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Circulation. 1999;99:1623-1629

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(Circulation. 1999;99:1623-1629.)
© 1999 American Heart Association, Inc.


Basic Science Reports

Effects of Ischemia on Discontinuous Action Potential Conduction in Hybrid Pairs of Ventricular Cells

Ronald Wilders, PhD; E. Etienne Verheijck, PhD; Ronald W. Joyner, MD, PhD; David A. Golod, MSc; Rajiv Kumar, PhD; Antoni C. G. van Ginneken, PhD; Lennart N. Bouman, MD; Habo J. Jongsma, PhD

From the Department of Medical Physiology and Sports Medicine, Utrecht University (R.W., E.E.V., H.J.J.), and the Academic Medical Center, University of Amsterdam, Department of Physiology, Amsterdam (R.W., E.E.V., A.C.G.v.G., L.N.B.), Netherlands; and Todd Franklin Cardiac Research Laboratory, The Children's Heart Center, Department of Pediatrics, Emory University, Atlanta, Ga (R.W.J., D.A.G., R.K.).

Correspondence to Ronald Wilders, Department of Medical Physiology and Sports Medicine, Utrecht University, Universiteitsweg 100, 3584 CG Utrecht, PO Box 80043, 3508 TA Utrecht, Netherlands. E-mail r.wilders{at}med.uu.nl


*    Abstract
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*Abstract
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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 µmol/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.


Key Words: arrhythmia • catecholamines • conduction • ischemia


*    Introduction
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up arrowAbstract
*Introduction
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down arrowDiscussion
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Many episodes of acute myocardial ischemia occur in tissue that is already abnormal, ie, that has spatially inhomogeneous distributions of membrane properties and intercellular coupling resulting from prior injury. Sudden cardiac death is commonly associated with a preexisting structural abnormality1 from prior infarction, hypertrophy, or myopathy that may serve as a substrate from which arrhythmias can arise. Conduction becomes slow and discontinuous, with an irregular (zigzag) spatial pattern.2 Surviving muscle fiber bundles are separated by connective tissue, and extracellular recordings show fractionated electrograms with discrete deflections.3 Action potentials in these regions have prepotentials and notches due to electrotonic interactions with nearby cells.4 During acute ischemia, excessive concentrations of catecholamines are observed within the unperfused myocardium.5 Depletion of catecholamines or treatment with ß-blockers decreases the incidence of ischemia-induced arrhythmias.6

In normal myocardium, fast sodium current (INa) is responsible for excitability and conduction. Under conditions of discontinuous conduction, however, L-type calcium current (ICa,L) may play a major role in sustaining conduction.7 8 9 10 For a pair of electrically coupled ventricular myocytes, we have previously shown that block of ICa,L significantly increased conduction delay when cells were relatively uncoupled but had no effect on conduction when cells were well coupled.7 Our further study using pharmacological modulation of ICa,L8 suggested that the facilitating effects on conduction produced by ß-agonist activity might counteract the inhibitory effects on conduction of acute ischemia.

Techniques have been developed11 to study isolated cardiac cells under conditions incorporating many of the known phenomena of myocardial ischemia, including hypoxia, elevated potassium, lowered pH, elevated lactate, and lack of glucose. Combining these techniques with our model-clamp technique,12 we have studied the effects of varying coupling conductance for a pair of electrically coupled cells in which the leader (stimulated) cell is a real isolated guinea pig ventricular cell (either in a normal Tyrode's solution, an "ischemic" solution, or an ischemic solution with a ß-agonist drug) and the follower cell is a model guinea pig ventricular cell represented by the Luo-Rudy model.13


*    Methods
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*Methods
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Cell Isolation
Single ventricular myocytes were prepared from adult guinea pigs weighing 200 to 800 g. After decapitation, the heart was excised and consecutively perfused with normal Tyrode's solution (5 mL/min, 3 to 5 minutes), nominally Ca2+-free Tyrode's solution (10 minutes), and nominally Ca2+-free enzyme solution (12 to 14 minutes). Both ventricles were cut into pieces, gently triturated in nominally Ca2+-free Tyrode's solution to which 180 µmol/L Ca2+ was added, and stored at room temperature. Samples of the cell suspension were placed in the recording chamber, and cells were allowed to settle for 5 to 10 minutes, after which superfusion with normal Tyrode's solution was started (1 mL/min, 35±0.5°C). Only single cells that were quiescent with preservation of their rod-shaped appearance were studied. Membrane capacitance, input resistance, and (2-Hz, 2-ms) stimulus current threshold were 163±15 pF, 15.2±1.4 M{Omega}, and 3.14±0.16 nA (mean±SEM, n=19), respectively.

