Ethics Statement

All experiments were performed in accordance with the guidelines for animal experimentation and were approved by the ethical committee of the Hôpital du Sacré-Coeur de Montréal.

Animal Preparation

Two large mongrel dogs (about 35 kg) were included in this pilot study. The first dog was used to create the computer model and the second to give some sense of experimental reproducibility. Each dog was anesthetized by sodium thiopental and maintained under positive pressure ventilation. After bilateral open chest surgery to expose the heart, anesthetic was changed to α-chloralose. Atrioventricular blockade was performed by formaldehyde injection to dissociate atrial and ventricular electrical activity, as in Armour et al. [10]. The right ventricle was electrically stimulated at 82 bpm to assure sufficient cardiac output. The atria were in sinus rhythm during the whole experiment.

Experimental Recording System

Two silicone plaques comprising 103 epicardial unipolar recording contacts were placed (1) in the right atrial free wall and lateral right atrial appendage (79 channels), and (2) in the Bachmann’s bundle and adjacent base of the medial atrial appendage (24 channels) [10]. The electrodes were connected to a multi-channel recording system (EDI 12/256, Institut de génie biomédical, École Polytechnique de Montréal). Signals were band-pass filtered (0.05–450 Hz) and digitized with a sampling rate of 1 kHz.

In parallel, a noncontact, endocardial balloon catheter (EnSite 3000 Multi Electrode Array with 64 channels; St Jude Medical Inc., St Paul, MN) was inserted in the right atrium. This device solves an inverse problem (see below) to compute endocardial electrograms at 2048 sites on a virtual closed surface representing the endocardium based on the potential at the 64 electrodes of the balloon [27]. This procedure requires reconstructing the endocardial geometry using a catheter localization system (EnSite NavX electroanatomical navigation system). Reconstruction of atrial geometry is shown in Fig. 1A for the dog considered in this study. The acquisition system outputs 2048 (virtual) endocardial electrograms as well as 3-lead ECG at a sampling rate of 1.2 kHz.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 1. Right atrium geometry and electrode configuration.

(A) Endocardial surface of a canine right atrium as reconstructed by the EnSite NavX system (left side: anterior view; right side: posterior view). Anatomical features identified by the catheter localization system are shown in red. Blue stars represent recording sites of the direct-contact endocardial catheter (B) 3D geometrical model (same views as panel A) of the right atrium after processing. Dashed circles represent the location of heterogeneity regions, shown here with a radius of 3 mm. (C) Epicardial electrode position for the two plaques in the computer model. (D) Left side: Balloon catheter with its 64 electrode. Right side: closed endocardial surface used for the inverse problem. RAA: right atrium appendage; SVC: superior vena cava; IVC: inferior vena cava; TV: tricuspid valve; CS: coronary sinus; SAN: sino-atrial node; RAGP: right atrium ganglionated plexus; IA: inter-atrial bundles.

https://doi.org/10.1371/journal.pone.0091165.g001

A second catheter in the right atrium served to measure direct-contact endocardial bipolar electrograms. This catheter, also localized and tracked by the system, was moved to record signals at 7 different locations (>5 sec stable recording at each location) near the superior vena cava, the right atrium ganglionated plexus, the inter-atrial bundles and the coronary sinus (stars in Fig. 1A).

Epi- and endocardial signals were simultaneously recorded using a separate digital acquisition system. To enable their synchronization, both systems had a “clock” input channel connected to a manually-driven tick generator.

Simulation of Electrical Propagation in the Right Atrium

The geometry extracted by the Ensite NavX system (Fig. 1A) formed the basis for constructing a 3D model of the canine right atrium. The dog that had the most accurate geometrical reconstruction (based on more acquisition points) was used for that purpose. The triangulated surface was processed and smoothed using VRMesh (VirtualGrid, Bellevue City, WA). Holes corresponding to the superior and inferior vena cava and to the tricuspid valve were created based on several points around their circumference identified using the catheter localization system (Fig. 1A). A thin-walled 3D cubic mesh (wall thickness: 1.75 mm; spatial resolution 0.25 mm; see Fig. 1B) was generated from the resulting triangulated surface as in our previous works [28]. Fiber orientation was specified following a rule-based approach [29]. There was no attempt to reproduce fine anatomical details and the trabecular structure of the right atrium (terminal crest and pectinate muscles) since no preparation-specific information was available for these anatomical features. Due to the limited spatial resolution of the NavX system, the details of the right atrium appendage anatomy were only grossly incorporated, as in older models [30].

