Vol. 283, Issue 2, H490-H500, August 2002
Mechanistic investigation of extracellular K+
accumulation during acute myocardial ischemia: a simulation
study
B.
Rodríguez,
J.
M.
Ferrero Jr., and
B.
Trénor
Laboratorio Integrado de Bioingeniería,
Departamento de Ingeniería Electrónica, Universidad
Politécnica de Valencia, 46021 Valencia, Spain
 |
ABSTRACT |
In
this study, we have used computer simulations to study the mechanisms
of extracellular K+ accumulation during acute
ischemia. A modified version of the Luo-Rudy phase II action
potential model was used to simulate the electrical behavior of one
ventricular myocyte during 14 min of simulated ischemia. Our
results show the following: 1) only the integrated effect of
activation of ATP-dependent K+ current, an ischemic
Na+ inward current, and inhibition of
Na+-K+ pump activity in the absence of coronary
flow replicates the biphasic time course of extracellular
K+ concentration observed during acute ischemia;
2) the time to onset of the plateau phase and the plateau
level value are determined by the rate of stimulation and by the rate
of alteration of the three mechanisms. However, acidosis and reduction
of extracellular volume produce only a slight anticipation of the
plateau phase; and 3) cellular K+ loss is mainly
due to an increase of K+ efflux via the time-independent
K+ current and ATP-dependent K+ current rather
than to a decrease of K+ influx.
cellular K+ loss; action potential model; computer
simulation
 |
INTRODUCTION |
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 (gK) or in K+ driving force
[(Vm
EK)]. An
increase of gK could be due to the lack of
oxygen that decreases the ATP-to-ADP ratio inducing the activation of
ATP-sensitive K+ currents (IK,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 (IK,Na) or free fatty
acid-activated K+ current (IK,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 IK,ATP would enhance
K+ efflux, it always has a repolarizing effect, which
therefore reduces (Vm
EK). Thus an increase in
gK is self-limiting and can only explain
extracellular K+ accumulation during ischemia if
(Vm
EK) 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 Vm 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 |
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
IK1, IK with its two
components IKS and IKR
(59), IKp,
INa, ICa,L, a
Na+ and K+ current through nonspecific
Ca2+-activated channels (Ins,Ca) and
several background currents (INa,b and
ICa,b). INaK, current
through sarcolemmal Ca2+ pump
(Ip,Ca), and INaCa 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
IK,ATP (9) and
INaS (see Simulation of ischemic
conditions).
To dynamically calculate ionic concentrations, ionic fluxes were
considered to flow between three compartments: the intracellular space,
the interstitial extracellular clefts, and a bulk extracellular medium,
in which concentrations were assumed to be constant (2). Dynamic changes in the extracellular (cleft) [S]o are
simulated with the equation
|
(1)
|
where Am is the area of the myocyte,
Vcleft is the volume of the interstitial cleft (per cell),
F is the Faraday constant, IS,tot is
the total ionic current associated to ion S, and [S]bulk is the [S] in the bulk.
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.
The formulation of IK,ATP proposed by Ferrero et
al. (9) was used to simulate the activation of this
current during ischemia. For this purpose, fATP was
linearly increased during 14 min from zero to different final maximum
values (fATP,final). Three different values of
fATP,final have been considered in our simulations: 0.8%,
1.7% and 3.5%, respectively. The first one is the most representative of acute myocardial ischemia (9, 49).
To simulate Na+-K+ pump inhibition,
INaK,max was substituted by the following
expression
|
(2)
|
where INaK,max,norm is the normoxic
value of INaK,max.
INaK,max,norm was increased to 2.75 µA/µF to
achieve zero net K+ efflux. This value of 2.75 µA/µF is
included in the range of experimentally observed
INaK,max (30). finhib
was progressively increased with time in a linear fashion during 14 min
from zero to its final value (finhib,final). We tested the
effect on extracellular K+ accumulation of three different
finhib,final: 21%, 35%, and 70%, respectively. A 35%
decrease of INaK,max after 14 min in the absence of coronary flow is in agreement with the experimental data recorded during acute myocardial ischemia (4).