Cell Chamber
Figure 1ADown and 1BDown illustrates the design of the cell chamber to produce the ischemic conditions for isolated cells. During ischemia, the cell chamber was layered with argon, preventing diffusion of atmospheric oxygen into the bath solution. Partial oxygen pressure was continuously monitored.



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Figure 1. A and B, Cell chamber for application of simulated ischemic conditions. C, Model clamp technique12 for coupling a real cell to a cell model.

Electrophysiological Recording
Whole-cell patch-clamp recordings were made with custom-built dual amplifiers using relatively high resistance patch pipettes (4 to 6 M{Omega} when filled with pipette solution) to minimize intracellular dialysis. Series resistance was compensated up to {approx}90%. Apart from zeroing the potential before touching the cell surface, no attempts were made to correct for liquid junction potential. In control experiments, action potential configuration and transmembrane currents remained stable for 40 to 60 minutes.

Solutions
Normal Tyrode's solution contained (in mmol/L) NaCl 140, KCl 5.4, CaCl2 1.8, MgCl2 1.0, HEPES 10.0, glucose 5.5 (pH 7.4 with NaOH) and was saturated with 100% O2. Nominally Ca2+-free Tyrode's solution was the same, without the CaCl2. Enzyme solution contained 0.06 U/mL collagenase-B, 0.19 U/mL collagenase-P, and 40 mg/mL trypsin inhibitor (Boehringer-Mannheim) in nominally Ca2+-free Tyrode's solution. During the last 5 minutes of the enzymatic isolation, 0.28 U/mL protease-XIV (Sigma Chemical Co) was added. Pipette solution contained (in mmol/L) KCl 140 and HEPES 10 (pH 7.2 with KOH). The ischemia solution contained (in mmol/L) NaCl 120, KCl 8.0, CaCl2 1.8, MgCl2 1.0, PIPES 10.0, and sodium lactate 20 (pH 6.8 with NaOH) and was saturated with 100% N2.

Coupling an Isolated Ventricular Cell to a Model Cell
Figure 1CUp diagrams our method of dynamically coupling a real cell to a real-time solution of a mathematical cell model with an ohmic coupling conductance Gc.12 The computer-controlled system, for each 80-µs time step {Delta}t, samples the membrane potential Vm,A, calculates the coupling current Ic=Gcx(Vm,A–Vm,B), injects this current into the real cell, and integrates the Luo-Rudy model with Ic as an additional ionic membrane current. To minimize effects of cell size, we scaled Ic such that the real cell and the model cell were of equal size, both exhibiting an effective current threshold of 2.6 nA.12

Statistics
For each cell, we compared action potential parameters, critical coupling conductance, and maximum conduction delay for control versus ischemia using a paired t test with a significance level of P<0.05. Comparison of action potential parameters between groups was performed with a Student-Newman-Keuls test after ANOVA. Data are presented as mean±SEM.


*    Results
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*Results
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Experimental Procedure
Figure 2Down illustrates our experimental procedure, with the Tyrode's solution bathing the cell switched to the ischemic solution for 17 minutes (horizontal bar). During the initial control period, PO2 was 215 Pa (158 mm Hg), action potential duration at 90% repolarization (APD90) was {approx}138 ms, and resting membrane potential (RMP) was -85 mV. During ischemia, PO2 rapidly falls to <13.6 Pa (<10 mm Hg) within 5 minutes. The APD90 shows some fluctuations, with a small decrease to {approx}125 ms until late in the ischemic period, when a large, rapid drop to {approx}60 ms occurs, at which time we switched back to control conditions. The RMP changes very rapidly with the ischemia (because of the elevated potassium) and remains stable at -76 mV. On reestablishment of control conditions, PO2 and RMP rapidly return to their initial control levels, whereas APD90 remains slightly shorter after recovering from the large drop at the end of the ischemic period.