These model limitations were deliberately introduced in order to ensure that: (1) there will be no real difference in epicardial and endocardial activation in the model; (2) the appendage (not taken into account by the Ensite device) will have a small influence on the simulation results. Consequently, the simulations represent a best-case scenario in which the loss of information due to the noncontact electrodes will be isolated from the effects of trabecular structure, epicardium-endocardium dissociation and heart contraction. These additional features may further reduce the accuracy of noncontact mapping.

Electrical propagation was simulated by solving the monodomain equation [31] in the cubic mesh using finite difference methods [32]. In the context of normal propagation in the absence of structural heart disease (e.g. fibrosis), this formulation, also used in previous works on atrial repolarization wave simulation [12], was shown to be sufficiently accurate, including for the computation of electrical signals [33]. Explicit time integration with a time step of 20 µs was used. Membrane kinetics was described by the Ramirez et al. model of canine atrial cell [34], [35]. Effective tissue conductivity was 12 mS/cm (longitudinal), anisotropy ratio was 3∶1, and membrane surface-to-volume ratio was 2000 cm⁻¹. Sinus rhythm propagation was elicited by injecting intracellular current at the anatomical location corresponding to the sino-atrial node (or more precisely to the focal point of activation) as identified using the catheter localization system (Fig. 1A).

To introduce repolarization heterogeneity in a way that replicates the Kneller et al. model of cholinergic atrial arrhythmia [34], we created circular zones of heterogeneity in membrane properties (Fig. 1B). Similarly to Vigmond et al. [11], zone radius was varied between 2 and 5 mm. In these zones (one at a time), acetylcholine (ACh) concentration was set to 0.03 µM based on Kneller et al. [34]. The resulting increase in ACh-dependent K+ current significantly shortened action potential durations in the zone, thus creating repolarization gradients [11].

For each substrate (control +7 zone locations × 3 zone radius = 22 simulations), sinus rhythm with a stable cycle length of 600 ms was simulated (experimentally-measured cycle length was 595±9 ms at baseline). Simulations were run until steady-state was reached, as determined by convergence of action potential durations (beat-to-beat variation <1%). Analysis was performed on the last simulated beat.

Simulation of Epicardial Electrograms

Epicardial mapping (“plaques”) was simulated using the same tools as in Jacquemet et al. [36]. Two plaques were used, as in the experiment: one in the right atrium free wall and one between Bachmann’s bundle and the appendage. Electrode configuration reproducing each experimental plaque was projected on the atrial epicardial surface on the basis of three manually-positioned control points (two electrodes at the extremities and one at the center of the plaque). The configuration is shown in Fig. 1C.

Electric potential at each of the 103 unipolar electrodes was computed using the current source approximation as in previous works [12], [36]. In this framework assuming an infinite uniform volume conductor, the potential φ of an electrode located at x is given by(1)where is σ_o the extracellular conductivity, I_m is the transmembrane current computed from the time course of the membrane potential in all simulated cardiac cells, and Vmyo is the integration domain (myocardium) [31]. The same formula (1) was used to compute potentials in the endocardium and in the blood cavity (see below).

Simulation of Noncontact Endocardial Electrograms

Since the EnSite software is proprietary, the noncontact mapping system was simulated using not exactly the same method, but a conceptually similar one based on Harley et al. [37]. In these approaches, the atrial geometry is specified by a closed surface S near the endocardium and whose interior V contains only blood. The surface S used by the EnSite software for the experiments is displayed in Fig. 1A; the one used for the simulations is shown on the right side of Fig. 1D. The 64 electrodes of the Ensite Array Catheter are located at x_i, i = 1 to 64, all inside the surface S (Fig. 1D, left side). Potentials at these 64 electrodes were computed using Eq. (1). Assuming homogeneity and isotropy of blood conductive properties and neglecting the effect of the catheter on volume conduction, the electric potential φ satisfies the Laplace equation Δφ  = 0 in V.

