Various ways to make phase singularities by electric shock

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

The Na+/K+ pump is an important modulator of refractoriness and rotor dynamics in human atrial tissue

Pharmacological treatment of atrial fibrillation (AF) exhibits limited efficacy. Further developments require a comprehensive characterization of ionic modulators of electrophysiology in human atria. Our aim is to systematically investigate the relative importance of ionic properties in modulating excitability, refractoriness, and rotor dynamics in human atria before and after AF-related electrical remodeling (AFER). Computer simulations of single cell and tissue atrial electrophysiology were conducted using two human atrial action potential (AP) models. Changes in AP, refractory period (RP), conduction velocity (CV), and rotor dynamics caused by alterations in key properties of all atrial ionic currents were characterized before and after AFER. Results show that the investigated human atrial electrophysiological properties are primarily modulated by maximal value of Na(+)/K(+) pump current (G(NaK)) as well as conductances of inward rectifier potassium current (G(K1)) and fast inward sodium current (G(Na)). G(NaK) plays a fundamental role through both electrogenic and homeostatic modulation of AP duration (APD), APD restitution, RP, and reentrant dominant frequency (DF). G(K1) controls DF through modulation of AP, APD restitution, RP, and CV. G(Na) is key in determining DF through alteration of CV and RP, particularly in AFER. Changes in ionic currents have qualitatively similar effects in control and AFER, but effects are smaller in AFER. The systematic analysis conducted in this study unravels the important role of the Na(+)/K(+) pump current in determining human atrial electrophysiology.

How hyperpolarization and the recovery of excitability affect propagation through a virtual anode in the heart

Researchers have suggested that the fate of a shock-induced wave front at the edge of a "virtual anode" (a region hyperpolarized by the shock) is a key factor determining success or failure during defibrillation of the heart. In this paper, we use a simple one-dimensional computer model to examine propagation speed through a hyperpolarized region. Our goal is to test the hypothesis that rapid propagation through a virtual anode can cause failure of propagation at the edge of the virtual anode. The calculations support this hypothesis and suggest that the time constant of the sodium inactivation gate is an important parameter. These results may be significant in understanding the mechanism of the upper limit of vulnerability.

The topology of defibrillation

We describe how Art Winfree's ideas about phase singularities can be used to understand the response of cardiac tissue with a random preexisting pattern of reentrant waves (fibrillation) to a large brief current stimulus. This discussion is organized around spatial dimension, beginning with a discussion of reentry on a periodic ring, followed by reentry in a two-dimensional planar domain (spiral waves), and ending with consideration of three-dimensional reentrant patterns (scroll waves). In all cases, we show how reentrant activity is changed by the application of a shock, describing conditions under which defibrillation is successful or not. Using topological arguments we draw the general conclusion that with a generic placement of stimulating electrodes, large-scale virtual electrodes do not give an adequate explanation for the mechanism of defibrillation.

Restitution Properties During Ventricular Fibrillation in the In Situ Swine Heart

Background— Although restitution has been hypothesized to determine action potential duration (APD) during ventricular fibrillation (VF), cardiac memory may also be important.

Methods and Results— Transmembrane recordings were made with a floating microelectrode from the anterior right ventricular wall in 6 pigs during up to 60 seconds of VF. The recordings were divided into 5-second intervals, and APD 60 and the diastolic interval (DI) were calculated for each activation cycle throughout each interval. Stepwise linear regression was used to determine how well each APD 60 [APD 60 (n)] was predicted by the 4 previous DIs (n−1, n−2, n−3, n−4) and the 3 previous APD 60 s (n−1, n−2, n−3). A mean±SD of 3±1.5 of the variables entered the regression equation. DI(n−1) (70% of intervals) and APD 60 (n−1) (71% of intervals) appeared most frequently in the regression equations and were the first or second variables entered during the stepwise regression in 87% and 76% of the intervals in which they were present, respectively. The coefficients of DI(n−1) and APD 60 (n−1) were positive 89% and 98% of the time, respectively. R 2 of the regression for all entered variables during all intervals was 0.39±0.05.

Conclusions— The high incidence and positive coefficient of DI(n−1) indicate that restitution is important in determining APD during VF, whereas the similarly high incidence and positive coefficient of APD(n−1) indicate that cardiac memory is equally important. The finding that the regression equation accounts for only 39% of the variability of APD indicates that factors other than restitution and memory are also important in determining APD during VF.

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 x 8 x 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.

Art Winfree and the bidomain model of cardiac tissue

This paper reviews Art Winfree's contributions to the bidomain model of cardiac tissue. Specifically, he first predicted quatrefoil reentry, he showed that an S1 refractory gradient is not required for an S2 stimulus to induce reentry, and his work on spiral wave meandering led to studies on how the path of the tip of a spiral wave is influenced by tissue anisotropy.

Interplay of ionic and structural heterogeneity on functional action potential duration gradients: Implications for arrhythmogenesis

Action potential duration (APD) dispersion in the heart is governed by the underlying cellular architecture and the spatial distribution of the membrane properties. Understanding the contribution of each factor is important in designing more effective methods for the control of arrhythmias. Recent experimental studies have shown that the insertion of structural barriers in ionically heterogeneous tissue facilitates the formation of unidirectional block and discordant alternans. In this work, computational modeling is used to examine the effect of internal obstacles on the formation of functional APD gradients in ionically heterogeneous tissue. Intrinsic APD differences are introduced by assigning two discrete cell types to each half of a square domain. The combined effect of structural and ionic heterogeneities is shown to produce gradients in APD that are oblique to both the intrinsic gradients in APD and the physical boundary. Simulation results are presented that show that the magnitude and spatial extent of the subsequent APD gradients are modulated by the size and orientation of the obstacle, the degree of anisotropy, and the location of the pacing site. Long, thin internal obstacles are found to produce the greatest dispersion in APD. The combination of internal obstacles and ionic heterogeneities is shown to produce a substrate for re-entrant excitation following a pair of near threshold point stimuli. (c) 2002 American Institute of Physics.

The pinwheel experiment re-revisited

Virtual electrode induced phase singularity hypothesis explains the origin of cardiac arrhythmias caused by artificial electrical induction of rotors, i.e. vortex-like self-sustained sources of activity. This mechanism is thought to underlie both stimulus-induced arrhythmias and shock defibrillation therapy. In this paper, we extend this hypothesis to three dimensions using the bidomain model of cardiac tissue. We predict that virtual electrode polarization can produce three topologically distinct types of rotors anchored to: (1) transmural I-shaped scroll wave filaments; (2) near-surface U-shaped scroll wave filaments; and (3) intramural O-shaped scroll wave filaments.

An S1 gradient of refractoriness is not essential for reentry induction by an S2 stimulus

This communication reports a numerical simulation of reentry induction by successive stimulation (S1-S2) that does not require an S1 gradient of refractoriness. The S1 action potential is uniform in space, so before the S2 stimulus there is no refractory gradient. Nevertheless, a unipolar S2 stimulus initiates quatrefoil reentry. The result supports the growing realization that virtual electrodes, hyperpolarization, de-excitation, and break excitation may be important during reentry induction.