INTRODUCTION

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DURING ACUTE MYOCARDIAL ISCHEMIA, interruption of coronary flow leads to a lack of oxygen and glucose in ventricular cardiomyocytes. Cellular metabolism is impaired and changes in ionic concentrations occur. Several studies (10, 46, 48, 51, 52, 58) have reported that ischemic interruption of coronary flow is followed by a fast increase in extracellular K⁺ concentration ([K⁺]_o). During the first 10-15 min of myocardial ischemia, [K⁺]_o increases from its normoxic value to a plateau level of 6-11 mmol/l above its initial value. During this plateau phase, [K⁺]_o remains almost constant during several minutes, and, in some preparations, it may eventually decrease (23, 54). Thereafter, a slower second increase of [K⁺]_o takes place simultaneously with the arrest of glycolytic activity and cell death (32, 33). This triphasic pattern is qualitatively similar in hearts of different species, but the time course is influenced by heart rate (46, 48, 51, 52) and experimental conditions (6, 51).

It is well known that extracellular K⁺ accumulation is related to profound modifications of the electrical behavior of ischemic cardiomyocytes (24). In particular, it contributes to the depolarization of resting membrane potential (53), to the decrease of the maximum upstroke velocity of action potential (AP) (24, 50), and to the shortening of AP duration (APD) (48). These electrophysiological changes are known to be pivotal in the genesis of reentrant arrhythmias and sudden cardiac death (13). However, despite the importance of this phenomenon, the mechanisms responsible for cellular K⁺ loss and its subsequent accumulation in the extracellular medium during acute myocardial ischemia are still uncertain (6, 51).

During normoxia, passive K⁺ efflux across the membrane is compensated by the inward movement accomplished by the Na⁺-K⁺ pump. Net K⁺ loss from ischemic cardiomyocytes could be due to increased K⁺ efflux, to reduced K⁺ influx, or both. Experimental studies (39) support the hypothesis that K⁺ efflux increases rapidly during acute myocardial ischemia. This increased K⁺ efflux could result from an increase in permeability of cell membrane to K⁺ ions (g_K) or in K⁺ driving force [(V_m  E_K)]. An increase of g_K could be due to the lack of oxygen that decreases the ATP-to-ADP ratio inducing the activation of ATP-sensitive K⁺ currents (I_K,ATP) (30). The activation of these channels has been proposed as a probable cause of shortening of APD during ischemia (9, 10, 49), and a possible contribution of this K⁺ current to extracellular K⁺ accumulation has also been suggested (51). In addition, other K⁺ currents, such as Na⁺-dependent K⁺ current (I_K,Na) or free fatty acid-activated K⁺ current (I_K,FFA) may be opened by ischemia-induced metabolic and ionic changes. However, during acute myocardial ischemia, activation of these two "new" K⁺ currents and their role in [K⁺]_o increase is unlikely (6, 51).

Although the increased I_K,ATP would enhance K⁺ efflux, it always has a repolarizing effect, which therefore reduces (V_m  E_K). Thus an increase in g_K is self-limiting and can only explain extracellular K⁺ accumulation during ischemia if (V_m  E_K) is maintained by an inward current. Several experimental results (3, 14, 16, 17) show that Na⁺ ions accumulate in the intracellular medium during the early phase of myocardial ischemia. Because net Na⁺ inward current might depolarize the cell membrane, this intracellular Na⁺ gain has been related to cellular K⁺ loss (39, 51).

As related above, it seems likely that ischemia elicits an increase in K⁺ efflux. However, a partial inhibition of the Na⁺-K⁺ pump has also been proposed as a possible cause of extracellular K⁺ accumulation during ischemia (54). A decreased Na⁺-K⁺ pump rate would decrease both K⁺ influx and Na⁺ efflux. Even in the presence of unchanged Na⁺ influx and K⁺ efflux, failure of the Na⁺-K⁺ pump could then increase [K⁺]_o and intracellular Na⁺ concentration ([Na⁺]_i).

