Effects of simulated ischemia on spiral wave stability

Regional hyperkalemia during acute myocardial ischemia is a major factor promoting electrophysiological abnormalities leading to ventricular fibrillation (VF). However, steep action potential duration restitution, recently proposed to be a major determinant of VF, is typically decreased rather than increased by hyperkalemia and acute ischemia. To investigate this apparent contradiction, we simulated the effects of regional hyperkalemia and other ischemic components (anoxia and acidosis) on the stability of spiral wave reentry in simulated two-dimensional cardiac tissue by use of the Luo-Rudy ventricular action potential model. We found that the hyperkalemic “ischemic” area promotes wavebreak in the surrounding normal tissue by accelerating the rate of spiral wave reentry, even after the depolarized ischemic area itself has become unexcitable. Furthermore, wavebreak and fibrillation can be prevented if the dynamical instability of the normal tissue is reduced significantly by targeting electrical restitution properties, suggesting a novel therapeutic approach.

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Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1999.276.1.h269 ◽

1999 ◽

Vol 276 (1) ◽

pp. H269-H283 ◽

Cited By ~ 111

Author(s):

Zhilin Qu ◽

James N. Weiss ◽

Alan Garfinkel

Keyword(s):

Action Potential ◽

Antiarrhythmic Drugs ◽

Cardiac Tissue ◽

Potential Model ◽

Spiral Wave ◽

Spiral Waves ◽

Two Dimensional ◽

Recovery From Inactivation ◽

Main Determinants ◽

The Stability

Spiral wave breakup is a proposed mechanism underlying the transition from ventricular tachycardia to fibrillation. We examined the importance of the restitution of action potential duration (APD) and of conduction velocity (CV) to the stability of spiral wave reentry in a two-dimensional sheet of simulated cardiac tissue. The Luo-Rudy ventricular action potential model was modified to eliminate its restitution properties, which are caused by deactivation or recovery from inactivation of K+, Ca2+, and Na+ currents ( I K, I Ca, and I Na, respectively). In this model, we find that 1) restitution of I Ca and I Na are the main determinants of the steepness of APD restitution; 2) for promoting spiral breakup, the range of diastolic intervals over which the APD restitution slope is steep is more important than the maximum steepness; 3) CV restitution promotes spiral wave breakup independently of APD restitution; and 4) “defibrillation” of multiple spiral wave reentry is most effectively achieved by combining an antifibrillatory intervention based on altering restitution with an antitachycardia intervention. These findings suggest a novel paradigm for developing effective antiarrhythmic drugs.

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Effects of Na+ and K+ channel blockade on vulnerability to and termination of fibrillation in simulated normal cardiac tissue

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00241.2005 ◽

2005 ◽

Vol 289 (4) ◽

pp. H1692-H1701 ◽

Cited By ~ 29

Author(s):

Zhilin Qu ◽

James N. Weiss

Keyword(s):

Action Potential ◽

Cardiac Tissue ◽

Theoretical Perspective ◽

Conduction Block ◽

Dynamical Instability ◽

K Channel ◽

Channel Blockade ◽

Wave Instability ◽

Transient Time ◽

Underlying Mechanisms

Na+ and K+ channel-blocking drugs have anti- and proarrhythmic effects. Their effects during fibrillation, however, remain poorly understood. We used computer simulation of a two-dimensional (2-D) structurally normal tissue model with phase I of the Luo-Rudy action potential model to study the effects of Na+ and K+ channel blockade on vulnerability to and termination of reentry in simulated multiple-wavelet and mother rotor fibrillation. Our main findings are as follows: 1) Na+ channel blockade decreased, whereas K+ channel blockade increased, the vulnerable window of reentry in heterogeneous 2-D tissue because of opposing effects on dynamical wave instability. 2) Na+ channel blockade increased the cycle length of reentry more than it increased refractoriness. In multiple-wavelet fibrillation, Na+ channel blockade first increased and then decreased the average duration or transient time (<Ts>) of fibrillation. In mother rotor fibrillation, Na+ channel blockade caused peripheral fibrillatory conduction block to resolve and the mother rotor to drift, leading to self-termination or sustained tachycardia. 3) K+ channel blockade increased dynamical instability by steepening action potential duration restitution. In multiple-wavelet fibrillation, this effect shortened <Ts> because of enhanced wave instability. In mother rotor fibrillation, this effect converted mother rotor fibrillation to multiple-wavelet fibrillation, which then could self-terminate. Our findings help illuminate, from a theoretical perspective, the possible underlying mechanisms of termination of different types of fibrillation by antiarrhythmic drugs.

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A computationally efficient electrophysiological model of human ventricular cells

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00731.2001 ◽

2002 ◽

Vol 282 (6) ◽

pp. H2296-H2308 ◽

Cited By ~ 94

Author(s):

O. Bernus ◽

R. Wilders ◽

C. W. Zemlin ◽

H. Verschelde ◽

A. V. Panfilov

Keyword(s):

Action Potential ◽

Cardiac Tissue ◽

Spiral Wave ◽

Ionic Currents ◽

Average Frequency ◽

Computationally Efficient ◽

Variable Model ◽

Potential Shape ◽

Ventricular Cells ◽

Ventricular Tissue

Recent experimental and theoretical results have stressed the importance of modeling studies of reentrant arrhythmias in cardiac tissue and at the whole heart level. We introduce a six-variable model obtained by a reformulation of the Priebe-Beuckelmann model of a single human ventricular cell. The reformulated model is 4.9 times faster for numerical computations and it is more stable than the original model. It retains the action potential shape at various frequencies, restitution of action potential duration, and restitution of conduction velocity. We were able to reproduce the main properties of epicardial, endocardial, and M cells by modifying selected ionic currents. We performed a simulation study of spiral wave behavior in a two-dimensional sheet of human ventricular tissue and showed that spiral waves have a frequency of 3.3 Hz and a linear core of ∼50-mm diameter that rotates with an average frequency of 0.62 rad/s. Simulation results agreed with experimental data. In conclusion, the proposed model is suitable for efficient and accurate studies of reentrant phenomena in human ventricular tissue.

