventricles corresponding to two propagating wavefronts initiated by dual-site pacing. C. Effects of the Geometry Uncertainties In order to evaluate the effects of heart-torso geometry uncertainties on the performance of the present TMP imaging approach, further simulation studies have been conducted using the modified (enlarge or reduce by 10%) torso models and shifted heart positions (by 10 mm) in the heart-torso model. In addition, 10 V potential GWN and 10-mm geometry GWN were added to the calculated BSPMs and the coordinates of body surface electrodes to simulate noise-contaminated body surface ECG recordings. The modified heart-torso models were used in the forward simulations to simulate measured BSPMs. The standard heart-torso model was used in the inverse

9 1198 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 Fig. 6. A typical example of TMP imaging results during dual-site ventricular pacing at the left ventricular intramural wall (one close to the epicardium and another close to the endocardium). The format of display is the same as that of Fig. 3. calculation. Table III shows the RE, CC, and AAD between the simulated true and the estimated TMP distributions following single-site pacing at three sites (1P1, 1P2, and 1P3) and dual-site pacing at two pairs (2P1 and 2P2). STM refers to the standard torso model, in which only measurement noise is introduced. STM+10% refers to the enlarged torso model by 10% from the STM. STM-10% refers to the reduced torso model by 10% from the STM. The heart position uncertainty was evaluated by shifting the heart position to the right (RSX) and left (LSX) by 10 mm. Averaged over all five cardiac source configurations induced by either a single or dual pacing, the RE, CC, and AAD for STM are,, and mv, respectively. Enlargement or reduction of the torso model by 10% resulted only an increase of in the RE, and an increase of 0.07 mv in the AAD. Shifting of the heart position by 10 mm resulted an increase of 0.02 in the RE, and an increase of 0.16 mv in the AAD. Table III suggests that the heart-torso geometry uncertainty showed negligible effect

10 HE et al.: NONINVASIVE IMAGING OF CARDIAC TMPS WITHIN 3-D MYOCARDIUM 1199 TABLE II SIMULATION RESULTS OF TMP IMAGING FOR DUAL-SITE VENTRICULAR PACING. 10 V GWN WAS ADDED INTO THE FORWARD SIMULATED BSPM. RE, CC, AND AAD BETWEEN THE FORWARD SIMULATED AND INVERSELY ESTIMATED TMP DISTRIBUTIONS THROUGHOUT THE VENTRICLES ARE SHOWN TABLE III EFFECTS OF THE TORSO GEOMETRY AND HEART POSITION UNCERTAINTIES ON THE TMP IMAGING PN: Potential noise; GN: Geometry noise. on the TMP distribution estimation as determined by the RE and AAD measures. IV. DISCUSSION In the present study, we have developed a new approach for noninvasive 3-D cardiac TMP imaging by means of a realistic geometry anisotropic heart-model. The present approach is based on our observation that a priori information regarding the distributed cardiac electrophysiological processes should be incorporated into the cardiac inverse solutions in order to obtain useful information on the distributed 3-D cardiac electrical activity from the two-dimensional electrocardiographic measurements made over the body surface. In the present study, the a priori information on cardiac electrophysiology is incorporated into the distributed heart-model, which is not an equivalent physical source model but rather an electrophysiological source model. The distributed electrophysiological processes within the heart are represented by cellular automata, on each of which the TMP is determined based on the knowledge of cardiac electrophysiology. The cardiac electrophysiological processes are linked with body surface ECGs via biophysical relationships. Through a nonlinear inverse estimation procedure, the electrophysiological properties of myocardial tissue are estimated as the heart model parameters from the noninvasive body surface electrocardiographic measurements. The TMP distribution within the 3-D myocardium is then reconstructed from the heart model parameters. The present study demonstrates, for the first time, that one can noninvasively estimate the spatial distribution of cardiac TMP over the 3-D myocardium from BSPMs in a realistic geometry inhomogeneous anisotropic heart-torso model. Since many cardiac abnormalities are associated with the change in shape of