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Figure 2. A, PO2; B, APD90; and C, RMP for an isolated guinea pig ventricular cell with ischemic conditions applied for period indicated by horizontal bar. Data obtained for every 10th action potential at 2-Hz stimulation when uncoupled from Luo-Rudy model cell.13 Single and double vertical arrows indicate times for which results obtained by coupling real cell to model cell are shown in Figures 3Up and 4Up, respectively.

We applied this procedure of an {approx}20-minute exposure to ischemic conditions to 11 cells. For times at 8 to 10 minutes into the ischemic period, these cells showed, in addition to the changes in RMP and APD90, a decrease in APD50, a decrease in maximum rate of rise of the action potential upstroke (max) (not significant, P=0.05), and a 4-mV reduction in overshoot potential (TableDown, left columns). The large, rapid drop in APD90 at the end of the ischemic period was observed for 5 of the 11 cells and is most likely due to hypoxia-induced activation of ATP-sensitive potassium current.14


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Table 1. Action Potential Parameters of Single Guinea Pig Ventricular Cells After 8 to 10 Minutes of Exposure to Simulated Ischemic Conditions

Conduction Under Ischemic Conditions
Figure 3Down shows results from coupling the real guinea pig ventricular cell of Figure 2Up to the Luo-Rudy model cell during the initial control period. Figure 3ADown shows membrane potential and coupling current for the 6-second period of coupling with a Gc of 6.6 nS as well as the preceding and following 2-second periods of uncoupling. The real cell is stimulated at 2 Hz, and no stimuli are applied to the model cell. After coupling has been established, some but not all action potentials of the real cell propagate to the model cell: action potentials 3, 6, and 11 fail to propagate, as indicated by their short duration and monophasic coupling current transient. At Gc=6.7 nS, however, every real cell action potential propagates to the model cell (Figure 3BDown), thus establishing 6.7 nS as the critical value of Gc for successful, uniform propagation under control conditions. At Gc<6.6 nS, action potentials propagate less frequently or not at all; at Gc>6.7 nS, conduction was uniformly successful (not shown).



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Figure 3. Action potential propagation from real guinea pig ventricular cell to Luo-Rudy model cell13 under control conditions. Vm of real cell (solid line; stimulated at 2 Hz) and model cell (dashed line; not directly stimulated) and coupling current (Ic). Real cell coupled to model cell with Gc for period indicated by horizontal arrow. A, Gc=6.6 nS. Vertical arrows indicate action potentials of real cell that do not propagate to model cell. B, Gc=6.7 nS. Asterisk indicates action potentials shown in Figure 5AUp.

For the same cell, we also determined critical Gc after 8 minutes of ischemia. At Gc=7.8 nS, action potentials 3 and 8 during coupling fail to propagate (Figure 4ADown), but at Gc=7.9 nS, there is uniform propagation (Figure 4BDown). Because of electrotonic interactions, the amount of depolarization of the real cell is slightly reduced during coupling. From Figures 3Up and 4Down, we see that critical Gc has been increased by the ischemic conditions from 6.7 to 7.9 nS.



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Figure 4. Action potential propagation from real guinea pig ventricular cell to Luo-Rudy model cell,13 in same format as Figure 3Up, after 8 minutes of exposure of real cell to ischemic conditions. A, Gc=7.8 nS. B, Gc=7.9 nS. Asterisk indicates action potentials shown in Figure 5BUp.

Figure 5Down contrasts propagation at critical Gc under control versus ischemic conditions by expanding Figures 3BUp and 4BUp, respectively, to illustrate only the last action potential propagated (asterisks). Under control conditions (Figure 5ADown), there is a rapid upstroke, followed by a partial repolarization of the real cell as current is transferred from real cell to model cell. When the model cell activates after a 28-ms delay, it rapidly depolarizes, producing a second phase of depolarization of the real cell. Under ischemic conditions (Figure 5BDown), the real cell shows a depolarized RMP and a slightly decreased peak amplitude, and the conduction time is decreased to 24 ms. Because for both Figure 5ADown and 5BDown, the value of Gc was the minimum value that allowed uniform conduction, these values of 28 and 24 ms represent the maximum conduction delay under control versus ischemic conditions, showing that the ischemia decreased the maximum conduction delay. Similar results were obtained for each of the 10 other cells studied under ischemic conditions.



