Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model

Functional reentry in the heart can be caused by a wave front of excitation rotating around its edge. Previous simulations on the basis of monodomain cable equations predicted the existence of self-sustained, vortex-like wave fronts (scroll waves) rotating around a filament in three dimensions. In our simulations, we used the more accurate bidomain model with modified Beeler-Reuter ionic kinetics to study the dynamics of scroll-wave filaments in a 16 × 8 × 1.5-mm slab of ventricular tissue with straight fibers. Wave fronts were identified as the areas with inward current. Their edges represented the filaments. Both transmural and intramural reentries with I- and U-shaped filaments, respectively, were obtained by the S1-S2 point stimulation protocol through the virtual electrode-induced phase singularity mechanism. The filaments meandered along elongated trajectories and tended to attach to the tissue boundaries exposed to air (no current flow) rather than to the bath (zero extracellular potential). They completely detached from electroporated (zero transmembrane potential) boundaries. In our simulations, the presence of the bath led to generation of only U-shaped filaments, which survived for the 1.5-mm-thick slab but not for the slabs of 0.5- or 3-mm thicknesses. Thus boundary conditions may be another determinant of the type and dynamics of reentry.

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Nozzles for Supersonic Flow Without Shock Fronts

Journal of Applied Mechanics ◽

10.1115/1.4009355 ◽

1944 ◽

Vol 11 (2) ◽

pp. A93-A100

Author(s):

Ascher H. Shapiro

Keyword(s):

Cross Section ◽

Compressible Fluids ◽

Three Dimensions ◽

Infinite Length ◽

Constant Cross Section ◽

Nozzle Design ◽

Wave Fronts ◽

A Value ◽

Parallel Stream ◽

Shock Fronts

Abstract Flow patterns for compressible fluids at supersonic velocities are discussed, and it is shown that shock fronts form when neighboring Mach lines (envelopes of wave fronts originating from point disturbances) intersect. A criterion for divergence of Mach lines is developed for cases in which the passage is symmetrical in two or three dimensions and has a straight axis. This criterion is used as the basis for designing supersonic nozzles and diffusers. The analysis indicates that only a nozzle of infinite length can discharge a parallel stream into a tube of constant cross section without the formation of shock fronts. Methods are presented for designing nozzles of finite length, with the intensity of shock fronts reduced to as small a value as possible, and it is shown that nozzles of reasonable length may be designed so that shock fronts are insignificant. Experimental observations indicate that the proposed method of nozzle design is a practical one. With regard to supersonic diffusers having a straight axis, it is shown that shock fronts cannot be avoided, even though the diffuser is of infinite length. However, the methods of this paper may be used as an aid in determining the best diffuser design.

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Focal extracellular potential: a means to monitor electrical activity in single cardiac myocytes

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.2000.278.4.h1383 ◽

2000 ◽

Vol 278 (4) ◽

pp. H1383-H1394 ◽

Cited By ~ 5

Author(s):

Tara L. Riemer ◽

Leslie Tung

Keyword(s):

Action Potential ◽

Cardiac Myocytes ◽

Transmembrane Potential ◽

Membrane Conductance ◽

Electrical Activation ◽

Ventricular Myocyte ◽

Extracellular Potential ◽

Whole Cell ◽

Cell Recording ◽

Electrophysiological Signal

The focal extracellular potential (FEP) described in this study is an electrophysiological signal related to the transmembrane potential ( V m) of cardiac myocytes that avoids the mechanical fragility, interference with contraction, and intracellular contact associated with conventional whole cell recording. One end of a frog ventricular myocyte was secured into a glass holding pipette. The FEP was measured differentially between this pipette and a bath pipette while the cell was voltage- or current-clamped by a third whole cell pipette. The FEP appeared as an amplitude-truncated action potential, while FEP duration accurately reflected the action potential duration (APD) at 90% repolarization (APD90). FEP magnitude increased as the holding pipette K+ concentration ([K+]) was increased. The FEP-voltage relation was quasi-linear at negative V m with a slope that increased with elevated holding pipette [K+]. Increasing the membrane conductance inside the holding pipette by adding amphotericin B or cromakalim linearized the FEP-voltage relation across all V m. The FEP accurately reported electrical activation and APD90 during changes of stimulation frequency and episodes of cellular stretch.

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Improvement of Electrical Stimulation Protocol for Simultaneous Measurement of Extracellular Potential with On-Chip Multi-Electrode Array System

Japanese Journal of Applied Physics ◽

10.7567/jjap.51.06fk02 ◽

2012 ◽

Vol 51 (6S) ◽

pp. 06FK02 ◽

Cited By ~ 24

Author(s):

Tomoyuki Kaneko ◽

Fumimasa Nomura ◽

Akihiro Hattori ◽

Kenji Yasuda

Keyword(s):

Electrical Stimulation ◽

Simultaneous Measurement ◽

Electrode Array ◽

Extracellular Potential ◽

Stimulation Protocol ◽

On Chip ◽

Multi Electrode Array

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Transmembrane Potential Properties at the Core of Functional Reentrant Wave Fronts in Isolated Canine Right Atria

Circulation ◽

10.1161/01.cir.98.15.1556 ◽

1998 ◽

Vol 98 (15) ◽

pp. 1556-1567 ◽

Cited By ~ 25

Author(s):

Charles A. Athill ◽

Takanori Ikeda ◽

Young-Hoon Kim ◽

Tsu-Juey Wu ◽

Michael C. Fishbein ◽

...