Because of the uniqueness of the solution to the Laplace equation with Dirichlet boundary conditions, the values of φ on S determine the value of φ at x_i, denoted by (c stands for catheter). An explicit formula can be derived from potential theory. From the Green’s second identity, if x is in the interior of V, then [37](2)where r is the distance between x and the surface element dS, E^e is the normal component of with respect to the surface S (the index e stands for endocardium), and is the solid angle subtended at x by the element dS located at y [31].

In order to compute these integrals numerically, S is discretized as a triangulated surface with N nodes located at y_j, j = 1 to N, where N is of the order of 2000. The field φ is approximated on the endocardium surface S using piecewise linear basis functions ψ_j:(3)where . If the 64-by-N matrices O^ec and S^ec are defined as:(4)then (2) can be written as

(5)Similarly, if x is on the boundary S, because of the singularity at r = 0,(6)and by defining the N-by-N matrices O^ee and S^ee as(7)the potential on the surface satisfies the equation

(8)After E^e is isolated in (8) and substituted in (5), the potential at the catheter electrodes is expressed as , where the 64-by-N forward transfer matrix is given by(9)where I is the identity matrix. Since the function ψ_j is linear on every triangle, the integrals from (4) and (7) are finite and can be computed analytically [38], [39], including in the presence of a singularity (i.e. when r = 0 in the integration domain). The auto-solid angle is defined such that the sum of each row of S^ee gives 1.

To estimate the potential at the endocardium from the potential at the catheter electrodes, the forward transfer matrix needs to be inverted. Because the system is underdetermined, Tikhonov regularization [31] was used to compute the inverse transfer matrix T^ce:(10)where λ is a positive regularization parameter. The parameter λ was set to 1.4 ·10⁻⁵ based on a comparison between electrograms computed directly using Eq. (1) and those obtained by solving the inverse problem.

Processing of Atrial Electrograms

Atrial activation times were identified in both epi- and endocardial electrograms using a dedicated event detector based on signal derivative [40]. Activation maps were validated manually by visual inspection of electrogram waveforms and activation times. Noncontact mapping sometimes produced fractionated endocardial waveforms (double potentials) that reduced the accuracy of detected activation times. To cope with that limitation, spatial filtering (Gaussian filter with a space constant of 5 mm) was applied to the resulting endocardial activation maps.

For each ventricular activation in the experimental signals, the onset of the Q wave and the offset of the T wave were identified manually on the ECG. For each atrial activation, the atrial activity interval was defined as the time interval between the earliest atrial activation time and the latest atrial activation +300 ms, assuming that atrial action potential durations were always shorter than 300 ms (which was a posteriori verified by inspecting the atrial T waves). Only atrial beats for which the atrial activity interval did not overlap with any QT interval were considered for subsequent analysis, in order to prevent the contamination of atrial signals by ventricular activity. This issue was not present in the simulated signals.

To quantify the local repolarization gradient, the area under the atrial T wave [7], [12] (ATa) was computed. The (non-dimensional) ATa of an electrogram waveform φ (t) was defined as:(11)where t_a is the activation time and σ_φ is the standard deviation of the whole signal φ. The integration bounds T₁ and T₂ were initialized to 50 and 300 ms. Further manual validation was performed to ensure appropriate positioning of integration bounds. After minor manual adjustments (mostly for the lower bound), the interval length T₂–T₁ was respectively 256±20 ms and 254±16 ms in epi- and endocardial experimental signals. For simulated signals, the bounds were set to T₁ = 35 ms and T₂ = 300 ms. Normalization by interval length was aimed at providing a non-dimensional ATa. It did not significantly influence the results since interval length was essentially the same across all electrodes. Amplitude normalization compensated epi-endo and between-channels amplitude differences that may be generated by the inverse problem solver, and facilitated the comparison between simulations and experiments. Baseline correction applied in (11) assumed that the point at the upper integration bound was isoelectric (just after the end of atrial repolarization and before the next onset of the Q wave). Since the previous and next atrial beats were typically partially masked by ventricular activity no interpolation of the isoelectric line was possible.

