Scroll wave with negative filament tension in a model of the left ventricle of the human heart and its overdrive pacing

Nonlinear waves of electrical excitation initiate cardiac contraction. Abnormal wave propagation in the heart, e.g., spiral waves, can lead to sudden cardiac arrest. This study analyzed the dynamics of spiral waves under the influence of an instability called negative filament tension, and examined how the spiral waves can be eliminated through high-frequency pacing. A generic anatomical model of the left ventricle of the human heart and the Aliev–Panfilov model for cardiac tissue were used. The study showed that the source of such arrhythmia is elongated filaments with lengths that can be 10–20 times greater than the characteristic thickness of the heart wall. In anisotropic tissue, the filament elongated before it was annihilated at the base of the heart. The spiral waves were eliminated through overdrive pacing with stimulation periods from 0.8 to 0.95 relative to the spiral wave period. The minimum time for the expulsion was about 10 s.

Figure 1

Examples of scroll wave filaments without the low-voltage pacing. (a) Isotropy, $t=21.5$ s; (b) anisotropy, $\eta =4, t=21.5$ s; (c) anisotropy, $\eta =9, t=12.2$ s; and (d) anisotropy, $\eta =9, t=22.4$ s. The epicardium is colored depending on the $z$ coordinate. The mesh is the endocardium. The apical thickness is 6 mm.

Figure 2

Filament length (mm) versus time (s) for isotropic [red (light gray)] and anisotropic [black and blue (dark gray)] LV models without pacing. The apical thickness is 6 mm.

Figure 3

High-frequency pacing of a scroll wave before (left, $t=3$ s) and during (right, $t=4.5$ s) the induced drift. Isotropic LV model with the apical thickness of 6 mm. Low-voltage pacing with the period $T_{\mathrm{stim}}=22.1$ MTU $=265$ ms. The potential $u$ is multiplied by 100 and color coded.

Figure 4

Filament trajectories at the endocardium [red (gray) curves] and filament examples (black curves). (a) Isotropy, (b) moderate anisotropy ($\eta =4$), and (c) high anisotropy ($\eta =9)$. Pacing period $T_{\mathrm{stim}}=22.1$ MTU, equal to $0.85T_{\mathrm{sw}}$. The filaments are shown at different times, and the later filaments are closer to the base and drawn thicker. The apical thickness is 6 mm. In (b), labels 1–4 denote filaments at times 1.34, 4.4, 5.0, and 5.4 s that are referred to in the text.

Figure 5

Length of the filaments (mm) versus time (s). The high-frequency pacing with the period 22.1 MTUs is enabled. The gray line shows the moment when the pacing started. Isotropy [red (light gray)], moderate anisotropy $\eta =4$ (black), and high anisotropy $\eta =9$ [blue (dark gray)]. The apical thickness is 6 mm.