In addition, during acute myocardial ischemia, osmotic changes produce the shrinkage of extracellular space (6, 23, 58). It seems likely that ischemia-induced restriction of extracellular water is ~15% after 10 min of interrupted coronary flow. In the absence of extracellular washout, a decrease in the extracellular volume could also contribute to the ischemic increase of [K⁺]_o.

Although experimental observations (6, 51) have tried to elucidate the exact role of these mechanisms on extracellular K⁺ accumulation during ischemia, the causes and mechanics of [K⁺]_o increase are still unknown. The simultaneous recording of all the individual ionic currents as well as the electrical V_m is impossible by experimental means. Because of their ability to simulate in precise detail the electrical behavior of the cell, AP mathematical models provide an alternative tool to explore the basic electrophysiological mechanisms that are responsible for the increase of [K⁺]_o during acute myocardial ischemia.

The goal of this work was to study, with the aid of computer simulations, the role on the ischemic increase of [K⁺]_o of each of its possible causes. For this purpose, simulations were carried out in which several degrees of activation of each mechanism were considered in the absence of coronary flow. During 14 min of simulated ischemia, ionic concentrations, K⁺ fluxes across the cell membrane, and the AP of one cardiomyocyte were monitored to elucidate the basis of cellular K⁺ loss during acute myocardial ischemia.

Glossary

EK	Nernst potential of K+
fATP	Fraction of activated ATP-sensitive K+ channels
fATP,final	Final value of fATP after 14-min linear increase
finhib	Degree of inihibition of Na+-K+ pump
finhib,final	Final value of finhib
ICa,L	L-type Ca2+ current
IK	Delayed time-dependent K+ current
IK,out	Sum of K+ efflux pathways
IKp	Time-independent plateau K+ current
IK1	Time-independent K+ current
INa	Fast Na+ current
INaCa	Current through the Na+/Ca2+ exchanger
INaK	Current through the Na+-K+ pump
INaK,max	Maximum current through the Na+-K+ pump
InsK	K+ current through the nonspecific Ca2+-activated channels
INaS	New ischemia-activated Na+ inward current
INaS,final	Final value of INaS
LR	Luo-Rudy
nIK	Number of K+ ions transported by IK
nIK,ATP	Number of K+ ions transported by IK,ATP
nIK,out	Number of K+ ions transported by IK,out
nIKp	Number of K+ ions transported by IKp
nIKl	Number of K+ ions transported by IK1
nINaK	Number of K+ ions transported by INaK
RnIK,out	Ratio between the number of K+ ions transported out of the cell by IK,out during simulated ischemia with respect to the amount of K+ transported during normoxia
RnINaK	Ratio between the number of K+ ions transported into the cell by INaK during simulated ischemia with respect to the amount of K+ introduced during normoxia
diff	Time constant for diffusion of ions from the interstitial clefts to the bulk extracellular medium
Tp	Time to onset of the plateau phase of [K+]o
Vcleft	Extracellular volume
Vcleft	Degree of reduction of extracellular volume after 14 min of ischemia
Vm	Membrane potential
[S]i	Intracellular concentration of generic ion S
[S]o	Extracellular concentration of generic ion S
[K+]o	Value of the plateau level of [K+]o

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

AP model. A modified version of LR phase II AP model (30) was used to simulate the electrical behavior of one single ventricular myocyte during 14 min of progressive ischemia. The LR model includes I_K1, I_K with its two components I_KS and I_KR (59), I_Kp, I_Na, I_Ca,L, a Na⁺ and K⁺ current through nonspecific Ca²⁺-activated channels (I_ns,Ca) and several background currents (I_Na,b and I_Ca,b). I_NaK, current through sarcolemmal Ca²⁺ pump (I_p,Ca), and I_NaCa are also considered in the model as well as calcium-induced calcium-released mechanism. In addition, the LR model has been completed by including new ionic currents, such as I_K,ATP (9) and I_NaS (see Simulation of ischemic conditions).

