Entropy Mapping Approach for Functional Reentry Detection in Atrial Fibrillation: An In-Silico Study

Abstract

Catheter ablation of critical electrical propagation sites is a promising tool for reducing the recurrence of atrial fibrillation (AF). The spatial identification of the arrhythmogenic mechanisms sustaining AF requires the evaluation of electrograms (EGMs) recorded over the atrial surface. This work aims to characterize functional reentries using measures of entropy to track and detect a reentry core. To this end, different AF episodes are simulated using a 2D model of atrial tissue. Modified Courtemanche human action potential and Fenton-Karma models are implemented. Action potential propagation is modeled by a fractional diffusion equation, and virtual unipolar EGM are calculated. Episodes with stable and meandering rotors, figure-of-eight reentry, and disorganized propagation with multiple reentries are generated. Shannon entropy ( S h E n ), approximate entropy ( A p E n ), and sample entropy ( S a m p E n ) are computed from the virtual EGM, and entropy maps are built. Phase singularity maps are implemented as references. The results show that A p E n and S a m p E n maps are able to detect and track the reentry core of rotors and figure-of-eight reentry, while the S h E n results are not satisfactory. Moreover, A p E n and S a m p E n consistently highlight a reentry core by high entropy values for all of the studied cases, while the ability of S h E n to characterize the reentry core depends on the propagation dynamics. Such features make the A p E n and S a m p E n maps attractive tools for the study of AF reentries that persist for a period of time that is similar to the length of the observation window, and reentries could be interpreted as AF-sustaining mechanisms. Further research is needed to determine and fully understand the relation of these entropy measures with fibrillation mechanisms other than reentries.

Keywords: Shannon entropy; approximate entropy; atrial fibrillation; entropy maps; fractionated electrograms; functional reentry; sample entropy.

Figure 1

(a) Stimulation protocol (i): the S2 stimulus occurs after S1, and it is applied to the inferior left corner of the domain. (b) Stimulation protocol (ii): S2 occurs after S1 and consists of two stimuli applied to the middle portion of the domain. For both protocols, S1 is a plane stimulus applied to the left boundary, and it generates a plane wave traveling from left to right.

Figure 2

Rotor propagation patterns generated by applying stimulation protocol (i) and (a) the paroxysmal atrial fibrillation (pAF) condition, (b) chronic AF 1 (cAF1) condition, (c) cAF2 condition. The maps correspond to the last 1000 ms of each simulation.

Figure 3

Reentry dynamics characterization maps corresponding to the rotors generated by applying stimulation protocol (i) and (a) pAF condition, (b) cAF1 condition, (c) cAF2 condition. The phase singularity (PS) trajectory is shown in the first column; Shannon entropy ($ShEn$), approximate entropy ($ApEn$), and sample entropy ($SampEn$) maps are shown from the second to the last column, respectively.

Figure 4

Figure-of-eight propagation patterns generated by applying stimulation protocol (ii) and (a) cAF2 condition, (b) cAF3 condition.

Figure 5

Reentry dynamics characterization maps corresponding to the figure-of-eight reentries generated by applying stimulation protocol (ii) and (a) cAF2 condition, (b) cAF3 condition. The PS trajectory is shown in the first column; $ShEn$, $ApEn$ and $SampEn$ maps are shown from the second to the last column, respectively.

Figure 6

Multiple-reentry propagation patterns generated by applying stimulation protocol (i) and (a) cAF4 condition, (b) cAF5 condition. Four consecutive frames are presented in each case.

Figure 7

Characterization of multiple-reentry dynamics resulting from the implementation of stimulation protocol (i) and the cAF4 condition. From (a) to (d), the maps correspond to four consecutive 1000 ms intervals. The PS trajectory is shown in the first column; $ShEn$, $ApEn$, and $SampEn$ maps are shown from the second to the last column, respectively. Red circles in the PS maps mark the occurrence of reentries. Black circles in the entropy maps mark detections matching the reentries defined in the PS maps.

Figure 8

Characterization of reentry breakup dynamics resulting from the implementation of stimulation protocol (i) and the cAF5 condition. From (a) to (d), the maps correspond to four consecutive 1000 ms intervals. The PS trajectory is shown in the first column; $ShEn$, $ApEn$, and $SampEn$ maps are shown from the second to the last column, respectively. Red contours in the PS maps mark the occurrence of reentries. Black contours in the entropy maps mark reentries detections.