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Attraction and repulsion of spiral waves by inhomogeneity of conduction anisotropy—a model of spiral wave interaction with electrical remodeling of heart tissue

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Abstract

Various forms of heart disease are associated with remodeling of the heart muscle, which results in a perturbation of cell-to-cell electrical coupling. These perturbations may alter the trajectory of spiral wave drift in the heart muscle. We investigate the effect of spatially extended inhomogeneity of transverse cell coupling on the spiral wave trajectory using a simple active media model. The spiral wave was either attracted or repelled from the center of inhomogeneity as a function of cell excitability and gradient of the cell coupling. High levels of excitability resulted in an attraction of the wave to the center of inhomogeneity, whereas low levels resulted in an escape and termination of the spiral wave. The spiral wave drift velocity was related to the gradient of the coupling and the initial position of the wave. In a diseased heart, a region of altered transverse coupling corresponds with local gap junction remodeling that may be responsible for stabilization-destabilization of spiral waves and hence reflect potentially important targets in the treatment of heart arrhythmias.

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References

  1. Zipes, D.P., Jalife, J.: Cardiac Electrophysiology: From Cell to Bedside, 4th edn. Saunders, Philadelphia (2004)

    Google Scholar 

  2. Fenton, F., Karma, A.: Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: filament instability and fibrillation (vol. 8, p. 20, 1998). Chaos 8, 879–879 (1998)

    Article  ADS  Google Scholar 

  3. Saffitz, J.E., Kanter, H.L., Green, K.G., Tolley, T.K., Beyer, E.C.: Tissue-specific determinants of anisotropic conduction velocity in canine atrial and ventricular myocardium. Circ. Res. 74, 1065–1070 (1994)

    Article  Google Scholar 

  4. de Bakker, J.M., van Capelle, F.J., Janse, M.J., Tasseron, S., Vermeulen, J.T., de Jonge, N., Lahpor, J.R.: Slow conduction in the infarcted human heart. ‘Zigzag’ course of activation. Circulation 88, 915–926 (1993)

    Article  Google Scholar 

  5. Polontchouk, L., Haefliger, J.A., Ebelt, B., Schaefer, T., Stuhlmann, D., Mehlhorn, U., Kuhn-Regnier, F., De Vivie, E.R., Dhein, S.: Effects of chronic atrial fibrillation on gap junction distribution in human and rat atria. J. Am. Coll. Cardiol. 38, 883–891 (2001)

    Article  Google Scholar 

  6. Saffitz, J.E., Corr, P.B., Sobel, B.E.: Arrhythmogenesis and ventricular dysfunction after myocardial infarction: is anomalous cellular coupling the elusive link? Circulation 87, 1742–1745 (1993)

    Article  Google Scholar 

  7. Paoletti, M.S., Solomon, T.H.: Front propagation and mode-locking in an advection-reaction-diffusion system. Phys. Rev. E 72(4), (2005). doi:10.1103/PhysRevE.72.046204

    Article  MathSciNet  Google Scholar 

  8. Winfree, A.T.: Varieties of spiral wave behavior: an experimentalist’s approach to the theory of excitable media. Chaos 1, 303–334 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  9. Zemlin, C., Mironov, S., Pertsov, A.: Delayed success in termination of three-dimensional reentry: role of surface polarization. J. Cardiovasc. Electrophysiol. 14, S257–S263 (2003)

    Article  Google Scholar 

  10. Kuklik, P., Wong, C.X., Brooks, A.G., Zebrowski, J.J., Sanders, P.: Role of spiral wave pinning in inhomogeneous active media in the termination of atrial fibrillation by electrical cardioversion. Comput. Biol. Med. 40, 363–372 (2010)

    Article  Google Scholar 

  11. Pumir, A., Krinsky, V.I.: How does an electric field defibrillate cardiac muscle? Physica D 91, 205–219 (1996)

    Article  MATH  Google Scholar 

  12. Lammers, W.J.E.P., Kirchhof, C., Bonke, F.I.M., Allessie, M.A.: Vulnerability of rabbit atrium to reentry by hypoxia - role of inhomogeneity in conduction and wavelength. Am. J. Physiol. 262, H47–H55 (1992)

    Google Scholar 

  13. Kuklik, P., Zebrowski, J.J.: Reentry wave formation in excitable media with stochastically generated inhomogeneities. Chaos 15, 33301 (2005)