Keyword(s):

Transmembrane Potential ◽

Wave Fronts ◽

The Core ◽

Right Atria

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Mechanisms of superiority of ascending ramp waveforms: new insights into mechanisms of shock-induced vulnerability and defibrillation

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.01117.2004 ◽

2005 ◽

Vol 289 (2) ◽

pp. H569-H577 ◽

Cited By ~ 15

Author(s):

Fujian Qu ◽

Li Li ◽

Vladimir P. Nikolski ◽

Vinod Sharma ◽

Igor R. Efimov

Keyword(s):

Optical Mapping ◽

Cellular Responses ◽

Electrode Polarization ◽

Bidomain Model ◽

Reentry Circuit ◽

Virtual Electrode

Monophasic ascending ramp (AR) and descending ramp (DR) waveforms are known to have significantly different defibrillation thresholds. We hypothesized that this difference arises due to differences in mechanisms of arrhythmia induction for the two waveforms. Rabbit hearts ( n = 10) were Langendorff perfused, and AR and DR waveforms (7, 20, and 40 ms) were randomly delivered from two line electrodes placed 10 mm apart on the anterior ventricular epicardium. We optically mapped cellular responses to shocks of various strengths (5, 10, and 20 V/cm) and coupling intervals (CIs; 120, 180, and 300 ms). Optical mapping revealed that maximum virtual electrode polarization (VEP) was reached at significantly different times for AR and DR of the same duration ( P < 0.05) for all tested CIs. As a result, VEP for AR were stronger than for DR at the end of the shock. Postshock break excitation resulting from AR generated faster propagation and typically could not form reentry. In contrast, partially dissipated VEP resulting from DR generated slower propagation; the wavefront was able to propagate into deexcited tissue and thus formed a shock-induced reentry circuit. Therefore, for the same delivered energy, AR was less proarrhythmic compared with DR. An active bidomain model was used to confirm the electrophysiological results. The VEP hypothesis explains differences in vulnerability associated with monophasic AR and DR waveforms and, by extension, the superior defibrillation efficacy of the AR waveform compared with the DR waveform.

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DYNAMICAL EFFECTS OF MYOCARDIAL ISCHEMIA IN ANISOTROPIC CARDIAC MODELS IN THREE DIMENSIONS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202507002534 ◽

2007 ◽

Vol 17 (12) ◽

pp. 1965-2008 ◽

Cited By ~ 18

Author(s):

PIERO COLLI FRANZONE ◽

LUCA F. PAVARINO ◽

SIMONE SCACCHI

Keyword(s):

Myocardial Ischemia ◽

Action Potential ◽

Numerical Simulations ◽

Cardiac Muscle ◽

Action Potential Duration ◽

Three Dimensions ◽

Extracellular Potential ◽

Anisotropic Structure ◽

Orthogonal Components ◽

Cardiac Excitation

The interaction between the presence of moderate or severe subendocardial ischemic regions and the anisotropic structure of the cardiac muscle is investigated here by means of numerical simulations based on anisotropic Bidomain and Monodomain models. The ischemic effects on cardiac excitation, recovery and distribution of action potential duration are discussed, showing the presence of ischemic epicardial markers. Extracellular potential distributions during the ST and TQ intervals are computed separately using non-stationary models. During the ST interval, the extracellular potential patterns differ from those simulated with stationary models used in the literature. These differences are explained by decomposing the cardiac current sources into conormal, axial and orthogonal components and by determining which component is dominant during the ST and TQ intervals.

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Mitochondrial depolarization and electrophysiological changes during ischemia in the rabbit and human heart

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00437.2014 ◽

2014 ◽

Vol 307 (8) ◽

pp. H1178-H1186 ◽

Cited By ~ 9

Author(s):

Matthew S. Sulkin ◽

Bas J. Boukens ◽

Megan Tetlow ◽

Sarah R. Gutbrod ◽

Fu Siong Ng ◽

...

Keyword(s):

Mitochondrial Membrane ◽

Human Heart ◽

Transmembrane Potential ◽

Optical Mapping ◽

Imaging Modality ◽

Ischemia Reperfusion ◽

Mitochondrial Depolarization ◽

Inner Mitochondrial Membrane ◽

Ventricular Tissue ◽

Direct Association

Instability of the inner mitochondrial membrane potential (ΔΨm) has been implicated in electrical dysfunction, including arrhythmogenesis during ischemia-reperfusion. Monitoring ΔΨm has led to conflicting results, where depolarization has been reported as sporadic and as a propagating wave. The present study was designed to resolve the aforementioned difference and determine the unknown relationship between ΔΨm and electrophysiology. We developed a novel imaging modality for simultaneous optical mapping of ΔΨm and transmembrane potential ( Vm). Optical mapping was performed using potentiometric dyes on preparations from 4 mouse hearts, 14 rabbit hearts, and 7 human hearts. Our data showed that during ischemia, ΔΨm depolarization is sporadic and changes asynchronously with electrophysiological changes. Spatially, ΔΨm depolarization was associated with action potential duration shortening but not conduction slowing. Analysis of focal activity indicated that ΔΨm is not different within the myocardium where the focus originates compared with normal ventricular tissue. Overall, our data suggest that during ischemia, mitochondria maintain their function at the expense of sarcolemmal electrophysiology, but ΔΨm depolarization does not have a direct association to ischemia-induced arrhythmias.

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