The maximum A posteriori approach to the inverse problem of electrocardiography.

In this paper we investigate the previously proposed maximum a posteriori (MAP) approach to the problem of determining epicardial potentials from measured body surface potentials, a form of the inverse problem of electrocardiography. The MAP inverse approach uses a priori knowledge of the covariances between epicardial electrograms in its estimate of epicardial potentials. However, in practice, this information is not generally available. In this paper we examined the effectiveness of this method when the covariances are estimated using one depolarization sequence and the MAP method is used with these covariances to estimate the epicardial potentials for a different depolarization sequence.

A new method for incorporating weighted temporal and spatial smoothing in the inverse problem of electrocardiography.

In this paper, we present a method for incorporating temporal smoothing (TS) into the estimate of epicardial potentials from body surface potential data. Our algorithm employs a different spatial smoothing parameter, chosen by the composite residual error and smoothing operator criteria, at each time step in the sequence. The total spatial smoothing term is then simply partitioned between temporal and spatial smoothing. The algorithm appears to be quite robust with regard to this partitioning. The new method was evaluated in the setting of additive Gaussian noise, but otherwise realistic conditions of body geometry and reference epicardial potentials. In examining the match between estimated and measured electrograms, or the match between estimated isopotential maps and measured isopotential maps, the estimates constructed using the new TS algorithm produced consistently smaller relative errors than those constructed using a quasi-static (QS) algorithm or those constructed by postprocessing the QS estimate with a moving average filter.

Parameter choice methods and temporal filtering for the generalized eigensystem method applied to the inverse problem of electrocardiography.

We have previously proposed the generalized eigensystem (GES) method as a modal expansion method for estimating electrical potentials on the heart outer surface from measurements of electrical potentials on the body surface. In this paper, we present an alternative formulation of GES more like that of classical Tikhonov regularization where a single continuous parameter needs to be chosen. We then compare this formulation of GES with zero order Tikhonov regularization on data collected from a swine experiment with the swine heart paced from six different sites. Although the inverse problems are solved at each time instant independently, we also incorporate temporal information by moving average filtering the estimates, and this is more effective for the GES methods than for Tikhonov.

Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging.

Various approaches to the solution to the inverse problem of electrocardiography have been proposed over the years. Recently, the use of inverse algorithms using measured body surface Laplacians has been proposed, and in various studies this technique has been shown to outperform the traditional use of body surface potentials in certain model problems. In this paper, we compare the use of body surface potentials and body surface Laplacians on two model problems with different assumed cardiac sources. For the spherical cap model problems with an anterior source, the epicardial estimates using body surface potentials had smaller average relative errors than when body surface Laplacians were used. For the spherical cap model problems with a posterior source, the epicardial estimates using body surface potential or body surface Laplacian sensors generally produced similar relative errors. For the radial dipole model, the epicardial estimates using body surface Laplacians had smaller errors than when body surface potentials were used. We introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.

Generalized eigensystem techniques for the inverse problem of electrocardiography applied to a realistic heart-torso geometry.

We have previously proposed two novel solutions to the inverse problem of electrocardiography, the generalized eigensystem technique (GES) and the modified generalized eigensystem technique (tGES), and have compared these techniques with other numerical techniques using both homogeneous and inhomogeneous eccentric spheres model problems. In those studies we found our generalized eigensystem approaches generally gave superior performance over both truncated singular value decomposition (SVD) and zero-order Tikhonov regularization (TIK). In this paper we extend the comparison to the case of a realistic heart-torso geometry. With this model, the GES and tGES approaches again provide smaller relative errors between the true potentials and the numerically derived potentials than the other methods studied. In addition, the isopotential maps recovered using GES and tGES appear to be more accurate than the maps recovered using either SVD and TIK.

Higher order regularization techniques for inverse electrocardiography.

We have previously presented the generalized eigensystem (GES) approach as an alternative to truncated singular value decomposition and zero order Tikhonov regularization methods for the ill-conditioned inverse problem of electrocardiography. In this paper we extend our comparison of GES with Tikhonov regularization utilizing higher order regularizers applied to a realistic heart/torso geometry with measured epicardial and body surface potentials. Utilizing higher order regularizers the results from Tikhonov regularization more closely match those of the GES techniques.