Correspondence between Epicardial and Endocardial Maps

One issue was to determine which endocardial electrode was closest to each epicardial electrode. In the computer model, this task was simply performed by identifying the endocardial electrode that minimized the Euclidian distance to the given epicardial electrode. In the experiment, the locations of epicardial electrodes in the EnSite endocardial coordinate system were not accurately known. The approximate location of some of the electrodes was however obtained using the catheter localization system.

The epi-endo correspondence was reconstructed iteratively. The grid of electrodes (plaques) was created based on three control points (like for the simulation of epicardial mapping, see above). The location of these three points was initialized using a priori knowledge about plaque placement. The position of these three points was then adjusted by random search within circular regions of diameter 5 mm around each initial control point position. The remaining points were positioned on the basis of the grid configuration, assuming regular inter-electrode spacing (this is similar to rigid registration). The optimization criterion was the root mean squared (RMS) difference between activation times in the epicardial map and at the corresponding electrodes of the endocardial map, summed up over three carefully-validated beats. Since anatomical reconstruction of the appendage was not accurate, electrodes located in the appendage were excluded in the computation of the optimization criterion.

Epicardial and endocardial maps were quantitatively compared using Pearson’s (product-moment) correlation coefficients [41] computed using Matlab. The software also outputted a p-value to exclude the hypothesis of no correlation.

Activation Maps

During the experiment in the first dog, the RR interval was 733±2 ms (ventricular pacing) and the QT interval was 353±22 ms. As a result, there were sequences of 380-ms intervals free of ventricular activity, while atrial depolarization time was <50 ms in the mapped area and repolarization always lasted less than 250–300 ms. In total, 12 atrial beats were found in these intervals free of ventricular activity. At least one suitable beat was identified for each of the 7 recording sites of the endocardial catheter. In the second dog, the RR interval was 733±6 ms (pacing) and the QT interval was 398±16 ms. Nine suitable beats were selected for the analysis.

Figure 2 shows examples of simultaneous epicardial and endocardial mapping. The location of epicardial electrodes on the endocardial surface (white dots in Fig. 2D) were obtained by optimization of the correspondence between epi- and endocardial map (Fig. 2F). The overall epi- and endocardial activation patterns were consistent. The RMS difference in activation time was 10 ms and the correlation coefficient was 0.8 in the first dog (p<0.001; see Fig. 2F). Due to a less accurate geometrical reconstruction (Fig. 2G), the correlation coefficient was 0.63 (p<0.001) in the second dog, with an RMS difference of nearly 20 ms. The main inconsistency between epi- and endocardial mapping was found in the appendage, a region that is distant from the balloon catheter and at the same time poorly geometrically represented for the inverse problem. Note that the sinus beat originates from a focal point located outside the epicardial plaques.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 2. Endo- and epicardial activation maps in the computer model (A–C) and in the experiments (D–I).

(A) Color-coded simulated endocardial activation map. White dots represent epicardial electrode positions. The white star denotes the earliest activation point. (B) Simulated epicardial activation map for the same atrial beat. (C) Epi- vs endocardial simulated activation times, along with the linear regression curve (dashed black line). (D) and (G) Experimental endocardial activation maps in two different dogs in control. (E) and (H) Corresponding experimental epicardial activation maps. (F) and (I) Epi- vs endocardial experimental activation times for the three beats (each shown with a different color) that served to identify epicardial plaque location. SVC: superior vena cava; IVC: inferior vena cava; RAA: right atrium appendage; BB: Bachmann’s bundle; RAGP: right atrium ganglionated plexus.

https://doi.org/10.1371/journal.pone.0091165.g002

In the computer model, exactly-known electrode location and geometry improved the consistency of the results. The endocardial activation map (Fig. 2A) was quantitatively similar to the epicardial map (Fig. 2B). Epi- and endocardial times (Fig. 2C) had a correlation coefficient of 0.96 and an RMS difference of 3.5 ms. The repolarization heterogeneities considered (changes in ACh concentration) had essentially no effect on the activation map at 100 bpm (maximum difference <0.8 ms).