    Article  Google Scholar 

  14. Bub, G., Shrier, A., Glass, L.: Spiral wave generation in heterogeneous excitable media. Phys. Rev. Lett. 88, 058101 (2002)

    Article  ADS  Google Scholar 

  15. Li, B.W., Zhang, H., Ying, H.P., Hu, G.: Coherent wave patterns sustained by a localized inhomogeneity in an excitable medium. Phys. Rev. E 79, 026220 (2009)

    Article  ADS  Google Scholar 

  16. Xu, A., Guevara, M.R.: Two forms of spiral-wave reentry in an ionic model of ischemic ventricular myocardium. Chaos 8, 157–174 (1998)

    Article  ADS  Google Scholar 

  17. Kuklik, P., Szumowski, L., Sanders, P., Zebrowsi, J.J.: Spiral wave breakup in excitable media with an inhomogeneity of conduction anisotropy. Comput. Biol. Med. 40, 775–780 (2010)

    Article  Google Scholar 

  18. Xie, F., Weiss, J.N.: Interaction and breakup of inwardly rotating spiral waves in an inhomogeneous oscillatory medium. Phys. Rev. E 75, 016107 (2007)

    Article  ADS  Google Scholar 

  19. Shajahan, T.K., Sinha, S., Pandit, R.: Spiral-wave dynamics depend sensitively on inhomogeneities in mathematical models of ventricular tissue. Phys. Rev. E 75, 011929 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  20. Hendrey, M., Ott, E., Antonsen, Jr., T.M.: Spiral wave dynamics in oscillatory inhomogeneous media. Phys. Rev. E 61, 4943–4953 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  21. Mikhailov, A.S., Davydov, V.A., Zykov, V.S.: Complex dynamics of spiral waves and motion of curves. Physica D 70, 1–39 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Jugdutt, B.I.: Remodeling of the myocardium and potential targets in the collagen degradation and synthesis pathways. Curr. Drug Targets Cardiovasc. Haematol. Disord. 3, 1–30 (2003)

    Article  Google Scholar 

  23. Davidenko, J.M., Pertsov, A.V., Salomonsz, R., Baxter, W., Jalife, J.: Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature 355, 349–351 (1992)

    Article  ADS  Google Scholar 

  24. Rogers, J.M., McCulloch, A.D.: Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation. J. Cardiovasc. Electrophysiol. 5, 496–509 (1994)

    Article  Google Scholar 

  25. Lim, Z.Y., Maskara, B., Aguel, F., Emokpae, R., Tung, L.: Spiral wave attachment to millimeter-sized obstacles. Circulation 114, 2113–2121 (2006)

    Article  Google Scholar 

  26. Cabo, C., Boyden, P.A.: Heterogeneous gap junction remodeling stabilizes reentrant circuits in the epicardial border zone of the healing canine infarct: a computational study. Am. J. Physiol. 291, H2606–H2616 (2006)

    Google Scholar 

  27. Panfilov, A.V., Keener, J.P.: Reentry in 3-dimensional Fitzhugh-Nagumo medium with rotational anisotropy. Physica D 84, 545–552 (1995)

    Article  Google Scholar 

  28. Qu, Z.L., Kil, K., Xie, F.G., Garfinkel, A., Weiss, J.N.: Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation. Biophys. J. 78, 2761–2775 (2000)

    Article  Google Scholar 

  29. Majumder R., Nayak A.R., Pandit R.: Scroll-wave dynamics in human cardiac tissue: lessons from a mathematical model with inhomogeneities and fiber architecture. PLoS ONE 6(4), e18052 (2011). doi:10.1371/journal.pone.0018052

    Article  ADS  Google Scholar 

  30. Fenton, F., Karma, A.: Fiber-rotation-induced vortex turbulence in thick myocardium. Phys. Rev. Lett. 81, 481–484 (1998)

    Article  ADS  Google Scholar 

  31. Davydov, V.A., Morozov, V.G., Davydov, N.V., Yamaguchi, T.: Propagation of autowaves in excitable media with chiral anisotropy. Phys. Lett. A 325, 334–339 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Beaudoin, D.L., Roth, B.J.: The effect of the fiber curvature gradient on break excitation in cardiac tissue. Pace 29, 496–501 (2006)