Vector expansion techniques for the inverse problem of electrocardiography: application to a realistic heart-torso geometry.

We have previously compared four numerical techniques utilizing both a homogeneous and inhomogeneous eccentric sphere model problem. In those studies we found that the Generalized Eigensystem approach generally gave superior performance over both truncated singular value decomposition and zero order Tikhonov regularization. In this paper we extend the comparison to the case of a realistic heart-torso geometry. With this model, the generalized eigensystem approach again provides superior performance as measured by both relative error and correlation coefficient.

The effects of errors in assumed conductivities and geometry on numerical solutions to the inverse problem of electrocardiography.

In this paper we used a previously proposed model problem to examine the effects of inhomogeneities on four techniques for numerically solving the inverse problem of electrocardiography. The layered inhomogeneous eccentric spheres system contains three regions representing the lungs, muscle, and subcutaneous fat, and is numerically modeled using finite elements. We simulated both anterior and posterior spherical cap activation fronts. We examined inverse solutions based on zero order Tikhonov regularization, truncated singular value decomposition, our new generalized eigensystem approach, and a modification of the generalized eigensystem approach. The effects on the inverse solutions of geometrical errors, errors in the assumed conductivities, and homogeneous torso assumptions were examined.

The effects of noise and errors in heart size on numerical techniques for the inverse problem of electrocardiography.

In this study we examine the effects of both noise and geometrical errors on four numerical methods proposed for solving the inverse problem of electrocardiography. The heart-body system is modeled using an inhomogeneous eccentric sphere model. The cardiac source is modeled as a double layer spherical cap with either an anterior or posterior location. Epicardial potentials determined using the numerical techniques were compared with the analytically determin potentials in the presence of both noise and errors in assumed geometry.

Scatter diagram analysis: a new technique for discriminating ventricular tachyarrhythmias.

With the increasing flexibility allowed by implantable cardioverter defibrillators that use tiered therapy, it is important to match the therapy with the arrhythmia. In this article we present scatter diagram analysis, a new computationally efficient two-channel algorithm for distinguishing monomorphic ventricular tachycardia (VT) from polymorphic ventricular tachycardia and ventricular fibrillation (VF). Scatter diagram analysis plots the amplitude from one channel versus the amplitude from another channel on a graph with a 15 x 15 grid. The fraction (percentage) of the 225 grid blocks occupied by at least one sample point is then determined. We found that monomorphic VT traces nearly the same path in space and occupies a smaller percentage of the graph than a nonregular rhythm such as polymorphic VT or VF. Scatter diagram analysis was tested on 27 patients undergoing intraoperative implantable cardioverter defibrillator testing. Passages of 4.096 seconds were obtained from rate (bipolar epicardial) and morphology (patch) leads, and digitized at 125 Hz. Scatter diagram analysis distinguished 13 episodes of monomorphic VT (28.6% +/- 4.0%) from 27 episodes of polymorphic VT or VF (48.0% +/- 8.2%) with P < 0.0005. There was overlap in only one monomorphic VT episode and one polymorphic VT or VF episode.

A generalized eigensystem approach to the inverse problem of electrocardiography.

We develop a new approach to the ill-conditioned inverse problem of electrocardiography which employs finite element techniques to generate a truncated eigenvector expansion to stabilize the inversion. Ordinary three-dimensional isoparametric finite elements are used to generate the conductivity matrix for the body. We introduce a related eigenproblem, for which a special two-dimensional isoparametric area matrix is used, and solve for the lowest eigenvalues and eigenvectors. The body surface potentials are expanded in terms of the eigenvectors, and a least squares fit to the measured body surface potentials is used to determine the coefficients of the expansion. This expansion is then used directly to determine the potentials on the surface of the heart. The number of measurement points on the surface of the body can be less than the number of finite element nodes on the body surface, and the number of modes employed in the expansion can be adjusted to reduce errors due to noise.

Efficient algorithms for detecting changes in intraventricular electrogram morphology.