With the exception of the appendage region, the computer model qualitatively reproduced experimental epi- and endocardial activation. Simulated and experimental epicardial maps (Figs. 2B vs 2E; 18 appendage data points excluded) had a correlation coefficient of 0.82 with an RMS difference of 6.8 ms (respectively 0.7 and 8.5 ms with all data points included). Since the computer model was derived from the experimental endocardial surface, endocardial activation could also be easily compared (data points in the valve and veins were excluded). Simulated and experimental endocardial activation times had a correlation coefficient of 0.91 with an RMS difference of 11 ms.

Morphology of Bipolar Electrograms

Direct-contact bipolar electrograms (Fig. 3, first row) were recorded at the 7 endocardial sites shown in Fig. 1A. Since noncontact endocardial electrograms were unipolar, noncontact bipolar electrograms were reconstructed by computing the difference between noncontact unipolar electrograms measured at two locations in the vicinity (<5 mm) of the bipolar recording site (Fig. 3, second row). Because bipolar waveform depends on the unknown orientation of the bipolar electrode, the location of these two sites were adjusted to better match direct-contact recording. The correlation coefficient between contact and noncontact waveforms was 0.88±0.06 (range: 0.8 to 0.95), except near the coronary sinus where the value was lower.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 3. Morphology of direct-contact (catheter) and non-contact bipolar electrograms for 7 recording sites in the experiment and in the computer model (normalized signals).

SVC: superior vena cava; RAGP: right atrium ganglionated plexus; IA: inter-atrial bundles; CS: coronary sinus.

https://doi.org/10.1371/journal.pone.0091165.g003

In the computer model, bipolar electrograms were also computed as the difference between unipolar electrograms at two close sites. Dipole orientation was selected to generate the same types of waveform morphology observed in the experiment (Fig. 3, third row). Noncontact bipolar electrograms (Fig. 3, fourth row) were computed as the difference between two noncontact unipolar electrograms measured at exactly the same location as the direct-contact unipolar electrograms. Correlation coefficient between contact and noncontact waveforms was 0.85±0.10 (range: 0.69 to 0.97), waveform in the coronary sinus excluded.

Area under the Atrial T Wave

The ATa provides a quantitative measure to assess atrial repolarization in experimental electrical recordings. Figure 4 illustrates the range of atrial T wave morphologies observed in the experiments and in the simulations at corresponding epi- and endocardial sites. Simulated atrial T waves had significantly lower normalized amplitude than the experimental ones (similarly to Vigmond et al. [12]) as revealed by smaller ATa values (Fig. 5), suggesting that canine atria contained stronger intrinsic heterogeneities than the model. Despite some differences in epicardial and noncontact endocardial atrial T wave morphology (notably atrial T wave did not become negative in experimental noncontact signals), epi- and endocardial ATa measurements appears to be correlated in these examples. Differences in signal amplitude, notably during the depolarization phase, may be due to inaccuracies in epi-endo electrode correspondence, or to volume conduction effects (e.g. Brody effect due to the higher blood conductivity [31]).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 4. Examples of unipolar epicardial and noncontact endocardial electrograms measured (normalized) at corresponding epi- and endocardial sites (both experimental and simulated).

The area under the atrial T wave is displayed as a shaded area. Simulated signals are saturated to highlight their atrial T wave.

https://doi.org/10.1371/journal.pone.0091165.g004

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 5. Endo- and epicardial ATa maps in the computer model (A–C) and in the experiments (D–I).

