Slow Recovery of Excitability Increases Ventricular Fibrillation Risk as Identified by Emulation

Figure 1. Behavior of rotor-driven re-entries varies significantly in response to electrophysiological variability. (A) Induction of a rotor via cross field S1–S2 stimulus, as demonstrated by the membrane potential field 5 and 125 ms after the S2 stimulus. The S1 stimulus creates a planar wave traveling to the right, and the square region stimulated by the S2 stimulus overlaps with the waveback of the initial wave, creating directional block. While excitation propagates upwards, tissue to the right eventually recovers and allows for excitation to curl into this region, forming the beginning of a rotor-driven re-entry. (B) Example rotor trajectories and the corresponding excitation field for different choices of some model parameters. All snapshots are taken at 3,000 ms (except for the helix, which terminates early). The last 1,200 ms of rotor tip movement in each case is visualized in red. Values for the spatial biomarkers maximum distance (MD), dominant frequency (DF), and organization indices (OI) are also presented.

Figure 2. The tissue-level biomarkers CV and APD fail to predict rotor-driven re-entry behavior. The classes of model behavior observed for different values of the tissue-level biomarkers, CV, and APD, with variability in all major model parameters. Classes are assigned according to Table 2, but with the “No Rotor” classification further separated into failure to propagate excitation and early termination (almost always due to APD being too long to successfully induce a rotor with the S1–S2 stimulus) in order to make the visualization more informative. There are regions of the biomarker space where behavior is largely predictable, but on the whole, the class of behavior cannot be predicted from these biomarkers alone and clearly depends on further electrophysiological factors. This is best demonstrated by regions like the one shown in the inset.

Figure 3. The class of re-entrant behavior exhibits complex dependence on ionic properties, but is well predicted by SVM classification. (A) Training and test data after classification using the rules in Table 2. Distinct parameter regimes that correspond to the different behaviors can be observed, but with small numbers of data points, predominantly in the fibrillatory region, that disrupt clean separations of the parameter space. (B) Combination of rotors that annihilate themselves with those that exhibit wave breakup into a single “chaotic” classification allows high-accuracy prediction of rotor behavior by an SVM classifier model. Also displayed are schematic diagrams indicating the different types of rotor path that can be generated in various regions throughout the parameter space.

Figure 4. Partitioned emulation successfully captures the complex dependencies of important descriptors of re-entry on the electrophysiological substrate. The response surfaces predicted by the partitioned emulator for each biomarker are shown, along with the training data (red) used in their construction. Null values for biomarkers are denoted by a value of −1. Performance can be judged by considering the unseen test data (white), which demonstrate great agreement with the surfaces that indicate the emulator's predictions. This is achieved despite the complex and non-monotonic nature of the dependence of these biomarkers on the two varied parameters.

Figure 5. Sustained re-entries respond more consistently to the recovery of tissue excitability than to fast inward current amplitude, but slowed recovery incurs an increased risk of wave breakup. Main effects of the parameters controlling tissue excitability and its recovery. Excitability strongly controls the shape of wavetip trajectories (OI1) and rotor stability (OI4), but has less consistent effect on the critical amount of tissue for sustained re-entry (maximum distance) and re-entrant frequency. On the other hand, by modulating ERP, recovery of fast inward channels does predictably control core size and frequency in sustained re-entries, but notably, slower recovery (increased ERP) is linked to an increased risk of wave breakup.

Figure 6. Slow inward current exhibits important effects on re-entrant behavior beyond its control of APD. Main effects of the parameters controlling tissue repolarization. The conductances of the two currents that control APD are seen to strongly affect the critical size and frequency of rotor-driven re-entry, according to their modulation of ERP. However, the strengths of both of these currents exhibit a similar effect on rotor stability despite their opposing influences on APD/ERP, highlighting the importance of subtler restitution effects controlling the risk of breakup. The slow inward current also emerges as an important controller of the complexity of wavetip trajectory in the case of stable spiral waves.

Figure 7. Variability in excitability critically determines the balance of slow current conductances that produces chaotic re-entrant behaviors. Parameter maps as predicted by the classifier model. As tissue excitability (as controlled by the conductance of the fast inward current) increases, the balance of inward and outward currents that triggers chaotic re-entry behaviors shifts, highlighting its importance in interpreting APD in terms of fibrillation risk. Increased slow inward current is here consistently associated with an increased risk of wave breakup.

Figure 8. Slower recovery of excitability widens the critical window of fast inward current density that can trigger breakup, and shifts this window to higher amounts of current density. Parameter maps as predicted by the classifier model. For the lower values of τv2- plotted, the existence of a critical window of fast inward current strength associated with highest risk of wave breakup is clearly seen. As slow inward current increases in strength, this window widens and shifts to lower gfi values. Slower recovery of fast inward channel availability (larger τv2-) corresponds on the whole to destabilization of functional re-entry, but the specific effect depends also on the conductance of this current.