Reconstruction of Endocardial Potentials and Activation Sequences From Intracavitary Probe Measurements
Localization of Pacing Sites and Effects of Myocardial Structure
Background Mapping of endocardial activation is an important procedure for diagnosing cardiac arrhythmias and locating the arrhythmogenic site before treatment. The objective of the present study was to develop and test a mathematical method to reconstruct the endocardial potentials and activation sequences (isochrones) from potential data measured with a noncontact, intracavitary multielectrode probe (the “inverse problem”).
Methods and Results A boundary element based mathematical method, combined with a numeric regularization technique, was developed for computing the inverse solution. Endocardial potentials were computed from intracavitary potentials measured with a multielectrode probe placed in the cavity of an isolated, perfused canine left ventricle. Data were acquired during rhythms induced by electrical stimuli applied at different locations and varying depths within the myocardium. Endocardial potentials were measured using intramural needles to evaluate the accuracy of the inverse solutions by direct comparison. Inversely computed endocardial potentials, from measured probe potentials, reconstruct with good accuracy the major features (potential maxima and minima, regions of negative and positive potentials) compared with the measured endocardial potentials. During early activation, the computed endocardial potentials exhibit a potential minimum in close proximity to the pacing site, determining the location of the stimulus with good accuracy (within 10-mm error). Multiple stimuli, as close as 10 to 20 mm to each other, can be distinguished and localized to their sites of origin by the inverse reconstruction. Similar to the measured endocardial potentials, the spatial distribution of the computed endocardial potentials reflects the underlying cardiac fiber direction, and dynamic changes of the computed endocardial potentials reflect the rotation of fibers with intramural depth. Maps of isochrones show good correspondence between the isochrones determined from the computed endocardial potentials and those determined directly from the measured endocardial potentials.
Conclusions Compared with actual, measured endocardial potentials and activation sequences, endocardial potential patterns and activation sequences can be reconstructed on a beat-by-beat basis from cavitary potentials measured with a multielectrode, noncontact probe. The approach presented here is shown to reconstruct, with 10-mm accuracy and resolution of 10 to 20 mm, local events of cardiac excitation (eg, pacing sites). In addition, the reconstructed endocardial potentials correctly reflect the underlying fibrous structure of the myocardium. These results demonstrate the feasibility of the approach. In the experiments, the probe position and endocardial geometry were determined invasively. To be clinically applicable, the reconstruction method should be combined with a noninvasive method for determining the probe-cavity geometry in the catheterization laboratory. It could then be developed into a catheter-based technique for locating arrhythmogenic sites and for studying and diagnosing conduction abnormalities, reentrant activity, and the effects of drugs and other interventions on cardiac activation and arrhythmias.
Techniques of intracardiac recording and stimulation during electrophysiological testing are aimed at studying the cardiac excitation process, analyzing the activation pattern, or locating arrhythmogenic sites and areas of abnormal activity or slow conduction. Identifying the mechanism of the underlying cardiac arrhythmia is paramount to the selection of an appropriate therapy for its management. Furthermore, accurate localization of the arrhythmogenic site in patients with ventricular arrhythmias is critical to the success of nonpharmacological approaches, such as surgical and nonsurgical (catheter) ablation methods, in the permanent abolition of tachycardia.
Current techniques of mapping the potentials directly from the endocardium present certain difficulties. At present, intravascular electrode-catheter mapping1 is limited in the number of recording sites, and the procedure is very time consuming. Moreover, mapping from multiple sites is carried out sequentially over several cardiac cycles without accounting for possible beat-to-beat variability in the activation pattern. A more complicated mapping procedure involves the use of an endocardial multielectrode balloon or sponge.2 3 4 The procedure requires open heart surgery, heart-lung bypass, emptying the blood from the heart, and inflating the balloon so that the electrodes are in direct contact with the endocardium. In addition to the difficult procedure and risk involved, very often the arrhythmia to be mapped cannot be induced during surgery. An alternative indirect mapping approach was introduced earlier by Taccardi and his colleagues5 through the development of an intracavitary multielectrode catheter-probe (olive shaped or cylindrical). Unlike the balloon, the probe can be introduced into the blood-filled ventricular cavity without occluding it. The probe permits the simultaneous recording of intracavitary potentials from multiple directions. However, unlike the balloon, the probe is not necessarily in direct contact with the endocardium. Probes based on the same principle, eg Foley-like inflatable catheters,6 carrying the electrodes on the surface of a small balloon, could be used during routine catheterization studies. It was demonstrated recently by Khoury and Rudy,7 in an idealized model of the probe-heart-torso volume conductor, that the spatial pattern of cardiac excitation is accurately reflected in the endocardial potentials but not in the associated cavitary probe potentials, which exhibit smoothed-out, low-amplitude distributions.
The overall objective of the present study was to develop and test a mathematical method to reconstruct the endocardial potential distribution from cavitary potentials measured with a multielectrode probe that is not in direct contact with the endocardium (the “inverse problem”). Endocardial potentials are computed during paced rhythms in the isolated, perfused canine left ventricle (LV). Specifically, the reconstruction procedure is assessed for its ability to locate the site of origin of single and multiple pacing stimuli, reflect the effect of cardiac fiber direction on the spatial pattern of the potentials, and reconstruct the major events during the spread of excitation.
The procedure of reconstructing endocardial potentials and, subsequently, the activation sequences from intracavitary, noncontact probe data can be divided into two subprocedures. The first consists of determining the probe-cavity geometry, which is required for determining the transfer relation between the probe and endocardial surfaces. The second consists of the actual computation of the endocardial potentials, assuming that the probe-cavity geometry is known. In this article, we focus on the second subprocedure of mathematically reconstructing the endocardial potentials from noncontact probe data. This essential step is difficult and crucial to the success of the entire approach. It must be carefully evaluated, with minimal effects from other complicating factors to assess feasibility of the technique. We therefore develop and test the reconstruction method, using a geometric relation that is determined invasively. Using specific protocols, we assess quantitatively the effects of errors in geometry (ie, errors in probe position and orientation) on the reconstructed endocardial potentials. Of course, to be clinically applicable the geometry must be determined during catheterization. Combining the reconstruction procedure with a noninvasive method for determining the geometry will be the next step in the development of this approach as a clinical tool.
The work presented here is a first step in the development of a catheter-based method for the simultaneous mapping of endocardial potentials and endocardial activation patterns (isochrones). If successful, such a method will permit detailed examination of global as well as regional cardiac electrical events in the clinical cardiac electrophysiology laboratory and in the intact experimental animal. With this approach, information can be obtained on the nature of conduction abnormalities, site of origin and type of arrhythmia, pathway of reentrant activity (including its spatial organization and its important components such as the area of slow conduction), and beat-to-beat dynamic changes during the arrhythmia (eg, initiation and termination). Moreover, the method will permit localization of the arrhythmogenic site before catheter ablation.
