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Effective dynamics of twisted and curved scroll waves using virtual filaments

Hans Dierckx (UGent) and Henri Verschelde (UGent)
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Abstract
Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.
Keywords
LINEAR-STABILITY, COMPUTATIONAL MODELS, VORTEX DYNAMICS, RESONANT DRIFT, FIBER ROTATION, ELECTRIC-FIELD, VENTRICULAR-FIBRILLATION, EXCITABLE MEDIA, 3-DIMENSIONAL CONTINUOUS MYOCARDIUM, ROTATING SPIRAL WAVES

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Citation

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MLA
Dierckx, Hans, and Henri Verschelde. “Effective Dynamics of Twisted and Curved Scroll Waves Using Virtual Filaments.” PHYSICAL REVIEW E 88.6 (2013): n. pag. Print.
APA
Dierckx, H., & Verschelde, H. (2013). Effective dynamics of twisted and curved scroll waves using virtual filaments. PHYSICAL REVIEW E, 88(6).
Chicago author-date
Dierckx, Hans, and Henri Verschelde. 2013. “Effective Dynamics of Twisted and Curved Scroll Waves Using Virtual Filaments.” Physical Review E 88 (6).
Chicago author-date (all authors)
Dierckx, Hans, and Henri Verschelde. 2013. “Effective Dynamics of Twisted and Curved Scroll Waves Using Virtual Filaments.” Physical Review E 88 (6).
Vancouver
1.
Dierckx H, Verschelde H. Effective dynamics of twisted and curved scroll waves using virtual filaments. PHYSICAL REVIEW E. 2013;88(6).
IEEE
[1]
H. Dierckx and H. Verschelde, “Effective dynamics of twisted and curved scroll waves using virtual filaments,” PHYSICAL REVIEW E, vol. 88, no. 6, 2013.
@article{4357650,
  abstract     = {Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.},
  articleno    = {062907},
  author       = {Dierckx, Hans and Verschelde, Henri},
  issn         = {1539-3755},
  journal      = {PHYSICAL REVIEW E},
  keywords     = {LINEAR-STABILITY,COMPUTATIONAL MODELS,VORTEX DYNAMICS,RESONANT DRIFT,FIBER ROTATION,ELECTRIC-FIELD,VENTRICULAR-FIBRILLATION,EXCITABLE MEDIA,3-DIMENSIONAL CONTINUOUS MYOCARDIUM,ROTATING SPIRAL WAVES},
  language     = {eng},
  number       = {6},
  pages        = {24},
  title        = {Effective dynamics of twisted and curved scroll waves using virtual filaments},
  url          = {http://dx.doi.org/10.1103/PhysRevE.88.062907},
  volume       = {88},
  year         = {2013},
}

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