(1)

Simulation of ischemic conditions. In the simulations, only the ischemic aspects that could contribute to extracellular K⁺ accumulation were taken into account. The interruption of coronary flow was simulated by steeply increasing _diff from its normoxic value (1,000 ms) to infinity. A nonelectrogenic Na⁺ influx, which could represent Na⁺ influx across Na⁺-H⁺ cotransport (28), was used to achieve zero net ionic fluxes before the onset of ischemia-induced alterations of ionic currents. Hence, even in the absence of washout between the extracellular clefts and the bulk extracellular medium, ionic concentrations were stabilized and remained constant during the first minute of the simulations. The alteration of ionic currents induced by metabolic changes during ischemia then began.

(2)

6

6

Simulation of the effect of pH on ionic currents. It is known that during acute myocardial ischemia, intracellular and extracellular acidosis decrease the single channel conductance of the I_Na and of the I_Ca,L (6). Because the reduction of the Na⁺ and Ca²⁺ influx across these currents could have consequences in extracellular K⁺ accumulation, the effect of pH has been considered by linearly decreasing the conductances of I_Na and I_Ca,L until 75% of their normoxic value during 14 min of simulated ischemia (20, 34, 37).

Study of K+ fluxes during simulated ischemia. One of our goals was to estimate the contribution of each K⁺ current to extracellular K⁺ accumulation during acute myocardial ischemia. For this purpose, we calculated the number of K⁺ ions transported across the membrane using the following expression for each K⁺ current (I_Kj)

(3)

where I_Kj is the generic K⁺ current (i.e., I_K1, I_K,ATP, and I_Kp). The total number of K⁺ ions transported out of the cell is represented by n_IK,out, which is the sum of all the n_IKj.

(4)

(5)

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Mechanisms of extracellular K+ accumulation during acute ischemia. To determine the causes of the ischemia-induced extracellular K⁺ accumulation, we have monitored the time course of [K⁺]_o under different conditions of alteration of I_K,ATP, I_NaK, and I_NaS. Figure 1 shows the results of these simulations. In this figure, traces I-III correspond to the activation of only one of these mechanisms, without considering the interactions with the others. Trace I represents the time course of [K⁺]_o for a linear activation of f_ATP from 0% to 0.8%, during 14 min of interrupted coronary flow. The final increase of [K⁺]_o is ~0.8 mmol/l, and the slope of the trace decreases with time until reaching a plateau level in the last minutes of I_K,ATP activation. Trace II shows extracellular K⁺ accumulation while I_NaK is being inhibited linearly during 14 min from its normoxic activity to a final degree of inhibition of 35%. K⁺ ions progressively accumulate in the extracellular medium and [K⁺]_o reaches a value of 8.4 mmol/l after 14 min of Na⁺-K⁺ pump inhibition. Trace III represents the rise of [K⁺]_o from 5.4 to 9.4 mmol/l during 12 min of linear activation of I_NaS from zero to its final value 1.2 µA/µF in the absence of coronary flow. Finally, the extracellular K⁺ accumulation produced by the effect of the three mechanisms separately and represented in traces I-III has been summed and plotted in trace IV.

View larger version (21K): [in this window] [in a new window]   Fig. 1.   Bottom, time course of extracellular K+ concentration ([K+]o) during 14 min of interrupted coronary flow under different conditions of alteration of ischemic mechanisms. Traces I-III show the individual effect on [K+]o of the alteration of ATP-sensitive K+ current (IK,ATP), current through the Na+-K+ pump (INaK), and new ischemia-activated Na+ inward current (INaS), respectively. Trace IV is the sum of traces I-III. Traces V-VII correspond to the simultaneous alteration of the two mechanisms indicated next to each trace. Trace VIII reproduces the concomitant effect of the three mechanisms on [K+]o. In all cases, when IK,ATP was activated, the final value of fraction of activated ATP-sensitive K+ (KATP) channels (fATP,final) was 0.8%. When INaS was activated, the final value of INaS (INaS,final) was 1.2 µA/µF, and when the maximum current through the Na+-K+ pump (INaK,max) inhibition was considered, the final value of the degree of inhibition of the Na+-K+ pump (finhib,final) was 35%. Top, changes in action potentials (APs) during simulated ischemia, also considering fATP,final = 0.8%, finhib,final = 35%, and INaS,final = 1.2 µA/µF. Time after the onset of ischemia is indicated above each trace. Vm, membrane potential.