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Figure 5. Action potential propagation from real guinea pig ventricular cell to Luo-Rudy model cell13 under control versus ischemic conditions. Vm of real cell (solid line) and model cell (dashed line) at critical value of coupling conductance (Gc). Arrows indicate maximum conduction delay. A, Control conditions. B, After 8 minutes of exposure of real cell to ischemic conditions.

Conduction Under Ischemic Conditions With Norepinephrine
For another 8 cells, we performed the same procedure of exposure to ischemic conditions but also including 1 µmol/L norepinephrine (ischemia+NA) in the ischemic solution. Like the 11 cells that were exposed to ischemic conditions without the norepinephrine, the cells showed a 9-mV depolarization of RMP, a decrease in max (not significant, P=0.09), and a 4-mV reduction in overshoot potential (TableUp, right columns). However, no changes in APD50 or APD90 were observed. Also, the large, rapid drop in APD90 at the end of the ischemic period was observed for only 1 of these 8 cells.

Figure 6Down illustrates, in the same format as Figure 5Up, results from 1 of the 8 cells exposed in the ischemia+NA solution. We determined that critical Gc was 6.2 nS in the control solution and 5.2 nS in the ischemia+NA solution (not shown). The results under control conditions (Figure 6ADown) are very similar to those shown for a different cell in Figure 5AUp. In the ischemia+NA solution (Figure 6BDown), the partial repolarization during the conduction process is much slower and is maintained at a higher voltage level, allowing for a much longer maximum conduction delay (60 ms). Similar results were obtained for each of the 7 other cells studied in the ischemia+NA solution.



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Figure 6. Action potential propagation from real guinea pig ventricular cell to Luo-Rudy model cell13 under control conditions versus ischemic conditions including norepinephrine. Vm of real cell (solid line) and model cell (dashed line) at critical value of Gc. Arrows indicate maximum conduction delay. A, Control conditions. B, After 8 minutes of exposure of real cell to ischemic conditions including 1 µmol/L norepinephrine (NA).

Statistical Comparison of Conduction in the Two Test Solutions
Effects on conduction of the application of ischemia or ischemia+NA are summarized in Figure 7Down. Note that each experimental intervention has its own control data. For the ischemia (n=11), the critical coupling conductance increases from 6.2±0.1 to 7.4±0.2 nS and the associated maximum conduction delay decreases from 31±1 to 23±1 ms. For the ischemia+NA (n=8), there is a decrease in critical coupling conductance from 5.9±0.2 to 5.0±0.1 nS and an increase in maximum conduction delay from 31±2 to 54±4 ms.



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Figure 7. A, Critical coupling conductance and B, maximum conduction delay for action potential propagation from real guinea pig ventricular cell to Luo-Rudy model cell13 under control versus ischemic conditions (control versus ischemia, n=11) and control conditions versus ischemic conditions including 1 µmol/L norepinephrine (control versus ischemia+NA, n=8). Bars show mean±SEM.

Conduction at a Constant Coupling Conductance in the Two Test Solutions
Figure 8Down emphasizes the differences in the discontinuous conduction process between control conditions, ischemia, and ischemia+NA at a constant coupling conductance of 8.0 nS. For the same real cell as used for Figures 2 through 5UpUpUpUp, we have plotted the results under control conditions (Figure 8ADown) versus ischemia (Figure 8CDown). Similarly, for the same real cell as used for Figure 6Up, we contrast propagation under control conditions (Figure 8BDown) and ischemia+NA (Figure 8DDown). Under control conditions (Figure 8ADown and 8BDown), coupling current flowing from each of the real cells to the model cell induces an early partial repolarization to +10 to +15 mV, and the conduction delay is 12 ms.



