Development of a computer algorithm for the detection of phase singularities and initial application to analyze simulations of atrial fibrillation.

Atrial fibrillation (AF) is a common cardiac arrhythmia, but its mechanisms are incompletely understood. The identification of phase singularities (PSs) has been used to define spiral waves involved in maintaining the arrhythmia, as well as daughter wavelets. In the past, PSs have often been identified manually. Automated PS detection algorithms have been described previously, but when we attempted to apply a previously developed algorithm we experienced problems with false positives that made the results difficult to use directly. We therefore developed a tool for PS identification that uses multiple strategies incorporating both image analysis and mathematical convolution for automated detection with optimized sensitivity and specificity, followed by manual verification. The tool was then applied to analyze PS behavior in simulations of AF maintained in the presence of spatially distributed acetylcholine effects in cell grids of varying size. These analyses indicated that in almost all cases, a single PS lasted throughout the simulation, corresponding to the central-core tip of a single spiral wave that maintained AF. The sustained PS always localized to an area of low acetylcholine concentration. When the grid became very small and no area of low acetylcholine concentration was surrounded by zones of higher concentration, AF could not be sustained. The behavior of PSs and the mechanisms of AF were qualitatively constant over an 11.1-fold range of atrial grid size, suggesting that the classical emphasis on tissue size as a primary determinant of fibrillatory behavior may be overstated. (c) 2002 American Institute of Physics.

[1]  N. D. Mermin,et al.  The topological theory of defects in ordered media , 1979 .

[2]  J Clémenty,et al.  Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins. , 1998, The New England journal of medicine.

[3]  N. Trayanova,et al.  Virtual electrode polarization in the far field: implications for external defibrillation. , 2000, American journal of physiology. Heart and circulatory physiology.

[4]  M. Courtemanche,et al.  Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. , 1998, The American journal of physiology.

[5]  W. Evans,et al.  LONE AURICULAR FIBRILLATION , 1954, British heart journal.

[6]  I R Efimov,et al.  Reversal of Repolarization Gradient Does Not Reverse the Chirality of Shock‐Induced Reentry in the Rabbit Heart , 2000, Journal of cardiovascular electrophysiology.

[7]  J Jalife,et al.  High-frequency periodic sources underlie ventricular fibrillation in the isolated rabbit heart. , 2000, Circulation research.

[8]  Walter E. Garrey THE NATURE OF FIBRILLARY CONTRACTION OF THE HEART.—ITS RELATION TO TISSUE MASS AND FORM , 1914 .

[9]  I R Efimov,et al.  Direct Evidence of the Role of Virtual Electrode‐Induced Phase Singularity in Success and Failure of Defibrillation , 2000, Journal of cardiovascular electrophysiology.

[10]  Igor R. Efimov,et al.  Transition from circular to linear rotation of a vortex in an excitable cellular medium , 1990 .

[11]  S Nattel,et al.  Ionic mechanisms of regional action potential heterogeneity in the canine right atrium. , 1998, Circulation research.

[12]  A. Winfree Electrical instability in cardiac muscle: phase singularities and rotors. , 1989, Journal of theoretical biology.

[13]  A. Skanes,et al.  Spatiotemporal periodicity during atrial fibrillation in the isolated sheep heart. , 1998, Circulation.

[14]  I R Efimov,et al.  The mechanisms of the vulnerable window: the role of virtual electrodes and shock polarity. , 2001, Canadian journal of physiology and pharmacology.

[15]  H. Karagueuzian,et al.  Cellular mechanism of reentry induced by a strong electrical stimulus: implications for fibrillation and defibrillation. , 2001, Cardiovascular research.

[16]  A Garfinkel,et al.  Role of pectinate muscle bundles in the generation and maintenance of intra-atrial reentry: potential implications for the mechanism of conversion between atrial fibrillation and atrial flutter. , 1998, Circulation research.

