Rotor termination is critically dependent on kinetic properties of I kur inhibitors in an in silico model of chronic atrial fibrillation

Abstract

Inhibition of the atrial ultra-rapid delayed rectifier potassium current (I Kur) represents a promising therapeutic strategy in the therapy of atrial fibrillation. However, experimental and clinical data on the antiarrhythmic efficacy remain controversial. We tested the hypothesis that antiarrhythmic effects of I Kur inhibitors are dependent on kinetic properties of channel blockade. A mathematical description of I Kur blockade was introduced into Courtemanche-Ramirez-Nattel models of normal and remodeled atrial electrophysiology. Effects of five model compounds with different kinetic properties were analyzed. Although a reduction of dominant frequencies could be observed in two dimensional tissue simulations for all compounds, a reduction of spiral wave activity could be only be detected in two cases. We found that an increase of the percent area of refractory tissue due to a prolongation of the wavelength seems to be particularly important. By automatic tracking of spiral tip movement we find that increased refractoriness resulted in rotor extinction caused by an increased spiral-tip meandering. We show that antiarrhythmic effects of I Kur inhibitors are dependent on kinetic properties of blockade. We find that an increase of the percent area of refractory tissue is the underlying mechanism for an increased spiral-tip meandering, resulting in the extinction of re-entrant circuits.

Figure 1. Electrophysiological properties of cAF tissue.

(A) Simulated AP recordings of isolated cells from normal (solid line) and remodeled atrial tissue (dashed line). (B) Restitution of ERP under physiological conditions (solid lines) and cAF (dashed lines). (C, D) CV and WL restitution for physiological conditions (solid lines) and cAF (dashed lines).

Figure 2. Pharmacological properties of simulated I _Kur inhibition.

(A) Effect of inhibition on I _Kur elicited by a simulated voltage step (500 ms) to +30 mV (see inset). (B) Effect of the different inhibitory model compounds on AP trajectories in cells from normal atrial tissue. (C) Depending on the kinetic properties, I _Kur inhibition resulted in an elevation of the plateau potential (#1, #2, and #3) as well as AP prolongation (#1, #2, #3, and #5) in cells from cAF tissue. (D) Effects of onset and recovery time constants on the non-blocked fraction of I _Kur blockade established at a pacing rate of 1 Hz. The underlying AP derived from a cAF cell is depicted in a dashed line.

Figure 3. Electrophysiological properties of remodeled atrial tissue under I _Kur inhibition.

Restitution curves of the APD (A), ERP (B), CV (C), and WL (D) under different types of I _Kur inhibition. Whereas APD, ERP, and WL restitution exhibits a strong dependence on kinetic properties of I _Kur inhibitors, the CV is not affected.

Figure 4. Percent area of refractory tissue.

(A) Spiral wave activity of a single rotor under control cAF conditions and after inhibition with all five test compounds displayed at the end of the 5^th second. The transmembrane voltage is color-coded with blue representing −80 mV and yellow representing 0 mV. (B) Summarized data of the mean percentage of refractory tissue quantified over the last 4 seconds of inhibition (control: 17.2%, #1: 22.2%, #2: 16.8%, #3: 19.1%, #4: 16.6%, #5: 16.2%).

Figure 5. Automated analysis of spiral wave activity.

(A) Sequence of images (in 20 ms steps) of spiral wave activity under control cAF conditions starting at the 10^th second. The transmembrane voltage is color-coded with blue representing −80 mV and yellow representing 0 mV. (B) Exemplary time interval (10^th to 15^th second) of the simulated unipolar pseudo-electrocardiogram (pseudo-ECG) recorded at the center of the atrial layer under control conditions. (C) Normalized power spectral density of atrial activation derived from the pseudo-ECG. (D) Number of rotors automatically detected by our analysis algorithm.

Figure 6. Rotor analysis under pharmacological I _Kur inhibition.

(A) Number of spiral waves followed over a time period of 30 seconds. (B) Normalized power spectral density of electrical activity in remodeled tissue under control conditions and under I _Kur inhibition.

Figure 7. Effects of I _Kur inhibition on spiral tip meandering.

Spatiotemporal arrangement of the spiral tips followed over a period of 30(color coded time scale: blue = early, red = late). Under control cAF conditions (A), five rotor centers were detected with high spatiotemporal stability. Similar results were obtained for the inhibitory compounds #2 (C), #4 (E), and #5 (F). However, when applying the compound #1 (B) or compound #3 (D), pronounced destabilization was observed paralleled by an extinction of rotors.