11 1200 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 TMP, the present approach suggests a new way of linking clinical ECG observation with the underlying cellular mechanisms within the myocardium. Note that a cellular automaton model was used in the present study to represent cardiac electrophysiological processes. With the rapid development in computing technology, it can be anticipated in the near future that more sophisticated heart models (e.g., [37]) will become available for the TMP imaging, providing further enhanced capability and resolution in imaging the spatio-temporal distribution of the TMP, and exploring the underlying cellular mechanisms associated with clinical ECG measurements. In our previous studies, we have developed a heart-model based localization approach to localize the site of origin of activation from body surface ECG recordings, and examined the applicability of the localization approach in a simulation study [19]. While some of the developed numerical techniques in that work have been used in the present study, the present work represents a distinctive piece of science in that we estimate the 3-D distribution of TMP instead of localizing the site of origin of the activation. We have also investigated the feasibility of imaging the activation time distribution, in which only the activation time at each myocardial tissue is considered [20]. In that work [20], no information on the shape of TMP is considered. In the present study, we estimate the spatio-temporal patterns of TMP distribution throughout the ventricles and over time. A recent study [21] also explored the estimation of distribution of activation time and approximate flat amplitude of TMP distribution from multi-channel MCG with a simplified action potential model, which provides a flat amplitude approximation of the TMP amplitude after activation, in an isotropic ventricle model. In that work [21], the Wiener estimation technique was used. In the present study, we have estimated the spatio-temporal distribution of TMPs [Figs. 3, 4 and 6], by means of a heart-model-based imaging approach. Such ability is important to image and study the cellular activities reflected in the shape of TMP. In another previous study, we have also addressed the imaging of 3-D distribution of current dipoles using weighted minimum norm algorithm [18], which provides a 3-D distribution of equivalent cardiac sources but without incorporating a priori information on cardiac electrophysiology. In the present simulation study, the primary objective function is a function of the temporally averaged CC between the true and candidate BSPMs, which represents spatio-temporal dissimilarity between the true and candidate BSPMs. Therefore, the present inverse solution is not an instantaneous inverse solution obtained from the BSPM at each time instant. It is a spatio-temporal inverse solution in that the spatio-temporal objective function (dissimilarity) of the true and candidate BSPMs is minimized. This spatio-temporal nature of the present inverse solution explains the good performance as observed in the present simulation study, especially considering the effects of geometry uncertainty. In addition, two constraints, the location difference in the minimum potential, and the difference in negative potential area, are used as the second and third criteria considering the nature of the pacing protocols. These two constraints have been selected based on experimental and clinical observations [32], [33] that suggested that the morphology of the BSPM is insensitive to inter-subject variation. In this spatio-temporal inverse solution, the a priori information on cardiac electrophysiology is also taken into consideration since the temporal and spatial patterns of the inverse solution in terms of heart model parameters are constrained by the heart model. In other words, the rich a priori knowledge embedded into the forward heart model is transformed into the accurate inverse solutions. A pacing protocol has previously been used in experimental or simulation settings to represent localized myocardial activation [19], [34] [36]. While a pacing protocol is used in the present study to demonstrate the feasibility of the present 3-D TMP imaging approach, it should be pointed out that the present 3-D TMP imaging technique is not necessarily limited to pace mapping, but also applicable to imaging other cardiac electrical activity, such as ischemia, infarction, repolarization abnormalities, and other arrhythmias. While it is beyond the scope of the present study to demonstrate the applicability of the proposed 3-D TMP imaging to other cardiac electrical activity, this issue should be addressed in future investigations. The present simulation results demonstrate the excellent performance of the present 3-D cardiac TMP imaging approach. Averaged over all 24 single-site pacing, the RE, CC, and AAD between the true and estimated TMP distributions were,, and mv, respectively, when 10 V potential GWN was added to the BSPMs. Averaged over all 12-pairs dual-site pacing, the RE, CC, and AAD between the true and estimated TMP distributions were,, and mv, respectively, with 10 V potential GWN being