[17]  L. J. Leon,et al.  Cholinergic Atrial Fibrillation in a Computer Model of a Two-Dimensional Sheet of Canine Atrial Cells With Realistic Ionic Properties , 2002, Circulation research.

[18]  P Coumel,et al.  Clinical approach to paroxysmal atrial fibrillation , 1990, Clinical cardiology.

[19]  B. Roth,et al.  Experimental and Theoretical Analysis of Phase Singularity Dynamics in Cardiac Tissue , 2001, Journal of cardiovascular electrophysiology.

[20]  J Jalife,et al.  A mechanism of transition from ventricular fibrillation to tachycardia : effect of calcium channel blockade on the dynamics of rotating waves. , 2000, Circulation research.

[21]  R. Gray,et al.  Spatial and temporal organization during cardiac fibrillation , 1998, Nature.

[22]  M. Fishbein,et al.  Pulmonary Veins and Ligament of Marshall as Sources of Rapid Activations in a Canine Model of Sustained Atrial Fibrillation , 2001, Circulation.

[23]  José Jalife,et al.  Vortices with linear cores in excitable media , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[24]  I R Efimov,et al.  Virtual electrode-induced phase singularity: a basic mechanism of defibrillation failure. , 1998, Circulation research.

[25]  S. Nattel New ideas about atrial fibrillation 50 years on , 2002, Nature.

[26]  M. Mansour,et al.  Left-to-Right Gradient of Atrial Frequencies During Acute Atrial Fibrillation in the Isolated Sheep Heart , 2001, Circulation.

[27]  F. Takens Detecting strange attractors in turbulence , 1981 .

[28]  J Jalife,et al.  Dynamics of wavelets and their role in atrial fibrillation in the isolated sheep heart. , 2000, Cardiovascular research.

[29]  S Nattel,et al.  Potential Ionic Mechanism for Repolarization Differences Between Canine Right and Left Atrium , 2001, Circulation research.

[30]  Kapral,et al.  Spiral waves in chaotic systems. , 1996, Physical review letters.

[31]  W. Rheinboldt,et al.  A COMPUTER MODEL OF ATRIAL FIBRILLATION. , 1964, American heart journal.

[32]  J Jalife,et al.  Reentry and fibrillation in the mouse heart. A challenge to the critical mass hypothesis. , 1999, Circulation research.

[33]  R. Gray,et al.  An Experimentalist's Approach to Accurate Localization of Phase Singularities during Reentry , 2004, Annals of Biomedical Engineering.

[34]  P. Welch The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[35]  José Jalife,et al.  Dynamics of rotating vortices in the Beeler-Reuter model of cardiac tissue , 1995 .

[36]  F. Roberge,et al.  Structural complexity effects on transverse propagation in a two-dimensional model of myocardium , 1991, IEEE Transactions on Biomedical Engineering.

[37]  J Jalife,et al.  Spatial and temporal organization in ventricular fibrillation. , 1999, Trends in cardiovascular medicine.

[38]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. , 1994, Circulation research.

[39]  Edward J. Vigmond,et al.  Computationally Efficient Model for Simulating Electrical Activity in Cardiac Tissue with Fiber Rotation , 1999, Annals of Biomedical Engineering.

[40]  S Nattel,et al.  Promotion of atrial fibrillation by heart failure in dogs: atrial remodeling of a different sort. , 1999, Circulation.

[41]  J Jalife,et al.  Stable microreentrant sources as a mechanism of atrial fibrillation in the isolated sheep heart. , 2000, Circulation.

[42]  Douglas L. Jones,et al.  Chronic rapid atrial pacing. Structural, functional, and electrophysiological characteristics of a new model of sustained atrial fibrillation. , 1995, Circulation.

[43]  S Nattel,et al.  Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodeling. , 2000, American journal of physiology. Heart and circulatory physiology.

[44]  G. W. Beeler,et al.  Reconstruction of the action potential of ventricular myocardial fibres , 1977, The Journal of physiology.

[45]  A. Winfree Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media. , 1991, Chaos.