The following is a short description of the mathematical procedure. Details of the mathematical methods can be found in our previous review articles.8 9 10 The potential field within the ventricular cavity is generated by the myocardial sources during excitation. To explain the relation between endocardial potentials and probe potentials, we recall an important property of the potential field, namely, that every electrode on the probe is influenced by the potential over the entire endocardium. However, endocardial regions that are closer to a particular probe electrode exert a stronger influence at this electrode compared with more distal regions. The geometric weight factors that represent these distance effects constitute the matrix A (see Equation 4 below). Note that there is no one-to-one correspondence between a specific electrode on the probe and a specific point on the endocardium and that all endocardial points contribute to the potential measured by a particular probe electrode.
The cavity potential distribution is described mathematically by Laplace’s equation. Computation of endocardial potentials from measured intracavitary probe potentials requires solving Laplace’s equation in the cavity volume (Ω) bounded by the probe surface (Sp) and the endocardial surface (Se), as illustrated in Fig 1⇓. The potential (v) is obtained by solving Laplace’s equation:
subject to the following Cauchy boundary conditions:
That is, the potential is known on the probe surface, and
That is, current cannot enter the probe, which is assumed to be nonconducting.
A standard boundary element method technique11 was used to discretize the probe and endocardial surfaces and to solve for the potentials in a realistic-geometry probe-cavity system. The method is the same as we previously applied to computing epicardial potentials from body surface potentials (“the electrocardiographic inverse problem”).8 9 10 12 13 14 Following the discretization of the surfaces, the ensuing relation is obtained:
where Vp is a vector of probe potentials of order Np (number of probe nodes or electrodes), Ve is a vector of endocardial potentials of order Ne (number of endocardial nodes or electrodes), and A is a matrix (Np×Ne) of influence coefficients that represents the geometric relation between the two (endocardial and probe) realistic surfaces. The problem of solving the endocardial potentials (Ve) for a given set of measured probe potentials (Vp) in Equation 4 is ill-posed in the sense that small perturbations in the data (Vp) due to measurement noise or to systematic errors in determining the geometry result in large variation in the solution (Ve). The solution of endocardial potentials (Ve) was therefore stabilized by applying zero-order Tikhonov regularization technique15 in conjunction with the CRESO a posteriori method16 for determining the regularization parameter (further explanation is provided in References 8 through 10). In this approach, the solution of endocardial potentials (Ve) is obtained as an optimal estimate of these potentials that is also stable. Stability is achieved by imposing a physiological constraint on the solution, which, for Tikhonov zero order, implies endocardial potentials of bounded amplitudes. This technique was previously applied, with good results, to the reconstruction of epicardial potentials from body surface potentials using a setup of an isolated dog heart in a human geometry electrolytic tank torso.13 14 The numeric algorithms used in the study presented here were initially tested by reconstructing endocardial potentials from intracavitary probe potentials in an idealized eccentric spheres model of the probe-heart-torso volume conductor.7 17
Experimental Model: Isolated Heart Preparation
The inverse method was applied to the reconstruction of LV endocardial potentials from actual, measured LV intracavitary probe potentials in the isolated canine heart. Two experiments were performed, with two dogs used in each experiment. The dogs were anesthetized with pentobarbital (30 mg/kg). Mechanical ventilation was maintained from an external respirator through an endotracheal tube. In each experiment, a large dog was used to support an isolated heart obtained from a smaller dog. The support dog was used to supply oxygenated blood, with blood flowing into the aorta of the isolated heart to perfuse the coronary arteries (similar to Langendorff perfusion; Fig 2⇓). The heart was suspended in a warm chamber and contracted freely. Heat exchangers maintained normal blood temperature. Arterial pressure was monitored for the support dog by cannulating the left femoral artery. Once the preparation was stable, the right ventricular (RV) wall was surgically removed to expose the septum, thereby providing an access for inserting needle electrodes from the right side of the heart through the septum to record septal potentials from the LV side. The preparation was stable for 4 hours on average. We implemented at least six preparations identical to the one described here (with the RV wall removed), for different purposes, and the preparation was stable for many hours. We also used dozens of “entire” heart preparations, and the duration was even longer.
Intracavitary and Endocardial Potential Measurements
Intracavitary potentials were measured using two different probes (one for each experiment). Recorded probe potentials served as the input data for the inverse reconstruction of LV endocardial potentials. In the first experiment (case 1; Fig 2⇑), a 65-electrode cylindrical probe was inserted through a purse string in the left atrial appendage of the isolated heart and positioned along the blood-filled LV cavity. The probe electrodes were distributed along 8 circumferential rings on the surface and a tip electrode at a tapered end. The probe was 11.5 mm wide, and the distance between the tip electrode and the proximal ring was 28 mm. In the second experiment (case 2; Fig 2⇑), an 89-electrode cylindrical probe was inserted through a purse string in the LV apex of the isolated LV preparation. The probe electrodes were distributed along 11 circumferential rings on the surface and a tip electrode at a tapered end. The probe was 12.5 mm wide, and the distance between the tip electrode and the proximal ring was 40.1 mm. A photograph of the actual probe used in case 2 is shown in Fig 3A⇓. In both probes, the electrodes in each ring were spaced 45 degrees from each other.
Endocardial potentials were measured by inserting 52 or 94 intramural multielectrode needles into the ventricular walls of the isolated LV from all directions (Fig 3B⇓; photograph of actual heart preparation used in case 2). The needles protruded slightly into the blood cavity, so that the tip electrodes measured potentials on the cavity side of the endocardium (the tip electrodes formed an “endocardial envelope” or an effective “endocardial balloon”). Recorded endocardial potentials served as the gold standard for evaluating the accuracy of the inversely computed potentials. Other intramurally located electrodes on the needles were used for recording and pacing at different depths in the myocardium. Two different types of electrode needles were used. A 13-mm-long needle, with 3 electrodes 1.6 mm apart at the endocardial end, was used for recording. A 14.4-mm-long needle, with 10 electrodes 1.6 mm apart, the 10th electrode being epicardial, was used for pacing and recording.
Potentials were recorded during rhythms induced by LV stimulation. Current pulses of just suprathreshold intensity, 2 ms in duration, were applied. The heart was paced at a cycle length of 360 ms in case 1 and at 350 ms in case 2. Pacing was performed from 12 (case 1) or 14 (case 2) pacing needles (at different intramural depths). The stimuli were applied between electrodes 1 and 2 (distal end of pacing needle) for subendocardial pacing, between electrodes 5 and 6 for midwall pacing, and between electrodes 9 and 10 (proximal end of pacing needle) for subepicardial pacing. The heart was paced from one needle or from two needles simultaneously. A total of 52 (pacing and recording) intramural needles were inserted throughout the LV wall and the septum in case 1, and 94 needles were inserted in case 2.
Unipolar electrographic signals from the probe electrodes and the intramural needle electrodes were simultaneously amplified, sampled at 1 kHz per channel, digitized (12 bits), and stored in a Microvax II computer. The common reference electrode was placed on the lump of noncontractile tissue close to the base of the isolated heart.