Effect of acidosis on the increase of [K+]_o. As shown in Table 1, simulation J considers the alteration of the three ischemic mechanisms in the same degree of simulation A and the inhibition of I_Na and I_Ca,L due to the effect of acidosis (see METHODS). Under these conditions, extracellular K⁺ accumulation follows the same biphasic pattern that in the other eight cases, and during the first 11.4 min, the time course of [K⁺]_o in simulations A and J is exactly the same. However, there are slight differences related to the final value of [K⁺]_o and the time to onset of the plateau phase that should be noted. First, in simulation J, the level reached during the plateau phase was 15.1 mmol/l in contrast with the 15.5 mmol/l obtained in simulation A. Second, the progressive inhibition of I_Na and I_Ca,L produced a slight anticipation of the plateau phase, which was reached after 11.4 min of the beginning of simulated ischemia.

Role of I_K,ATP on ischemic cellular K+ loss. Figure 2A depicts the time course of [K⁺]_o during simulations A-C (see Table 1), which only differ in the f_ATP,final value (0.8%, 1.7%, and 3.5%, respectively). As shown in this figure, a faster activation of I_K,ATP produces a faster rise of [K⁺]_o during the first minutes of simulated ischemia. After this rapid increase, the slope of the three traces decreases until reaching a plateau phase. The [K⁺]_o and T_p are shown in Table 1.

View larger version (12K): [in this window] [in a new window]   Fig. 2.   A: effect of IK,ATP on extracellular K+ accumulation during acute myocardial ischemia. Data were recorded during simulations A-C, in which fATP,final was 0.8%, 1.7%, and 3.5%, respectively. In the three simulations, INaK was inhibited to a degree of inhibition of 35% and INaS was linearly activated from 0 to 1.2 µA/µF. B: effect of heart rate on extracellular K+ accumulation during simulated ischemia. Five different heart rates were considered (120, 90, 60, 45, and 0 beats/min) to investigate the effect of heart rate on the rise of [K+]o produced by the simultaneous effect of IK,ATP (fATP,final was 0.8%), INaK (finhib,final was 35%), and INaS (INaS,final was 1.2 µA/µF).

Effect of heart rate on extracellular K+ accumulation during acute ischemia. Experimental studies (21, 46, 48, 51, 52) have established that during acute myocardial ischemia, the increase of [K⁺]_o is rate dependent, especially in the lower range of heart rates (0-90 beats/min). To determine the effect of heart rate on extracellular K⁺ accumulation, myocardial ischemia was simulated under several rates of stimulation (120, 90, 60, 45, and 0 beats/min). For this purpose, f_ATP, f_inhib, and I_NaS have been increased in a linear manner from zero to their final values of 0.8%, 35%, and 1.2 µA/µF (simulation A), in the absence of coronary flow.

View larger version (51K): [in this window] [in a new window]   Fig. 3.   Comparison between experimental measures of the ischemic increase of [K+]o and the results of simulation A (fATP,final = 0.8%, finhib,final = 3 5%, INaS,final = 1.2 µA/µF). The first of each group of bars represents the data of simulation A, whereas the other bars correspond to the measures obtained in cardiac tissues of rabbit, pig, and guinea pig after 6, 8, 10, and 11 min of ischemia (21, 44, 46, 48, 58). The rate of stimulation applied in each case is specified at the top of the bars (in beats/min).

