Skip to main content
Log in

Homogenization of an Electrophysiological Model for a Strand of Cardiac Myocytes with Gap-Junctional and Electric-Field Coupling

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We derive a homogenized description of the electrical communication along a single strand of myocytes in the presence of gap-junctional and electric-field coupling. In the model, cells are electrically coupled through narrow clefts that are resistively connected to extracellular space. Cells are also coupled directly through gap junctions. We perform numerical simulations of this full model and its homogenization. We observe that the full and homogenized descriptions agree when gap-junctional coupling is at physiologically normal levels. When gap-junctional coupling is low, the two descriptions disagree. In this case, only the full model captures the behavior that the ephaptic mechanism can speed up action potential propagation. A strength of our homogenized description is that it is a macroscale model that can account for the preferential localization of Na+ channels at the ends of cells.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Copene, E., Keener, J., 2008. Ephaptic coupling of cardiac cells through the junctional electric potential. J. Math. Biol. 57(2), 265–284.

    Article  MATH  MathSciNet  Google Scholar 

  • Evans, L., 2002. Partial Differential Equations. American Mathematical Society, Providence, pp. 218–221

    Google Scholar 

  • Faber, G., 2008. Cardiac Bioelectricity Research and Training Center (CBRTC). The Luo-Rudy dynamic (LRd) model of the mammalian ventricular action potential. Available at: http://www.cwru.edu/med/CBRTC/LRdOnline/. Accessed December 2008

  • Faber, G., Rudy, Y., 2000. Action potential and contractility changes in [Na+] i overloaded cardiac myocytes: a simulation study. Biophys. J. 78, 2392–2404.

    Article  Google Scholar 

  • Gutstein, D., Morley, G., Tamaddon, H., Vaidya, D., Schneider, M., Chen, J., Chien, K., Stuhlmann, H., Fishman, G., 2001. Conduction slowing and sudden arrhythmic death in mice with cardiac-restricted inactivation of connexin43. Circ. Res. 88, 333–339.

    Google Scholar 

  • Hand, P., 2009. Homogenization in cardiac electrophysiology and blow-up in bacterial chemotaxis. Doctoral dissertation. New York University, New York.

  • Henriquez, C., 1993. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit. Rev. Biomed. Eng. 21, 1–77.

    Google Scholar 

  • Hornung, U., 1997. Homogenization and Porous Media. Springer, New York.

    MATH  Google Scholar 

  • Kucera, J., Rorh, S., Rudy, Y., 2002. Localization of sodium channels in intercalated disks modulates cardiac conduction. Circ. Res. 91, 1176–1182.

    Article  Google Scholar 

  • Luo, C., Rudy, Y., 1991. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ. Res. 68, 1501–1526.

    Google Scholar 

  • Mori, Y., Fishman, G., Peskin, C., 2008. Ephaptic conduction in a cardiac strand model with 3D electrodiffusion. Proc. Nat. Acad. Sci. 105, 6463–6468.

    Article  Google Scholar 

  • Neu, J., Krassowska, W., 1993. Homogenization of syncytial tissues. Crit. Rev. Biomed. Eng. 21, 137–199.

    Google Scholar 

  • Picone, J., Sperelakis, N., Mann, J., 1991. Expanded model of the electric field hypothesis for propagation in cardiac muscle. Math. Comput. Model. 15(8), 13–35.

    Article  Google Scholar 

  • Ramasamy, L., Sperelakis, N., 2007. Cable properties and propagation velocity in a long single chain of simulated myocardial cells. Theor. Biol. Med. Model. 4, 36.

    Article  Google Scholar 

  • Rohr, S., 2004. Role of gap junctions in the propagation of the cardiac action potential. Cardiovasc. Res. 62, 309–322.

    Article  Google Scholar 

  • Sperelakis, N., Mann, J., 1977. Evaluation of electric field changes in the cleft between excitable cells. J. Theor. Biol. 64, 71–96.

    Article  Google Scholar 

  • Sperelakis, N., McConnell, K., 2002. Electric field interactions between closely abutting excitable cells. IEEE Eng. Med. Biol. Mag. 21, 77–89.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paul E. Hand.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hand, P.E., Peskin, C.S. Homogenization of an Electrophysiological Model for a Strand of Cardiac Myocytes with Gap-Junctional and Electric-Field Coupling. Bull. Math. Biol. 72, 1408–1424 (2010). https://doi.org/10.1007/s11538-009-9499-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-009-9499-2

Navigation