Volume Conductor Geometry Measurements
At the end of the experiment and after the completion of different pacing protocols, the LV cavity was filled with gelatin to preserve the geometry of the endocardial surface. The needles were then replaced by metal rods that were 101.6 mm long, and the heart was stored in a formalin solution. A few days later, the geometry of the endocardial envelope formed by the needle tips (approximating the endocardial surface) was digitized. This was accomplished by determining the cylindrical coordinates of the needle tips (see schematic illustration of the measurement setup in Fig 4⇓). The coordinates were determined for two points on the exterior portion of the metal rod (external end point and entry point on the epicardium); the coordinates of the tip (electrode 1) were subsequently computed by linear extrapolation (ie, using the equation of a straight line in three-dimensional space). Similarly, the probe surface was digitized by determining the cylindrical coordinates of the electrodes on its surface using the same setup shown in Fig 4⇓.
The probe and endocardial surfaces were reconstructed by connecting the electrodes (nodes) with triangles (the electrodes being the vertices of the triangles). The probe position and orientation relative to the endocardial surface (including horizontal and vertical shifts, rotation, and tilt with respect to the vertical axis of the LV) were mathematically determined using measured endocardial and probe potential data. This was accomplished by minimizing the root-mean-square error between the actual measured probe potentials and the forward-computed probe potentials (using the forward relation between endocardial potentials and probe potentials in Equation 4 in “Mathematical Formulation”). The root-mean-square error was minimized over five consecutive time frames early in the activation process. This approach is similar in concept to an earlier method by Macchi et al18 19 where the site of origin of ectopic events was localized by minimizing the difference between measured probe potentials and potentials computed for an oblique dipole layer model that approximated cardiac sources during early ectopic activation.20 Fig 5⇓ is an anterior view of the discretized (triangulated) probe and LV endocardial surfaces with the probe positioned within the cavity (anterior wall is removed in Fig 5⇓ to show the probe). The two surfaces describe the geometry required for the boundary value problem illustrated in Fig 1⇑. A separate probe position was determined for each pacing protocol, as the position changed over the period of the experiment due to ventricular contraction, variation in the location of the pacing site, and changes in ventricular blood filling. This served as a best-case scenario for each protocol for computing endocardial potentials from probe potentials while minimizing error due to inaccuracy in probe position. Using this best-case scenario as a baseline, study of the effects of error in probe position and orientation on the accuracy of reconstruction was conducted by displacing or reorienting the probe from its original position and/or orientation. Note that the above method of determining the probe position and orientation within the cavity cannot be extrapolated to clinical application, as it requires a priori knowledge of the actual endocardial potentials. Clinically, a noninvasive method for determining probe position and orientation (eg, echocardiography) will have to replace the invasive approach used in the present experiment.
Data Processing and Display
After the experiment, recorded unipolar electrographic signals were baseline adjusted, calibrated, and signal averaged (6 cycles). Few electrode needles were discarded due to malfunction during the experiment. In case 1, a total of 50 actual recording needles were used, and the endocardial surface was therefore represented by 50 nodes. In case 2, a maximum of 76 actual recording needles were used (some pacing protocols had more malfunctioning needles than others). An additional 6 nodes were used to completely close off the endocardial surface at the base and apex, resulting in a total of 82 nodes to represent the endocardial surface. The probe surface was closed off by adding a node at the proximal end of the probe. In both cases, potentials at nodes with missing data were interpolated by minimizing the laplacian at all nodes of the surface considered.21 During subendocardial pacing (stimulus applied between electrodes 1 and 2 of the pacing needle), the tip electrode of the pacing needle was assigned the value of the potential measured by the third electrode. In case 2, the 8 electrodes in the proximal circumferential ring of the probe were removed, as they were touching the myocardium in the apical region. This, in effect, resulted in an 81-electrode probe. Therefore, the matrix A in Equation 4 was of order 66×50 for case 1 and 82×82 for case 2. All the needle tips were in the cavity, some very close to the real endocardium, and some a few millimeters into the blood. Thus, the reconstructed surface was not the real endocardial surface but rather an envelope that closely lined the endocardium.
The instantaneous potential distribution on the unrolled surface of the probe is displayed in the form of equipotential contour maps. The probe and endocardial potentials are presented as seen by an observer looking at the probe surface and endocardial surface from within the probe. The endocardial potential maps are displayed on the actual endocardial surface; cut at the left lateral LV, and projected on a two-dimensional surface with a view of the anterior LV, septum, and posterior LV as illustrated in Fig 6⇓. Equipotential contour maps are presented for every millisecond. Regions bounded by the most positive or least negative equipotential contour are shaded. Endocardial isochrone (activation) maps were obtained by determining the time of occurrence of the negative peak of the first derivative of QRS at every electrode site on the endocardial surface. Maps of isochrones determined on the probe surface are called “pseudoisochrones,”5 as the probe electrodes were not in direct contact with the endocardium. The end of the stimulus pulse was selected as the reference point. The sites where the stimuli were delivered are indicated by asterisks on all the endocardial maps.
Localizing Single Ectopic Events in Different Regions and at Different Intramural Depths
Probe and endocardial potentials generated by a subendocardial stimulus applied at an anteroseptal location are shown in Fig 7⇓. At 13 ms, the measured endocardial potential distribution (Fig 7A⇓-I) exhibits a potential minimum of −34.44 mV located at the pacing site indicated by the asterisk (potential measured by the third distal electrode on the pacing needle). This location of the potential minimum is in agreement with the results of previous reports on the close proximity of the potential minimum to the site of the stimulus early in the activation sequence.4 22 23 24 25 26 27 28 29 30 31 32 33 The alignment of the region of peak positive potentials (shaded in the figure) with respect to the potential minimum and the region of negative potentials agrees qualitatively with the subendocardial fiber direction.34 This potential pattern is in accord with previous studies demonstrating the effect of myocardial anisotropy (fiber orientation) on propagation of excitation and on the resulting potential fields; excitation spreads faster in a direction parallel to the long axes of the cardiac fibers than perpendicular to them and generates positive potentials and potential maxima in the areas toward which excitation propagates along fibers.23 24 25 26 27 28 29 30 31 32 33 The simultaneously measured intracavitary probe potentials (Fig 7A⇓-II) exhibit a potential minimum −1.91 mV in magnitude that faces the pacing region on the endocardium. The inversely computed endocardial potentials from the measured probe potentials, at 13 ms, are shown in Fig 7A⇓-III. A potential minimum −5.02 mV in magnitude appears on the endocardial surface at the pacing site, thereby accurately identifying the location of the pacing site. In addition, the position of the region of peak positive potentials and its orientation relative to the potential minimum correlate well with that of the measured potentials. At 18 ms (5 ms later than the time instant depicted in Fig 7A⇓), the magnitudes of the potential minima become −23.02 mV, −2.49 mV, and −7.43 mV in Fig 7B⇓-I (measured endocardial), Fig 7B⇓-II (measured probe), and Fig 7B⇓-III (reconstructed endocardial), respectively. Furthermore, the positive region expands in a counterclockwise direction with respect to the potential minimum, as reflected in the potentials on both the endocardial (measured and reconstructed) and probe surfaces. At a later time frame (23 ms), the potential minima become −23.17 mV, −22.75 mV, and −25.21 mV in Fig 7C⇓-I, Fig 7C⇓-II, and Fig 7C⇓-III, respectively. In addition, the positive and negative regions on the endocardial surface are oriented horizontally (circumferentially). A sequence of successive histological sections of the ventricular wall in the anteroseptal region (containing the pacing needle) showing fiber directions are provided in Fig 8⇓. The fibers, viewed from the endocardial side, rotate counterclockwise from endocardium to epicardium (top to bottom in Fig 8⇓), as demonstrated earlier by Streeter et al.34 The counterclockwise rotary expansion of the positive region reflects the effect of fiber rotation on the spread of excitation through deep myocardial layers, from the endocardium toward the epicardium. This effect of transmural fiber rotation (“rotational anisotropy”) on the initial spread of activation and the resulting potential field was reported earlier in conjunction with measured epicardial potentials.28 29 30 31 32 33 Our results (Fig 7⇓) demonstrate a similar effect on endocardial potentials and show that this is captured correctly in the reconstructed potential distributions.
