Commenced in January 2007
Paper Count: 30382
Obstacles as Switches between Different Cardiac Arrhythmias
Authors: Daniel Olmos-Liceaga
Abstract:Ventricular fibrillation is a very important health problem as is the cause of most of the sudden deaths in the world. Waves of electrical activity are sent by the SA node, propagate through the cardiac tissue and activate the mechanisms of cell contraction, and therefore are responsible to pump blood to the body harmonically. A spiral wave is an abnormal auto sustainable wave that is responsible of certain types of arrhythmias. When these waves break up, give rise to the fibrillation regime, in which there is a complete loss in the coordination of the contraction of the heart muscle. Interaction of spiral waves and obstacles is also of great importance as it is believed that the attachment of a spiral wave to an obstacle can provide with a transition of two different arrhythmias. An obstacle can be partially excitable or non excitable. In this talk, we present a numerical study of the interaction of meandering spiral waves with partially and non excitable obstacles and focus on the problem where the obstacle plays a fundamental role in the switch between different spiral regimes, which represent different arrhythmic regimes. Particularly, we study the phenomenon of destabilization of spiral waves due to the presence of obstacles, a phenomenon not completely understood (This work will appear as a Chapter in a Book named Cardiac Arrhytmias by INTECH under the name "Spiral Waves, Obstacles and Cardiac Arrhythmias", ISBN 979-953-307-050-5.).
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330413Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1255
 B. L. Zaret, M. Moser and L.S. Cohen. Yale University School of Medicine Heart Book, New York: Hearst books, 1992.
 F. H. Fenton, E. Cherry, H. M. Hastings and S. J. Evans (2002). "Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity", CHAOS, Vol. 12, No. 3, pp. 852-892, September 2002.
 G. D. Veenhuyzen, C. S. Simpson and H. Abdollah, "Atrial Fibrillation", CMAJ, Vol. 171, No. 7, pp. 755-760, September 2004.
 A. S. Tang, H. Ross, C. S. Simpson, L. B. Mitchell, P. Dorian, R. Goeree, B. Hoffmaster, M. Arnold and M. Talajic. "Canadian cardiovascular society / Canadian heart rhythm society position paper on implantable cardioverter defibrillator use in Canada". Can J. Cardiol, Vol. 21, Suppl A, pp. 11A-18A, May 2005.
 D. P. Zipes. Epidemiology and mechanisms of sudden cardiac death. Can J. Cardiol, Vol. 21, Suppl A,(May 2005) (37A-40A),
 S. G. Priori, E. Aliot, C. Bl├©mstrom-Lundqvist, L. Bossaert, G. Breithardt, P. Brugada, J. A. Camm, R. Cappato, S. M. Cobbe, C. Di Mario, B. J. Maron, W. J. McKenna, A. K. Pedersen, U. Ravens, P. J. Schwartz, M. Trusz-Gluza, P. Vardas, H. J. J. Wellens, H. and D. P. Zipes, "Task Force on Sudden Cardiac Death", European Society of Cardiology. Europace, Vol. 4, pp 3-18. January 2002.
 J. F. Starobin, Y. I. Zilberter, E. M. Rusnak, and C. F. Starmer. "Wavelet formation in excitable cardiac tissue: the role of wavefrontobstacle interactions in initiating high-frequency fibrillatory-like arrhythmias", Biophys. J., Vol. 70, No. 2, pp. 581-594, February 1996.
 K. H. W. J. Ten Tusscher and A. V. Panfilov. "Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model", Am J. Physiol. Heart Circ. Physiol., Vol. 284, No. 2, pp. H542- H548, February 2002.
 M. Valderr├íbano, Y.-H. Kim, M. Yashima, T.-J. Wu, H. S. Karagueuzian, and P.-S. Chen. "Obstacleinduced transition from ventricular fibrillation to tachycardia in isolated swine right ventricles: Insights into the transition dynamics and implications for the critical mass", J. Am. Col. Cardiol., Vol. 36, No. 6, pp. 2000-2008, November 2000.
 E. M. Azene, N. A. Trayanova and E. Warman. "Wave Front-obstacle interactions in cardiac tissue: a computational study". Ann. Biomed. Eng., Vol. 29, No. 1, pp. 35-46, January 2001.