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VULNERABILITY TO REENTRY, AND DRIFT, STABILITY AND BREAKDOWN OF SPIRAL WAVES IN A LINEAR GRADIENT OF GK IN A LUO–RUDY 1 VIRTUAL VENTRICULAR TISSUE

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127403009010 ◽

2003 ◽

Vol 13 (12) ◽

pp. 3865-3871 ◽

Cited By ~ 2

Author(s):

O. V. ASLANIDI ◽

R. H. CLAYTON ◽

A. V. HOLDEN ◽

H. K. PHILLIPS ◽

R. J. WARD

Keyword(s):

Action Potential ◽

Velocity Component ◽

Action Potential Duration ◽

Cardiac Tissue ◽

Spiral Wave ◽

Spiral Waves ◽

Linear Gradient ◽

Wave Solutions ◽

Ventricular Tissue ◽

Vulnerable Window

The vulnerable window in a heterogeneous virtual LRl cardiac tissue, with a linear gradient in GK, is wider when following propagation down the gradient, towards tissue with longer action potential duration, than when following propagation up the gradient. Spiral wave solutions in a uniform linear gradient in GK drift, with a velocity component along the gradient of the order of mm/s, towards tissue with a longer APD.

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Spiral wave stability in cardiac tissue with biphasic restitution

Physical Review E ◽

10.1103/physreve.68.021917 ◽

2003 ◽

Vol 68 (2) ◽

Cited By ~ 9

Author(s):

O. Bernus ◽

H. Verschelde ◽

A. V. Panfilov

Keyword(s):

Cardiac Tissue ◽

Spiral Wave ◽

Wave Stability

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Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00608.2002 ◽

2003 ◽

Vol 284 (2) ◽

pp. H542-H548 ◽

Cited By ~ 68

Author(s):

K. H. W. J. Ten Tusscher ◽

A. V. Panfilov

Keyword(s):

Action Potential ◽

Cardiac Tissue ◽

Potential Model ◽

Phase 1 ◽

Spiral Wave ◽

Spiral Waves ◽

Local Current ◽

Gradient Component ◽

Reentrant Excitation ◽

Ventricular Action Potential

Heterogeneity of cardiac tissue is an important factor determining the initiation and dynamics of cardiac arrhythmias. In this paper, we studied the effects of gradients of electrophysiological heterogeneity on reentrant excitation patterns using computer simulations. We investigated the dynamics of spiral waves in a two-dimensional sheet of cardiac tissue described by the Luo-Rudy phase 1 (LR1) ventricular action potential model. A gradient of action potential duration (APD) was imposed by gradually varying the local current density of K+ current or inward rectifying K+ current along one axis of the tissue sheet. We show that a gradient of APD resulted in spiral wave drift. This drift consisted of two components. The longitudinal (along the gradient) component was always directed toward regions of longer spiral wave period. The transverse (perpendicular to the gradient) component had a direction dependent on the direction of rotation of the spiral wave. We estimated the velocity of the drift as a function of the magnitude of the gradient and discuss its implications.

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Electrical refractory period restitution and spiral wave reentry in simulated cardiac tissue

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00898.2001 ◽

2002 ◽

Vol 283 (1) ◽

pp. H448-H460 ◽

Cited By ~ 41

Author(s):

Fagen Xie ◽

Zhilin Qu ◽

Alan Garfinkel ◽

James N. Weiss

Keyword(s):

Refractory Period ◽

Cardiac Tissue ◽

Cell Model ◽

Experimental Studies ◽

Spiral Wave ◽

Transmembrane Potentials ◽

Wave Stability ◽

Cardiac Action ◽

Ventricular Tissue ◽

Atrial Cell

Theoretical and experimental studies have shown that restitution of the cardiac action potential (AP) duration (APD) plays a major role in predisposing ventricular tachycardia to degenerate to ventricular fibrillation, whereas its role in atrial fibrillation is unclear. We used the Courtemanche human atrial cell model and the Luo-Rudy guinea pig ventricular model to compare the roles of electrical restitution in destabilizing spiral wave reentry in simulated two-dimensional homogeneous atrial and ventricular tissue. Because atrial AP morphology is complex, we also validated the usefulness of effective refractory period (ERP) restitution. ERP restitution correlated best with APD restitution at transmembrane potentials greater than or equal to −62 mV, and its steepness was a reliable predictor of spiral wave phenotype (stable, meandering, hypermeandering, and breakup) in both atrial and ventricular tissue. Spiral breakup or single hypermeandering spirals occurred when the slope of ERP restitution exceeded 1 at short diastolic intervals. Thus ERP restitution, which is easier to measure clinically than APD restitution, is a reliable determinant of spiral wave stability in simulated atrial and ventricular tissue.

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