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Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205
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ABSTRACT |
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Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
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Mechanoelectric
coupling in the heart is well documented and has been suggested as a
cause of arrhythmia. One hypothesized mechanism for the stretch
sensitivity of cardiac muscle is the presence of stretch-activated
channels (SACs). This study uses modeling to explore the influence of
SACs on cardiac resting potential, excitation threshold, and action
potential in the context of arrhythmia. We added a putative SAC,
modeled as a linear, time-independent conductance with reversal
potential of 
20 or 50 mV, to guinea pig and frog
ventricular membrane models. Increased stretch conductance led to
resting potential depolarization, a decreased excitation threshold,
altered action potential duration, and, under certain conditions, early
afterdepolarizations. We conclude that stretch increases cellular
excitability, making the heart prone to ectopic activity. Regional
effects of stretch on action potential duration can vary and are
influenced by factors such as the SAC reversal potential, ionic
conditions, and baseline currents, all of which may lead to an
increased dispersion of refractoriness throughout the heart and
therefore an increased risk of arrhythmia.
mechanoelectric coupling; electrical stimulation; cardiac myocytes; stretch-activated channels; mathematical model
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INTRODUCTION |
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Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
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THE EXISTENCE of cardiac mechanoelectric coupling (the influence of mechanical events on the electrical state of the heart) is well established (for reviews, see Refs. 13 and 27). Clinically, an increased prevalence of arrhythmia is reported for hearts that have been mechanically compromised by congestive heart failure (12, 34) or for hearts that have been exposed to pressure overload through hypertension (46) or aortic valve disease (9). In vitro studies have shown that sudden incidents of cardiac tissue stretch can result in extrasystoles or the formation of arrhythmia (14, 19). It has been hypothesized that stretch-activated channels (SACs) contribute to cellular membrane potential changes and therefore are the underlying cellular substrate for mechanoelectric coupling and stretch-induced arrhythmias (15, 47).
Stretch of cardiac tissue, cells, or cell membranes has been repeatedly observed to alter resting potential (Vrest) and action potentials. Stretch-induced changes in Vrest, although varied in magnitude, generally act to depolarize the transmembrane potential (Vm). Rapid, pulsatile increases in muscle length or ventricular volume produce transient depolarizations of Vrest that can lead to extrasystoles (15, 47). Contrary to this consistent pattern of changes in Vrest, stretch-induced action potential changes are highly variable (13, 27). Because a change in action potential duration (APD) through the consequent heterogeneity of refractoriness (18), dispersion of repolarization (24), formation of early afterdepolarizations (EADs) (36), or wavelength shortening (38) may be a critical factor involved in arrhythmia formation, the variability in action potential shape and duration is important to characterize. An accelerated repolarization caused by tissue or cellular stretch, indicated by a reduction in APD as measured near final repolarization [i.e., APD at 90% repolarization (APD90)], has been observed in whole rabbit heart (37), frog ventricle (26), guinea pig papillary muscle (32), frog ventricular myocytes (50), guinea pig ventricular myocytes (54), and in vivo human studies (48). Paradoxically, other studies show shortening of early repolarization (decreased APD at 20% repolarization) followed by a prolonged plateau and delay in final repolarization (increased APD90), resulting in an overall lengthening of the action potential in canine heart (14), rabbit heart (55), and frog ventricle (25).
Because these experimental studies were conducted on various animal preparations by different investigators, it is difficult to reconcile the apparently conflicting effects of stretch on the action potential. It is unclear whether a single mechanism causes all of these stretch effects or whether different mechanisms act in the various preparations and conditions. Modeling of cellular membrane currents and membrane potentials is one approach to address this question because it allows the methodical variation of any number of parameters to permit a thorough and efficient examination.