Computing a correlation coefficient between a stored template of a normal beat and subsequent beats is a widely used indicator of changes in electrogram morphology. While effective, this method is quite computationally demanding, particularly for use in implantable devices with limited available power. We investigated methods for computing a normalized autocorrelation as efficient template matching alternatives to the correlation coefficient. These four algorithms, polarity incidence (PI), hybrid sign (HS), modified hybrid sign (MHS), and relative magnitude (RM) are compared with the correlation coefficient (CC) for detecting changes in intraventricular electrogram morphology. We sought to determine the number of instances in which 75% (or 90%) of a patient's sinus rhythm beats could be distinguished from 75% (or 90%) of the patient's ventricular tachycardia beats at the 95% confidence level in 30 patients. The relative magnitude method performs nearly as well as the correlation coefficient in nearly every case but requires only 3 multiplies per application. Hence the relative magnitude algorithm may be more appropriate for implantable devices.

Detecting ventricular fibrillation using efficient techniques for computing a normalized autocorrelation.

With the introduction of the multifunction implantable pacemaker/cardioverter/defibrillator, it is increasingly important to detect and identify arrhythmias automatically. Detection of ventricular fibrillation by analysis of the autocorrelation function is widely used on surface lead ECG analysis, but due to the computational demand is not practical for use in an implantable defibrillator. In this paper, results using three computationally efficient algorithms for estimating the normalized autocorrelation are compared with the true normalized autocorrelation for discriminating polymorphic ventricular tachycardia/ventricular fibrillation (PMVT/VF) from monomorphic ventricular tachycardia (MVT) using signals available to an implantable defibrillator.

Autoregressive modeling of epicardial electrograms during ventricular fibrillation.

During ventricular fibrillation (VF), electrograms from bipolar epicardial electrodes generally appear to have little organization or structure. We sought to identify any well defined organization or structure in these signals by determining if they could be modeled as an autoregressive stochastic process with a white noise excitation during the short time period (6.5-8 s) typically used by automatic implantable defibrillators. The autoregressive model is then used to synthesize VF signals using a white noise excitation with the same probability distribution function as the estimated excitation determined from the autoregressive model for that particular true VF episode. Both the original and ten synthesized VF signals for each patient are then compared using root mean square (rms) amplitude, the number of zero crossings per second, the amplitude distribution of the signals, the rate, and percent variation of rate. The results of examining the synthesized VF waveforms indicate that the rms amplitudes are similar to the true VF waveforms. While the synthesized VF signals had higher rate, more regular RR intervals, more zero crossings per second, and spent less time at baseline than the VF signal from which they were generated, these differences are generally not significant (p > or = 0.05). The use of such synthesized VF signals may allow more thorough testing of VF detection algorithms than is possible with the present limited libraries of human VF recordings.

A comparison of four new time-domain techniques for discriminating monomorphic ventricular tachycardia from sinus rhythm using ventricular waveform morphology.

Electrical management of intractable tachycardia via implantable antitachycardia devices has become a major form of therapy. Newly advanced methods of ventricular tachycardia detection propose examination of changes in intraventricular electrogram morphology in addition to or in combination with earlier rate-based detection algorithms. Unfortunately, most of the proposed morphology analysis techniques have computational demands beyond the capabilities of present devices or may be adversely affected by amplitude and baseline fluctuations of the intraventricular electrogram. We have designed four new computationally efficient time-domain algorithms for distinguishing ventricular electrograms during monomorphic ventricular tachycardia (VT) from those during sinus rhythm using direct analysis of the ventricular electrogram morphology. All four techniques are independent of amplitude fluctuations and three of the four are independent of baseline changes. These new techniques were compared to correlation waveform analysis, a previously proposed method for distinction of VT from sinus rhythm. Evaluation of these four new algorithms was performed on data from 19 consecutive patients with 31 distinct monomorphic ventricular tachycardia morphologies. Three of the algorithms performed as well or better than correlation waveform analysis but with one-tenth to one-half the computational demands.

Identification of ventricular tachycardia using intracardiac electrograms: a comparison of unipolar versus bipolar waveform analysis.

