One of the mechanisms of cardiac arrhythmias is the self-organization of electrical waves in the heart. These waves can anchor to scar tissue, collagen fibers, and coronary vessels. The anchoring generates stationary electrical signals that compete with the heart's natural pacemakers. When anchored, the electrical wave acquires a geometry of a spiral in a two-dimensional system and of a scroll in three-dimensions. These patterns are also observed in the chemical medium provided by the Belousov-Zhabotinsky reaction. These two systems share the property of excitability. Reason for which, the chemical system is used as a model medium to determine the effects and mechanisms during the anchoring of scroll waves. This dissertation describes experimental and numerical results of the dynamics of three-dimensional waves in heterogeneous Belousov-Zhabotinsky reaction media. Here, the focus is on scroll rings which are scroll waves with circular geometry. These waves are characterized by their rotation around a closed filament loop. In a homogeneous medium with positive filament tension, these free filament rings contract and collapse at a rate that is a function of their curvature. In non-homogeneous media, scroll rings can anchor to hetero- geneities (i.e. unexcitable regions within the reaction medium); depending on the obstacle's size, the pinning can be a success or a failure. In this research cylindrical, spherical and toroidal-shaped heterogeneities are used to pin scroll rings. The pinning process affects the stability and the collapsing time of the filament loops. This stability means that the contraction and collapse of the filament are prevented; consequently the filament loop becomes stationary. The stabilization may be induced by filament-filament interaction in the proximity of the pinning sites. This interaction seems to induce the self-wrapping of the filament along the heterogeneity. In general, this dissertation reports the characterization of these stationary filaments and the discussion of the possible mechanism that allows the vortex stabilization. The dynamics of pinned scroll rings is also analyzed in terms of the curvature-flow model, the Burgers' equation and the Barkley model. The unpinning of filament loops anchored to spherical heterogeneities is also investigated. For this purpose electric fields of different strength are applied to the BZ-medium. In general, the electric field forces the pinned scroll ring to change its initial shape, unpin, rotate, and drift. Strong fields induces the scroll wave to expand instead of collapse and also the formation of new filaments by a wavebreak mechanism. More experimental and computational research is needed to a) explain in detail the mechanism behind the stabilization of vortices by pinning, b) understand the role of the excitability of the heterogeneity in the pinning process, and c) elucidate the robustness of the pinned structure and its dependence on the heterogeneity's characteristics. / A Dissertation submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for the degree of Doctor of
Philosophy. / Fall Semester, 2012. / November 6, 2012. / Belousov-Zhabotinsky, Excitabile media, Filament dynamics, Scroll waves, Spiral waves, Ventricular Arrhythmias / Includes bibliographical references. / Oliver Steinbock, Professor Directing Thesis; Richard Bertram, University Representative; Naresh Dalal, Committee Member; Lei Zhu, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_183571 |
| Contributors | Jiménez, Zulma A. (authoraut), Steinbock, Oliver (professor directing thesis), Bertram, Richard (university representative), Dalal, Naresh (committee member), Zhu, Lei (committee member), Department of Chemistry and Biochemistry (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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