Probe and endocardial potentials generated by a subepicardial stimulus applied at an anteroseptal location (same pacing needle as in Fig 7⇑) are shown in Fig 9⇓. Initially, at 17 ms, a potential minimum −1.97 mV in magnitude appears in the measured endocardial potential distribution (Fig 9A⇓-I) that is 8 mm away from the endocardial tip of the pacing needle. As the wave front moves from the epicardium to the endocardium, the potential minimum progressively increases in magnitude, becoming −18.18 mV at 28 ms (Fig 9B⇓-I) and −40.11 mV at 33 ms, when it appears at the endocardial site of the pacing needle (Fig 9C⇓-I). Similarly, the simultaneously measured probe potentials exhibit a potential minimum facing the pacing region that progressively increases in magnitude: −0.52 mV at 17 ms (Fig 9A⇓-II), −2.78 mV at 28 ms (Fig 9B⇓-II), and −38.39 mV at 33 ms (Fig 9C⇓-II). The potential minimum, in the corresponding inversely computed endocardial potentials, appears from the start at the endocardial position of the pacing needle. It increases in magnitude with time progression: −0.67 mV at 17 ms (Fig 9A⇓-III), −10.01 mV at 28 ms (Fig 9B⇓-III), and −41.97 mV at 33 ms (Fig 9C⇓-III).
The alignment of the peak positive region with respect to the negative region, early in the activation process, is similar in the measured and inversely computed endocardial potentials. However, the alignment is different for a subepicardial stimulus (Fig 9A⇑-I and Fig 9A⇑-III) from that for a subendocardial stimulus (Fig 7A⇑-I and Fig 7A⇑-III). The initial pattern of activation due to a stimulus at a certain depth within the myocardium is generally a reflection of the local fiber direction at that level. In Fig 9A⇑-I and 9A-III, the alignment of the positive and negative regions on the endocardium is more circumferential than expected based on the direction of the epicardial fibers themselves (see fiber directions in Fig 8⇑). This difference probably results from the fact that by the time distinct negative and positive potential regions can be detected on the endocardial surface, the wave front has penetrated into deeper subepicardial layers that are rotated clockwise and are more circumferential than the epicardial fibers. As time progresses, a clockwise expansion of the positive region with respect to the negative region is observed in both the measured and the computed endocardial potentials as well as in the measured probe potentials. This is a consequence of the clockwise rotation of the fibers with depth from the epicardium to the endocardium (as viewed from the endocardial surface), as illustrated in Fig 8⇑. Later in the activation process (33 ms), the positive potential region expands to form a circular pattern, with the potential minimum located at the endocardial node of the pacing needle in both the measured and the computed endocardial potentials. The formation of a circular pattern with high degree of symmetry and no obvious positive-negative axis probably results from the cumulative (averaging) effect of the rotating fibers, as activation spreads from epicardium to endocardium through many layers of different fiber directions.35 36 A similar effect, as seen from the epicardium, was described by Watabe et al31 and recently by Taccardi and colleagues.32 33
A map of isochrones determined from the measured endocardial potentials for the pacing protocol of Fig 7⇑ (subendocardial stimulus) is shown in Fig 10A⇓. The earliest activation time is 2 ms, as determined from the electrogram of the third distal electrode on the pacing needle (see “Methods”). The corresponding inversely reconstructed isochrone map, determined from the inversely computed endocardial potentials, is shown in Fig 10B⇓; the earliest activation time is 23 ms. Both isochrone maps indicate that activation starts in the anteroseptal region (in the vicinity of the pacing needle) and progresses to the posterior region toward the base of the LV. A map of pseudoisochrones (see “Methods”) determined on the probe surface is shown in Fig 11A⇓. The earliest activation time determined directly from the measured probe potentials is 22 ms. For subepicardial pacing (Fig 9⇑), a map of isochrones determined from the measured endocardial potentials is shown in Fig 12A⇓. The earliest activation time is 29 ms, later than that for subendocardial stimulation (Fig 10A⇓). The corresponding isochrone map, determined from the inversely computed endocardial potentials, is shown in Fig 12B⇓; the earliest activation time is 32 ms. A map of pseudoisochrones determined on the probe surface is shown in Fig 11B⇓ for subepicardial pacing. The earliest activation time determined directly from the measured probe potentials is 32 ms.
Endocardial and probe potential distributions during the initial phase of activation due to stimuli applied at varying depths along the same transmural needle are presented in Fig 13⇓. The pacing needle, indicated by the asterisk, is located in the anterolateral LV region. The potential distributions generated 11 ms after a subendocardial pacing stimulus are shown in Fig 13A⇓. The measured endocardial potentials (Fig 13A⇓-I) exhibit a potential minimum −19.77 mV in magnitude located at the pacing site (potential measured by the third distal electrode on the pacing needle). A −0.32 mV minimum appears in the measured probe potential distribution (Fig 13A⇓-II). The inversely computed endocardial potentials display a −2.63 mV potential minimum that is 8.2 mm away from the pacing site (Fig 13A⇓-III). A sequence of successive histological sections of the ventricular wall in the anterolateral region (containing the pacing needle) showing fiber directions (viewed from the endocardial side) are provided in Fig 14⇓. Note that in the endocardial potential maps of Fig 13A⇓-I and 13A-III, the peak positive regions are aligned with respect to the negative region in a direction that is parallel, in a qualitative sense, to the subendocardial fiber direction. A single positive area appears in the computed endocardial potentials as opposed to two positive regions in the measured potentials. The potential distributions, generated by a midwall stimulus at 10 ms after stimulation, are shown in Fig 13B⇓. The magnitude of the measured endocardial potential minimum is −7.27 mV, and the relative minimum in the probe potential is 0 mV. A potential minimum −1.11 mV in magnitude is reconstructed in the computed endocardial potential distribution and is located at the endocardial node of the pacing needle (3.6 mm away from the minimum of the corresponding measured potentials). Notice that the positive and the negative regions reflected in the measured and computed endocardial potential maps (in Fig 13B⇓-I and 13B-III, respectively) are oriented parallel to the circumferential (horizontal) fiber direction at the midwall level, as can be deduced from Fig 14⇓. The inversely computed potentials are generally noisy at low levels of measured probe potentials. For a subepicardial stimulus (Fig 13C⇓), the measured and computed endocardial potential distributions at 14 ms reflect an alignment of the positive and negative regions that is indicative of the fiber direction at the subepicardial level (see Fig 14⇓). The measured and reconstructed potential minima, −1.56 mV in Fig 13C⇓-I and −0.67 mV in Fig 13C⇓-III, are at the same node, 4.1 mm from the pacing needle. The corresponding probe potential minimum is −0.06 mV.