 J. M. Davidenko, A. V. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, "Stationary and drifting spiral waves of excitation in isolated cardiac muscle", Nature, Vol. 355, No. 6358, pp. 349-351, January 1992.
 T. Ikeda, M. Yashima, T. Uchida, D. Hough, M. C. Fishbein, W. J. Mandel, P. S. Chen and H. Karagueuzian. "Attachment of meandering reentrant wave fronts to anatomic obstacles in the atrium - Role of the obstacle size", Circ. Res., Vol. 81, No. 5, pp. 753-764, November 1997.
 Z. Y. Lim, B. Maskara, F. Aguel, R. Emokpae and L. Tung. "Spiral wave attachment to millimeter-sized obstacles", Circulation, Vol 114, No. 20, pp. 2113-2121, November 2006.
 Y. Kim, F. Xie, M. Yashima, T. Wu, M. Valderr├íbano, M. Lee, T. Ohara, O. Voroshilovsky, R. N. Doshi, M. C. Fishbein, Z. Qu, A. Garfinkel, J. N. Weiss, H. S. Karagueuzian and P. Chen. "Role of papillary muscle in the generation and maintenance of reentry during ventricular tachycardia and fibrillation in isolated swine right ventricle." Circulation, Vol. 100, No. 13, pp. 1450-1459, September 1999.
 A. M. Pertsov, J. M. Davidenko, R. Salomonsz, W. T. Baxter, and J. Jalife. "Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle", Circ. Res., Vol. 72, No. 3, pp. 631-650, March 1993.
 T. K. Shajahan, S. Sinha and R. Pandit. "Spiral-wave dynamics depend sensitively on inhomogeneities in mathematical models of ventricular tissue", Phys. Rev. E, Vol. 75, No. 1, pp. 011929(1-8), January 2007.
 P. Comtois and A. Vinet. "Multistability of reentrant rhythms in an ionic model of a two-dimensional annulus of cardiac tissue". Phys. Rev. E, Vol. 72, No. 5, pp. 051927(1-11), November 2005.
 T. K. Shajahan, A. R. Nayak and R. Pandit. "Spiral-Wave Turbulence and its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue", Plos One, Vol. 4, No. 3, pp. 1-21, March 2009.
 F. Xie, Z. Qu, A. Garfinkel and J. N. Weiss. "Effects of simulated ischemia on spiral wave stability", Am. J. Heart Circ. Physiol., Vol. 280, No. 4, pp. H1667-H1673, April 2001.
 D. Olmos. "Reflection and attachment of spirals at obstacles for the Fitzhugh-Nagumo and Beeler-Reuter models", Phys. Rev. E, Vol. 81, No. 4, pp. 041924 (1-9), April 2010.
 D. Olmos and B. D. Shizgal. "Annihilation and reflection of spiral waves at a boundary for the Beeler-Reuter model", Phys. Rev. E, Vol. 77, No. 3, pp. 031918 1-14, March 2008.
 Y. A. Yermakova and A. M. Pertsov. "Interaction of rotating spiral waves with a boundary", Biophysics, Vol. 31, No. 5, pp. 932-940, 1986.
 A. L. Hodgkin and A. F. Huxley. "A quantitative description of membrane current and its application to conduction and excitation in nerve", J. Physiol, Vol. 117, pp. 500-544, August 1952.
 A. G. Kléber and Y. Rudy. "Basic Mechanisms of cardiac impulse propagation and associated arrhythmias", Physiol. Rev., Vol. 84, No. 2, pp. 431-488, April 2004.
 C.-S. Luo and Y. Rudy. "A Dynamic Model of the Cardiac Ventricular Action Potential. I. Simulations of ionic currents and concentration changes", Circ. Res., Vol. 74, No. 8, pp. 1071-1096, June 1994.
 L. Priebe and D. J. Beuckelmann. "Simulation Study of Cellular Electric Properties in Heart Failure", Circ. Res., Vol. 82, No. 11, pp. 1206-1223, June 1998.
 M. Courtemanche, R. J. Ramirez. and S. Nattel. "Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model", Am. J. Physiol. and Heart Circ. Physiol., Vol. 275, No. 1, pp. H301-H321, July 1998.
