EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 18 (2023) Math. Model. Nat. Phenom., 18 (2023) 14 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 18, 2023
Article Number 14
Number of page(s) 25
Section Mathematical physiology and medicine
DOI https://doi.org/10.1051/mmnp/2023012
Published online 28 April 2023
  1. R.R. Aliev and A.V. Panfilov, A simple two-variable model of cardiac excitation. Chaos Solitons Fractals 7 (1996) 293–301. [CrossRef] [Google Scholar]
  2. J.D. Bayer, R.C. Blake, G. Plank and N.A. Trayanova, A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann. Biomed. Eng. 40 (2012) 2243–2254. [CrossRef] [PubMed] [Google Scholar]
  3. M. Boulakia, S. Cazeau, M.A. Fernández et al., Mathematical modeling of electrocardiograms: a numerical study. Ann. Biomed. Eng. 38 (2010) 1071–1097. [CrossRef] [PubMed] [Google Scholar]
  4. Y. Bourgault, Y. Coudière and C. Pierre, Existence and uniqueness of the solution for the bidomain model used in cardiac electrophysiology. Nonlinear Anal., Real World Appl. 10 (2009) 458–482. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Bucelli, M. Salvador, L. Dede and A. Quarteroni, Multipatch isogeometric analysis for electrophysiology: simulation in a human heart. Comput. Methods Appl. Mech. Eng. 376 (2021) 113666. [CrossRef] [Google Scholar]
  6. P. Colli Franzone and G. Savaré, Degenerate evolution systems modeling the cardiac electric field at micro and macroscopic level. In: A. Lorenzi, B. Ruf (eds.), Evolution Equations, Semigroups and Functional Analysis: In Memory of Brunello Terreni, vol. 50. Birkhäuser, Basel (2002), pp. 49–78. [CrossRef] [Google Scholar]
  7. P. Colli Franzone, L. Guerri and S. Tentoni, Mathematical modeling of the excitation process in myocardial tissue: Infiuence of fiber rotation on wavefront propagation and potential field. Math. Biosci. 101 (1990) 155–235. [CrossRef] [Google Scholar]
  8. R. Fitzhugh, Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1 (1961) 445–465. [CrossRef] [Google Scholar]
  9. A. Fraguela, R. Felipe-Sosa, J. Henry and M.F. Márquez, Existence of a T-periodic solution for the monodomain model corresponding to an isolated ventricle due to ionic-diffusive relations. Acta Appl. Math. 177 (2022) https://doi.org/10.1007/s10440-022-00465-2. [CrossRef] [Google Scholar]
  10. Y. Giga, N. Kajiwara and K. Kress, Strong time-periodic solutions to the bidomain equations with arbitrary large forces. Nonlinear Anal., Real World Appl. 47 (2019) 398–413. [CrossRef] [MathSciNet] [Google Scholar]
  11. D. Henry, Geometric theory of semilinear parabolic equations, LNM, vol. 840, Springer-Verlag (1981). [CrossRef] [Google Scholar]
  12. O. Hernandez, A. Fraguela and R. Felipe-Sosa, Existence of global solutions in a model of electrical activity of the monodomain type for a ventricle. Nova Scientia 10 (2018) 17. [CrossRef] [Google Scholar]
  13. M. Hieber, N. Kajiwara, K. Kress and P. Tolksdorf, The periodic version of the Da Prato-Grisvard theorem and applications to the bidomain equations with FitzHugh-Nagumo transport. Ann. Mat. Pura Appl. (2020). https://doi.org/10.1007/s10231-020-00975-6. [Google Scholar]
  14. J. Keener and J. Sneyd, Mathematical Physiology. Springer, Berlin (1998). [CrossRef] [Google Scholar]
  15. J.L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires. Paris, Dunod (1969). [Google Scholar]
  16. C. Luo and Y. Rudy, A model of the ventricular cardiac action potential. Circ. Res. 68 (1991) 1501–1526. [CrossRef] [PubMed] [Google Scholar]
  17. Y. Mori, A multidomain model for ionic electrodiffusion and osmosis with an application to cortical spreading depression. Physica D: Nonlinear Phenomena 308 (2015) 94–108. [CrossRef] [MathSciNet] [Google Scholar]
  18. R. O’Connell and Y. Mori, Effects of glia in a triphasic continuum model of cortical spreading depression. Bull. Math. Biol. 78 (2016) 1943–1967. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  19. A. Panfilov and A. Holden, Computational Biology of the Heart. Wiley, New York (1997). [Google Scholar]
  20. P.A. Raviart and J.M. Thomas, Introduction ál’analyse numriéque des équations aux dérivées partielles, Masson (1988). [Google Scholar]
  21. T. Rubíček, Nonlinear Partial Differential Equations with Applications. Birkhäuser Verlag, Basel (2005). [Google Scholar]
  22. J.M. Rogers and A.D. McCulloch, A collocation-Galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 41 (1994) 743–757. [CrossRef] [Google Scholar]
  23. J. Sneyd, M. Falcke, V. Kirk and G. Dupont, Models of Calcium Signalling. Springer (2016). [Google Scholar]
  24. J. Sundnes, G.T. Lines, X. Cai, B.F. Nielsen, K.A. Mardal and A. Tveito, Computing the Electrical Activity in the Heart. Monographs in Computational Science and Engineering. Springer-Verlag, Berlin, Heidelberg (2006). [Google Scholar]
  25. L. Tung, A bidomain model for describing ischemic myocardial D-C potentials. Ph.D. dissertation, Massachusetts Inst. Technol, Cambridge, MA (1978). [Google Scholar]
  26. M. Veneroni, Reaction-diffusion systems for the macroscopic bidomain model of the cardiac electric field. Nonlinear Anal., Real World Appl. 10 (2009) 849–868. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.