Results of subendocardial stimulation in the apical region are shown in Fig 15⇓. The measured endocardial potentials at 10 ms for a pacing stimulus (asterisk) applied in the posteroseptal portion of the apex (Fig 15A⇓-I) exhibit a potential minimum −22.25 mV in magnitude that is located at the pacing node (potential measured by the third distal electrode on the pacing needle). A corresponding broad potential minimum −3.43 mV in magnitude appears in the measured probe potentials (Fig 15A⇓-II). The inversely computed endocardial potentials (Fig 15A⇓-III) reveal a potential minimum −7.40 mV in magnitude located 4.2 mm away from the pacing site. For a stimulus applied in the posterolateral portion of the apex (Fig 15B⇓-I), the measured endocardial potentials at 14 ms reveal a potential minimum −1.55 mV in magnitude located at the pacing node. Measured probe potentials (Fig 15B⇓-II) reflect a minimum −1.31 mV in magnitude. The inversely computed endocardial potentials (Fig 15B⇓-III) reconstruct a potential minimum −2.27 mV in magnitude that is exactly at the same pacing node. Note that the probe position and orientation were the same for both pacing protocols in Fig 15⇓.
Thus far, the results of the pacing protocols of Figs 7⇑, 9⇑, 13⇑, and 15⇑ demonstrate that measured endocardial potentials exhibit a potential minimum, early in activation, at or in close proximity to the pacing site. This is in keeping with the observations of Harada et al.4 Measured probe potentials exhibit minima that appear on its surface at electrodes facing the pacing sites. More important, the location of the pacing site can be reconstructed with good accuracy (less than 10 mm error) on the endocardial surface from the inverse solution. Early during activation, the magnitudes of the measured probe potentials are small. This results in low magnitude and low signal-to-noise ratio of the input data for the inverse reconstruction. As a result, the inversely computed potential maps are generally noisy and do not depict the activation pattern at this early stage. As the cardiac sources become more extensive with the progression of activation, probe potentials and, consequently, the inversely computed endocardial potentials increase in magnitude and reflect the activation pattern. In effect, an apparent delay appears in the computed endocardial potential maps compared with the measured ones (see “Discussion”). This phenomenon is a manifestation of the volume conductor geometric and conductive effects that attenuate the probe potentials.7
Early in the activation process, the relative orientation of the positive and negative regions on the endocardial surface is generally a reflection of the fiber direction at the intramural depth of the stimulating electrode. In addition, for subsequent time frames, regions of positive potentials expand around the negative regions in a rotary fashion, reflecting the rotation of the fibers as the activation penetrates increasing depths within the myocardium. These characteristics are clearly reflected in the inversely reconstructed endocardial potentials. For the relatively large probe sizes used in these experiments, a broad pattern of rotational expansion can be deduced from the measured probe potentials as well.
Distinguishing Multiple Cardiac Events
The ability to resolve and localize multiple ectopic events was investigated by pacing the LV from two sites simultaneously and recording the instantaneous potentials generated by pacing stimuli at varying distances from each other. This provides a measure of the spatial resolution capability of the reconstruction procedure. In Fig 16⇓, two pacing stimuli separated by 29.5 mm were applied subendocardially: one stimulus in the anterobasal region, and the other in the posterobasal region (asterisks). At 15 ms, the measured endocardial potentials reveal two minima at the two pacing sites: a −46.44 mV minimum on the anterior surface and a −28.82 mV minimum on the posterior surface (potentials measured by the third distal electrode on the pacing needle). Two potential minima also appear in the simultaneously measured probe potentials (Fig 16C⇓): a −2.66 mV minimum facing the anterior wall and −2.36 mV minimum facing the posterior wall. The inversely computed endocardial potentials reconstruct the two potential minima exactly at the location of the pacing nodes (Fig 16B⇓): a −15.23 mV minimum on the anterior wall and a −7.71 mV minimum on the posterior wall. Single pacing stimuli were then applied separately at the same pacing sites. Measured probe potentials generated at 15 ms by the single anterior stimulus are shown in Fig 16D⇓ and for the single posterior stimulus in Fig 16E⇓. The potential minimum is −3.00 mV in Fig 16D⇓ and −3.71 mV in Fig 16E⇓. It can be observed that probe potentials generated by the two simultaneous stimuli of Fig 16C⇓ approximate a superposition of the potentials generated by the application of the stimuli separately (Fig 16D⇓ plus 16E).
A map of isochrones determined from the measured endocardial potentials for the pacing protocol of Fig 16⇑ is shown in Fig 17A⇓. The map indicates two sites of early activation: the earliest activation time is 9 ms in the anterior region and 6 ms in the posterior region. The corresponding inversely reconstructed isochrone map, determined from the inversely computed endocardial potentials, is shown in Fig 17B⇓. Two distinct regions of early activation can be observed in Fig 17B⇓: the earliest activation time is 20 ms in the anterior region and 14 ms in the posterior region. A map of pseudoisochrones determined on the probe surface from the measured probe potentials themselves is shown in Fig 18⇓ for the double stimuli protocol of Fig 16C⇑. Notice that a single broad region of early activation is reflected on the probe surface; the earliest activation time is 14 ms. This suggests that for multiple cardiac events, maps of pseudoisochrones constructed directly from the measured probe potentials do not always reflect the complexity of the underlying cardiac sources and can be misleading in determining the cardiac activation pattern.