 A. Nygren, C. Fiset, L. Firek, J. W. Clark, D. S. Lindblad, R. B. Clark, W. R. Giles. "Mathematical Model of an Adult Human Atrial Cell: The Role of K+ Currents in Repolarization", Circ. Res., Vol 82, No. 1, pp. 63-81, January 1998.
 K. Yanagihara, A. Noma and H. Irisawa. "Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments", Jap. J. Physiology, Vol. 30, No. 6, pp. 841-857, 1980.
 D. DiFrancesco and D. Noble. "A model of cardiac electrical activity incorporating ionic pumps and concentration changes", Phil. Trans. R. Soc. Lond., Vol. 307, No. 1133, pp. 353-398, January 1985.
 F. H. Fenton and E. M. Cherry. "Models of cardiac cell", Scholarpedia, Vol. 3, No. 8, p. 1858, 2008.
 F. H. Fenton and A. Karma. "Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation", CHAOS, Vol. 8, No. 1, pp. 20-47, March 1998.
 K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge: Cambridge University Press, 2005.
 A. Isomura, M. Hörning, K. Agladze and K. Yoshikawa. "Eliminating spiral waves pinned to an anatomical obstacle in cardiac myocytes by high-frequency stimuli". Phys. Rev. E. Vol. 78, No. 6. pp. 066216(1-6), December 2008.
 N. F. Otani. "Mini Review: Computer Modeling in Cardiac Electrophysiology" J. Comput. Phys., Vol. 161, No. 1, pp. 21-34, June 2000.
 A. V. Panfilov, A. V. and J. P. Keener. "Effects of high frequency stimulation on cardiac tissue with an inexcitable obstacle", J. Theor. Biol, Vol. 163, No. 4, pp. 439-448, August 1993.
 Benson, A. P. and A. V. Holden. "Calcium oscillations and ectopic beats in virtual ventricular myocytes and tissues: bifurcations, autorhythmicity and propagation", in: Lecture Notes in Computer Science, F. Frangi, P. Radeva, A. Santos and M. Hernandez, Berlin: Springer-Verlag Berlin, 2005, pp. 895-897.
 C.-S. Luo, and Y. Rudy. "A Dynamic Model of the Cardiac Ventricular Action Potential.II. Afterdepolarizations, triggered activity, and potentiation", Circ. Res., Vol. 74, No. 8, pp. 1097-1113, June 1994.
 K. J. Lee. "Wave Pattern Selection in an Excitable System", Phys. Rev. Lett. Vol. 79, No. 15, pp. 2907-2910, October 1997.
 D. Olmos. Ph. D. Thesis: "Pseudospectral solutions of reaction-diffusion equations that model excitable media: convergence of solutions and Applications". University of British Columbia, Canada, 2007.
 I. R. Efimov, V. I. Krinsky and J. Jalife. "Dynamics of rotating vortices in the Beeler-Reuter model of cardiac tissue". Chaos, Sol. and Frac., Vol. 5, No.3-4, pp. 513-526, March-April 1995.
 V. N. Biktashev. "Drift of spiral waves", Scholarpedia, Vol. 2, No. 4, p. 1836.
 G. W. Beeler and H. Reuter. "Reconstruction of the action potential of ventricular myocardial fibres". J.Physiol., Vol. 268, No. 1, pp. 177-210, June 1977.
 A. S. Mikhailov, V. A. Davydov, V. S. Zykov. "Complex dynamics of spiral waves and motion of curves", Physica D, Vol 70, No. 1-2, pp. 1- 39, January 1994.
 C. Cabo, A. M. Pertsov, J. M. Davidenko, W. T. Baxter, R. A. Gray and J. Jalife. "Vortex shedding as a precursor of turbulent electrical activity in cardiac muscle", Biophys. J., Vol 70, No. 3, pp. 1105-1111, March 1996.
 D. A. Leal-Soto. M. Sc. Thesis: "Interacci├│n de ondas en espiral y obst├ículos en medios excitables con la ecuaci├│n de Fitzhugh-Nagumo" (In Spanish). Universidad de Sonora, México, 2011