Committee Chair

Cox, Christopher

Committee Member

Belinskiy, Boris; Rubenstein, Donald

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

The objective of this study is to model spirals arising in atrial fibrillation. Spiral wave fronts, known to cardiologists as cardiac rotors, are responsible for heart arrhythmias. The modeling of the path of the spiral will ultimately assist in understanding why arrhythmias occur and how to treat them. This study involved first developing a linear ray model to provide basic understanding of a rotating wave front, then generalizing to spiral models. Both the Archimedean spiral and a spiral derived from the diffusion equation are used as possible candidates to resemble cardiac rotors found in the heart. We conclude by comparing the two spirals strike frequencies to electrodes and discuss their non-Doppler anomalies.

Acknowledgments

This work would not have been possible without the help and advice of many people. I would like to thank the Department of Mathematics and the Graduate School at UTC for giving me the opportunity to continue my studies. I would like to thank Dr. Rubenstein for his discoveries, and willingness to share his research with myself and faculty at UTC. I would also like to thank Dr. Cox and Dr. Belinskiy for their invaluable knowledge.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

5-2022

Subject

Atrial fibrillation--Mathematical models; Differential equations, Parabolic

Keyword

Diffusion Equation; Atrial Fibrillation; Doppler Effect; excitable media; Differential Equations

Document Type

Masters theses

DCMI Type

Text

Extent

xii, 56 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

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