In the pacing protocol of Fig 19⇓, the two pacing sites were moved closer to each other (separated by 22.4 mm); the posterior pacing site (in Fig 14⇑) was moved toward the lateral LV while maintaining the anterior site in the same location as before. Probe position was the same as in the previous protocol. At 11 ms, measured endocardial potentials display two minima at the anterior and lateral sites (Fig 19A⇓-I), −44.16 mV and −21.84 mV in magnitude, respectively. Two potential minima initially appear on the probe surface (Fig 19A⇓-II): −0.76 mV and −0.08 mV in magnitude for the respective anterior and lateral sites (at 11 ms). The inversely computed endocardial potentials (Fig 19A⇓-III) accurately depict the pacing sites by the location of the potential minima: −4.79 mV for the anterior and −2.88 mV for the lateral. At 16 ms, measured endocardial potentials reveal two minima in Fig 19B⇓-I: −44.96 mV for the anterior site and −23.30 mV for the lateral site. Notice that the simultaneously measured probe potentials reveal only a single broad minimum −5.2 mV in magnitude (Fig 19B⇓-II). This demonstrates the smoothing effect of the volume conductor on probe potentials; an observation that was presented earlier in an idealized model of the probe-heart-torso volume conductor for different configurations of equivalent myocardial sources.7 However, when the probe potential data of Fig 19B⇓-II are used to compute the inverse solution, the reconstructed endocardial potentials (Fig 19B⇓-III) exhibit two potential minima at the locations of the two pacing nodes. The anterior potential minimum is −19.26 mV and the lateral minimum is −9.05 mV in magnitude.
Probe Position and Orientation
In the clinical environment, the probe position and orientation will have to be determined using noninvasive imaging methods. This will introduce an uncertainty in the geometry that will translate to an error in the matrix A of Equation 4 (in “Methods”) and, in turn, in the computed endocardial potentials. It is important, therefore, to study the sensitivity of the approach to uncertainty in the geometry. The effect of error in determining probe position on the inversely recovered endocardial potentials was assessed by adding a 5-mm shift (error) to the probe position determined in the experiment (see “Methods”). The measured probe potentials of Fig 7⇑ were used to inversely compute the endocardial potentials in the presence of a 5-mm shift of the probe, toward the anterior LV (Fig 20⇓). The potentials in Fig 20⇓ were computed at the same time frames of Fig 7⇑. The results of Fig 7⇑ provided a baseline for comparison in the absence of the imposed geometric error. In Fig 20A⇓ (at 13 ms), a potential minimum −3.84 mV in magnitude appears at the pacing node; the same location as in Fig 7A⇑-III. Furthermore, note the similarity in the orientation of the positive region with respect to the negative region in the two figures. At a later time frame (18 ms), the positive region expands in a counterclockwise fashion with respect to the negative region (Fig 20B⇓) in a similar fashion as in Fig 7B⇑-III. The potential minimum is −4.08 mV and is located at the pacing node. At 23 ms (Fig 20C⇓), the negative region becomes more extensive with a potential minimum of −24.25 mV, accompanied by further counterclockwise expansion of the positive region.
The effect of error in probe position due to 5-mm shift toward the septum (instead of toward anterior LV, the situation explored in Fig 20⇑) was studied in Fig 21⇓ for the same pacing protocol of Fig 7⇑. The inversely computed potentials in Fig 21⇓ exhibit a similar potential distribution to that of Fig 7⇑ (in the absence of position error) in terms of the orientation of the positive and negative regions, as well as the counterclockwise expansion. The potential minimum appears 9 mm away (at the closest septal node) from the pacing site in both Fig 21A⇓ (13 ms) and Fig 21B⇓ (18 ms) (−3.21 mV and −4.58 mV in magnitude, respectively). The potential minimum in Fig 21C⇓ (23 ms) is −36.68 mV and appears 1.2 mm away from the pacing site.
The effect of error in determining the probe orientation (rotation along its axis) on the inverse solution was tested by rotating the probe by a certain angle relative to the orientation as determined in the experiment and using the measured probe potential data to compute the inverse solution. The data of the pacing protocol of Fig 16⇑ were used in evaluating the effect of error in probe orientation. For an error of 5 degrees (Fig 22A⇓), the potential minima (anterior, −14.57 mV; posterior, −5.85 mV) do not change in location. For an error of 10 degrees (Fig 22B⇓), the anterior potential minimum (−10.91 mV) remains in the same location, whereas the posterior minimum (−3.66 mV) shifts toward the septum (direction of the rotational error) by 11 mm, to the node closest to the pacing site.
Important information on the electrophysiolgical condition of the heart can be obtained from the endocardial potential distribution and its evolution in time. Mapping the potentials from the entire endocardial surface, on a beat-by-beat basis, is therefore a very desirable procedure during electrophysiological testing. As reviewed in the introduction, current techniques of simultaneous mapping from many endocardial sites (eg, using an endocardial balloon) require open heart surgery. Our goal is to develop a catheter-based, nonsurgical technique for simultaneous mapping of endocardial potentials and activation sequences (isochrones). Our general approach is to reconstruct mathematically the endocardial potentials from potentials measured in the cavity by a noncontact catheter probe. Implementing this approach clinically, in the electrophysiology laboratory, requires not only measuring the cavity potentials with a multielectrode catheter but also noninvasive determination of the probe position and orientation relative to the endocardial surface. In this article, we focus on the difficult key step of computing the endocardial potentials from potentials measured with a noncontact intracavitary probe. Developing the methodology and demonstrating the ability to reconstruct endocardial potentials with acceptable accuracy are essential to the development of the entire approach as a clinical tool.
The endocardial surface is easily accessible with intravascular electrode catheters during routine electrophysiology studies. However, current electrode catheter mapping techniques are limited in the number of recording sites, are time consuming, and do not account for possible beat-to-beat variations in the activation pattern or changes in the mechanism of the arrhythmia. In addition, brief arrhythmias may not be adequately mapped. The endocardial balloon or sponge mapping technique provides direct measurements of the endocardial surface potentials from multiple sites simultaneously. However, the balloon (or sponge) mapping procedure is limited in use, as it requires a complicated surgery. It is not always possible to induce sustained tachycardias in the operating room, and, furthermore, arrhythmias induced during surgery may be of different morphology or mechanism than those observed preoperatively. The approach presented in this study, for the inverse reconstruction of endocardial potentials from intracavitary potential data, involves the use of multielectrode catheter probes that can be percutaneously introduced into the cavity in a way that is similar to electrode catheters used in electrophysiology studies. Although the probes used in the present study were relatively large, the same methodology used here for the inverse reconstruction could be applied to a smaller size cylindrical catheter probe, such as the 9F (3 mm) multielectrode catheter used earlier by Taccardi and his colleagues.5 This “noncontact” mapping approach is aimed at providing isopotential and isochronal maps of the endocardial surface in a way that is similar to the endocardial balloon approach but without using the balloon or without the need for surgery. In addition, similar to the balloon, the inverse problem mapping technique is carried out over a single cardiac cycle. That is, mapping would be conducted on a beat-by-beat basis and could essentially allow for mapping nonsustained arrhythmias or infrequent ectopic events during routine electrophysiology studies. Moreover, with the advent of catheter-based ablation techniques,37 38 the inverse mapping approach would be ideal for localizing arrhythmogenic sites and specific components in these sites (eg, the area of slow conduction in a reentry pathway) before ablation, without the need for surgery.
