Skip to main content
SpringerLink
Log in

Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction

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

Abstract

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.

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

Access this article

Log in via an institution

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

  • Bordas, R., Carpentieri, B., Fotia, G., Maggio, F., Nobes, R., Pitt-Francis, J., & Southern, J. (2009). Simulation of cardiac electrophysiology on next-generation high-performance computers. Philos. Trans. R. Soc. A, 367, 1951–1969.

    Article  MathSciNet  MATH  Google Scholar 

  • Boron, W., & Boulpaep, E. (2005). Medical physiology. Philadelphia: Saunders.

    Google Scholar 

  • Cherry, E., Greenside, H., & Henriquez, C. (2000). A space-time adaptive method for simulating complex cardiac dynamics. Phys. Rev. Lett., 84, 1343–1346.

    Article  Google Scholar 

  • Cherry, E., Greenside, H., & Henriquez, C. (2003). Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method. Chaos, 13, 853–865.

    Article  MathSciNet  MATH  Google Scholar 

  • Colli Franzone, P., Deuflhard, P., Erdmann, B., Lang, J., & Pavarino, L. (2006). Adaptivity in space and time for reaction-diffusion systems in electrocardiology. SIAM J. Sci. Comput., 28, 942–962.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Fenton, F., & Karma, A. (1998). Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. Chaos, 8, 20–47.

    Article  MATH  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., & Griffith, B. (2010). Adaptive multiscale model for simulating cardiac conduction. Proc. Natl. Acad. Sci. USA, 107(33), 14603–14608.

    Article  Google Scholar 

  • Hand, P., & Peskin, C. (2010). Homogenization of an electrophysiological model for a strand of cardiac myocytes with gap-junctional and electric-field coupling. Bull. Math. Biol., 72, 1408–1424.

    Article  MathSciNet  MATH  Google Scholar 

  • Hand, P., Griffith, B., & Peskin, C. (2009). Deriving macroscopic myocardial conductivities by homogenization of microscopic models. Bull. Math. Biol., 71, 1707–1726.

    Article  MathSciNet  MATH  Google Scholar 

  • Keener, J., & Sneyd, J. (1998). Mathematical physiology. Berlin: Springer.

    MATH  Google Scholar 

  • Keldermann, R., ten Tusscher, K., Nash, M., Bradley, C., Hren, R., Taggart, P., & Panfilov, A. (2009). A computational study of mother rotor VF in the human ventricles. Am. J. Physiol., Heart Circ. Physiol., 296(2), H370–H379.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lin, J., & Keener, J. (2010). Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling. Proc. Natl. Acad. Sci. USA, 107(49), 20935–20940.

    Article  Google Scholar 

  • Luo, C., & Rudy, Y. (1994). A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ. Res., 74(6), 1071–1096.

    Google Scholar 

  • Mori, Y., Fishman, G., & Peskin, C. (2008). Ephaptic conduction in a cardiac strand model with 3d electrodiffusion. Proc. Natl. Acad. Sci. USA, 105, 6463–6468.

    Article  Google Scholar 

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

    Google Scholar 

  • Peters, N., Green, C., Poole-Wilson, P., & Severs, N. (1993). Reduced content of connexin43 gap junctions in ventricular myocardium from hypertrophied and ischemic human hearts. Circulation, 88(3), 864–875.

    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, 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 

  • Severs, N., Coppen, S., Dupont, E., Yeh, H., Ko, Y., & Matsushita, T. (2004). Gap junction alterations in human cardiac disease. Cardiovasc. Res., 62(2), 368–377.

    Article  Google Scholar 

  • Severs, N., Bruce, A., Dupont, E., & Rothery, S. (2008). Remodelling of gap junctions and connexin expression in diseased myocardium. Cardiovasc. Res., 80(1), 9–19.

    Article  Google Scholar 

  • Smith, J., Green, C., Peters, N., Rothery, S., & Severs, N. J. (1991). Altered patterns of gap junction distribution in ischemic heart disease. An immunohistochemical study of human myocardium using laser scanning confocal microscopy. Am. J. Pathol., 139(4), 801–821.

    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 

  • Yao, J., Gutstein, D., Liu, F., Fishman, G., & Wit, A. (2003). Cell coupling between ventricular myocyte pairs from connexin43-deficient murine hearts. Circ. Res., 93(8), 736–743.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leon H. Charney Division of Cardiology, New York University School of Medicine, New York, NY, 10016, USA

    Paul E. Hand & Boyce E. Griffith

Authors
  1. Paul E. Hand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Boyce E. Griffith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul E. Hand.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hand, P.E., Griffith, B.E. Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction. Bull Math Biol 73, 3071–3089 (2011). https://doi.org/10.1007/s11538-011-9661-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-011-9661-5

Keywords

Search

Navigation