Termination of Scroll Waves by Surface Impacts

Niels F. Otani, Kayleigh Wheeler, Valentin Krinsky, and Stefan Luther

Phys. Rev. Lett. 123, 068102 – Published 7 August 2019

Abstract

Three-dimensional scroll waves direct cell movement and gene expression, and induce chaos in the brain and heart. We found an approach to terminate multiple three-dimensional scrolls. A pulse of a properly configured electric field detaches scroll filaments from the surface. They shrink due to filament tension and disappear. Since wave emission from small heterogeneities is not used, this approach requires a much lower electric field. It is not sensitive to the details of the excitable medium. It may affect future studies of low-energy chaos termination in the heart.

Received 13 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.068102

Physics Subject Headings (PhySH)

Cardiac dynamics Heart diseases

Coherent structures Front propagation Heart

Electrical techniques Spiral & scroll waves

Nonlinear DynamicsPhysics of Living Systems

Authors & Affiliations

Niels F. Otani^1,*, Kayleigh Wheeler¹, Valentin Krinsky^2,3,†, and Stefan Luther^3,‡

¹School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
²CNRS, INPHYNI, 1361, route des Lucioles, 06560 Valbonne France
³Max Planck Institute for Dynamics and Self-Organization, Research Group of Biomedical Physics, Am Fassberg, 17, 37077, Göttingen, Germany

^*nfosma@rit.edu
^†valentin.krinsky@ds.mpg.de
^‡stefan.luther@ds.mpg.de

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Vol. 123, Iss. 6 — 9 August 2019

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Images

Figure 1
Simultaneous termination of multiple scroll waves. In (b)–(f) only filaments are shown (green). (b) A radial electric field pulse ( $0.92 V / cm$ ) is delivered at time $t = 0$ . (c) All filaments are disconnected from the outer hemisphere. (d)–(f) They shrink and disappear. (a) Same as (b) with the leading (red) and trailing (blue) edges of waves shown. Notations. White arrows show the sense of rotation of the waves.The membrane potential $u$ on the boundaries is displayed in muted colors (see colorbar). In (b)–(f), the ends of the filaments are color-coded blue, pink or black, depending on whether they terminate on the inner, top or outer surface, respectively. Dimensionless time $t = \hat{t} / T_{s}$ is used, where $T_{s}$ is the approximate scroll wave rotation period.
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Figure 2
Success rate of termination of all scroll waves in the hemispherical shell. The red trace shows the results for a radially directed $E$ field pulse, the blue trace, for a $z$ -directed pulse. Error brackets indicate standard error of the mean. We see that, for a radial $E$ pulse, the $E$ field amplitude, $E_{50}$ , that produces a success rate of 0.5, is approximately the same ( $1 V / cm$ ) irrespective of the number of vortices.
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Figure 3
Panel A: Mechanisms of scroll termination by a surface impact. (a) and (b) A circular cylinder: (a) Numbers near each curve indicate the angle $α$ the $E$ field makes with the filament of the scroll. (b) The rotational symmetry forces the terminating threshold to be independent of phase for $α = 0$ . (c) A graph similar to (a) measured in an elliptical cylinder. There is no rotational symmetry here. (d)–(g) The dynamics of filament detachment: (d) A scroll wave. The filament is shown in green. (e) An $E$ pulse depolarizes the rear surface. The filament disconnects from it. (f) A new segment of the filament is created (green dashed), which attaches to the upper surface. (g) The $C$ -shaped filament shrinks due to the filament tension, and eventually disappears. Panel B: Mechanisms affecting termination of a scroll. (a) Immediately after the $E$ pulse. Green dashed lines denote newly created filament segments. (b) After $1 / 4$ th of a scroll wave period. Mechanism 1. A uniform, $z$ -directed field fails to terminate a single filament. Mechanism 2. Two filaments with the opposite topological charge are terminated by the $z$ -directed field. Mechanism 3. Termination of a single filament by the radial field. Mechanism 4. Reattachment of a filament end. Mechanism 5. Reattachment of the center of a filament.
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