A comparison of noninvasive reconstruction of epicardial versus transmembrane potentials in consideration of the null space.

We compare two source formulations for the electrocardiographic forward problem in consideration of their implications for regularizing the ill-posed inverse problem. The established epicardial potential source model is compared with a bidomain-theory-based transmembrane potential source formulation. The epicardial source approach is extended to the whole heart surface including the endocardial surfaces. We introduce the concept of the numerical null and signal space to draw attention to the problems associated with the nonuniqueness of the inverse solution and show that reconstruction of null-space components is an important issue for physiologically meaningful inverse solutions. Both formulations were tested with simulated data generated with an anisotropic heart model and with clinically measured data of two patients. A linear and a recently proposed quasi-linear inverse algorithm were applied for reconstructions of the epicardial and transmembrane potential, respectively. A direct comparison of both formulations was performed in terms of computed activation times. We found the transmembrane potential-based formulation is a more promising source formulation as stronger regularization by incorporation of biophysical a priori information is permitted.

A new spatiotemporal regularization approach for reconstruction of cardiac transmembrane potential patterns.

The single-beat reconstruction of electrical cardiac sources from body-surface electrocardiogram data might become an important issue for clinical application. The feasibility and field of application of noninvasive imaging methods strongly depend on development of stable algorithms for solving the underlying ill-posed inverse problems. We propose a novel spatiotemporal regularization approach for the reconstruction of surface transmembrane potential (TMP) patterns. Regularization is achieved by imposing linearly formulated constraints on the solution in the spatial as well as in the temporal domain. In the spatial domain an operator similar to the surface Laplacian, weighted by a regularization parameter, is used. In the temporal domain monotonic nondecreasing behavior of the potential is presumed. This is formulated as side condition without the need of any regularization parameter. Compared to presuming template functions, the weaker temporal constraint widens the field of application because it enables the reconstruction of TMP patterns with ischemic and infarcted regions. Following the line of Tikhonov regularization, but considering all time points simultaneously, we obtain a linearly constrained sparse large-scale convex optimization problem solved by a fast interior point optimizer. We demonstrate the performance with simulations by comparing reconstructed TMP patterns with the underlying reference patterns.

ECG mapping and imaging of cardiac electrical function.

Inverse electrocardiography has been developed for several years. By coupling electrocardiographic mapping and 3D-time anatomical data, the electrical excitation sequence can be imaged completely non-invasively in the human heart. In this study, a bidomain theory based surface heart model activation time imaging approach was applied to single beat data of atrial and ventricular depolarization. For sinus and paced rhythms, the sites of early activation and the areas with late activation were estimated with sufficient accuracy. In particular for focal arrhythmias, this model-based imaging approach might allow the guidance and evaluation of antiarrhythmic interventions, for instance, in case of catheter ablation or drug therapy.

Atrial noninvasive activation mapping of paced rhythm data.

INTRODUCTION: Atrial arrhythmias have emerged as a topic of great interest for clinical electrophysiologists. Noninvasive imaging of electrical function in humans may be useful for computer-aided diagnosis and treatment of cardiac arrhythmias, which can be accomplished by the fusion of data from ECG mapping and magnetic resonance imaging (MRI). METHODS AND RESULTS: In this study, a bidomain-theory-based surface heart model activation time (AT) imaging approach was applied to paced rhythm data from four patients. Pacing sites were the right superior pulmonary vein, left inferior pulmonary vein, left superior pulmonary vein, coronary sinus, posterior wall of right atrium, and high right atrium. For coronary sinus pacing, the AT pattern of the right atrium was compared with a CARTO map. The root mean square error between CARTO geometry (85 nodal points) and the surface model of the right atrium was 8.6 mm. The correlation coefficient of the noninvasively obtained AT map of the right atrium and the CARTO map was 0.76. All pulmonary vein pacing sites were identified. The reconstructed pacing site of right posterior atrial pacing correlates with the invasively determined pacing catheter position with a localization distance of 4 mm. CONCLUSION: The individual anatomic model of the atria of each patient enables accurate noninvasive AT imaging within the atria, resulting in a localization error for the pacing sites within 10 mm. Our findings may have implications for imaging of atrial activity in patients with focal arrhythmias or focal triggers.

Electrocardiographic imaging of atrial and ventricular electrical activation.

Inverse electrocardiography has been developing for several years. By combining measurements obtained by electrocardiographic body surface mapping with three-dimensional anatomical data, one can non-invasively image the electrical activation sequence in the human heart. In this study, an imaging approach that uses a bidomain theory-based surface heart model was applied to single-beat data of atrial and ventricular activation. We found that for sinus and paced rhythms, the sites of early activation and the areas with late activation were estimated with sufficient accuracy. In particular, for focal arrhythmias, this model-based imaging approach might allow the guidance and evaluation of antiarrhythmic interventions, for instance, in case of catheter ablation or drug therapy.

Model-based imaging of cardiac electrical excitation in humans.

Activation time (AT) imaging from electrocardiographic (ECG) mapping data has been developing for several years. By coupling ECG mapping and three-dimensional (3-D) + time anatomical data, the electrical excitation sequence can be imaged completely noninvasively in the human heart. In this paper, a bidomain theory-based surface heart model AT imaging approach was applied to single-beat data of atrial and ventricular depolarization in two patients with structurally normal hearts. In both patients, the AT map was reconstructed from sinus and paced rhythm data. Pacing sites were the apex of the right ventricle and the coronary sinus (CS) ostium. For CS pacing, the reconstructed AT pattern on the endocardium of the right atrium was compared with the CARTO map in both patients. The localization errors of the origins of the initial endocardial breakthroughs were determined to be 6 and 12 mm. The sites of early activation and the areas with late activation were estimated with sufficient accuracy. The reconstructed sinus rhythm sequence was in good qualitative agreement with the pattern previously published for the isolated Langendorff-perfused human heart.

Clinical ECG mapping and imaging of cardiac electrical excitation.

Combining electrocardiographic mapping and 3D+time anatomical data enables noninvasively the imaging of the electrical excitation sequence in the human heart. A bidomain-theory based surface heart model activation time imaging approach was employed to image single beat data of atrial and ventricular depolarisation. Activation time maps were reconstructed for three patients who underwent an electrophysiologic study. The sinus rhythm and a rhythm according to a pacing protocol were reconstructed for two patients. For the third patient the accessory pathway of the WPW syndrome was localized. For focal arrhythmias, this model-based imaging approach might allow the guidance and evaluation of antiarrhythmic interventions, for instance, in case of catheter ablation or drug therapy.