Role of spiral wave pinning in inhomogeneous active media in the termination of atrial fibrillation by electrical cardioversion Pawel Kuklik a,b,Ã , Christopher X. Wong a , Anthony G. Brooks a , Jan Jacek Z ˙ ebrowski b , Prashanthan Sanders a a Cardiovascular Research Centre, Department of Cardiology, L5 McEwin Building, Royal Adelaide Hospital and the Disciplines of Medicine and Physiology, University of Adelaide, Adelaide, SA 5000, Australia b Faculty of Physics, Warsaw University of Technology, Warsaw, Poland article info Article history: Received 13 May 2009 Accepted 1 February 2010 Keywords: Excitable media Spiral wave pinning Electrical cardioversion Atrial fibrillation Arrhythmia mechanisms abstract Atrial fibrillation is the most common type of arrhythmia to affect humans. One of the treatment modalities for atrial fibrillation is an electrical cardioversion. Electrical cardioversion can result in one of three outcomes: an immediate termination of arrhythmic activity, a delayed termination or unsuccessful termination. The mechanism of delayed termination is unknown. Here we present a model of an atrial fibrillation as a coexistence of several spiral waves pinned to the inhomogeneities in active media. We show that in inhomogeneous system delayed termination can be explained as the unpinning of a spiral wave from inhomogeneities and its termination after collision with the edge of the system. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction Atrial fibrillation is the most common type of arrhythmia to affect humans. The underlying mechanism is still not clear despite extensive experimental and theoretical studies aiming to char- acterize the spatiotemporal organization of electrical activity during this type of arrhythmia. Several mechanisms have been proposed. However, three dominate: a coexistence of multiple spiral waves (multiple wavelets hypothesis) [1], a stationary, high frequency spiral wave (mother wavelet hypothesis) [2] and a point sources of periodic activity [3]. One of the treatments for atrial fibrillation is electrical cardioversion. During this procedure, a monophasic or biphasic electrical shock is applied to the chest to reset the abnormal forms of electrical activity within the atria and restore spontaneous sinus rhythm [4]. Several studies have previously investigated the effect of cardioversion on the electro- physiology of myocardial cells with evidence supporting altera- tion of cell membrane potential [5], a prolongation of the repolarization time [6] and a heterogeneous distribution of the electrical field within muscle [7]. Electrical cardioversion is a frequently used technique to restore sinus rhythm. It can result in one of three outcomes: an immediate, delayed or unsuccessful termination. However, de- spite significant research devoted to the explanation and characterization of electrical cardioversion, its effect on the spatiotemporal organization of activation waves is not fully understood. Two mechanisms have been proposed to explain the ability of electrical cardioversion to terminate atrial fibrilla- tion: the depolarization of a critical mass of the myocardium [8] and a prolongation of the action potential duration leading to an increase in the wave size, causing a termination of the fibrillation due to the resultant decrease in the spatial area available for wave propagation [9]. One of the unexplained phenomena occurring in clinical practice is the delayed termination of electrical activity following the application of the cardioversion shock. In this phenomenon, electrical cardioversion does not terminate all abnormal activity but, instead, renders it unstable before leading to a spontaneous termination. The details of this instability and the resulting delayed termination are not known. An understanding of this phenomenon may give insight into the mechanism of atrial fibrillation itself and provide new ideas for its treatment. A hypothesis providing a mechanism of the delayed termina- tion was proposed by Zemlin et al. [10]. Using a mathematical model, they showed how a three-dimensional scroll wave self- terminates within a few cycles after the application of the electric shock. However, their result is only applicable to 3D systems (the ventricular wall) since such self-termination is driven by filament curvature dynamics, negligible in the thin atrial muscle. An important hypothesis for the 2D system was provided by Pumir and Krinsky in [11] where authors showed an unpinning of the spiral wave from a heterogeneity in the active media after the ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/cbm Computers in Biology and Medicine 0010-4825/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2010.02.001 Ã Corresponding author at: Cardiovascular Research Centre, Department of Cardiology, L5 McEwin Building, Royal Adelaide Hospital and the Disciplines of Medicine and Physiology, University of Adelaide, Adelaide, SA 5000, Australia. Tel.: + 61 8 822 22723; fax: + 61 8 8222 2722. E-mail address: pawel.kuklik@adelaide.edu.au (P. Kuklik). Computers in Biology and Medicine 40 (2010) 363–372