Paradoxical Onset of Arrhythmic Waves from Depolarized Areas in Cardiac Tissue Due to Curvature-Dependent Instability

Figures

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  Fig. 1. Optogenetic induction of quasistable depolarized zones (red areas) leads to ectopic waves emanating from the most curved portions of the interface between tissue with ultralong and normal action potentials. (a) Time series of a single experiment showing ectopic waves originating from the corners of a square quasistable depolarized region after a first wave has passed. (b) Distribution of the oscillations amplitude during ectopic activity at the positions indicated by the green, blue, and magenta dot. (c) Generation of an ectopic wave from the “jaw tip of a Pacman.” (d) Generation of an ectopic wave from the vertex of an elliptic interface. In all figures, the symmetry is broken by the first wave passing through the medium.

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  Fig. 2. Numerical modeling of ectopic wave generation from corners of a square quasistable depolarized region in four different cardiac tissue models. For each model, a snapshot of ectopic activity and voltage signals at three different locations, indicated by the green, blue, and magenta dots, are presented. (a) Majumder-Korhonen model of neonatal rat ventricular myocytes. (b) ten Tusscher–Noble–Noble–Panfilov model of adult human ventricular myocytes. Both detailed physiological models contained an increased conductance and slow inactivation variable of the late Na+ current in the QSD tissue. (c) Aliev-Panfilov model. (d) FitzHugh-Nagumo model. Both of these simplified models contained a slow repolarizing variable, in addition to the bistable kinetics of the QSD tissue. In all snapshots of ectopic activity, the symmetry is broken by the first wave passing through the medium.

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  Fig. 3. Numerical modeling of ectopic waves in the FitzHugh-Nagumo model. (a) Modeling scheme. White zones with ultralong action potentials (i.e., quasistable depolarization) are represented by a bistable system (γ = 14), while the surrounding black zone (normal tissue) is modeled as a monostable system (γ = 1.5). (b) Snapshots of ectopic beat generation from the corner of a quasistable depolarized square after passing of an initial wave [compare to Fig. 1(a)]. (c) Distribution of oscillation amplitude for oscillatory activity in (b); [compare to Fig. 1(b)]. (d),(e) Preferential generation of ectopic activity from the highest curvature areas of Pacman-shaped (d) and elliptic (e) regions [compare to Figs. 1(c) and 1(d), respectively]. The symmetry is broken by the first wave passing through the medium in (b) and (d). The wave was coming from the bottom of the domain. (f),(g) Ectopic wave potentiation by the curvature of the border zone in radially symmetric cases. Time traces, corresponding to snap-shots, are indicated by green, blue, and magenta lines. (f) Sub-threshold nonpropagating oscillatory response from a disc of large size (low curvature). (g) Propagating periodic response from a…

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  Fig. 4. Influence of the nullcline slope 1/γ of the bistable zone on ectopic wave generation. (a)–(c) Induction of ectopic activity for γ = 20 (a), 14 (b), or 11 (c). Left panels: Nullclines. Middle panels: Space-time plots of 1D simulation. Right panels: Snap-shot from 2D simulation. (a) For γ = 20, only the stationary solution is found in 1D and 2D. (b) For γ = 14, subthreshold oscillatory activity is seen in 1D and periodic waves emanating from the corners in 2D. (c) For γ = 11, a propagating response is observed both in 1D and 2D. Like in (b), the ectopic origins are located in the corners of the bistable regions. (d) Bifurcation diagram for a curved (R = 36.0, red line) and flat (blue line) interface between the monostable (i.e., excitable) and bistable (i.e., quasistable depolarized) regions.

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  Fig. 5. (a) Localization of oscillations in corners of a bistable domain with zero Dirichlet boundary condition and γ = 8.9. (b) Schrödinger potential wells with ground energy (dashed lines) values for γ = 6.6 (red line) and γ = 13 (blue line). (c) Stability parameter Reλ for different values of γ, from the ground energy calculation of the Schrödinger eigenvalue problem. The points corresponding to γ = 6.6 and γ = 13 are indicated by red and blue dots, respectively, for matching with the potential well profiles in (b).