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A Fast Numerical Method for Large-Scale Modeling of Cardiac Tissue and Linear Perturbation Theory for the Study and Control of Cardiac Spiral Wave Breakup

Allexandre, Didier
http://rave.ohiolink.edu/etdc/view?acc_num=case1094046834

Abstract Details

2004, Doctor of Philosophy, Case Western Reserve University, Biomedical Engineering.
Ventricular fibrillation and tachycardia are the leading causes of sudden cardiac death in the United States. Yet, despite extensive research, their nature as well as the electrophysiological mechanisms responsible for their initiation and sustenance are not fully understood. Researchers have suggested that the breakup of a spiral wave, a vortex-like electrical wave, may be one major mechanism by which tachycardia can evolve into fibrillation. We therefore apply linear perturbation theory, a mathematical technique, to gain new insights into the electrophysiological and dynamical mechanisms underlying this phenomenon. We found spiral wave perturbation dynamics to be composed of a multitude of characteristic and independent behaviors, called eigenmodes. Along with one meandering mode, not just one but several unstable alternans modes were found with differing growth rates, frequencies and spatial structures, suggesting different electrophysiological properties. We also explored a promising new approach, based on the theory, for the design of an energy efficient electrical stimulus protocol to control spiral wave breakup. We show a particular example in which the instability of an entire spiral wave can be controlled in the linear regime over several rotation periods using a single localized stimulus applied at one instant in time. Computer simulation of cardiac activity has been another popular approach used to study arrhythmia. However, due to various numerical constraints, these simulations are computationally costly when modeling large tissue size using realistic ionic cell models. We have therefore developed a new fast variable timestep method. The method is explicit, yet highly stable, permitting the use of adaptive timesteps much larger than the limit imposed by conventional explicit methods. We perform a thorough study of computational efficiency of the method, by examining how the grid spacing, tissue size and error tolerance affect runtimes obtained for the Hodgkin-Huxley (HH) and Luo-Rudy (LRd) ion channel models. We find the method to be 2-10 times faster for the HH model and typically an order of magnitude (30-40 times) faster for LRd when compared to the conventional fixed timestep forward Euler method. It is also about twice as fast as currently available methods when applied to the LRd model.
Niels Otani (Committee Chair)
Yoram Rudy (Other)
Igor Efimov (Other)
Daniela Calvetti (Other)
216 p.
Cardiac Arrhythmia; Spiral Wave; Reentry; Fibrillation; Modeling; Computer model; Control; Electrode; Action Potential; Algorithm; Numerical method; Simulation; Finite Difference; Eigenmode; Linear Perturbation; Hodgkin-Huxley; Heart

Recommended Citations

Citations

  • Allexandre, D. (2004). A Fast Numerical Method for Large-Scale Modeling of Cardiac Tissue and Linear Perturbation Theory for the Study and Control of Cardiac Spiral Wave Breakup [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1094046834

    APA Style (7th edition)

  • Allexandre, Didier. A Fast Numerical Method for Large-Scale Modeling of Cardiac Tissue and Linear Perturbation Theory for the Study and Control of Cardiac Spiral Wave Breakup. 2004. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1094046834.

    MLA Style (8th edition)

  • Allexandre, Didier. "A Fast Numerical Method for Large-Scale Modeling of Cardiac Tissue and Linear Perturbation Theory for the Study and Control of Cardiac Spiral Wave Breakup." Doctoral dissertation, Case Western Reserve University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=case1094046834

    Chicago Manual of Style (17th edition)

case1094046834
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© 2004, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.