A spontaneously active focus drives a model atrial sheet more easily than a model ventricular sheet.

Tachycardias can be produced when focal activity at ectopic locations in either the atria or the ventricles propagates into the surrounding quiescent myocardium. Isolated rabbit atrioventricular nodal cells were coupled by an electronic circuit to a real-time simulation of an array of cell models. We investigated the critical size of an automatic focus for the activation of two-dimensional arrays made up of either ventricular or atrial model cells. Over a range of coupling conductances for the arrays, the critical size of the focus cell group for successful propagation was smaller for activation of an atrial versus a ventricular array. Failure of activation of the arrays at smaller focus sizes was due to the inhibition of pacing of the nodal cells. At low levels of coupling conductance, the ventricular arrays required larger sizes of the focus due to failure of propagation even when the focus was spontaneously active. The major differences between activation of the atrial and ventricular arrays is due to the higher membrane resistance (lower inward rectifier current) of the atrial cells.

Measurements of calcium transients in ventricular cells during discontinuous action potential conduction.

The L-type calcium current (I(Ca)) is important in sustaining propagation during discontinuous conduction. In addition, I(Ca) is altered during discontinuous conduction, which may result in changes in the intracellular calcium transient. To study this, we have combined the ability to monitor intracellular calcium concentration ([Ca(2+)](i)) in an isolated cardiac cell using confocal scanning laser fluorescence microscopy with our "coupling clamp" technique, which allows action potential propagation from the real cell to a real-time simulation of a model cell. Coupling a real cell to a model cell with a value of coupling conductance (G(C) = 8 nS) just above the critical value for action potential propagation results in both an increased amplitude and an increased rate of rise of the calcium transient. Similar but smaller changes in the calcium transient are caused by increasing G(C) to 20 nS. The increase of [Ca(2+)](i) by discontinuous conduction is less than the increase of I(Ca), which may indicate that much of [Ca(2+)](i) is the result of calcium released from the sarcoplasmic reticulum rather than the integration of I(Ca).

Electrical interactions between a real ventricular cell and an anisotropic two-dimensional sheet of model cells.

We have extended our "coupling clamp" technique, in which we couple a real cell to a real-time simulation of a model cell, to now incorporate a real cardiac cell as the central element of a two-dimensional sheet of model cells, in which the coupling conductances may be different in the x and y directions and a specific region of lack of coupling conductance may serve as a resistive barrier. We stimulated the real cell in the central location and determined the critical size of the real cell for successful activation of the entire sheet. We found that this critical size was decreased when anisotropy was present compared with the isotropic case and was further decreased when the central site of stimulation was close to the resistive barrier. The heart normally has some degree of anisotropy, and it has been shown that the remodeling that occurs in peri-infarction zones produces a particular loss of lateral connections compared with end-to-end connections among heart cells. We propose that the normal existence of anisotropy and enhancement of the degree of anisotropy both by loss of lateral gap junctions and the development of resistive barriers may play a facilitating role in the development of ectopic foci that may lead to cardiac arrhythmias.

Effects of anisotropy on the development of cardiac arrhythmias associated with focal activity.

The anisotropy that normally exists in the myocardium may be either enhanced in peri-infarction zones by loss of lateral cell connections or reduced by redistribution of gap junctions. To test how the degree of anisotropy affects the development of ectopic focal activity, we carried out computer simulations in which a model of an ectopic focus is incorporated as the central element of a two-dimensional sheet of ventricular cells. At low values of intercellular coupling conductance (Gc), the focus region is spontaneously active, but the limited intercellular current flow inhibits propagation. At high Gc, automaticity is suppressed by the loading effects of the surrounding cells. At intermediate Gc, the ectopic activity may propagate into the sheet. In the case of isotropic coupling, the minimum size of the focus region for propagation to occur (in terms of number of collaborating cells within the focus) is as small as approximately ten cells, and this number decreases with increasing anisotropy. Thus, the presence of anisotropy facilitates the development of ectopic focal activity. We conclude that the remodeling that occurs in peri-infarction zones may create a substrate that either facilitates (enhanced anisotropy) or inhibits (reduced anisotropy) the development of cardiac arrhythmias associated with ectopic focal activity.

Effects of ischemia on discontinuous action potential conduction in hybrid pairs of ventricular cells.

BACKGROUND: Acute ischemia often occurs in cardiac tissue that has prior injury, resulting in spatially inhomogeneous distributions of membrane properties and intercellular coupling. Changes in action potential conduction with ischemia, which can be associated with release of catecholamines, may be particularly important in tissue that has discontinuous conduction resulting from prior infarction, hypertrophy, or myopathy. METHODS AND RESULTS: Isolated guinea pig ventricular myocytes were electrically coupled by a coupling-clamp circuit to a comprehensive computer model of a guinea pig ventricular myocyte to assess alterations in the critical value of coupling conductance required for action potential conduction from the real cell to the model cell when the real cell was exposed to a solution that included hypoxia, acidosis, and an elevated extracellular potassium concentration to simulate acute ischemia. The "ischemic" solution increased critical coupling conductance from 6.2+/-0.1 to 7.4+/-0.2 nS and decreased the associated maximum conduction delay from 31+/-1 to 23+/-1 ms (mean+/-SEM, n=11). The ischemic solution plus 1 micromol/L norepinephrine decreased critical coupling conductance from 5.9+/-0.2 to 5.0+/-0.1 nS and increased maximum conduction delay from 31+/-2 to 54+/-4 ms (mean+/-SEM, n=8). CONCLUSIONS: The release of catecholamines with ischemia, in a setting of partially uncoupled cells, may play a major role in producing long conduction delays, which may allow reentrant pathways.

