title: Modeling for cardiac excitation propagation based on the Nernst-Planck equation and homogenization.
abstract: The bidomain model is a commonly used mathematical model of the electrical properties of the cardiac muscle that takes into account the anisotropy of both the intracellular and extracellular spaces. However, the equations contain self-contradiction such that the update of ion concentrations does not consider intracellular or extracellular ion movements due to the gradient of electric potential and the membrane charge as capacitive currents in spite of the fact that those currents are taken into account in forming Kirchhoff's first law. To overcome this problem, we start with the Nernst-Planck equation, the ionic conservation law, and the electroneutrality condition at the cellular level, and by introducing a homogenization method and assuming uniformity of variables at the microscopic scale, we derive rational bidomain equations at the macroscopic level.
authors.affiliation: Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8563, Japan. okada@sml.k.u-tokyo.ac.jp
authors.forename: Jun-ichi
authors.initials: J
authors.lastname: Okada
authors.forename: Seiryo
authors.initials: S
authors.lastname: Sugiura
authors.forename: Toshiaki
authors.initials: T
authors.lastname: Hisada
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006329:Heart Conduction System / Q000502:physiology*; D006801:Humans; D015640:Ion Channel Gating / Q000502:physiology; D007473:Ion Channels / Q000502:physiology*; D008564:Membrane Potentials / Q000502:physiology*; D008955:Models, Cardiovascular; D009431:Neural Conduction / Q000502:physiology*
chemical_list: D007473:Ion Channels