Furthermore, INaS was introduced into the
model to simulate altered Na+ fluxes during myocardial
ischemia. In agreement with experimental findings,
INaS represents a Na+ inward
current, which progressively increases with time of ischemia and its activation begins 2 min after the onset of simulated
ischemia (14, 19). Thereafter, this current was
increased linearly with time during 12 min from zero to several
INaS,final:
0.6,
1.2, and
2.4 µA/µF.
In the simulations in which shrinkage of the extracellular space was
considered, Vcleft was linearly decreased by 21% in 14 min
of interrupted coronary flow. The initial value of Vcleft was its normal value 5.182 × 10
6 µl (30)
and its final value 4.094 × 10
6 µl.
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 INa and of the
ICa,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 INa and
ICa,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
(IKj)
|
(3)
|
where IKj is the generic K+
current (i.e., IK1,
IK,ATP, and IKp). The
total number of K+ ions transported out of the cell is
represented by nIK,out, which is the
sum of all the nIKj.
In addition, to determine whether the activation of
ischemic mechanisms modifies K+ fluxes, the ratio
between the number of K+ ions transported across the cell
membrane during simulated ischemia with respect to the amount
of K+ transported during normoxia was calculated using the
variables RnIK,out(t) and
RnINaK(t), which were
defined as
|
(4)
|
|
(5)
|
where
nIK,out,norm(t) and
nINaK,norm(t) are
nIK,out(t), and
nINaK(t) in the
absence of coronary flow but without considering other ischemic
mechanisms (under "normoxic" conditions).
The program was written in Advanced Continuous Simulation
Language. The nonlinear system of different equations was solved using
the Gear stiff method (11). A maximum time step of 0.01 ms
was allowed.
 |
RESULTS |
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 IK,ATP,
INaK, and INaS. 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 fATP 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
IK,ATP activation. Trace II shows
extracellular K+ accumulation while
INaK 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 INaS 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.

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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.
|
|
Traces V-VII describe the changes in
[K+]o produced by the activation of two of
the three ischemic mechanisms considered. Trace V depicts the progressive increase of
[K+]o during the activation of
IK,ATP (fATP,final = 0.8%)
together with the inhibition of INaK
(finhib,final = 35%). The final value of
[K+]o after 14 min of simulation was 10 mmol/l. Trace VI shows how the simultaneous activation of
IK,ATP (fATP,final = 0.8%) and INaS (INaS,final =
1.2 µA/µF) also leads to the rise of
[K+]o. In this case, the value of
[K+]o reached after 14 min of simulation was
11.25 mmol/l. Finally, trace VII represents the increase of
[K+]o produced by the activation of
INaS (INaS,final =
1.2 µA/µF) and the simultaneous inhibition of
Na+-K+ pump until a 35% reduction of its
maximal current. The final value of [K+]o in
this case was 17.9 mmol/l. As shown, the activation of two of the three
ischemic mechanisms considered in our simulations produces in
all cases a continuous rise of [K+]o.
However, the rate of rise of [K+]o in
trace VII is much faster than in the other traces.
Trace VIII shows the concomitant effect of the three
mechanisms on extracellular K+ accumulation during 14 min
of interrupted washout. In this case, fATP,final was 0.8%,
finhib,final was 35%, and
INaS,final was
1.2 µA/µF. This trace is
eventually different from the previous ones. Indeed, a progressive rise
of [K+]o follows the activation of
IK,ATP simultaneously with the inhibition of
INaK. Two minutes later, this increase of
[K+]o is enhanced by the activation of
INaS. The rise of
[K+]o lasts for 11.6 min and, thereafter, a
plateau phase takes place during which [K+]o
remains almost constant in 15.5 mmol/l. By comparison of traces IV and VIII, it is clear that the concomitant
activation of the three mechanisms presents a certain synergy, which
enhances cellular K+ loss during simulated ischemia.
In conclusion, the simultaneous effect of the three mechanisms
(IK,ATP, INaK, and
INaS) replicates the changes in
[K+]o experimentally observed during acute
myocardial ischemia (46, 48, 51, 52). Only the
simultaneous activation of the three mechanisms produces the
electrophysiological changes in cardiac cells necessary to induce the
biphasic time course of [K+]o. Figure 1,
top, represents changes in the AP of one single ventricular
cardiomyocyte before the interruption of coronary flow and after 3, 7, and 11 min of simulated ischemia (as in trace VIII,
fATP,final = 0.8%, finhib,final = 35%, and INaS,final =
1.2 µA/µF).