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Figure 8. Action potential propagation from real guinea pig ventricular cell to Luo-Rudy model cell13 under control versus ischemic conditions (left) and control conditions versus ischemic conditions including norepinephrine (right). Vm of real cell (solid line) and model cell (dashed line) at a Gc of 8.0 nS. Single-headed arrows indicate minimum value of Vm for early partial repolarization of real cell during conduction process. Double-headed arrows indicate conduction delay. A and B, Control conditions. C, After 8 minutes of exposure of real cell to ischemic conditions. D, After 8 minutes of exposure of real cell to ischemic conditions including 1 µmol/L norepinephrine (NA).

During ischemia (Figure 8CUp), both the peak amplitude of the real cell action potential and the potential after this peak amplitude are reduced. Because the driving force for coupling current is the difference in membrane potential, less coupling current is flowing from real cell to model cell during the process of propagation. The real cell continues to repolarize to -18 mV until, with a 22-ms delay, the model cell reaches its activation threshold and fires its action potential.

During ischemia+NA (Figure 8DUp), the potential after the peak of the real cell action potential is maintained at a higher level than in control solution, with a small repolarization during conduction to only +25 mV. As a consequence, coupling current is larger than under control conditions, and it takes less time (11 ms) to activate the follower cell. Thus, Figure 8Up demonstrates that, for discontinuous conduction at constant Gc, impulse propagation is largely impaired in the ischemia solution but enhanced in the ischemia+NA solution.

Changes in Ionic Currents
To unmask changes in ionic currents underlying the changes in conduction properties shown in Figures 3 through 8UpUpUpUpUpUp, we tested for changes in INa, ICa,L, and the inward rectifier and delayed rectifier potassium currents (IK1 and IK, respectively) as major contributors to the activation and plateau phase of the action potential.13 15 In accordance with data from the literature,15 the transient outward current (Ito) appeared to be absent in our cells (not shown). Under both ischemic conditions and ischemic conditions plus norepinephrine, only a slight decrease in max, reflecting activation of INa, was observed (TableUp).

For 4 of the 19 cells studied—2 cells exposed to the ischemia solution and 2 cells exposed to the ischemia+NA solution—we applied voltage clamp protocols under control conditions and after 10 to 15 minutes of ischemia, ie, directly after the determination of action potential parameters, critical coupling conductance, and maximum conduction delay at 8 to 10 minutes of ischemia. Resulting current-voltage relations are shown in Figure 9Down, which contrasts data from a cell exposed to the ischemia solution (Figure 9ADown and 9BDown) and a separate cell exposed to the ischemia+NA solution (Figure 9CDown and 9DDown).



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Figure 9. Current-voltage relations of single guinea pig ventricular cells after 10 to 15 minutes of exposure to ischemic conditions: peak current (left) and quasi–steady-state current (right) elicited on 500-ms depolarizing voltage clamp steps from holding potentials of -40 and -80 mV, respectively. Step interval was 1 second. A and B, Control versus ischemic conditions. C and D, Control conditions versus ischemic conditions including 1 µmol/L norepinephrine (NA).

The amplitude of the peak current, reflecting ICa,L, decreased in the ischemic solution (Figure 9AUp) but showed an {approx}4-fold increase in the ischemia+NA solution (Figure 9CUp). Under ischemic conditions, the quasi–steady-state current, reflecting IK1 and IK, shows a shift in reversal potential and a crossover in the negative voltage range, as expected from the effects of increased extracellular potassium concentration on IK1,16 whereas no major changes are observed in the voltage range positive to -10 mV (Figure 9BUp). Under ischemic conditions including norepinephrine, however, quasi–steady-state current shows a large increase in the latter voltage range (Figure 9DUp).


*    Discussion
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up arrowAbstract
up arrowIntroduction
up arrowMethods
up arrowResults
*Discussion
down arrowReferences
 
We have used isolated guinea pig ventricular myocytes in an experimental system in which an isolated cell exposed to either normal Tyrode's solution or an ischemic solution can be dynamically coupled to a real-time solution of a mathematical model of a guinea pig ventricular cell. Our use of the ischemic solution attempts to recreate the major modulators of acute ischemia to be tested in terms of critical coupling conductance and maximum conduction delay for action potential propagation across a pair of cells in which coupling conductance is much lower than the normal value. We are basically asking: If action potential conduction is already discontinuous, perhaps from some prior injury, what is the effect of the acute imposition of a simulated ischemic condition? Our use of "normal" cells and a normal ventricular model for this experimental model is based on previous work showing that in healed myocardial infarctions, the resting membrane potential has returned to nearly normal values,3 although the membrane properties of surviving cells may be somewhat abnormal, with decreased calcium currents, sodium current, and Ito.17 18

