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A comparison of two boundary conditions used with the bidomain model of cardiac tissue

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Abstract

In the bidomain model, two alternative sets of boundary conditions at the interface between cardiac tissue and a saline bath have been used. It is shown that these boundary conditions are equivalent if the length constant of the tissue in the direction transverse to the fibers is much larger than the radius of the individual cardiac cells. If this is not the case, the relative merits of the two boundary conditions are closely related to the question of the applicability of a continuum model, such as the bidomain model, to describe a discrete multicellular tissue.

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References

  1. Clerc, L. Directional differences of impulse spread in trabecular muscle from mammalian heart. J. Physiol. 255:335–346; 1976.

    CAS  PubMed  Google Scholar 

  2. Colli Franzone, P.; Guerri, L.; Rovida, S. Wavefront propagation in an activation model of the an-isotropic cardiac tissue: Asymptotic analysis and numerical simulations. J. Math. Biol. 28:121–176; 1990.

    Article  CAS  PubMed  Google Scholar 

  3. Henriquez, C.S. Structure and volume conduction effects on propagation in cardiac tissue. Durham, NC: Duke University; 1988. Dissertation.

    Google Scholar 

  4. Henriquez, C.S.; Trayanova, N.; Plonsey, R. Potential and current distributions in a cylindrical bundle of cardiac tissue. Biophys. J. 53:907–918; 1988.

    CAS  PubMed  Google Scholar 

  5. Henriquez, C.S.; Trayanova, N.; Plonsey, R. A planar slab bidomain model for cardiac tissue. Ann. Biomed. Eng. 18:367–376; 1990.

    Article  CAS  PubMed  Google Scholar 

  6. Henriquez, C.S.; Plonsey, R. Simulation of propagation along a bundle of cardiac tissue. I. Mathematical formulation. IEEE Trans. Biomed. Eng. 37:850–860; 1990.

    CAS  PubMed  Google Scholar 

  7. Henriquez, C.S. Plonsey, R. Simulation of propagation along a bundle of cardiac tissue. II. Results of simulation. IEEE Trans. Biomed. Eng. 37:861–875; 1990.

    CAS  PubMed  Google Scholar 

  8. Kleber, A.G.; Riegger, C.B. Electrical constants of arterially perfused rabbit papillary muscle. J. Physiol. 385:307–324; 1986.

    Google Scholar 

  9. Peskoff, A. Electric potential in three-dimensional electricall syncytial tissues. Bull. Math. Biol. 41:163–181; 1979.

    CAS  PubMed  Google Scholar 

  10. Plonsey, R. Bioelectric sources arising in excitable fibers. Ann. Biomed. Eng. 16:519–546; 1988.

    Article  CAS  PubMed  Google Scholar 

  11. Plonsey, R.; Barr, R.C. Interstitial potentials and their change with depth into cardiac tissue. Biophys. J. 51:547–555; 1987.

    CAS  PubMed  Google Scholar 

  12. Roth, B.J. Longitudinal resistance in strands of cardiac muscle. Nashville, TN: Vanderbilt University; 1987. Dissertation.

    Google Scholar 

  13. Roth, B.J. The electrical potential produced by a strand of cardiac muscle: A bidomain analysis. Ann. Biomed. Eng. 16:609–637; 1988.

    Article  CAS  PubMed  Google Scholar 

  14. Roth, B.J. Action potential propagation in a thick strand of cardiac muscle. Circ. Res. 68:162–163; 1991.

    CAS  PubMed  Google Scholar 

  15. Roth, B.J.; Guo, W.-Q.; Wikswo, J.P., Jr. The effects of spiral anisotropy on the electric potential and the magnetic field at the apex of the heart. Math. Biosci. 88:159–189; 1988.

    Google Scholar 

  16. Roth, B.J.; Wikswo, J.P., Jr. A bidomain model for the extracellular potential and magnetic field of cardiac tissue. IEEE Trans. Biomed. Eng. 33:467–469; 1986.

    CAS  PubMed  Google Scholar 

  17. Spach, M.S.; Miller, W.T., III; Geselowitz, D.B.; Barr, R.C.; Kootsey, J.M.; Johnson, E.A. The discontinuous nature of propagation in normal canine cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents. Circ. Res. 48:39–54; 1981.

    CAS  PubMed  Google Scholar 

  18. Sommer, J.R. Implications of structure and geometry on cardiac electrical activity. Ann. Biomed. Eng. 11:149–157; 1983.

    CAS  PubMed  Google Scholar 

  19. Suenson, M. Interaction between ventricular cells during the early part of excitation in the ferret heart. Acta. Physiol. Scand. 125:81–90; 1985.

    CAS  PubMed  Google Scholar 

  20. Tung, L. A bi-domain model for describing ischemic myocardial dc potentials. Cambridge, MA: Massachusetts Institute of Technology; 1978. Dissertation.

    Google Scholar 

  21. Weidmann, S. Electrical constants of trabecular muscle from mammalian heart. J. Physiol. 210:1041–1054; 1970.

    CAS  PubMed  Google Scholar 

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  1. Biomedical Engineering and Instrumentation Program, National Institutes of Health, Building 13, Room 3W13, 20892, Bethesda, MD

    Bradley J. Roth

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  1. Bradley J. Roth
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Roth, B.J. A comparison of two boundary conditions used with the bidomain model of cardiac tissue. Ann Biomed Eng 19, 669–678 (1991). https://doi.org/10.1007/BF02368075

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  • DOI: https://doi.org/10.1007/BF02368075

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