(A) Color-coded simulated endocardial ATa map in the presence of repolarization heterogeneity with a radius of 3 mm around the white star. White dots represent epicardial electrode positions. (B) Simulated epicardial ATa map for the same beat. (C) Epi- vs endocardial simulated ATa for all simulations with different repolarization heterogeneity distributions, along with the linear regression curve and 50% confidence interval. Data point density estimated by kernel-based method is displayed as contour lines. (D) and (G) Examples of experimental endocardial ATa maps in two different dogs. (E) and (H) Experimental epicardial ATa map for the same beat. (F) and (I) Epi- vs endocardial ATa for all beats combined in each of the two dogs. SVC: superior vena cava; IVC: inferior vena cava; RAA: right atrium appendage; BB: Bachmann’s bundle; RAGP: right atrium ganglionated plexus.

https://doi.org/10.1371/journal.pone.0091165.g005

To further investigate this question, epi- and endocardial ATa maps were compared (Figs. 5D and E). The epi- and endocardial ATa patterns were found to be qualitatively comparable, except in the right appendage where signals were less reliable. The correspondence between epi- and endocardial ATa is summarized in Fig. 5F for all electrodes and 12 beats. To facilitate the interpretation, data point density was estimated using a kernel-based method [42] (kde2d Matlab script implementation by Z. I. Botev, available on Matlab Central website) and displayed as contour lines. The correlation coefficient between epi- and endocardial ATa values was 0.57 in the first dog (Fig. 5F) and 0.46 in the second (Fig. 5I). In both dogs, the hypothesis of no correlation between epi- and endocardial ATa was rejected at p<0.001.

The same analysis was performed on simulated data. Note that there was no attempt to match experimental repolarization properties. Instead, heterogeneities were introduced at predefined locations to assess whether these changes could be identified using mapping systems. Figures 5A and B show endo- and epicardial ATa maps for a simulated beat with a heterogeneity region of radius 3 mm around the white star in Fig. 5C. This region of increased repolarization gradients was characterized by higher ATa values. Epi- and endocardial ATa maps were consistent. The correlation coefficient between epi- and endocardial ATa values from the 22 simulations with different repolarization heterogeneity distributions was 0.92, as illustrated in Fig. 5C.

Temporal Changes in Area under the Atrial T Wave

Experimental endocardial ATa maps were similar in the 12 analyzed beats. The correlation coefficient between any pair of them was always >0.9. The differences between ATa maps (separated by a few seconds or minutes) may reflect autonomic neural modulation [10]. To illustrate how endocardial ATa maps may be used to identify changes that occur outside the region covered by epicardial mapping, Figs. 6A–C displays ATa maps for two beats as well as their difference (ΔATa). On the ΔATa map, regions where changes occur can be easily identified.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Figure 6. Endocardial ATa maps.

(A) First experimental beat. (B) Another beat at a later time. (C) Difference between maps A and B. (D) Simulated ATa map during sinus rhythm in a uniform substrate. (E) Simulated ATa map with repolarization heterogeneity (3 mm radius in the right atrium ganglionated plexus; shown as a dashed circle). (F) Difference between maps D and E.

https://doi.org/10.1371/journal.pone.0091165.g006

In the simulations (Figs. 6D–F), repolarization gradients were induced by increasing ACh concentration in a circular zone, which affected ATa values. In the control beat (Fig. 6D), spatial variations in ATa were observed due to small repolarization gradients created by wavefront curvature or collision (this effect was |ΔATa| <0.04 in epicardial signals), and also due to distortions caused by the inverse problem. After subtraction, though, the pattern became clearer (Fig. 6F), thus enabling localization of the altered region. The distance between the center of the altered region and the maximum of the ΔATa map was <5 mm for the 4 regions in the right atrium ganglionated plexus and the inter-atrial bundles (Fig. 1B), and <9 mm for the 3 regions closest to the venae cavae. For the region near the superior vena cava, changes in repolarization were detectable only for a radius >3 mm. Otherwise, the radius of the region did not significantly affect the results in the range of parameters considered.