Geometrical Considerations
The slow conduction and fractionated waveforms characteristic of conduction in ischemic tissue are indications of successive activation of groups of cells for which the intergroup conductance is limiting the conduction. Our use of a model of 2 cells can be scaled to represent the conduction between 2 groups of cells under the conditions that within each group the cells are well coupled and essentially isopotential. That this condition is met under certain ischemic conditions is indicated by the brief duration of each component of the fractionated signals and also from direct microelectrode recordings of cells within the groups.4 Thus, 2 groups of 1000 cells connected by a conductance of 8000 nS would have the same characteristics of conduction as 2 single cells connected by a conductance of 8 nS. In the case of connections between large groups of cells, the interconnections might be a short bridge of cells, rather than a direct electrical connection between 1 cell of each group. The major geometrical limitation of our model system is that we are currently restricted to a pair of cells without connections to other cells or groups of cells. Thus, the effects of tissue loading19 are not taken into account.

Conduction Under Ischemic Conditions
Our results show that the application of ischemia increases the critical value of coupling conductance required for action potential propagation and decreases the associated maximum conduction delay. The analysis is somewhat complex, because it involves 3 factors: the ability of a proximal cell (leader cell) to supply current, the coupling conductance, and the requirements for charge to activate the distal cell (follower cell). For this experimental model system, we used the Luo-Rudy model cell as the distal cell, and we did not modify the model description during the ischemia so that the requirements for activation of the distal cell would be unchanged. During the experiment, we controlled the coupling conductance, and this became a dependent variable to characterize the amount of coupling conductance required for successful propagation. The actual mechanism by which the ischemia decreases the ability of the real cell to supply current to the distal cell (as shown by the increased value of critical coupling conductance) cannot be uniquely determined by these experiments but is probably explained by an {approx}50% decrease in ICa,L during the metabolic inhibition, as observed in our voltage-clamp experiments (Figure 9AUp). A similar decrease in ICa,L was observed by Cordeiro et al.11 As a result, the amount of partial repolarization of the proximal cell during the conduction process is increased and the driving force for coupling current is lowered, as we have previously shown with pharmacological modulation of ICa,L.8

Conduction Under Ischemic Conditions With Norepinephrine
Our results with the application of ischemic conditions including 1 µmol/L norepinephrine show that the presence of the norepinephrine completely reverses the effects of the simulated ischemic condition with respect to discontinuous propagation. With the norepinephrine, the critical coupling conductance is decreased, and the maximum conduction delay is increased. The actual mechanism by which the ability of the real cell to supply current to the distal cell is increased (as shown by the decreased value of critical coupling conductance) is probably explained by an increase in ICa,L (Figure 9CUp), which, despite the concomitant increase in outward current (Figure 9DUp), results in a slower rate of partial repolarization of the proximal cell during the conduction process and an increased driving force for coupling current.

Limitations of This Study
Our results suggest that the release of catecholamines with ischemia, in a setting of partially uncoupled cells, may play a major role in producing the long conduction delays that may allow the establishment of a reentrant pathway. In our experimental model system, the application of simulated ischemia, without the catecholamine, actually decreased the maximum conduction delay that could occur. Nevertheless, it is important not to extrapolate these results for cell pairs too literally for the much more complex situation of the spatially inhomogeneous application of ischemia as well as the spatial inhomogeneity of coupling conductance and intrinsic action potential properties.


*    Acknowledgments
 
This study was supported by Netherlands Heart Foundation grant 92.310, Netherlands Organization for Scientific Research grant 805-06-152, National Institutes of Health grant HL-22562, the Georgia Affiliate of the American Heart Association, and the Emory Egleston Children's Research Center.

Received July 1, 1998; revision received November 10, 1998; accepted November 23, 1998.


*    References
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up arrowIntroduction
up arrowMethods
up arrowResults
up arrowDiscussion
*References
 
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