added. These promising simulation results suggest the robustness of the present approach in imaging TMP distributions for cardiac activation corresponding to one or two activation wavefronts. The effect of torso and heart geometry uncertainty is evaluated in the present study by enlarging or reducing the torso size and shifting the heart position. In addition, electrode placement uncertainty is assessed by adding GWN of 10 mm to the electrode positions. Compared with the standard heart-torso geometry model, the present simulation results suggest that the enlargement or reduction in the torso size results in little change in the performance of the present TMP imaging approach. Averaged over five cardiac source configurations, shifting of the heart position to the right or the left by 10 mm resulted in an increase in the RE of 2% and in the AAD of 0.16 mv (Table III), suggesting the robustness of the present TMP imaging approach. When higher estimation accuracy is desired, it will be necessary to build the realistic geometry heart-torso model for each individual subject based on CT or MR images, to obtain more accurate heart and torso geometry information. A thorough investigation on the effects of geometry uncertainty, including the heart rotation, on the accuracy of TMP imaging is beyond the scope of the present study but needed in the future investigation. The effect of cardiac anisotropy has been taken into consideration in the present study as the goal is to characterize and image the distribution of TMP instead of localization of site of origin of activation. It has been known that the fiber orientation within the myocardium plays an important role in shaping the excita-

12 HE et al.: NONINVASIVE IMAGING OF CARDIAC TMPS WITHIN 3-D MYOCARDIUM 1201 tion wavefronts within the ventricles [30]. The anisotropic heart model is, therefore, important for modeling detailed cardiac excitation and conduction within the ventricles [24] [29], [39]. Note that we have not attempted to model the abnormal conduction paths in the present study, since the goal of the present work is to demonstrate the merits of the 3-D TMP imaging approach we have proposed. A heart model incorporating TMPs on conduction deficient cardiac tissue will need to be used, if one would like to deduce information about conduction paths. In conclusion, we have developed a novel spatio-temporal imaging approach for imaging cardiac TMP distribution over the 3-D myocardium from noninvasive body surface ECGs by means of a realistic geometry anisotropic heart-model embedded in a realistic geometry inhomogeneous torso model. We have demonstrated, by computer simulation, the feasibility of the 3-D TMP imaging approach to estimate the TMP distribution with good accuracy over the 3-D ventricles and enable the inclusion of myocardial anisotropy in the TMP imaging. While computational loads may represent a limitation for the present TMP imaging approach in providing on-line imaging results due to the computational burden in the heart modeling, this limitation may be overcome in the near future considering the rapidly growing computer power. Future investigations should also include in-depth examination of the effects of geometry uncertainty on the imaging accuracy, and experimental validation of the present heart-model based TMP imaging approach in an experimental and clinical setting. The present promising results suggest that the present 3-D TMP imaging approach may become a useful alternative for noninvasive imaging of cardiac electrophysiological processes within the 3-D myocardium. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their constructive comments on the original version of the manuscript. REFERENCES [1] R. M. Gulrajani, Bioelectricity and Biomagnetism. New York: Wiley, [2] R. C. Barr, M. Ramsey, and M. S. Spach, Relating epicardial to body surface potential distributions by means of transfer coefficients based on geometry measurements, IEEE Trans. Biomed. Eng., vol. BME-24, pp. 1 11, [3] P. C. Frazone, B. Taccardi, and C. Viganotti, An approach to the inverse calculation of epicardial potentials from body surface maps, Adv. Cardiol., vol. 21, pp , [4] A. V. Shahidi, P. Savard, and R. Nadeau, Forward and inverse problems of electrocardiography: Modeling and recovery of epicardial potentials in humans, IEEE Trans. Biomed. Eng., vol. 41, pp , Mar [5] R. D. Throne and L. G. Olson, A generalized eigensystem approach to the inverse problem of electrocardiography, IEEE Trans. Biomed. Eng., vol. 41, pp , June [6] P. R. Johnston and R. M. Gulrajani, A new method for regularization parameter determination in the inverse problem of electrocardiography, IEEE Trans. Biomed. Eng., vol. 44, pp , Jan [7] H. S. Oster, B. Taccardi, R. L. Lux, P. R. Ershler, and