In this investigation, we explore the relationship between stretch and
possible cellular substrates for arrhythmia, such as increased
dispersion of repolarization or the formation of EADs. To explore the
potential role of SACs in excitability and arrhythmogenesis, we
combined a putative SAC model with the Luo-Rudy membrane model for
guinea pig ventricle (GPV model) (28, 58). We also formulated and
implemented the SAC model into a new biophysical membrane model for
frog ventricle (FV model) because the only quantitative report of
stretch effects on cellular excitability is with field excitation of
frog ventricular cells (50). Moreover, implementation of the FV model
permitted us to explore the potential role of the sarcoplasmic
reticulum (SR), which has little function in the frog compared with the
mammal (10, 31). The two models illustrate that stretch increases
cellular excitability and dispersion of both repolarization and
refractoriness
all potentially arrhythmogenic factors.
A preliminary version of this study was presented in abstract form (40).
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METHODS |
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Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
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Guinea Pig Ventricular Membrane Model
We implemented the mammalian membrane model of Luo and Rudy (28, 58) for the guinea pig ventricle (GPV model), a formulation based on whole cell and single-channel experimental data. To account for stretch sensitivity, a putative SAC was added to the membrane model. Both single-channel (6, 21, 41) and whole cell (21, 44) current recordings have associated a linear current-voltage relation with SACs. These currents have been shown to be carried by cations (6, 21, 41) and to be generally time independent (21, 44). Reported single-channel reversal potentials are15 (44), 27 (6), 70 and 2
(21), and 35 to 70 (41) mV. Whole cell reversal
potentials have been measured to be 15 (44) and 16
(21) mV.
Thus the stretch channel current
(Is) was
assumed to be linear and time independent with variable conductance
(gs) and reversal potential (Es)
with representative values of 50 and 20 mV
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(1) |
Standard model conditions.
Ionic conditions for the GPV model were (in mM) 140 [Na]o, 5.4 [K]o, and 1.8 [Ca]o (extracellular
Na, K, and Ca concentration, respectively), and temperature was
37°C. At steady-state resting conditions,
Vrest was
86.5 mV, and intracellular concentrations were (in mM) 18 [Na]i, 145 [K]i, and 1.784 × 10
4
[Ca]i. Membrane
conductances were normalized to membrane capacitance and expressed in
microsiemens per microfarad. Standard capacitive membrane area (1.534 × 104
cm2), cell volume (38 × 106 µl), and cellular
subvolumes were used (28).
Frog Ventricular Membrane Model
To explore the potential role of SR in stretch responses and to compare excitation threshold (ET) results with experimental data, we also formulated and implemented a new membrane model for the frog ventricle (FV model) as described in the APPENDIX. To account for stretch sensitivity, the membrane model was modified by the addition of a linear, time-independent SAC as in Eq. 1.Field excitation framework. It is essential to use an appropriate model to determine ET when comparing modeling results to experimental studies that apply field stimuli (50). Therefore, the membrane models were implemented in an 11-patch field excitation framework to determine cellular excitation under conditions of simulated field stimulation. The details of this framework are presented in the APPENDIX.
Standard model conditions.
Ionic conditions for the FV model were (in mM) 110 [Na]o, 3.0 [K]o, 1.0 [Ca]o, and 2.5 [Mg]i and temperature
of 22°C. At steady-state resting conditions,
Vrest was
85.5 mV, and intracellular concentrations were (in mM) 10 [Na]i, 90 [K]i, and 1.099 × 104
[Ca]i. Model
conductances were expressed in microsiemens for a cell with a
capacitance of 0.1 nF and a volume of 2.5 × 106 µl. Membrane
conductances were normalized to membrane capacitance and expressed in
microsiemens per microfarad.
Validation of FV model.
Experimental data were obtained using whole cell voltage and current
clamp of single frog ventricular myocytes, isolated as previously
described (30). The bath Ringer solution contained (in mM) 110 NaCl, 3 KCl, 1.0 CaCl2, 10 glucose, and 10 HEPES, pH 7.25. Pipette solution consisted of (in mM) 40 KCl, 70 K-glutamate, 10 HEPES, and 10 EGTA, pH 7.18. Experiments were conducted
at room temperature (19-23°C) using a commercial patch-clamp
unit (Dagan 3900 Integrating Patch Clamp, Dagan, Minneapolis, MN). Action potentials were generated by a 10-ms current pulse;
voltage-clamp pulses were applied from a holding potential of
85.5 mV. Parameters for the ionic currents of the FV model were
adjusted until a close fit of the model to the data was obtained.