Electrical interactions among real cardiac cells and cell models in a linear strand.

Previous work with model systems for action potential conduction have been restricted to conduction between two real cells or conduction between a model cell and a real cell. The inclusion of additional elements to make a linear strand has allowed us to investigate the interactions between cells at a higher level of complexity. When, in the simplest case of a linear strand of three elements, the conductance between elements 2 and 3 (GC2) is varied, this affects the success or failure of propagation between elements 1 and 2 (coupled by GC1) as well as the success or failure of propagation between elements 2 and 3. Several major features were illustrated. 1) When GC1 was only slightly greater than the coupling conductance required for successful propagation between a model cell and a real cell, addition of a third element of the strand either prevented conduction from element 1 to element 2 (when GC2 was high) or allowed conduction from element 1 to element 2 but not conduction from element 2 to element 3 (when GC2 was low). 2) For higher levels of GC1, there was an allowable "window" of values of GC2 for successful conduction from element 1 through to element 3. The size of this allowable window of GC2 values increased with increasing values of GC1, and this increase was produced by increases in the upper bound of GC2 values. 3) When the size of the central element of the strand was reduced, this facilitated conduction through the strand, increasing the range of the allowable window of GC2 values. The overall success or failure of conduction through a structure of cells that has a spatially inhomogeneous distribution of coupling conductances cannot be predicted simply by the average or the minimum value of coupling conductance but may depend on the actual spatial distribution of these conductances.

Electrical interactions between a rabbit atrial cell and a nodal cell model.

Atrial activation involves interactions between cells with automaticity and slow-response action potentials with cells that are intrinsically quiescent with fast-response action potentials. Understanding normal and abnormal atrial activity requires an understanding of this process. We studied interactions of a cell with spontaneous activity, represented by a "real-time" simulation of a model of the rabbit sinoatrial (SA) node cell, simultaneously being electrically coupled via our "coupling clamp" circuit to a real, isolated atrial myocyte with variations in coupling conductance (Gc) or stimulus frequency. The atrial cells were able to be driven at a regular rate by a single SA node model (SAN model) cell. Critical Gc for entrainment of the SAN model cell to a nonstimulated atrial cell was 0.55 +/- 0.05 nS (n = 7), and the critical Gc that allowed entrainment when the atrial cell was directly paced at a basic cycle length of 300 ms was 0.32 +/- 0.01 nS (n = 7). For each atrial cell we found periodic phenomena of synchronization other than 1:1 entrainment when Gc was between 0.1 and 0.3 nS, below the value required for frequency entrainment, when the atrial cell was directly driven at a basic cycle length of either 300 or 600 ms. In conclusion, the high input resistance of the atrial cells allows successful entrainment of nodal and atrial cells at low values of Gc, but further uncoupling produces arrhythmic interactions.

Determinants of action potential initiation in isolated rabbit atrial and ventricular myocytes.

Action potential conduction through the atrium and the ventricle of the heart depends on the membrane properties of the atrial and ventricular cells, particularly with respect to the determinants of the initiation of action potentials in each cell type. We have utilized both current- and voltage-clamp techniques on isolated cells to examine biophysical properties of the two cell types at physiological temperature. The resting membrane potential, action potential amplitude, current threshold, voltage threshold, and maximum rate of rise measured from atrial cells (-80 +/- 1 mV, 109 +/- 3 mV, 0.69 +/- 0.05 nA, -59 +/- 1 mV, and 206 +/- 17 V/s, respectively; means +/- SE) differed significantly (P < 0.05) from those values measured from ventricular cells (-82.7 +/- 0.4 mV, 127 +/- 1 mV, 2.45 +/- 0.13 nA, -46 +/- 2 mV, and 395 +/- 21 V/s, respectively). Input impedance, capacitance, time constant, and critical depolarization for activation also were significantly different between atrial (341 +/- 41 M omega, 70 +/- 4 pF, 23.8 +/- 2. 3 ms, and 19 +/- 1 mV, respectively) and ventricular (16.5 +/- 5.4 M omega, 99 +/- 4.3 pF, 1.56 +/- 0.32 ms, and 36 +/- 1 mV, respectively) cells. The major mechanism of these differences is the much greater magnitude of the inward rectifying potassium current in ventricular cells compared with that in atrial cells, with an additional difference of an apparently lower availability of inward Na current in atrial cells. These differences in the two cell types may be important in allowing the atrial cells to be driven successfully by normal regions of automaticity (e.g., the sinoatrial node), whereas ventricular cells would suppress action potential initiation from a region of automaticity (e.g., an ectopic focus).