Y. Rudy, Noninvasive electrocardiographic imaging: Reconstruction of epicardial potentials, electrograms, and isochrones and localization of single and multiple electrocardiac events, Circulation, vol. 96, pp , [8] B. He and D. Wu, A bioelectric inverse imaging technique based on surface Laplacians, IEEE Trans. Biomed. Eng., vol. 44, pp , July [9] F. Greensite and G. Huiskamp, An improved method for estimating epicardial potentials from the body surface, IEEE Trans. Biomed. Eng., vol. 45, pp , [10] Z. W. Liu, P. Jia, P. R. Ershler, B. Taccardi, R. L. Lux, D. S. Khoury, and Y. Rudy, Noncontact endocardial mapping: Reconstruction of electrograms and ischrones from intracavitory probe potentials, J. Cardiovasc. Electrophsyiol., vol. 8, pp , [11] D. S. Khoury, K. L. Berrier, S. M. Badruddin, and W. A. Zoghbi, Three-dimensional electrophysiological imaging of the intact canine left ventricle using a noncontact multielectrode cavitary probe: Study of sinus, paced, and spontaneous premature beats, Circulation, vol. 97, pp , [12] J. J. M. Cuppen and A. V. Oosterom, Model studies with inversely calculated isochrones of ventricular depolarization, IEEE Trans. Biomed. Eng., vol. BME-31, pp , [13] G. Huiskamp and F. Greensite, A new method for myocardial activation imaging, IEEE Trans. Biomed. Eng., vol. 44, pp , June [14] F. Greensite, Myocardial activation imaging, in Computational Inverse Problems in Electrocardiography, P. Johnston, Ed. Brisol, U.K.: WIT, 2001, pp [15] A. J. Pullan, L. K. Cheng, M. P. Nash, C. P. Bradley, and D. J. Paterson, Noninvasive electrical imaging of the heart: Theory and model development, Ann. Biomed. Eng., vol. 29, pp , [16] R. Modre, B. Tilg, G. Fischer, and P. Wach, An iterative algorithm for myocardial activation time imaging, Comput. Meth. Programs Biomed., vol. 64, pp. 1 7, [17] P. Wach, B. Tilg, G. Lafer, and W. Rucker, Magnetic source imaging in the human heart: Estimating cardiac electrical sources from simulated and measured magnetocardiogram data, Med. Biol. Eng. Comput., vol. 35, pp , [18] B. He and D. Wu, Imaging and visualization of 3-D cardiac electric activity, IEEE Trans. Inform. Technol. Biomed., vol. 5, pp , Sept [19] G. Li and B. He, Localization of the site of origin of cardiac activation by means of a heart-model-based electrocardiographic imaging approach, IEEE Trans. Biomed. Eng., vol. 48, pp , June [20] B. He, G. Li, and X. Zhang, Noninvasive three-dimensional activation time imaging of ventricular excitation by means of a heart-excitationmodel, Phys. Med. Biol., vol. 47, pp , [21] S. Ohyu, Y. Okamoto, and S. Kuriki, Use of the ventricular propagated excitation model in the magnetocardiographic inverse problem for reconstruction of electrophysiological properties, IEEE Trans Biomed Eng., vol. 49, pp , June [22] W. Lu, Z. Xu, and Y. Fu, Microcomputer-based cardiac field simulation model, Med. Biol. Eng. Comput., vol. 31, pp , [23] M. Aoki, Y. Okamoto, T. Musha, and K. Harumi, Three-dimensional simulation of the ventricular depolarization and repolarization processes and body surface potentials: Normal heart and bundle branch block, IEEE Trans. Biomed. Eng., vol. BME-34, pp , [24] J. Nenonen, J. Edens, L. J. Leon, and B. M. Horacek, Computer model of propagated excitation in the anisotropic human heart I: Implementation and algorithms, Comput. Cardiol., pp , [25] M. Lorange and R. M. Gulrajani, A computer heart model incorporating anisotropic propagation. I. Model construction and simulation of normal activation, J Electrocardiol., vol. 26, pp , [26] D. Wei, O. Okazaki, K. Harumi, E. Harasawa, and H. Hosaka, Comparative simulation of excitation and body surface electrocardiogram with isotropic and anisotropic computer heart model, IEEE Trans. Biomed. Eng., vol. 42, pp , Apr [27] P. C. Franzone, L. Guerri, M. Pennacchio, and B. Taccardi, Spread of excitation in 3-D models of the anisotropic cardiac tissue III: Effects of ventricular geometry and fiber structure on the potential distribution, Math. Biosci., vol. 151, pp , [28] G. Huiskamp, Simulation of depolarization in a membrane-equationsbased model of the anisotropic ventricle, IEEE Trans. Biomed. Eng., vol. 45, pp , July [29] G. Fischer, B. Tilg, R. Modre, G. Huiskamp, J. Fetzer, W. Rucker, and P. Wach, A bidomain model based BEM-FEM coupling formulation for anisotropic cardiac tissue, Ann Biomed Eng., vol. 28, pp , [30] D. D. Streeter Jr., H. M. Spotnitz, D. P. Patel Jr., J. Ross, and E. H. Sonnenblick, Fiber orientation in the canine left ventricle during diastole and systole, Circ. Res., vol. 24, pp , [31] B. He, T. Musha, Y. Okamoto, S. Homma, Y. Nakajima, and T. Sato, Electric dipole tracing in the brain by means of the boundary element method and its accuracy, IEEE Trans Biomed. Eng., vol. BME-34, pp , 1987.