Simulations
Simulations were initiated with a zero-stretch conductance using standard model conditions unless otherwise indicated. To determine Vrest under stretch conditions, gs was set to the test value and the membrane potential was allowed to settle to its new value over a period of 250 ms. To initiate action potentials, monophasic, rectangular electrical waveforms of 5-ms duration were applied to the field excitation model for cells initially at steady-state Vrest. For each value of gs tested, Vrest was allowed to settle for a period of 150 ms before application of the electrical stimulus. To stretch trigger action potentials, the simulation was initiated with gs = 0 and the membrane potential at rest; after 100 ms, gs was stepped to the test value for a specified duration and then returned to zero.Action potentials were simulated for a wide range of values for
gs. Using the FV
model, we varied
gs from 0 to 300 µS/µF for an
Es of 20
and 50 mV. With the GPV model,
gs was varied
from 0 to 100 µS/µF for the same
Es, 20 and
50 mV.
ET was defined as the minimum half-cell-length potential (HCLP) for which excitation occurred and differs from the transmembrane potential at which regenerative activity occurred, i.e., the "takeoff potential." The HCLP is the potential difference generated by the applied field over a distance equal to one-half of the cell length. An action potential was defined to occur when the membrane potential exceeded 0 mV within 100 ms after the onset of the stimulus.
APD90 was used as a measure of the duration of the action potential and was calculated by determining the time elapsed from the action potential upstroke to the point of 90% repolarization from the maximum overshoot. The upstroke was defined as the instant of maximum rate of rise in membrane potential.
The membrane response for a given stimulus waveform was computed using a second-order Runge-Kutta-Fehlberg algorithm with variable step size no greater than 10 µs (Advanced Computer Simulation Language, Mitchell and Gauthier, Concord, MA) running on a computer workstation (Indy/R4400, Silicon Graphics, Mountain View, CA).
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RESULTS |
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Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
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Validation of FV Model
Two types of experimental recordings from frog ventricular myocytes using the whole cell variation of the patch-clamp method were obtained for fitting the parameters of the FV model. The first was the ventricular action potential, obtained with a stimulus pulse under current-clamp conditions. The second was the 400-ms isochronal current-voltage relation obtained under voltage clamp. Here, the membrane potential was initially held at rest (85.5 mV), clamped
to the test potential for 400 ms, and then returned to rest.
Experimental data were acquired at a sampling rate of 2 kHz, and the
current values were sampled between 398 and 402 ms after the onset of
the test potential and averaged. The resulting value was then plotted
against the test pulse voltage.
The model-simulated action potentials and 400-ms isochronal current-voltage relations were determined under clamp protocols and extracellular and intracellular ionic conditions identical to those in the experiments and fit iteratively to the experimental recordings by adjusting the delayed rectifier potassium current (IK), inward rectifier potassium current (IK1), and sodium-potassium pump current (INaK). All of the remaining currents were constrained according to findings in the literature as described in the APPENDIX. The experimental and model-simulated frog ventricular action potentials are shown in Fig. 1A and compare favorably in height, duration, Vrest, and overall shape. The model-generated 400-ms isochronal current-voltage relation shown in Fig. 1B also faithfully reproduces the experimental voltage-clamp findings.
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Action Potential Changes
Stretch-mediated changes in APD and action potential shape were explored in both the GPV and FV models by implementing a stretch channel with an Es of20
and 50 mV. The stretch channel was activated, and
Vrest was allowed
to stabilize for a period of 150 ms. An electrical field stimulus of a
fixed intensity equal to 1.1 times that of the control (unstretched) ET
was then applied to trigger an action potential.
Figure 2 shows the results of adding a
stretch channel with an
Es of 50
mV in both guinea pig and frog. For guinea pig ventricle, as
gs was increased
from 0 to 50 µS/µF,
Vrest gradually
depolarized and APD90 consistently
decreased from 193 to 144 ms (Fig.
2A). A similar trend is seen for the
frog ventricle. As
gs increased from
0 to 10 µS/µF,
Vrest depolarized
slightly and APD90 decreased to an
even larger degree, from 716 to 185 ms (Fig.