As mentioned above, the same mathematical methods used in this study would be applied to a smaller catheter probe. Although a smaller probe would result in greater smoothing of its potentials,39 certain computational procedures would improve. For example, the surface elements of the probe (triangles) will be smaller, and error due to interpolation over the probe surface elements will be reduced in the mathematical formulation of the boundary element method.11 Qualitatively, the inverse solutions obtained in case 1 (65-electrode probe) were as good as the solutions obtained in case 2 (81-electrode probe, effectively). In both cases, the pacing sites could be localized with good accuracy. The effect of rotational anisotropy of the fibers was reflected in the inverse solutions in both cases equally well (in terms of clockwise and counterclockwise rotation). Further experiments are needed to compare the inverse solution obtained with different probe diameters and designs, as well as to determine the minimum number of electrodes on the probe surface required for obtaining sufficient resolution.
The computational methods used in this work were very efficient. All computations were run on a desk-top workstation. The total time to construct the geometry matrix A (in Equation 4) and to compute the inverse solution for all the equipotential maps throughout the cardiac cycle (sampled at 1 frame per millisecond) takes less than 60 seconds. This makes the inverse reconstruction method practical for mapping in the clinical as well as the experimental laboratory.
The specific objective of the present study was to develop and test a mathematical method to reconstruct the endocardial potential distribution from intracavitary potentials measured with a noncontact, multielectrode probe. Intracavitary probe potentials were measured, in an isolated and perfused canine LV, during rhythms induced by electrical stimuli applied at different locations and varying depths within the myocardium. These measured probe potentials, together with a knowledge of the geometry of the probe-cavity volume conductor, were used to reconstruct the potentials on the endocardial surface. The actual endocardial potentials were also measured simultaneously and served as the gold standard for evaluating the accuracy of the reconstruction. The reconstructed endocardial potentials were assessed for their ability to locate the site of origin of electrical stimuli; to distinguish between multiple, simultaneous cardiac events at different sites; to reflect the effect of the underlying cardiac fiber direction; and to recover the sequence of endocardial activation.
The results confirm that LV wall pacing gives rise to a potential minimum on the probe surface, facing the region of stimulation. Moreover, the results demonstrate that the inversely computed endocardial potentials, from the measured probe potentials, reconstruct with good accuracy the major features (potential maxima and minima, regions of negative and positive potentials) compared with the actual measured endocardial potentials. Note that the reconstructed potential magnitudes are reduced compared with the measured amplitudes. This is a property of the regularization scheme that constrains the magnitudes of the reconstructed potential in a least-squares sense. However, the spatial pattern of the potential distribution and the sequence of activation (isochrones) are preserved by the regularization approach. During early activation, the computed endocardial potentials exhibit a potential minimum on the endocardial surface in close proximity to the pacing site, determining the location of the stimulus with good accuracy (within 10-mm error) in a similar way to the measured endocardial potentials. Simultaneously applied stimuli from multiple locations, as close as 10 to 20 mm apart, can be separated (distinguished) from each other and localized to their corresponding sites of origin by the reconstruction procedure. The ability to reconstruct local cardiac events would be valuable in locating the site of origin of ventricular arrhythmias. This includes tachycardias resulting from ectopic activity or from circus movement reentry.40 Furthermore, the reconstruction method could detect changes in the mechanism of the tachycardia or a shift in the ectopic focus to a new site. The resolution of the reconstructed maps suggests that a reentrant circuit, with a radius as small as 10 to 20 mm, could be detected. Mapping the Wolff-Parkinson-White syndrome with one or, more important, two Kent bundles and two preexcitation sites is another possible clinical application, particularly when one of the sites is septal and therefore is more difficult to detect with the usual procedures.
Previously, Macchi and colleagues18 19 attempted to localize the site of origin of paced ventricular beats in the canine heart using a similar intracavitary probe. The approach was to represent the cardiac ectopic source by two equivalent dipoles of equal strength and opposite polarity, with the ectopic focus located at the midpoint of the line connecting the dipoles. The position and moment of the equivalent source were then obtained by minimizing the difference between the computed (forward problem) and the measured potentials on the surface of the intracavitary probe in an infinite conducting medium. This approach is limited to locating a single site of ectopic activity at an early time frame (QRS onset); unlike the reconstruction method presented here, it does not provide a spatial distribution of the potentials on the endocardial surface and cannot be used to locate multiple sites of ectopic activity. Furthermore, the method is not suited for studying the sequence of activation or progression of excitation.
The results of this study demonstrate that the spatial distribution of the reconstructed endocardial potentials (positions and relative orientation of maxima and minima and of the negative and positive regions) correlates well, in a qualitative sense, with the measured potentials and reflects the underlying cardiac fiber direction. The measured and computed endocardial potentials show that the initial pattern of activation due to a stimulus at a certain level (depth) within the myocardium reflects the fiber direction at that level. Earlier investigations23 24 25 26 27 28 29 30 31 32 33 showed that myocardial tissue anisotropy affects the potentials generated during cardiac excitation by determining the shape of the activation wave front (the isochrone), influencing the strength and distribution of the cardiac sources and modifying the potential fields generated by these sources. Studies showed that as a consequence of anisotropy, ectopic excitation spreads faster in a direction parallel to the cardiac fibers than perpendicular to them (resulting in ellipsoidal-like isochrones). The axial component of the cardiac sources due to point (ectopic) stimulation plays a dominant role in determining the associated potential field compared with the much weaker transverse component. As a result, the orientation of the region of positive endocardial potentials with respect to the negative region reflects the direction of the fibers at the level of the stimulus within the myocardium. This property is captured in the reconstructed endocardial potential distribution. In addition, the progression of depolarization is reflected well in the development of both the measured and computed endocardial potentials. As depolarization progresses, the negative potentials increase in magnitude and, at the same time, regions of positive potentials expand in a clockwise or counterclockwise fashion around the negative regions, as a consequence of the influence of the fiber rotation on the spread of the excitation wave fronts. The influence of fiber rotation through deep myocardial layers (“rotational anisotropy”) on wave front propagation was demonstrated in the canine myocardium28 29 30 31 32 33 and in a macroscopic model of the ventricular tissue that incorporates the anisotropic properties of the myocardium.35 36 In the present study, the measured and the computed endocardial potential distributions show that for a subendocardial stimulus, the region of positive potentials expands in a counterclockwise fashion around the negative region. This is due to the influence of counterclockwise rotation of the fibers, from endocardium to epicardium, on the propagating wave front. Conversely, the potential distributions exhibit a clockwise rotation for stimuli originating from subepicardial sites. Stimuli applied at midwall tend to result in rotational expansion of the positive regions in both directions. These results demonstrate that not only do the reconstructed endocardial potentials localize the pacing site on the endocardial surface but they can also detect the depth of the site of origin as revealed by the relative orientation of positive and negative regions and by the progression of the potential pattern during depolarization.
The limited spatial resolution we achieved in our experiments, particularly in the experiment of Fig 7⇑, where only 52 needles were distributed through the entire wall plus septum, made it difficult to define the potential distributions in the positive areas in great detail. Despite this, correlation between endocardial potential patterns and fiber direction can be inferred from the data presented as discussed above and demonstrated in “Results” by direct correlation with fiber direction determined histologically.
