Incorporating Inductances in Tissue-Scale Models of Cardiac Electrophysiology
| Autor: | Simone Rossi, Boyce E. Griffith |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
0301 basic medicine
Time Factors Discretization Quantitative Biology::Tissues and Organs Action Potentials General Physics and Astronomy 030204 cardiovascular system & hematology 03 medical and health sciences 0302 clinical medicine Heart Conduction System FOS: Mathematics Humans Focus Issue: Complex Cardiac Dynamics Heart Atria Mathematics - Numerical Analysis Anisotropy Electrodes Monodomain model Mathematical Physics Physics Cardiac electrophysiology Applied Mathematics Mathematical analysis Models Cardiovascular Bidomain model Heart Numerical Analysis Computer-Assisted Statistical and Nonlinear Physics Numerical Analysis (math.NA) Action (physics) Finite element method Electrophysiological Phenomena Nonlinear system 030104 developmental biology |
| Popis: | In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and [...]. 20 pages, 12 figures |
| Databáze: | OpenAIRE |
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