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Induced drift of scroll waves in the Aliev-Panfilov model and in an axisymmetric heart left ventricle

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Abstract
The low-voltage cardioversion-defibrillation is a modern sparing electrotherapy method for such dangerous heart arrhythmias as paroxysmal tachycardia and fibrillation. In an excitable medium, such arrhythmias relate to appearance of spiral waves of electrical excitation, and the spiral waves are superseded to the electric boundary of the medium in the process of treatment due to high-frequency stimulation from the electrode. In this paper we consider the Aliev Panfilov myocardial model, which provides a positive tension of three-dimensional scroll waves, and an axisymmetric model of the left ventricle of the human heart. Two relations of anisotropy are considered, namely, isotropy and physiological anisotropy. The periods of stimulation with an apical electrode are found so that the electrode successfully entrains its rhythm in the medium, the spiral wave is superseded to the base of the ventricle, and disappears. The results are compared in two-dimensional and three-dimensional media. The intervals of effective stimulation periods are sufficiently close to each other in the two-dimensional case and in the anatomical model. However, the use of the anatomical model is essential in determination of the time of superseding.
Keywords
IMPLANTABLE CARDIOVERTER-DEFIBRILLATORS, FIBRILLATION, TACHYCARDIA, SIMULATION, DIFFUSION, DYNAMICS, RINGS, Spiral wave, paroxysmal tachycardia, mathematical cardiology, electrotherapy, implantable cardioverter-defibrillator

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MLA
Pravdin, Sergei F., et al. “Induced Drift of Scroll Waves in the Aliev-Panfilov Model and in an Axisymmetric Heart Left Ventricle.” RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, vol. 35, no. 5, Walter De Gruyter Gmbh, 2020, pp. 273–83, doi:10.1515/rnam-2020-0023.
APA
Pravdin, S. F., Epanchintsev, Timofei, I., Nezlobinskii, T., & Panfilov, A. (2020). Induced drift of scroll waves in the Aliev-Panfilov model and in an axisymmetric heart left ventricle. RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 35(5), 273–283. https://doi.org/10.1515/rnam-2020-0023
Chicago author-date
Pravdin, Sergei F., I Epanchintsev, Timofei, Timur Nezlobinskii, and Alexander Panfilov. 2020. “Induced Drift of Scroll Waves in the Aliev-Panfilov Model and in an Axisymmetric Heart Left Ventricle.” RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING 35 (5): 273–83. https://doi.org/10.1515/rnam-2020-0023.
Chicago author-date (all authors)
Pravdin, Sergei F., I Epanchintsev, Timofei, Timur Nezlobinskii, and Alexander Panfilov. 2020. “Induced Drift of Scroll Waves in the Aliev-Panfilov Model and in an Axisymmetric Heart Left Ventricle.” RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING 35 (5): 273–283. doi:10.1515/rnam-2020-0023.
Vancouver
1.
Pravdin SF, Epanchintsev, Timofei I, Nezlobinskii T, Panfilov A. Induced drift of scroll waves in the Aliev-Panfilov model and in an axisymmetric heart left ventricle. RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING. 2020;35(5):273–83.
IEEE
[1]
S. F. Pravdin, I. Epanchintsev, Timofei, T. Nezlobinskii, and A. Panfilov, “Induced drift of scroll waves in the Aliev-Panfilov model and in an axisymmetric heart left ventricle,” RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, vol. 35, no. 5, pp. 273–283, 2020.
@article{8689433,
  abstract     = {{The low-voltage cardioversion-defibrillation is a modern sparing electrotherapy method for such dangerous heart arrhythmias as paroxysmal tachycardia and fibrillation. In an excitable medium, such arrhythmias relate to appearance of spiral waves of electrical excitation, and the spiral waves are superseded to the electric boundary of the medium in the process of treatment due to high-frequency stimulation from the electrode. In this paper we consider the Aliev Panfilov myocardial model, which provides a positive tension of three-dimensional scroll waves, and an axisymmetric model of the left ventricle of the human heart. Two relations of anisotropy are considered, namely, isotropy and physiological anisotropy. The periods of stimulation with an apical electrode are found so that the electrode successfully entrains its rhythm in the medium, the spiral wave is superseded to the base of the ventricle, and disappears. The results are compared in two-dimensional and three-dimensional media. The intervals of effective stimulation periods are sufficiently close to each other in the two-dimensional case and in the anatomical model. However, the use of the anatomical model is essential in determination of the time of superseding.}},
  author       = {{Pravdin, Sergei F. and Epanchintsev, Timofei, I and Nezlobinskii, Timur and Panfilov, Alexander}},
  issn         = {{0927-6467}},
  journal      = {{RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING}},
  keywords     = {{IMPLANTABLE CARDIOVERTER-DEFIBRILLATORS,FIBRILLATION,TACHYCARDIA,SIMULATION,DIFFUSION,DYNAMICS,RINGS,Spiral wave,paroxysmal tachycardia,mathematical cardiology,electrotherapy,implantable cardioverter-defibrillator}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{273--283}},
  publisher    = {{Walter De Gruyter Gmbh}},
  title        = {{Induced drift of scroll waves in the Aliev-Panfilov model and in an axisymmetric heart left ventricle}},
  url          = {{http://dx.doi.org/10.1515/rnam-2020-0023}},
  volume       = {{35}},
  year         = {{2020}},
}

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