{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T09:05:58Z","timestamp":1791104758776,"version":"4.1.0"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>\n                    An efficient finite element method is developed to model the spreading of excitation in ventricular myocardium by treating the thin region of rapidly depolarizing tissue as a propagating wavefront. The model is used to investigate excitation propagation in the full canine ventricular myocardium. An eikonal-curvature equation and an eikonal-diffusion equation for excitation time are compared. A Petrov--Galerkin finite element method with cubic Hermite elements is developed to solve the eikonal-diffusion equation on a reasonably coarse mesh. The oscillatory errors seen when using the Galerkin weighted residual method with high mesh P\u00e9clet numbers are avoided by supplementing the Galerkin weights with C\n                    <jats:sup>0<\/jats:sup>\n                    functions based on derivatives of the interpolation functions. The ratio of the Galerkin and supplementary weights is a function of the P\u00e9clet number such that, for one-dimensional propagation, the error in the solution is within a small constant factor of the optimal error achievable in the trial space. An additional no-inflow boundary term is developed to prevent spurious excitation from initiating on the boundary. The need for discretization in time is avoided by using a continuation method to gradually introduce the nonlinear term of the governing equation. A simulation is performed in an anisotropic model of the complete canine ventricular myocardium, with 2355 degrees of freedom for the dependent variable.\n                  <\/jats:p>","DOI":"10.1137\/s0036139901389513","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"324-350","source":"Crossref","is-referenced-by-count":79,"title":["A Finite Element Method for an Eikonal Equation Model of Myocardial Excitation Wavefront Propagation"],"prefix":"10.1137","volume":"63","author":[{"given":"Andrew J.","family":"Pullan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karl A.","family":"Tomlinson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter J.","family":"Hunter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61257-2"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(84)90152-X"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(82)90071-8"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620100617"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"P. Colli Franzone and L. Guerri,\n                      Models of the spreading of excitation in myocardial tissue\n                      , in High\u2010Performance Computing in Biomedical Research, T. C. Pilkington, B. Loftis, J. F. Thompson, S. L.\u2010Y. Woo, T. C. Palmer, and T. F. Budinger, eds., CRC Press, Boca Raton, FL, 1993, pp. 359\u2013401.","DOI":"10.1201\/9781003068136-18"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(93)90001-Q"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(97)00093-X"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00163143"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(90)90020-Y"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139992233069"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1161\/01.CIR.84.6.2513"},{"key":"R12","first-page":"1","volume":"21","author":"Henriquez C. S.","year":"1993","journal-title":"Crit. Rev. Biomed. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0278-940X","issn-type":"print"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00163916"},{"key":"R14","unstructured":"J. P. Keener and A. V. Panfilov,\n                      Three\u2010dimensional propagation in the heart: The effects of geometry and fiber orientation on propagation in myocardium\n                      , in Cardiac Electrophysiology: From Cell to Bedside, 2nd ed., D. P. Zipes and J. Jalife, eds., Saunders, Philadelphia, 1995, pp. 335\u2013347."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1109\/10.284925"},{"key":"R16","unstructured":"I. J. Le Grice,\n                      A Finite Element Model of Myocardial Structure: Implications for Electrical Activation in the Heart\n                      , Ph.D. thesis, The University of Auckland, Auckland, New Zealand, 1992."},{"key":"R17","volume-title":"Numerical solution of convection\u2010diffusion problems","author":"Morton K.","year":"1996"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90002-2"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0736(87)80019-5"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"O. H. Schmitt,\n                      Biological information processing using the concept of interpenetrating domains\n                      , in Information Processing in the Nervous System, K. N. Leibovic, ed., Springer\u2010Verlag, New York, 1969, pp. 325\u2013331.","DOI":"10.1007\/978-3-662-25549-0_18"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"James Sethian, Theory, algorithms, and applications of level set methods for propagating interfaces, Acta Numer., Vol. 5, Cambridge Univ. Press, Cambridge, 1996, 309\u201339599d:65397","DOI":"10.1017\/S0962492900002671"},{"key":"R23","unstructured":"K. A. Tomlinson,\n                      Finite Element Solution of an Eikonal Equation for Excitiation Wavefront Propagation in Ventricular Myocardium\n                      , Ph.D. thesis, The University of Auckland, Auckland, New Zealand, 2000."},{"key":"R24","volume-title":"El m\u00e9todo de los elementos finitos. Vol. 1","author":"Zienkiewicz O.","year":"1994"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036139901389513","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:47:57Z","timestamp":1787338077000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036139901389513"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S0036139901389513"],"URL":"https:\/\/doi.org\/10.1137\/s0036139901389513","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}