The resting membrane potential was shifted to less negative potentials,
from its normoxic value
86 to
58 mV. This depolarization of cell
membrane was accompanied by a progressive shortening of APD, a decrease
of its amplitude and of the maximum upstroke velocity of AP. All of
these changes in the shape of AP are similar to the observed during the
first minutes of myocardial ischemia (22, 46), and
they are related to extracellular K+ accumulation.
To further investigate the causes of the biphasic increase of
[K+]o, simulations have been carried out to
study the effect of different degrees of activation of each mechanism
on the
[K+]o and
Tp. Table 1
summarizes the results of these simulations.
Simulation H considers IK,ATP and
INaS activation, Na+-K+
pump inhibition, and the decrease of extracellular space volume with the final value of each parameter being in the range observed experimentally.
[K+]o and
Tp are 15.5 mmol/l and 11.4 min, respectively,
in agreement with experimental observations.
Although simulation A did not consider the shrinkage of
extracellular space, the increase of [K+]o in
simulations A and H was very similar. The effect
of shrinkage of extracellular space was only to slightly anticipate the
plateau phase. This small effect is in accordance with the results
obtained by Yan et al. in 1996 (58).
Simulations A-C consider different rates of
activation of IK,ATP to test the effect of this
current on extracellular K+ accumulation. Our results show
that the plateau level of [K+]o is lower for
faster degrees of activation of IK,ATP. In
contrast, higher finhib,final (simulations D,
A, and E) or INaS,final
(simulations F, A, and G)
both produce an increase in the final value of
[K+]o, and faster rates of activation of the
three mechanisms provoke an anticipated onset of the plateau phase. In
all of the cases,
[K+]o and
Tp are in the range of the experimental data
obtained during the acute phase of myocardial ischemia.
Because extracellular K+ accumulation has been hypothesized
to be related to a net Na+ gain (39),
[Na+]i was monitored under different
conditions of ischemia. Our simulations show a progressive
increase of [Na+]i simultaneously with the
increase of [K+]o. The last column of Table 1
provides the value of [Na+]i at the onset of
the plateau phase. As shown, this value is always in the range of
12.3-12.8 mmol/l, according to experimental results (1, 8,
17, 26, 41).
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
INa and ICa,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 INa and
ICa,L produced a slight anticipation of the
plateau phase, which was reached after 11.4 min of the beginning of
simulated ischemia.
Role of IK,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
fATP,final value (0.8%, 1.7%, and 3.5%, respectively).
As shown in this figure, a faster activation of
IK,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 Tp are
shown in Table 1.

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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,
fATP, finhib, and INaS
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.
Figure 2B depicts the results of these simulations. As it
can be observed, the time course of [K+]o was
biphasic at all the heart rates tested, except for 0 beats/min, for
which a plateau was not reached. As the rate of stimulation decreased,
the rise of [K+]o was slower and the time to
onset of the plateau phase increased. However, the plateau level
reached similar values at all the heart rates considered. These results
are in agreement with experimental studies of the effect of heart rate
on extracellular K+ accumulation during acute myocardial
ischemia (48, 52). Quantitatively, the first rise
of [K+]o finished 10.6 and 13.83 min after
the beginning of simulated ischemia for 120 and 45 beats/min,
respectively. In addition, the plateau level was 15.3, 15.5, 16, and
16.2 mmol/l for 120, 90, 60, and 45 beats/min, respectively.
Furthermore, Fig. 3 provides a more
precise comparison between the increase of
[K+]o observed in simulation A and
the experimental results obtained in different preparations after 6, 8, 10, and 11 min of ischemia under a similar heart rate. The
first of each group of bars represents the data of simulation
A, whereas the following bars correspond to the measures obtained
in ischemic cardiac tissues of rabbit, pig, and guinea pig
(21, 44, 46, 48, 58). The rate of stimulation (in
beats/min) applied in each case is specified on the top of the bars.