Implantable antitachycardia devices suffer a high false-positive rate of delivery of therapy because current detection schemes based upon ventricular rate and rate variations are excessively sensitive at the cost of specificity. Several methods have been proposed for providing complementary information derived from morphologic analysis of intraventricular electrograms in order to increase specificity. The majority of these techniques have utilized bipolar electrogram analysis to detect changes in ventricular activation indicative of ventricular tachycardia. Whether bipolar or unipolar intracardiac electrogram analysis might be preferred for discriminating ventricular tachycardia from sinus rhythm has not been determined. In this study, a previously demonstrated method for identification of ventricular tachycardia using intracardiac electrograms, correlation waveform analysis, was used to analyze both unipolar and bipolar signals during sinus rhythm and ventricular tachycardia recorded during electrophysiology studies of 15 patients with inducible sustained monomorphic ventricular tachycardia. Correlation waveform analysis consistently discriminated between all depolarizations during ventricular tachycardia in 14/15 patients (93%) using either electrogram configuration; 13 of the 14 patients were common to both groups. Of these patients, 8/15 (53%) had greater separation between sinus rhythm and ventricular waveforms with bipolar electrogram analysis while 7/15 (47%) had greater separation with unipolar electrogram analysis. We conclude that morphologic analysis of unipolar and bipolar electrograms may be equally effective in distinguishing ventricular tachycardia from sinus rhythm. For individual patients, either a unipolar or bipolar ventricular configuration may be preferable, and should be chosen on a patient-specific basis during electrophysiology study prior to antitachycardia device implantation.

A time-domain analysis of intracardiac electrograms for arrhythmia detection.

The analysis of intracardiac electrogram morphology has been proposed as a complementary method for accurate discrimination between sinus rhythm (SR), supraventricular dysrhythmias, and ventricular dysrhythmias by automatic antitachycardia and cardioverter defibrillator devices. In this study, the performance of a traditional time-domain method for surface electrocardiogram interpretation--Correlation Waveform Analysis (CWA) and a newly developed technique--Bin Area Method (BAM) were used to analyze unfiltered intraatrial and intraventricular electrograms obtained from 47 patients during routine cardiac electrophysiology studies. Nineteen patients had 31 distinct, sustained, monomorphic ventricular tachycardias (VTs) induced; 13 patients had paroxysmal bundle branch block of supraventricular origin (BBB) induced; 19 patients had retrograde atrial activation during ventricular overdrive pacing. Three patients were common to two or more groups. Using a best fit electrogram alignment, both CWA and BAM distinguished VT from SR in 28/31 cases (90%), BBB from SR in 15/15 patients (100%), and anterograde from retrograde atrial activation in 19/19 patients (100%). We conclude that the use of time-domain techniques that are independent of amplitude and baseline fluctuations appear to be reliable for discrimination of retrograde atrial activation, paroxysmal BBB, and VT from SR using intracardiac electrograms. Reduction of computational time and power constraints, without sacrificing reliable dysrhythmia discrimination, is possible. These features may make real-time morphology analysis of intracardiac electrograms feasible for automatic antitachycardia and cardioverter-defibrillator devices.

Intraventricular electrogram analysis for ventricular tachycardia detection: statistical validation.

Time-domain analysis of intraventricular electrogram morphology during ventricular tachycardia (VT) and sinus rhythm or atrial fibrillation (SR/AF) has been proposed as a method for increasing the specificity of pathological tachycardia detection by antitachycardia devices. However, few studies have validated the use of such analysis with statistical methods. When statistical methods have been utilized, it has been assumed that the distribution of the values derived from analysis of the intracardiac electrograms have had a normal (gaussian) distribution. In this study, we sought to determine whether: (1) the distribution of values derived from analysis of intracardiac electrogram during SR/AF and VT is gaussian or nongaussian; and (2) the discrimination of monomorphic VT from SR/AF using SR/AF templates can be validated statistically. Two previously proposed time-domain methods--correlation waveform analysis (CWA) and area of difference (AD)--were selected for evaluation of 29 patients with 33 distinct, sustained monomorphic VTs. An initial SR/AF template was used to analyze subsequent SR/AF and VT passages with a minimum of 50 consecutive depolarizations using a "best-fit" alignment. The values derived from each analysis were examined subsequently for skewness (asymmetry) and kurtosis (shape) using two-tailed tests (P less than 0.02). For passages of SR/AF, a normal (gaussian) distribution was present in only 24% (CWA), and 45% (AD); for passages of VT, normal distribution was present in only 58% for both CWA and AD. Using appropriate statistical testing with nonparametric tolerance intervals, CWA and AD discriminated VT from SR/AF in 29 out of 33 (88%), and 30 out of 33 (91%) instances, respectively, with 95% confidence.(ABSTRACT TRUNCATED AT 250 WORDS)

The Bin Area Method: a computationally efficient technique for analysis of ventricular and atrial intracardiac electrograms.