Theoretically, according to the oblique dipole layer theory,10 20 one expects a pacing stimulus to produce a potential pattern with one minimum and two maxima. However, this typical pattern was not necessarily observed in all of the measured and reconstructed potential maps for one or more of the following reasons: (1) low resolution due to the limited number of recording needles or probe electrodes may have obscured one of the maxima. (2) Due to the convoluted shape of the real endocardial surface, the endocardial fibers were not necessarily parallel to the “endocardial” surface defined by the tips of the needles. Also, the direction of the intramural fibers is not perfectly parallel to the endocardium (ie, they form an angle of attack at the endocardial surface). (3) Purkinje involvement during endocardial pacing may indeed have complicated the potential patterns because of additional wave fronts. However, previously recorded epicardial maps32 33 showed that Purkinje involvement did not suppress the rotation-expansion of the epicardial potential pattern. (4) Blood attenuates the potentials, a property that was demonstrated earlier by the authors in an idealized model of the probe-heart-torso geometry.
Results of isochrone maps show a good correspondence between the isochrones determined from the reconstructed endocardial potentials and those determined from the actual measured endocardial potentials. Pattern of activation (propagation of the wave front) and regions of earliest and latest activation can be observed from the isochrones determined from both the measured and the computed potentials. Regions of earliest activation are located in the vicinity of the pacing site. Earliest activation times (time of endocardial breakthrough) for pacing stimuli that originate deep in the myocardium are longer than activation times for subendocardial stimuli. However, pseudoactivation times determined directly from the probe surface, as well as activation times determined from the reconstructed endocardial potentials, appear delayed compared with the activation times determined directly from the measured endocardial potentials. Similar behavior was observed in the potential distributions, where probe potentials and, consequently, the computed endocardial potentials increase sufficiently in magnitude when the cardiac sources become sufficiently developed. The probe-cavity volume conductor geometric and conductive effects result in smoothed-out and low-amplitude probe potentials. As depolarization progresses, the signal-to-noise ratio in the reconstructed endocardial potentials improves, and primary features can then be realized, after an “apparent delay.” In this study, the regularization method is formulated under the assumption of time-independent quasistationary conditions, that is, steady-state conditions apply at any instant of time. Taking advantage of the fact that the process of cardiac excitation is continuous in time, Oster and Rudy41 incorporated information from the time progression of excitation in the regularization procedure. Results of using the temporal information in the inverse reconstruction of epicardial potentials from body surface potential data demonstrated a marked improvement in the inverse solution. In particular, physiological events not detected early enough by the quasistatic approach could be detected at the time of their occurrence using the temporal approach. A similar approach that incorporates temporal information in the inverse solution can also be adopted to the probe-endocardium inverse problem discussed here.
Although attempts were made to obtain as accurate a discretization of the endocardial surface as possible, determining the geometry of the endocardium and the probe position within the cavity were major sources of error. Ideally, the exact endocardial geometry and probe position should be determined at the time of the potential measurements. In our experiments, the endocardial geometry was obtained at a later time. After the completion of the experiment, the cavity was filled with gelatin wax to preserve its geometry. However, the myocardium changed its properties on termination of perfusion, resulting in alteration of the position of the intramural needles (distances between neighboring needle tip electrodes were in the order of 0.5 to 1.0 cm). Furthermore, all of the computations were made under the assumption of a single cavity geometry (end-diastolic volume) throughout the experiment, whereas the amount of blood filling varied from one pacing protocol to another. The probe-endocardium geometric relation was determined by finding the probe position that minimized the differences between the measured probe potentials and those computed from the measured endocardial potentials (the latter constitutes a solution to the forward problem). The position so determined approximates the actual position of the probe during the experiments. However, an error is introduced since the endocardial geometry used in the computation differs somewhat from the endocardial geometry at the time of the potential measurement, as explained above. Despite this error, and considering the results of simulating additional error in probe position and orientation (Figs 20⇑, 21⇑, and 22⇑), the results demonstrate that the inverse solution is robust in the presence of geometric errors. This property is very encouraging in terms of the clinical application of the approach. In fact, using existing noninvasive techniques in the clinical electrophysiology laboratory, the probe position can be determined at the time of the potential measurement. Consequently, the geometry determination is likely to be more accurate in patients than we could achieve in the experiments. Recent reports by Derfus et al42 43 to assess the effect of uncertainty in probe position on estimating endocardial potentials in an idealized geometry and, subsequently, in an exposed canine heart have presented concerns in regard to the feasibility of the inverse reconstruction of endocardial potentials from the measured probe potentials. Our results, from the present study as well as previous simulations,17 suggest that actual potential magnitudes computed by the inverse solution are sensitive to error in geometry and probe position. Nevertheless, the potential distribution itself and its spatial characteristics (eg, locations of maxima and minima) are not as sensitive to error in geometry. Even in the presence of geometric uncertainties, the reconstructed endocardial potential patterns determine, with good accuracy, the location of pacing sites at different positions and intramural depths. The potential distributions also reflect correctly the fibrous structure of the myocardium (“rotational anisotropy”) and its effect on the activation wave front and the associated myocardial sources. In addition, isochronal maps constructed from the inversely computed endocardial potentials provide accurate information on the sequence and pattern of endocardial activation.
In summary, in the present study we developed methodology, tested the accuracy, and demonstrated the feasibility of reconstructing endocardial potential maps from intracavitary potentials measured by a noncontact multielectrode probe. The reconstruction procedure is the key step in the development of a catheter-based technique that can be applied in the clinical electrophysiology laboratory. It must be emphasized that, in the present study, the probe position/orientation and cavity geometry were determined invasively in a way that cannot be applied clinically. However, the demonstrated feasibility and good performance of the reconstruction procedure and its robustness in the presence of geometric errors indicate that it can be combined with noninvasive imaging methods for determining the geometry. In fact, noninvasive methods used clinically in patients may yield probe-cavity geometry measurements that are more accurate than our experimental method. One such technique that can determine the endocardial geometry and probe position with high measurement accuracy is transesophageal echocardiography.44 45 Other imaging techniques that are available in the clinical electrophysiology laboratory should also be examined. The successful performance of the potential reconstruction procedure developed here suggests that combining it with a clinically applicable method for determining the geometry should be the next step in its development as a clinical tool.
This study was supported by National Institutes of Health grants HL-33343 (Dr Rudy) and HL-43276 (Dr Taccardi), American Heart Association National Center Grant-in-Aid 91006370 (Dr Rudy), and awards from the Nora Eccles Treadwell Foundation and the Richard A. and Nora Eccles Harrison Fund for Cardiovascular Research. The authors would like to thank Yonild Lian, BS, for her assistance in the experiments.
Reprint requests to Prof Yoram Rudy, Department of Biomedical Engineering, 505 Wickenden Bldg, Case Western Reserve University, Cleveland, OH 44106-7207.
- Received June 10, 1994.
- Accepted August 19, 1994.
- Copyright © 1995 by American Heart Association
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