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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
IK,ATP, finhib, and
INaS 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
nIK,
nIKp,
nIK,ATP, and
nIK1, which represent the number of
K+ ions transported across the plasmatic membrane by
IK, IKp,
IK,ATP, and IK1. 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).

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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).
|
|
A preliminary analysis of Fig. 4, A and B, shows
that the main part of K+ efflux during simulated
ischemia is accomplished by IK1 and
IK,ATP. At the end of simulation A
(Fig. 4A), nIKATP and
nIK1 represent 25% and 49%,
respectively, of total K+ efflux. The contribution of
IK to cellular K+ loss is also
considerable, even if it decreases from 33% to a 13% during the 14 min of simulation A. K+ efflux across other
K+ currents like IKp and
InsK represent <10% of total K+ efflux.
It is important to note that the number of K+ ions
transported across IK1 and
IK,ATP continuously increases during 14 min of simulated ischemia. However, the slope of the traces of
nIK and nIKp decreases with time, and this
effect is more evident for a higher value of fATP,final
(Fig. 4B). The comparison of Fig. 4, A and
B, shows that a higher degree of activation of
IK,ATP increases
nIK,ATP but reduces the rate of
K+ ions transported across other K+ currents,
such as IK1, IK, or
IKp.
Furthermore, Fig. 5, A and
B, depicts the time course of
RnIK,out and
RnInaK during simulations
A and C (see Table 1). These variables (see
METHODS) represent the ratio between the amount of
K+ ions transported across the cell membrane, out of and
into the cell, respectively, during simulated ischemia with
respect to the amount of K+ transported during normoxia.

View larger version (13K):
[in this window]
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|
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).
|
|
Figure 5A shows that K+ efflux is enhanced very
early after the onset of simulated ischemia and that this
increase is faster under a higher degree of activation of
IK,ATP. However, in the last minutes of
simulations A and C, the time course of
RnIK,out changes and the rate of
K+ ions transported out of the cell becomes higher for a
lower value of fATP,final.
Figure 5B depicts the time course of
RnINaK during simulations
A and C. For only 2 min, K+ influx is
slightly inhibited in ischemia with respect to normoxia. Subsequently, the increase of RnINaK
reflects the enhancement of the number of K+ ions
transported into the cell, which is faster for a higher degree of
activation of IK,ATP. However, at the end of the
simulations, as for RnIKout, the
time course of RnINaK changes and
Na+-K+ pump current is higher for
fATP,final 0.8% than for 3.5%.
 |
DISCUSSION |
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
IK,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.
Different experimental studies (6, 51) have proposed three
mechanisms to be the more probable causes of extracellular K+ accumulation during acute myocardial ischemia,
namely, activation of IK,ATP, inhibition of
INaK, and altered Na+ fluxes
(INaS). These three factors have been introduced
in our simulations so we could study their possible contribution to the increase of [K+]o in the absence of coronary
flow. Our results show that only the simultaneous activation of the
three mechanisms leads to the experimentally observed pattern of
[K+]o: an initial fast rise, followed by a
plateau phase. Furthermore, the plateau level and the time to onset of
the plateau phase in our simulations were in the range of experimental
data obtained during acute myocardial ischemia (21, 22,
46, 48). It is important to note that even if the alteration of
ischemic mechanisms continued during the whole ischemic
period, [K+]o remained constant during the
plateau phase. In addition, accordingly with several experimental
reports (21, 48, 51), the increase of heart rate in our
simulations accelerates the first rise of [K+]o and anticipates the plateau phase.
As shown in Fig. 3, the increase of [K+]o
after 6 and 8 min of ischemia is very similar to that observed
in simulation A, and the difference is always
<10% under all the heart rates considered (21, 46, 48,
58). For longer periods of ischemia, experimental data
differ significantly between them, and the comparison with the results
of the simulation is much more difficult. Ten minutes after the onset
of myocardial ischemia, [K+]o in
simulation A is the same as that in rabbit cardiac tissue under 60 beats/min (48). In contrast, under 90 beats/min,
Vanheel et al. (44) observed an extracellular
K+ accumulation very different, not only from the data of
simulation A, but also from other experimental results
(48, 58). This discrepancy could be originated by the
influence of factors that are known to affect extracellular
K+ accumulation, such as the experimental model of
ischemia, oxygen availability, or conditions that change
intracellular pH (51). These experimental conditions could
determine the evolution of cellular metabolism and consequently the
degrees of alteration of IK,ATP,
INaK, and INaS. In
addition, K+ electrode measurements involve puncturing the
myocardium to create an artificial space. The subsequent dilutional and
diffusional effects could distort the changes in
[K+]o recorded.