2B).
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Figure 3 illustrates the analogous case of
adding a stretch channel with
Es = 20 mV
to the GPV and FV models. Here, the effect of the stretch channel on
APD was qualitatively different for the two models. For the guinea pig
ventricle (Fig. 3A),
Vrest again
depolarized as gs
increased from 0 to 50 µS/µF. However, with increased
gs,
APD90 gradually lengthened and
final repolarization was delayed; at the same time, the APD measured at
plateau levels decreased. These simultaneous events resulted in a
characteristic "crossover" of the action potentials during the
repolarization phase that was not seen for the case of
Es = 50
mV. The action potential plateau lengthening led to the appearance of
an EAD (gs = 49.6 µS/µF; Fig. 3A,
trace c). At a slightly higher level of stretch conductance (gs = 50 µS/µF; Fig. 3A,
trace d), the EAD triggered a
premature action potential. For the frog ventricle (Fig.
3B),
Vrest depolarized
and APD became progressively shorter as
gs increased from
0 to 10 µS/µF. This result is similar to that seen for
Es = 50
mV.
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The ionic basis underlying the EAD and slow action potential upstroke is shown in Fig. 4. During the prolonged plateau (termed the EAD conditional phase; Refs. 22 and 59) preceding the EAD of Fig. 4A, inactivation gates of the L-type calcium current (ICa) recover while the activation gate closes, permitting reactivation (Fig. 4B). The SR calcium release current (Irel) was not triggered during EAD formation. Therefore, the stretch-induced premature action potential seen in the guinea pig is the result of the recovery and subsequent reactivation of ICa.
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Cellular Excitability
To explore the change in excitability of the cell models under stretch, we recorded resting potential (Vrest) and ET with increasing gs. In our simulations using the GPV model, gs was varied over a range of 0 to 40 µS/µF using an Es of20
or 50 mV (Fig. 5). As expected from
the results shown in Figs. 2 and 3,
Vrest depolarized
from 86.5 to 78.0 mV over this range for Es = 20 mV
and from 86.5 to 82.7 mV for
Es = 50
mV. Concurrent with this depolarization of
Vrest, the cell
became more excitable; ET decreased by 23.4% for
Es = 20 mV
and by 10.4% for
Es = 50 mV. Analogous simulations were performed using the FV model. Results similar to those of Fig. 5 were obtained with only minor differences in
the curvature of the plots.
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A comparison of the effects of
gs on the FV and
GPV models is displayed in Table 1. For
Es = 20
and 50 mV, the change in Vrest
(
Vrest) and
the change in ET (ET) are given for each model for an increase in
gs from 0 to 40 µS/µF. As a measure of comparison, the
gs needed to
cause a 12% decrease in ET
[gs(12%
ET)] was also determined for both models for
Es = 20
and 50 mV.
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By applying stretch conductances with magnitudes larger than those
already discussed, we found that both transient and sustained stretches
could directly trigger action potentials in the absence of any
electrical stimulus (Fig. 6). Figure
6A shows a guinea pig ventricular
action potential triggered by a transient, 30-ms activation of a
gs of 70 µS/µF with
Es = 20
mV. Figure 6B shows a frog ventricular
action potential triggered by a 30-ms, 80 µS/µF stretch, also with
Es = 20
mV. Similar results were obtained for both guinea pig and frog with
Es = 50
mV. A sustained stretch of a slightly lower conductance
results in a pacemaker-like activity for guinea pig
ventricle. Figure 6C shows the
response of the guinea pig ventricular membrane potential to the
sustained activation of a
gs of 60 µS/µF with Es = 20 mV.
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Dispersion of APD
The difference between the changes in APD with stretch obtained with the GPV and FV membrane models at Es =20 mV
(Fig. 3) prompted further investigation. For example, ionic conditions for the FV model were varied to determine whether lengthening of
APD90 with stretch (behavior never
observed under normal ionic conditions for the FV model but seen for
the GPV model in Fig. 3A) could be
observed. Indeed, if the magnitude of ICa were
increased, either by simply scaling the current or by increasing
[Ca]o from 1 to 4 mM,
stretch with Es = 20 mV now caused a lengthening of the action potential (Fig.
