Electrical waves that rotate in the heart organize dangerous cardiac arrhythmias. Finding the region around which such rotation occurs is one of the most important practical questions for arrhythmia management. For many years, the main method for finding such regions was so-called phase mapping, in which a continuous phase was assigned to points in the heart based on their excitation status and defining the rotation region as a point of phase singularity. Recent analysis, however, showed that in many rotation regimes there exist phase discontinuities and the region of rotation must be defined not as a point of phase singularity, but as a phase defect line. In this paper, we use this novel methodology and perform a comparative study of three different phase definitions applied to in silico data and to experimental data obtained from optical voltage mapping experiments on monolayers of human atrial myocytes. We introduce new phase defect detection algorithms and compare them with those that appeared in literature already. We find that the phase definition is more important than the algorithm to identify sudden spatial phase variations. Sharp phase defect lines can be obtained from a phase derived from local activation times observed during one cycle of arrhythmia. Alternatively, similar quality can be obtained from a reparameterization of the classical phase obtained from observation of a single timeframe of transmembrane potential. We found that the phase defect line length was (35.9 ± 6.2)mm in the Fenton-Karma model and (4.01 ± 0.55)mm in cardiac human atrial myocyte monolayers. As local activation times are obtained during standard clinical cardiac mapping, the methods are also suitable to be applied to clinical datasets. All studied methods are publicly available and can be downloaded from an institutional web-server.

Intracardiac electrograms (iEGMs) are time traces of the electrical potential recorded close to the heart muscle. We calculate unipolar and bipolar iEGMs analytically for a myocardial slab with parallel myofibers and validate them against numerical bidomain simulations. The analytical solution obtained via the method of mirrors is an infinite series of arctangents. It goes beyond the solid angle theory and is in good agreement with the simulations, even though bath loading effects were not accounted for in the analytical calculation. At a large distance from the myocardium, iEGMs decay as 1/R (unipolar), 1/R2 (bipolar and parallel), and 1/R3 (bipolar and perpendicular to the endocardium). At the endocardial surface, there is a mathematical branch cut. Here, we show how a thicker myocardium generates iEGMs with larger amplitudes and how anisotropy affects the iEGM width and amplitude. If only the leading-order term of our expansion is retained, it can be determined how the conductivities of the bath, torso, myocardium, and myofiber direction together determine the iEGM amplitude. Our results will be useful in the quantitative interpretation of iEGMs, the selection of thresholds to characterize viable tissues, and for future inferences of tissue parameters.

Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): FWO-Flanders, KU Leuven internal starting grant Introduction and Purpose Cardiac electrograms (EGMs) are one of the most important recordings obtained during electroanatomical voltage mapping and lie at the basis for planning most clinical electrophysiological interventions. Despite its widespread use, the relation of EGM shape and amplitude to the underlying excitation patterns and properties of cardiac tissue is not completely understood. Recent clinical studies [1] have provided important new guidelines on the relation between EGM amplitudes and the thickness of myocardial walls. The aim of this study is to quantify the effect of the wall thickness on EGM amplitudes and duration using analytical and in-silico approaches. Methods We study bipolar EGMs both in-silico and analytically in a homogeneous slab of cardiac tissue (70 x 70 x L mm), where L = 2, 5, or 10 mm, with parallel fiber direction. Simulations were performed using the cardiac electrophysiology simulator openCARP [2]. Cardiac cells were described by the ten Tusscher-Panfilov 2006 model (TP06) [4] with epicardial tissue parameters. A plane wave propagating along the fiber direction was initiated. The extracellular voltage at 147 points arranged in a hemisphere around a point was measured to study the effect of bipolar electrode orientation (see Fig. 1A [3]). In addition, we developed an analytical approach to obtain an EGM, using an equivalent dipole representation of the depolarization wavefront and analytical evaluation of the corresponding integrals. Results Fig. 1B and 1C show the dependency of the EGM properties on the electrode orientation, as represented by the angles α (incidence angle) and β (angle between electrode and propagation direction) [3]. Solid lines represent data from a state-of-the-art numerical methodology, the dashed lines show our analytical estimations. Both the peak-to-peak amplitude and EGM width are well approximated by our theory for all orientations of the electrodes. Fig. 2 shows how the EGM is influenced by the myocardial wall thickness L. Both the amplitude and the duration are in good agreement with our theory. We observe that the amplitude as well as the width increase with the slab thickness, confirming the result in [1] but also delivering an accurate analytical expression for this change. It may thus allow to discriminate effects of thickness and other factors affecting the EGMs, such as substrate abnormalities, for example. Conclusion We developed an analytical approach which can correctly describe the amplitude, duration, and shape of the depolarization part of the EGM. Our theory agrees with the previous in-silico and clinical studies on the influence of catheter orientation [3,5], and wall thickness [1,3]. Subsequent work in this direction is expected to provide better guidelines for clinical interpretation of EGMs, accounting for the effects of the thickness of myocardial wall in the characterization of the substrate of cardiac arrhythmias.

Electrical waves that rotate in the heart organize dangerous cardiac arrhythmias. Finding the region around which such rotation occurs is one of the most important practical questions for arrhythmia management. For many years, the main method for finding such regions was so-called phase mapping, in which a continuous phase was assigned to points in the heart based on their excitation status and defining the rotation region as a point of phase singularity. Recent analysis, however, showed that in many rotation regimes there exist phase discontinuities and the region of rotation must be defined not as a point of phase singularity, but as a phase defect line. In this paper we use this novel methodology and perform comparative study of three different phase definitions applied to in-silico data and to experimental data obtained from optical voltage mapping experiments on monolayers of human atrial myocytes. We introduce new phase defect detection algorithms and compare them with those that appeared in literature already. We find that the phase definition is more important than the algorithm to identify sudden spatial phase variations. Sharp phase defect lines can be obtained from a phase derived from local activation times observed during one cycle of arrhythmia. Alternatively, similar quality can be obtained from a reparameterization of the classical phase obtained from observation of a single timeframe of transmembrane potential. We found that the phase defect line length was (35.9 ± 6.2) mm in the Fenton-Karma model and (4.01 ± 0.55) mm in cardiac human atrial myocyte monolayers. As local activation times are obtained during standard clinical cardiac mapping, the methods are also suitable to be applied to clinical datasets. All studied methods are publicly available and can be downloaded from an institutional web-server.