Electrophysiological mechanisms of cellular
K+ loss.
During the first minutes of simulated ischemia, the activation
of IK,ATP represents an increase of
gK, 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 IK,ATP is not
sufficient to cause the extracellular K+ accumulation
observed during acute ischemia has already been proven by the
use of KATP openers such as cromakalim (39,
44). An explanation of this small effect of
IK,ATP activation could be that the increase of
gK reduces K+ driving force and APD,
limiting K+ efflux across other K+ currents
like IK, IKp,
IK1, or even IK,ATP.
Accordingly, our results show that during simulated ischemia, a
faster activation of IK,ATP reduces the rate of
K+ ions transported across these currents to the
extracellular space.
However, experiments using IK,ATP blockers such
as glibenclamide (52) and 5-hydroxydecanoate
(33) have shown a decrease in the rate of extracellular
K+ accumulation during the first phase of acute
ischemia. In some animal species (e.g., rabbit), glibenclamide
almost abolishes the plateau phase of [K+]o
(52), leading to a higher degree of K+
accumulation after 15 min of ischemia despite the
IK,ATP blockade. Our simulations are in
agreement with these effects as shown in Fig. 1 (traces VII
and VIII).
As discussed before, the self-limiting effect of
gK on K+ efflux has to be
counteracted by a net inward current, which would maintain
K+ driving force (39). The nature of this
inward current is still being debated (6, 51), but several
evidences suggest that altered Na+ fluxes could be related
to cellular K+ loss during acute ischemia.
In this way, altered Na+ fluxes could contribute to
intracellular Na+ accumulation observed very early after
the onset of myocardial ischemia (3, 8, 14, 16).
Recent data (8, 14) show an important rise of
[Na+]i in the first minutes of myocardial
ischemia that is significantly prevented by specific inhibitors
of Na+ channels. In addition, experimental studies
(5, 19, 35, 42, 55, 56) support the hypothesis that
Na+ channels are profoundly modified by amphiphiles like
lysophosphatidylcoline and palmitoylcarnitine. Indeed, a fourfold
accumulation of these substances occurs after 2 min of myocardial
ischemia (7). This increase of long-chain
acylcarnitine concentration is coincident with the development of
electrophysiological alterations leading to reentrant arrhythmias and
has also been related to cellular K+ loss
(12). In conclusion, it seems probable that
ischemia-induced accumulation of amphiphiles could alter ionic
currents and, among them, Na+ channels causing an increase
of [Na+]i. The consequent inward
Na+ current would have a depolarization effect, which would
increase K+ driving force and, hence, K+
efflux. In 1997, Shivkumar et al. (39) established that
inhibition of Na+ pathways during hypoxia prevented
cellular K+ loss. In addition, in 1988, Tosaki et al.
(41) showed that lidocaine, a Na+ channel
inhibitor, lessened both intracellular Na+ and
extracellular K+ accumulations during myocardial
ischemia. In 1997, experiments (43) with the same
drug, lidocaine, in rat hearts proved its antiarrhythmic effect
accompanied by a lower increase of [Na+]i
during myocardial ischemia. Our theoretical considerations support the experimental hypothesis according to which
Na+-related mechanisms could contribute in a large extent
to the cellular K+ loss during acute myocardial
ischemia. However, other inward currents could also be involved
in this phenomenon. Connexin hemichannels have recently been shown to
open after 8 min of metabolic inhibition (18, 25). The
consequent nonselective depolarizing current could also contribute to
the enhancement of K+ driving force during ischemia.
In addition to the increase of K+ efflux, a decrease of
K+ influx would also contribute to extracellular
K+ accumulation during acute myocardial ischemia.
