{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1929"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1929","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Modeling of Spiral Waves Arising in Atrial Fibrillation","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Cummins, James"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Cox, Christopher","Belinskiy, Boris; Rubenstein, Donald","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:47:06Z","subjects":["Atrial fibrillation--Mathematical models","Differential equations, Parabolic"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/747","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Cox, Christopher","Belinskiy, Boris; Rubenstein, Donald","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Cummins, James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05-01T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Atrial fibrillation--Mathematical models","Differential equations, Parabolic"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/747"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","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."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Modeling of Spiral Waves Arising in Atrial Fibrillation"]}]}],"canonical_facts":{"dc:contributor":["Cox, Christopher","Belinskiy, Boris; Rubenstein, Donald","College of Arts and Sciences"],"dc:creator":["Cummins, James"],"dc:date":["2022-05-01T07:00:00Z"],"dc:description":["Dept. of Mathematics","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."],"dc:description.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."],"dc:identifier":["https://scholar.utc.edu/theses/747"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Atrial fibrillation--Mathematical models","Differential equations, Parabolic"],"dc:title":["Modeling of Spiral Waves Arising in Atrial Fibrillation"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:47:06Z"}