Pacemaker synchronization of electrically coupled rabbit sinoatrial node cells.

The effects of intercellular coupling conductance on the activity of two electrically coupled isolated rabbit sinoatrial nodal cells were investigated. A computer-controlled version of the "coupling clamp" technique was used in which isolated sinoatrial nodal cells, not physically in contact with each other, were electrically coupled at various values of ohmic coupling conductance, mimicking the effects of mutual interaction by electrical coupling through gap junctional channels. We demonstrate the existence of four types of electrical behavior of coupled spontaneously active cells. As the coupling conductance is progressively increased, the cells exhibit: (a) independent pacemaking at low coupling conductances, (b) complex dynamics of activity with mutual interactions, (c) entrainment of action potential frequency at a 1:1 ratio with different action potential waveforms, and (d) entrainment of action potentials at the same frequency of activation and virtually identical action potential waveforms. The critical value of coupling conductance required for 1:1 frequency entrainment was <0.5 nS in each of the five cell pairs studied. The common interbeat interval at a relatively high coupling conductance (10 nS), which is sufficient to produce entrainment of frequency and also identical action potential waveforms, is determined most by the intrinsically faster pacemaker cell and it can be predicted from the diastolic depolarization times of both cells. Evidence is provided that, at low coupling conductances, mutual pacemaker synchronization results mainly from the phase-resetting effects of the action potential of one cell on the depolarization phase of the other. At high coupling conductances, the tonic, diastolic interactions become more important.

Experimental model for an ectopic focus coupled to ventricular cells.

BACKGROUND: We used a mathematical model of a sinoatrial nodal cell (SAN model) electrically coupled to real ventricular cells (VCs) to investigate action potential conduction from an automatic focus. METHODS AND RESULTS: Since input resistance of a VC is less than that of an SAN cell, coupling of the SAN model, with a size factor of 1, to a VC produced either (1) spontaneous pacing at the slower rate of the SAN model but without driving (activation) of the VC for lower values of coupling conductance (Gj) or (2) inhibition of pacing of the SAN model by electrical coupling to the VC for higher values of Gj. When the SAN model was adjusted in size to be 3 to 5 times larger than a sinoatrial nodal cell, thus making effective SAN model capacitance 3 to 5 times larger and input resistance 3 to 5 times smaller, the SAN model propagated activity to the coupled VC for Gj above a critical value. When the VC was paced at 1 Hz, the coupled cell pair demonstrated a stable rhythm of alternating cycle lengths and alternating conduction directions. By increasing pacing frequency to 2 Hz, we converted this rhythm to a regular 2-Hz frequency in which each action potential originated in the VC. More complex periodic interactions were observed at intermediate cycle lengths and lower or higher values of Gj. CONCLUSIONS: The phenomena we observed demonstrate the critical role of the size of an automatic focus as well as the coupling in the propagation of activity from the focus into surrounding myocardium.

Modulating L-type calcium current affects discontinuous cardiac action potential conduction.

We have used pairs of cardiac cells (i.e., one real guinea pig ventricular cell and a real-time simulation of a numerical model of a guinea pig ventricular cell) to evaluate the effects on action potential conduction of a variable coupling conductance in combination with agents that either increase or decrease the magnitude of the L-type calcium current. For the cell pairs studied, we applied a direct repetitive stimulation to the real cell, making it the "leader" cell of the cell pair. We have demonstrated that significant delays in action potential conduction for a cell pair can occur either with a decreased value of coupling conductance or with an asymmetry in size such that the follower cell is larger than the leader cell. In both conditions we have shown that isoproterenol, applied to the real cell at very low concentrations, can reversibly decrease the critical coupling conductance (below which action potential conduction fails) for a cell pair with fixed cell sizes, or, for a fixed value of coupling conductance, increase the maximum allowable asymmetry in cell size for successful conduction. For either of these effects, we were able to show that treatment of the real cell with BayK 8644, which more specifically increases the magnitude of the L-type calcium current, was able to mimic the actions of isoproterenol. Treatment of the leader cell of the cell pair (the real cell) with nifedipine, which selectively lowers the magnitude of the L-type calcium current, had effects opposite those of isoproterenol or BayK 8644. The actions of nifedipine, isoproterenol, and BayK 8644 are all limited to conditions in which the conduction delay is on the order of 5 ms or more, whether this delay is caused by limited coupling conductance or by asymmetry in size of the cells. This limitation is consistent with the time course of the L-type calcium current and suggests that the effects of calcium channel blockers or beta-adrenergic blocking drugs, in addition to being selective for regions of the heart that depend on the L-type calcium current for the upstroke of the action potential, would also be somewhat selective for regions of the heart that have discontinuous conduction, either normally or because of some pathological condition.

Image-based display of activation patterns derived from scattered electrodes.

Presentation of electrophysiologic data, such as activation patterns, can take many forms, the most common of which are hand- or machine-drawn isochronal maps. We present an image-based method which provides accurate matching between electrophysiologic data and the anatomic sites from which the data were derived. This method is linear, simple, and straightforward to implement, and presents results in a format which is easy to understand and interpret.