Controversial experimental results make it difficult to determine the
role of INaK on the increase of
[K+]o during ischemia. On the one
hand, metabolic impairment during ischemia leads to a decrease
of intracellular pH, an accumulation of inorganic phosphates into the
cell, and reduced intracellular ATP levels (26, 43, 45, 49,
57). Experimental reports show that all these metabolic
alterations could be considered as Na+-K+ pump
inhibitors (15, 27, 36, 40). Furthermore, in 1982, Bersohn
et al. (4) measured a 25% inhibition of the activity of
Na+-K+-ATPase in sarcolemmal vesicles of rabbit
myocardium 10 min after the onset of myocardial ischemia. On
the contrary, other experimental studies evidenced that during acute
myocardial ischemia, K+ influx persists (31,
38) and even is enhanced (1) suggesting that
Na+-K+ pump is not totally inhibited.
Our results are in accordance with all these experimental data and
could explain this apparent contradiction. In fact, even if
INaK,max is reduced during 14 min up to 65% of
its normoxic value, K+ influx accomplished by
INaK is only reduced for a few seconds after the
onset of myocardial ischemia. Once INaS
is activated, intracellular Na+ and extracellular
K+ accumulations enhance Na+-K+
pump activity and produce a considerable increase of K+
influx that counteracts cellular K+ loss during acute
myocardial ischemia. As already suggested by experimental
results (46), this enhancement of
Na+-K+ pump activity plays an important role in
the onset of the plateau phase.
Paradoxically, the activation of the IK,ATP
seems to also contribute to dynamically counterbalance K+
fluxes. As related above, the increase of gK has
a self-limiting effect on K+ efflux because it reduces
K+ driving force and APD, limiting K+ efflux
across other K+ currents. These electrophysiological
changes explain the fact that a faster activation of the
IK,ATP leads to a smaller increase of
[K+]o, because it can be observed in our
simulations and in experimental studies of the effect of
IK,ATP openers such as pinacidil on
[K+]o during acute ischemia
(21).
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
IK,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.
First, the interruption of coronary flow induces a wide variety of
changes in the electrophysiological and metabolic activity of
cardiomyocytes. In this work, only the aspects of ischemia related to extracellular K+ accumulation in scientific
literature were taken into account in the simulations. Accordingly, the
activation of IK,ATP, the inhibition of
INaK, an INaS, the
shrinkage of extracellular space, and the lack of diffusion between the
interstitial space and the bulk extracellular medium were considered in
our study. Even if these conditions of simulated ischemia are
sufficient to replicate the extracellular K+ accumulation
experimentally observed, other mechanisms like
IK,FFA, IK,Na, or
Na+-K+-2Cl
cotransport could also
contribute to this phenomenon. However, their activation under
ischemic conditions is still uncertain. In addition, other
components of ischemia like acidosis could indirectly influence
cellular K+ loss during ischemia.
Na+-H+ cotransporter (28) has been
related to the intracellular Na+ accumulation observed
during ischemia and hypoxia. This exchanger also affects pH
regulation, something that is not fully contemplated in the LR model.
Furthermore, because of the lack of direct measurements that could
provide more precise information about the rate of variation of
IK,ATP, INaK,
INaS, or Vcleft during acute
myocardial ischemia, the activation of all the mechanisms in
our simulation was linear with time. This linearity probably influenced
the slope of the first increase of [K+]o in
our simulations. However, although the rate of activation of the
mechanisms is possibly not exactly linear during ischemia, the
extracellular K+ accumulation shown in our simulations is
quantitatively and qualitatively similar to the observed during acute
myocardial ischemia in a wide variety of experiments.
 |
ACKNOWLEDGEMENTS |
This study was supported by Grant GV-98-12-78 from the
Consellería de Cultura, Educació i Ciencia de la
Generalitat Valenciana, and by a grant from the Universidad
Politécnica de Valencia.
 |
FOOTNOTES |
Address for reprint requests and other correspondence:
J. M. Ferrero, Jr., Laboratorio Integrado de
Bioingeniería, Departamento de Ingeniería
Electrónica, Universidad Politécnica de Valencia, Camino de
Vera s/n, 46021 Valencia, Spain (E-mail:
cferrero{at}eln.upv.es).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
February 14, 2002;10.1152/ajpheart.00625.2001
Received 18 July 2001; accepted in final form 7 February 2002.
 |
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