Obstacles as Switches between Different Cardiac Arrhythmias

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.).




References:
[1] B. L. Zaret, M. Moser and L.S. Cohen. Yale University School of
Medicine Heart Book, New York: Hearst books, 1992.
[2] 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.
[3] G. D. Veenhuyzen, C. S. Simpson and H. Abdollah, "Atrial
Fibrillation", CMAJ, Vol. 171, No. 7, pp. 755-760, September 2004.
[4] 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.
[5] D. P. Zipes. Epidemiology and mechanisms of sudden cardiac death.
Can J. Cardiol, Vol. 21, Suppl A,(May 2005) (37A-40A),
[6] 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.
[7] 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.
[8] 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.
[9] M. Valderrábano, 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.
[10] 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.
[11] 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.
[12] 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.
[13] 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.
[14] Y. Kim, F. Xie, M. Yashima, T. Wu, M. Valderrábano, 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.
[15] 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.
[16] 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.
[17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22] Y. A. Yermakova and A. M. Pertsov. "Interaction of rotating spiral
waves with a boundary", Biophysics, Vol. 31, No. 5, pp. 932-940, 1986.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] 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.
[28] 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.
[29] 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.
[30] 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.
[31] F. H. Fenton and E. M. Cherry. "Models of cardiac cell", Scholarpedia,
Vol. 3, No. 8, p. 1858, 2008.
[32] 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.
[33] K. W. Morton and D. F. Mayers, Numerical Solution of Partial
Differential Equations, Cambridge: Cambridge University Press, 2005.
[34] 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.
[35] N. F. Otani. "Mini Review: Computer Modeling in Cardiac
Electrophysiology" J. Comput. Phys., Vol. 161, No. 1, pp. 21-34, June
2000.
[36] 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.
[37] 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.
[38] 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.
[39] K. J. Lee. "Wave Pattern Selection in an Excitable System", Phys. Rev.
Lett. Vol. 79, No. 15, pp. 2907-2910, October 1997.
[40] 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.
[41] 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.
[42] V. N. Biktashev. "Drift of spiral waves", Scholarpedia, Vol. 2, No. 4, p.
1836.
[43] 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.
[44] 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.
[45] 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.
[46] D. A. Leal-Soto. M. Sc. Thesis: "Interacci├│n de ondas en espiral y
obstáculos en medios excitables con la ecuación de Fitzhugh-Nagumo"
(In Spanish). Universidad de Sonora, México, 2011