    Article  Google Scholar 

  33. Tseng, W.I., Reese, T.G., Weisskoff, R.M., Wedeen, V.J.: Cardiac diffusion tensor MRI in vivo without strain correction. Magn. Reson. Med. 42, 393–403 (1999)

    Article  Google Scholar 

  34. Ho, S.Y., Anderson, R.H., Sanchez-Quintana, D.: Atrial structure and fibres: morphologic bases of atrial conduction. Cardiovasc. Res. 54, 325–336 (2002)

    Article  Google Scholar 

  35. Fitzhugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445–466 (1961)

    Article  ADS  Google Scholar 

  36. Tobon, C., Ruiz, C., Saiz, J., Heidenreich, E., Hornero, F.: Reentrant mechanisms triggered by ectopic activity in a three-dimensional realistic model of human atrium. A computer simulation study. Comput. Cardiol. 1–2, 629–632, 1112 (2008)

    Google Scholar 

  37. Seemann, G., Höper, C., Sachse, F.B., Dossel, O., Holden, A.V., Zhang, H.G.: Heterogeneous three-dimensional anatomical and electrophysiological model of human atria. Philos. Trans. R. Soc. A 364, 1465–1481 (2006)

    Article  ADS  Google Scholar 

  38. Roberts, D.E., Hersh, L.T., Scher, A.M.: Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ. Res. 44, 701–712 (1979)

    Article  Google Scholar 

  39. Ten Tusscher, K.H., Panfilov, A.V.: Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model. Am. J. Physiol. 284, H542–H548 (2003)

    Google Scholar 

  40. Krinsky, V.V., Hamm, E., Voignier, V.V.: Dense and sparse vortices in excitable media drift in opposite directions in electric field. Phys. Rev. Lett. 76, 3854–3857 (1996)

    Article  ADS  Google Scholar 

  41. Pazo, D., Kramer, L., Pumir, A., Kanani, S., Efimov, I., Krinsky, V.: Pinning force in active media. Phys. Rev. Lett. 93(16), (2004). doi:10.1103/PhysRevLett.93.168303

    Article  Google Scholar 

  42. Lin, J.W., Garber, L., Qi, Y.R., Chang, M.G., Cysyk, J., Tung, L.: Region of slowed conduction acts as core for spiral wave reentry in cardiac cell monolayers. Am. J. Physiol. 294, H58–H65 (2008)

    Google Scholar 

  43. Tanaka, M., Isomura, A., Horning, M., Kitahata, H., Agladze, K., Yoshikawa, K.: Unpinning of a spiral wave anchored around a circular obstacle by an external wave train: common aspects of a chemical reaction and cardiomyocyte tissue. Chaos 19, 043114 (2009)

    Article  ADS  Google Scholar 

  44. Agladze, K., Kay, M.W., Krinsky, V., Sarvazyan, N.: Interaction between spiral and paced waves in cardiac tissue. Am. J. Physiol. 293, H503–H513 (2007)

    Google Scholar 

  45. Bittihn, P., Squires, A., Luther, G., Bodenschatz, E., Krinsky, V., Parlitz, U., Luther, S.: Phase-resolved analysis of the susceptibility of pinned spiral waves to far-field pacing in a two-dimensional model of excitable media. Philos. Trans. A Math. Phys. Eng. Sci. 368, 2221–2236 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. Bian, W.N., Bursac, N.: Engineered skeletal muscle tissue networks with controllable architecture. Biomaterials 30, 1401–1412 (2009)

    Article  Google Scholar 

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Authors and Affiliations

  1. Centre for Heart Rhythm Disorders, Royal Adelaide Hospital, University of Adelaide, Adelaide, Australia

    Pawel Kuklik & Prashanthan Sanders

  2. Institute of Cardiology, Warsaw, Poland

    Lukasz Szumowski

  3. Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, ul. Koszykowa 75, Warsaw, Poland

    Jan J. Żebrowski

Authors
  1. Pawel Kuklik
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  2. Prashanthan Sanders
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  4. Jan J. Żebrowski
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Correspondence to Pawel Kuklik.

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Kuklik, P., Sanders, P., Szumowski, L. et al. Attraction and repulsion of spiral waves by inhomogeneity of conduction anisotropy—a model of spiral wave interaction with electrical remodeling of heart tissue. J Biol Phys 39, 67–80 (2013). https://doi.org/10.1007/s10867-012-9286-4

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  • DOI: https://doi.org/10.1007/s10867-012-9286-4

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