Recent studies have reported a significant false positive rate in delivery of therapy by implantable antitachycardia devices utilizing detection algorithms based on sustained high rate. More selective decision schemes for the recognition of life-threatening arrhythmias have been recently proposed that use analysis of the intrinsic electrogram rather than rate alone. Morphological discrimination of abnormal electrograms using correlation waveform analysis (CWA) has been proposed as an effective method of intracardiac electrogram analysis, but its computational demands limit its use in implantable devices. A new method for intracardiac electrogram analysis, the bin area method (BAM), was created to detect abnormal cardiac conduction with computational requirements of one-half to one-tenth those of CWA. Like CWA, BAM is a template matching method that is sensitive to conduction changes revealed in the electrogram morphology and is independent of amplitude and baseline fluctuations. Performance of BAM and CWA were compared using bipolar right ventricular and right atrial electrode recordings from 47 patients undergoing clinical cardiac electrophysiology studies. Nineteen patients had 31 distinct monomorphic ventricular tachycardias (VTs) induced (group I), thirteen patients had paroxysmal bundle branch block of supraventricular origin (BBB) induced (group II), and 19 patients had retrograde atrial activation during right ventricular overdrive pacing (group III). (One patient was common to all three groups, and two patients were common to groups II and III.) Using the ventricular electrogram, both BAM and CWA distinguished VT from sinus rhythm in 28/31 (90%) cases, and BBB from Normal Sinus Rhythm (NSR) in 13/13 (100%) patients. Using the atrial electrogram, both BAM and CWA distinguished anterograde from retrograde atrial activation in 19/19 (100%) patients. BAM achieves similar performance to CWA with significantly reduced computational demands, and may make real-time analysis of intracardiac electrograms feasible for implantable pacemakers and antitachycardia devices.

Paroxysmal bundle branch block of supraventricular origin: a possible source of misdiagnosis in detecting ventricular tachycardia using time domain analyses of intraventricular electrograms.

Current implantable antitachycardia devices use several methods for differentiating sinus rhythm (SR) from supraventricular tachycardia (SVT) or ventricular tachycardia (VT). These methods include sustained high rate, the rate of onset, changes in cycle length, and sudden onset. Additional methods for detecting VT include techniques based upon ventricular electrogram morphology. The morphological approach is based on the assumption that the direction of cardiac activation, as sensed by a bipolar electrode in the ventricle, is different when the patient is in SR as compared to VT. Whether paroxysmal bundle branch block of supraventricular origin (BBB) can be differentiated from VT has not been determined. In this study, we compared the morphology of the ventricular electrogram during sinus rhythm with a normal QRS (SRNIQRS) or SVT with a normal QRS (SVTNIQRS) with the morphologies of BBB and VT in 30 patients undergoing cardiac electrophysiology studies. Changes in ventricular electrogram morphology were determined using three previously proposed time domain methods for VT detection: Correlation Waveform Analysis (CWA), Area of Difference (AD), and Amplitude Distribution Analysis (ADA). CWA, AD, and ADA distinguished VT from SRNIQRS or SVTNIQRS in 16/17 (94%), 14/17 (82%), and 12/17 (71%) patients, and BBB from SRNIQRS or SVTNIQRS in 15/15 (100%), 13/15 (87%), and 6/15 (40%) patients, respectively. However, the ranges of values during BBB using these methods overlapped with ranges of values during VT in all cases for CWA, AD, and ADA. Hence, BBB may be a source of misdiagnosis in detecting VT when these time domain methods are used for ventricular electrogram analysis.