A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation

Abstract

In the context of cardiac electrophysiology, we propose a novel computational approach to highlight and explain the long-debated mechanisms behind atrial fibrillation (AF) and to reliably numerically predict its induction and sustainment. A key role is played, in this respect, by a new way of setting a parametrization of electrophysiological mathematical models based on conduction velocities; these latter are estimated from high-density mapping data, which provide a detailed characterization of patients' electrophysiological substrate during sinus rhythm. We integrate numerically approximated conduction velocities into a mathematical model consisting of a coupled system of partial and ordinary differential equations, formed by the monodomain equation and the Courtemanche-Ramirez-Nattel model. Our new model parametrization is then adopted to predict the formation and self-sustainment of localized reentries characterizing atrial fibrillation, by numerically simulating the onset of ectopic beats from the pulmonary veins. We investigate the paroxysmal and the persistent form of AF starting from electro-anatomical maps of two patients. The model's response to stimulation shows how substrate characteristics play a key role in inducing and sustaining these arrhythmias. Localized reentries are less frequent and less stable in case of paroxysmal AF, while they tend to anchor themselves in areas affected by severe slow conduction in case of persistent AF.

Keywords: arrhythmia; atrial fibrillation; cardiac electrophysiology; mathematical models; numerical simulation.

Figure 1

Overview of AF mechanisms generated by the interplay between functional (electrical remodeling and triggering) and structural factors (structural remodeling generated by the hemodynamics and mechanics dysfunction). We refer to Schotten et al. (2011) for the details of those mechanisms.

Figure 2

CV vector approximation procedure based on a least-squares approach.

Figure 3

Hexahedral meshes with different levels of refinement. The geometry was obtained from Zygote solid 3D heart model (Zygote Media Group Inc., 2014).

Figure 4

Feeding the model with data: numerical approximation of CV field from patient activation map and its projection onto the computational geometry.

Figure 5

LDRBM fibers distribution and projected CV field for the two patients considered in this work.

Figure 6

Comparison of activation maps numerically approximated using different space and time discretizations.

Figure 7

Persistent AF: examples of two localized reentries with different anchoring sites. An anchor point, located in an area of severe slow conduction, allows rotor's stabilization (top). Tissue heterogeneity, instead, force the rotor to travel along a functional line of block (bottom) .

Figure 8

Role of the electrical and structural remodeling in the formation of localized reentries. The formation of functional lines of block occurs in areas of heterogeneous tissue, where the wavefront is likely to meet its tail due to conduction and APD heterogeneity. In areas of severe slow conduction, the rotor stabilize thanks to the low wavefront's speed and the short APD.

Figure 9

Anchor points stabilization in area of severe slow conduction and enhanced electrical remodeling.

Figure 10

Position of localized reentry anchor points or functional lines of block in the analyzed cases generated from the CV field of the persistent patient. The progression of the disease (bottom) generates more anchor points, which sustain the localized reentries.

Figure 11

Non sustained localized reentry in paroxysmal AF.

Figure 12

Effect of a stimulus delivered before (left), after (center) or in the vulnerable window (right). Only in the latter case, the instability creates rotors that might form reentrant circuits.

Figure 13

Rotors position in unstable localized reentry in paroxysmal AF.

Figure 14

Rotors position in unstable localized reentry in paroxysmal AF. The reentry is interrupted by head-tail interaction.