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dc.creatorUgarte J.P.
dc.creatorTobón C.
dc.creatorLopes A.M.
dc.creatorMachado J.A.T.
dc.descriptionCardiac tissue is characterized by structural and cellular heterogeneities that play an important role in the cardiac conduction system. Under persistent atrial fibrillation (persAF), electrical and structural remodeling occur simultaneously. The classical mathematical models of cardiac electrophysiological showed remarkable progress during recent years. Among those models, it is of relevance the standard diffusion mathematical equation, that considers the myocardium as a continuum. However, the modeling of structural properties and their influence on electrical propagation still reveal several limitations. In this paper, a model of cardiac electrical propagation is proposed based on complex order derivatives. By assuming that the myocardium has an underlying fractal process, the complex order dynamics emerges as an important modeling option. In this perspective, the real part of the order corresponds to the fractal dimension, while the imaginary part represents the log-periodic corrections of the fractal dimension. Indeed, the imaginary part in the derivative implies characteristic scales within the cardiac tissue. The analytical and numerical procedures for solving the related equation are presented. The sinus rhythm and persAF conditions are implemented using the Courtemanche formalism. The electrophysiological properties are measured and analyzed on different scales of observation. The results indicate that the complex order modulates the electrophysiology of the atrial system, through the variation of its real and imaginary parts. The combined effect of the two components yields a broad range of electrophysiological conditions. Therefore, the proposed model can be a useful tool for modeling electrical and structural properties during cardiac conduction. © 2020 World Scientific Publishing Company.
dc.publisherWorld Scientific
dc.subjectAtrial Electrophysiologyspa
dc.subjectAtrial Fibrillationspa
dc.subjectComplex Order Derivativesspa
dc.subjectMyocardium Heterogeneitiesspa
dc.subject.keywordStructural propertieseng
dc.subject.keywordCardiac conductionseng
dc.subject.keywordComplex-order derivativeseng
dc.subject.keywordElectrical and structural propertieseng
dc.subject.keywordElectrical propagationeng
dc.subject.keywordElectrophysiological propertieseng
dc.subject.keywordMathematical equationseng
dc.subject.keywordNumerical procedureseng
dc.subject.keywordStructural remodelingeng
dc.subject.keywordFractal dimensioneng
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.affiliationUgarte, J.P., GIMSC, Facultad de Ingenieriás, Universidad de San Buenaventura, Medellín, Colombia
dc.affiliationTobón, C., MATBIOM, Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
dc.affiliationLopes, A.M., UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal
dc.affiliationMachado, J.A.T., Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugal
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