13 1202 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 [32] M. S. Spach, R. C. Barr, C. F. Lanning, and P. C. Tucek, Origin of body surface QRS and T wave potentials from epicardial distribution in the intact chimpanzee, Circulation, vol. 52, pp , [33] D. W. Benson, R. Sterba, J. J. Gallagher, A. I. I. Walston, and M. S. Spach, Localization of the site of ventricular preexcitation with body surface maps in patients with Wolff-Parkinson-White syndrome, Circulation, vol. 65, pp , [34] M. Dubuc, R. Nadeau, G. Tremblay, T. Kus, F. Molin, and P. Savard, Pace mapping using body surface potential maps to guide catheter ablation of accessory pathways in patients with Wolff-Parkinson-White syndrome, Circulation, vol. 87, pp , [35] S. G. Larry, L. L. Robert, R. E. Philip, A. F. Roger, I. M. Fran, and G. Kathleen, Resolution of pace mapping stimulus site separation using body surface potentials, Circulation, vol. 90, pp , [36] R. Hren, B. B. Punske, and G. Stroink, Assessment of spatial resolution of pace mapping when using body surface potentials, Med. Biol. Eng. Comput., vol. 37, pp , [37] R. M. Gulrajani, M. C. Trudel, and L. J. Leon, A membrane-based computer heart model employing parallel processing, Biomedizinische Technik Brand 46 Erganzungsband, vol. 2, pp , [38] G. Li and W. Lu, Improved neural network optimization algorithm for classification of imbalanced-exemplar patterns, ACTA Eletronica SIN., vol. 16, pp , [39] M. Thivierge, R. M. Gulrajani, and P. Savard, Effects of rotational myocardial anisotropy in forward potential computations with equivalent heart dipoles, Ann. Biomed. Eng., vol. 25, no. 3, pp , Bin He (S 87 M 88 SM 97) received the Ph.D. degree in bioelectrical engineering with the highest honors from the Tokyo Institute of Technology, Tokyo, Japan, and completed the postdoctoral fellowship in biomedical engineering at Harvard University Massachusetts Institute of Technology (M.I.T.), Cambridge. After working as a Research Scientist at M.I.T, he joined the faculty of the University of Illinois at Chicago, where he is currently a Professor of Bioengineering, Electrical and Computer Engineering, and Computer Science, and the Director of Biomedical Functional Imaging and Computation Laboratory. His major research interests include biomedical functional imaging and source imaging, cardiovascular engineering, neural engineering, and computational biomedicine. He has published over 150 scientific papers in peer-reviewed journals and conference proceedings. He is the Founding Editor of the Book Series on Bioelectric Engineering, being published by Kluwer Academic Publisher. He also holds an appointment of Visiting Professor at Zhejiang University, China, and has been active in developing domestic and international collaborative research projects. Dr. He is the recipient of NSF CAREER Award, American Heart Association Established Investigator Award, the University of Illinois University Scholar Award, and the University of Illinois at Chicago College of Engineering Faculty Research Award. He is listed in Who s Who in Science and Engineering, Who s Who in America, and Who s Who in the World. He has been active in professional activities in the field of biomedical engineering and bioelectromagnetism. He currently serves as the President of International Society of Bioelectromagnetism, and the Member-at-Large of the ADCOM of the IEEE Engineering in Medicine and Biology Society. He serves as the General Chair of the 5th International Conference on Bioelectromagnetism, and served as the General Chair of the 3rd International Workshop on Biosignal Interpretation, and Technical Program Chair of the first IEEE-EMBS Asian-Pacific Conference on Biomedical Engineering. He has served as Associate Editor for IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE. He served as the sole Guest Editor for special issues at IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE, IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, Electromagnetics, Critical Reviews in Biomedical Engineering, and Methods of Information in Medicine. Guanglin Li (M 01) received the B.S. and M.S. degrees in electrical engineering from Shangdong University of Technology, Jinan, China, in 1983 and 1988, respectively, and the Ph.D. degree in biomedical engineering from Zhejiang Univeristy, Hangzhou, China, in In 1988, he joined the faculty of the Electrical Engineering Department, ShanDong University of Technology and has been an Associate Professor since He worked as a Research Fellow in Department of Electrical Engineeering and Computer Science at the University of Illinois at Chicago from 1999 to 2000, and as a Research Associate in Department of Bioengineering at the University of Illinois at Chicago from 2000 to He is currently a Senior Scientist with BioTechPlex Corporation, Elk Grove Village, IL. His research interests include biomedical signal processing, biomedical instrumentation, electrocardiography forward and inverse problem, and modeling and simulation of electrophysiological system. animal experimentation. Xin Zhang (S 00) received the B.S and M.S. degrees in biomedical engineering from Zhejiang University, Hangzhou, China, in 1996 and 1999, respectively. Since 1999, he has been a Ph.D. degree student in the Department of Bioengineering at the University of Illinois at Chicago. He has been conducting research in electrocardiography modeling and simulation, and electroencephalographic inverse problem. His research interests include biological signal processing and analysis, computer simulation, and human and