Insights into the intracardiac electrogram from analytical and numerical modelling

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.

Estimation of the uncertainty in internal dose calculation for two contamination cases

The assessment of internal dose is subject to a large uncertainty due to the limits of measuring technique and to the assumptions made by the expert. Here, we propose an approach to report the confidence interval associated with the evaluated dose. The sources of uncertainties considered so far include the date of intake, the physico-chemical characteristics of the radioactive material, the counting error and the stochastic variability of excretion. Three successive levels of approximation are suggested, depending on the expected dose, for which increasingly realistic parameter values should be sought and applied. Finally, the results of a Monte Carlo dose calculation are presented in the form of a statistical distribution of possible dose values. This approach has been applied to two cases of uranium and caesium exposure.

In situ measurements of optical parameters in Lake Baikal with the help of a Neutrino telescope

We present results of an experiment performed in Lake Baikal at a depth of approximately 1 km. The photomultipliers of an underwater neutrino telescope under construction at this site were illuminated by a distant laser. The experiment not only provided a useful cross-check of the time calibration of the detector but also allowed us to determine inherent optical parameters of the water in a way that was complementary to standard methods. In 1997 we measured an absorption length of 22 m and an asymptotic attenuation length of 18 m. The effective scattering length was measured as 480 m. By use of (cos theta) = 0.95 (0.90) for the average scattering angle, this length corresponds to a geometric scattering length of 24 (48) m.

Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart

BACKGROUND

Ventricular tachycardia may result from vortexlike reentrant excitation of the myocardium. Our general hypothesis is that in the structurally normal heart, these arrhythmias are the result of one or two nonstationary three-dimensional electrical scroll waves activating the heart muscle at very high frequencies.

METHODS AND RESULTS

We used a combination of high-resolution video imaging, electrocardiography, and image processing in the isolated rabbit heart, together with mathematical modeling. We characterized the dynamics of changes in transmembrane potential patterns on the epicardial surface of the ventricles using optical mapping. Image processing techniques were used to identify the surface manifestation of the reentrant organizing centers, and the location of these centers was used to determine the movement of the reentrant pathway. We also used numerical simulations incorporating Fitzhugh-Nagumo kinetics and realistic heart geometry to study how stationary and nonstationary scroll waves are manifest on the epicardial surface and in the simulated ECG. We present epicardial surface manifestations (reentrant spiral waves) and ECG patterns of nonstationary reentrant activity that are consistent with those generated by scroll waves established at the right and left ventricles. We identified the organizing centers of the reentrant circuits on the epicardial surface during polymorphic tachycardia, and these centers moved during the episodes. In addition, the arrhythmias that showed the greatest movement of the reentrant centers displayed the largest changes in QRS morphology. The numerical simulations showed that stationary scroll waves give rise to monomorphic ECG signals, but nonstationary meandering scroll waves give rise to undulating ECGs characteristic of torsade de pointes.

CONCLUSIONS

Polymorphic ventricular tachycardia in the healthy, isolated rabbit heart is the result of either a single or paired ("figure-of-eight") nonstationary scroll waves. The extent of the scroll wave movement corresponds to the degree of polymorphism in the ECG. These results are consistent with our numerical simulations that showed monomorphic ECG patterns of activity for stationary scroll waves but polymorphic patterns for scroll waves that were nonstationary.

Rotating Spiral Waves Created by Geometry

The Belousov-Zhabotinsky reagent and numerical simulations were used to show that under high-frequency stimuli, rotating spiral waves can be initiated in a homogeneous excitable medium in the vicinity of domain boundaries or inexcitable barriers with sharp corners.