@Article{RSM:Rog94,
  author =       "J.M. Rogers and A.D. McCulloch",
  title =        "A collocation--Galerkin finite element model of
                 cardiac action potential propagation.",
  journal =      j-BME,
  year =         "1994",
  month =        aug,
  volume =       "41",
  number =       "8",
  pages =        "743--757",
  robnote =      "A new computational method was developed for modeling
                 the effects of the geometric complexity, nonuniform
                 muscle fiber orientation, and material inhomogeneity of
                 the ventricular wall on cardiac impulse propagation.
                 The method was used to solve a modification to the
                 FitzHugh-Nagumo system of equations. The geometry,
                 local muscle fiber orientation, and material parameters
                 of the domain were defined using linear Lagrange or
                 cubic Hermite finite element interpolation. Spatial
                 variations of time-dependent excitation and recovery
                 variables were approximated using cubic Hermite finite
                 element interpolation, and the governing finite element
                 equations were assembled using the collocation method.
                 To overcome the deficiencies of conventional
                 collocation methods on irregular domains, Galerkin
                 equations for the no-flux boundary conditions were used
                 instead of collocation equations for the boundary
                 degrees-of-freedom. The resulting system was evolved
                 using an adaptive Runge-Kutta method. Converged
                 two-dimensional simulations of normal propagation
                 showed that this method requires less CPU time than a
                 traditional finite difference discretization. The model
                 also reproduced several other physiologic phenomena
                 known to be important in arrhythmogenesis including:
                 Wenckebach periodicity, slowed propagation and
                 unidirectional block due to wavefront curvature,
                 reentry around a fixed obstacle, and spiral wave
                 reentry. In a new result, we observed wavespeed
                 variations and block due to nonuniform muscle fiber
                 orientation. The findings suggest that the finite
                 element method is suitable for studying normal and
                 pathological cardiac activation and has significant
                 advantages over existing techniques.",
  bibdate =      "Mon Jan 8 18:24:04 2007",
}

{"_id":"STixwEExLwrBgkz4x","bibbaseid":"rogers-mcculloch-acollocationgalerkinfiniteelementmodelofcardiacactionpotentialpropagation-1994","downloads":0,"creationDate":"2016-07-01T21:38:39.952Z","title":"A collocation–Galerkin finite element model of cardiac action potential propagation.","author_short":["Rogers, J.","McCulloch, A."],"year":1994,"bibtype":"article","biburl":"http://www.sci.utah.edu/~macleod/Bibtex/biglit.bib","bibdata":{"bibtype":"article","type":"article","author":[{"firstnames":["J.M."],"propositions":[],"lastnames":["Rogers"],"suffixes":[]},{"firstnames":["A.D."],"propositions":[],"lastnames":["McCulloch"],"suffixes":[]}],"title":"A collocation–Galerkin finite element model of cardiac action potential propagation.","journal":"j-BME","year":"1994","month":"August","volume":"41","number":"8","pages":"743–757","robnote":"A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.","bibdate":"Mon Jan 8 18:24:04 2007","bibtex":"@Article{RSM:Rog94,\n author = \"J.M. Rogers and A.D. McCulloch\",\n title = \"A collocation--Galerkin finite element model of\n cardiac action potential propagation.\",\n journal = j-BME,\n year = \"1994\",\n month = aug,\n volume = \"41\",\n number = \"8\",\n pages = \"743--757\",\n robnote = \"A new computational method was developed for modeling\n the effects of the geometric complexity, nonuniform\n muscle fiber orientation, and material inhomogeneity of\n the ventricular wall on cardiac impulse propagation.\n The method was used to solve a modification to the\n FitzHugh-Nagumo system of equations. The geometry,\n local muscle fiber orientation, and material parameters\n of the domain were defined using linear Lagrange or\n cubic Hermite finite element interpolation. Spatial\n variations of time-dependent excitation and recovery\n variables were approximated using cubic Hermite finite\n element interpolation, and the governing finite element\n equations were assembled using the collocation method.\n To overcome the deficiencies of conventional\n collocation methods on irregular domains, Galerkin\n equations for the no-flux boundary conditions were used\n instead of collocation equations for the boundary\n degrees-of-freedom. The resulting system was evolved\n using an adaptive Runge-Kutta method. Converged\n two-dimensional simulations of normal propagation\n showed that this method requires less CPU time than a\n traditional finite difference discretization. The model\n also reproduced several other physiologic phenomena\n known to be important in arrhythmogenesis including:\n Wenckebach periodicity, slowed propagation and\n unidirectional block due to wavefront curvature,\n reentry around a fixed obstacle, and spiral wave\n reentry. In a new result, we observed wavespeed\n variations and block due to nonuniform muscle fiber\n orientation. The findings suggest that the finite\n element method is suitable for studying normal and\n pathological cardiac activation and has significant\n advantages over existing techniques.\",\n bibdate = \"Mon Jan 8 18:24:04 2007\",\n}\n\n","author_short":["Rogers, J.","McCulloch, A."],"key":"RSM:Rog94","id":"RSM:Rog94","bibbaseid":"rogers-mcculloch-acollocationgalerkinfiniteelementmodelofcardiacactionpotentialpropagation-1994","role":"author","urls":{},"metadata":{"authorlinks":{}},"downloads":0,"html":""},"search_terms":["collocation","galerkin","finite","element","model","cardiac","action","potential","propagation","rogers","mcculloch"],"keywords":[],"authorIDs":[],"dataSources":["5HG3Kp8zRwDd7FotB"]}