Examples of numerically generated vortices and their
Examples of numerically generated vortices and their organizing centers in 3-D excitable media are illustrated in Fig. 1. Panels a to d show 4 different configurations of 3-D scroll waves that were computed using the FitzHugh–Nagumo model [39,40]. Panel a shows an example of the simplest configuration of a scroll wave, which rotates around a central I-shaped filament spanning the entire myocardial wall. As shown in panel b, the filament of the scroll waves can bend into an L-shape that appears as a single spiral wave on 1 surface of the excitable medium, and breakthrough or 1-way propagation on the opposite surface. Panel c shows an example of a U-shaped filament scroll wave that is identified when a “figure-of-8” is seen on the surface and likely a breakthrough or 1-way propagation on the opposite surface. The variety of 3-D configurations may set a stage for diverse dynamic behaviors of scroll waves, even in homogeneous myocardial tissue. Under conditions of normal excitability, the filament of scroll waves is subjected to the action of “positive tension” and tends to shrink. On the other hand, under low excitability conditions, the filament is subjected to “negative tension” and tends to enlarge. Such phenomena have been predicted in a modeling study,  and we first confirmed them experimentally in isolated sheep hearts by using a simultaneous endocardial and epicardial high-resolution optical mapping setup . In these experiments, 3 CCD cameras and a cardio-endoscope enabled simultaneous recording from the epicardium of the RAA, and the LAA epicardium and endocardium.
Fig. 2 illustrates an example of an atrial scroll wave with an I-shaped filament, which rotated clockwise when viewed from the epicardial surface and counterclockwise when viewed from the endocardial surface. Phase maps of the 2 recording surfaces made it possible to detect concurrent epicardial and endocardial phase singularities (PSs) around which functional reentry was organized. Interestingly, I-shaped filament scroll waves are generally stable and long lasting, with minimal twisting under normal conditions since their butein are subject to positive tension.
Acute stretch-related AF AF is commonly associated with acute atrial dilatation and stretch [9,10,41,42]. In patients with acute myocardial infarction, heart failure and/or mitral valve disease, atrial dilatation and stretch have been widely recognized as the major pathophysiological factor of AF initiation and maintenance. Despite many studies demonstrating a significant relationship between stretch of the posterior left atrium (PLA) and PV and the dynamics of AF, [43,44] a clear role of stretch-activated channels (SACs) in these regions has not yet been established. Activation of SACs that have an ohmic IV relationship (i.e., linear voltage dependency of the ion channel conductance) causes a shortening of the action potential duration (APD) at 50% repolarization (APD50), a prolongation of APD at 90% repolarization (APD90), and a depolarization of the resting membrane potential, which may potentially result in spontaneous activity. To investigate the hypothesis that atrial dilatation is associated with arrhythmogenic sources at the PVs, we implemented in a well-characterized acute stretch-related AF (SRAF) model in sheep [45,46] that was originally described by Ravelli et al.  in a rabbit model. In this model, the intra-atrial septum was perforated and all venous orifices were closed with the exception of the inferior vena cava, which was connected to a cannula controlling the level of intra-atrial pressure (IAP). As reported previously, [45,46] sustained episodes of AF (>1h) were reproducibly induced by burst pacing when the IAP was raised to more than 10cm H2O. In Fig. 3, panels A and B depict representative DF maps from the LA free wall (LAFW) and the PLA, including the junction to the left superior PV (LSPV) during SRAF induced at IAPs of 18 and 5cm H2O, respectively. At 18cm H2O, the DF of fibrillatory activity during SRAF was higher in the PLA than in the LAFW (panel A). In contrast, the DF was roughly similar in both regions at an IAP of 5cm H2O (i.e., atrial flutter). Panel C shows representative signals recorded from the PLA (site a) and LAFW (site b) during SRAF at an IAP of 18cm H2O. The cycle length of AF activity was shorter in the PLA (site a) than in the LAFW (site b). Panel D summarizes DFmax data from 8 experiments: At IAP >10cm H2O, the PLA DFmax (12.0±0.2Hz) was significantly higher than the LAFW DFmax (10.5±0.2Hz, p<0.001), whereas at IAP less than 10cm H2O there was no significant difference in the PLA DFmax (10.8±0.3Hz) and LAFW DFmax (10.2±0.3Hz). Notably, these DFmax values in the PLA and LAFW were appreciably higher than in the RAA (7.8±0.3Hz). These results strongly suggest that a high frequency AF driver exists in the PLA near the junction to the PVs in SRAF. An analysis of spatio-temporal excitation patterns during SRAF revealed that the normalized number of spatio-temporally periodic waves in the PLA was strongly correlated with IAP (p=0.002). Furthermore, a significant positive correlation was found between IAP and the number of waves appearing from the LSPV junction in the PLA (p=0.02), but not with those emanating from the LAFW (p=0.09).