Contribution of K+ currents on cellular K⁺ loss during acute ischemia. In view of the above, the concomitant effect of the increase of I_K,ATP, f_inhib, and I_NaS replicates qualitative and quantitatively the rise of [K⁺]_o during the early phase of myocardial ischemia. To further investigate the causes of cellular K⁺ loss, the number of K⁺ ions transported across the membrane by each K⁺ current was continuously monitored under conditions of simulated ischemia. Figure 4 depicts the time course of n_IK, n_IKp, n_IK,ATP, and n_IK1, which represent the number of K⁺ ions transported across the plasmatic membrane by I_K, I_Kp, I_K,ATP, and I_K1. These variables have been monitored during 14 min of simulation A (Fig. 4A), simulation C (Fig. 4B), and in the absence of diffusion between the interstitial clefts and the bulk extracellular medium under otherwise nonischemic conditions (Fig. 4C).

View larger version (21K): [in this window] [in a new window]   Fig. 4.   Role of K+ currents on cellular K+ loss during the early phase of myocardial ischemia. The time course of the variables nIK, nIKp, nIK,ATP, and nIK1 represents the number of K+ ions transported across the plasmatic membrane by IK, IKp, IK,ATP, and IK1, respectively. A and B: data recorded during simulation A (fATP,final = 0.8%, finhib,final = 35%, INaS,final = 1.2 µA/µF) and simulation C (fATP,final = 3.5%, finhib,final = 35%, INaS,final = 1.2 µA/µF), respectively. C: data recorded in the absence of coronary flow under otherwise nonischemic conditions (fATP,final = 0%, finhib,final = 0%, INaS,final = 0 µA/µF).

View larger version (13K): [in this window] [in a new window]   Fig. 5.   Time course of ratios RnIKout and RnINaK (see METHODS) during 14 min of simulated ischemia. Two different degrees of activation of IK,ATP were considered recording data from simulation A (fATP,final = 0.8%, finhib,final = 35%, and INaS = 1.2 µA/µF) and simulation C (fATP,final = 3.5%, finhib,final = 35%, and INaS,final = 1.2 µA/µF).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Extracellular K+ accumulation during simulated ischemia. During acute myocardial ischemia, cellular K⁺ loss and the absence of washout produce an important increase of [K⁺]_o. Because extracellular K⁺ accumulation has been proven to be a major cause of reentrant arrhythmias, much attention has been paid to clarify this phenomenon. However, the mechanisms responsible for ischemia-induced increase of [K⁺]_o are still uncertain (6, 51). In this study, we have used computer simulations of AP models to investigate the intimate mechanisms of K⁺ loss during acute ischemia. LR phase II AP model (29), along with a formulation of I_K,ATP from our group (9), reproduces the electrical activity of cardiac cells with high degree of electrophysiological detail, thus providing a helpful tool to analyze the changes induced in ventricular cells very early after the onset of myocardial ischemia.

Electrophysiological mechanisms of cellular K+ loss. During the first minutes of simulated ischemia, the activation of I_K,ATP represents an increase of g_K, which could enhance K⁺ efflux. However, the activation of this current on its own only leads to a final increase of [K⁺]_o of 0.8 mmol/l. The idea that the activation of the I_K,ATP is not sufficient to cause the extracellular K⁺ accumulation observed during acute ischemia has already been proven by the use of K_ATP openers such as cromakalim (39, 44). An explanation of this small effect of I_K,ATP activation could be that the increase of g_K reduces K⁺ driving force and APD, limiting K⁺ efflux across other K⁺ currents like I_K, I_Kp, I_K1, or even I_K,ATP. Accordingly, our results show that during simulated ischemia, a faster activation of I_K,ATP reduces the rate of K⁺ ions transported across these currents to the extracellular space.

Study limitations. The AP model used in this work is a modified version of LR phase II AP model for ventricular cardiomyocytes that includes a formulation of the I_K,ATP. This useful tool allows the simulation of the electrophysiological behavior of one cardiomyocyte in precise detail. However, because a mathematical model is always a simplification of the complex reality, this study has some limitations.