7A). A
similar crossover and increase of APD could also be obtained by a
combination of a smaller increase in
[Ca]o (2 mM) and a
decrease in IK1
by a factor of 2 (Fig. 6B). However,
with either the increase of
[Ca]o to 2 mM or the
decrease of IK1
alone, APD shortening (and not lengthening) was observed. Despite
significant lengthening of the action potential plateau, no EAD was
observed for the FV model under any conditions.
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Regional differences in action potential duration in cardiac tissue
create a situation of "dispersion of repolarization." Dispersion
of repolarization may be caused by any number of mechanisms, including
a gradient in tissue stretch or variance in local extracellular ionic
conditions, as suggested by our results. To quantify the potential
dispersion of repolarization that might be found in stretched tissue,
APD was plotted over a range of
gs for the FV model (Es = 20 mV, Fig. 8).
APD90 is seen to decrease to less than one-half of its original value with a
gs of 10 µS/µF under normal ionic conditions. However, increasing
[Ca]o to 4 mM or a
combination of increasing
[Ca]o to 2 mM and
decreasing IK1 leads to an
increase in APD90 as
gs increases.
Figure 8 illustrates how these
APD90 changes interact and how
given either a gradient in
gs (variation
along the abscissa on a single curve) or a regional variation in ionic
conditions (variation among curves at a single point on the abscissa),
significant dispersion of repolarization can exist in tissue.
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DISCUSSION |
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Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
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In this study we implemented two biophysical membrane models, the
Luo-Rudy GPV model and a newly formulated FV model, to explore the
arrhythmogenic effects of adding a linear, time-independent, stretch-sensitive current. This current consistently caused a depolarization of
Vrest and a
reduction in ET, thus increasing excitability to the point where a
mechanical stimulus alone could elicit an extrasystole. APD changes, as
measured by APD90, were more
variable. The guinea pig action potential shortened with stretch for
Es = 50
mV. However, the action potential lengthened with stretch for
Es = 20
mV, leading to a crossover of the action potentials and formation of
EADs. In contrast, the frog action potential consistently shortened
with increased stretch for both Es = 20 mV
and Es = 50 mV, and neither action potential crossover nor lengthening
was seen. Under altered ionic conditions, the frog action potential
could lengthen with increased stretch, although EADs were never seen.
The highly variable APD response observed in this study suggests that
stretch is a possible substrate for arrhythmia in terms of an increased
dispersion of repolarization throughout a region of stretched tissue.
In addition, the formation of EADs indicates a mechanism for
stretch-induced extrasystoles or initiation of reentry.
Effect of Stretch Conductance on ET and Vrest
Depolarization of Vrest occurs with an increase in the conductance of the stretch channel, a finding that was independent of the membrane model or stretch channel Es. At times, the depolarization of the membrane potential by the stretch current was sufficient to trigger an action potential independent of any electrical stimulus (Fig. 6), a behavior that corresponds to that seen experimentally in isolated rabbit heart and frog ventricle (15, 25). The ubiquitous Vrest depolarization is paralleled by a decrease in ET. Over a range of gs, a close relationship exists between the extent of depolarization and the percent decrease of ET. The ratio of percent change in ET per millivolt change in Vrest was nearly constant and varied only from 2.49 to 2.75 for the range of conductance changes reported (Fig. 5, Table 1).Such decreases in ET and depolarizations in Vrest that occur with applied stretch are consistent with previous findings in cell-based experiments. A recent study of whole cell currents in guinea pig ventricular myocytes has shown the activation of inward stretch-sensitive currents for stretch of 10-20% from resting length (44). Another cell-based study, in which direct mechanical stretch was applied to guinea pig ventricular myocytes, reported a slight depolarization (<4 mV) of Vrest with stretch (54).
We, too, have observed small depolarizations of
Vrest and found
~12% change in ET for a 10% stretch in single frog ventricular myocytes during direct mechanical stretch (Ref. 50; Table 1). These
findings, combined with those from the FV model, can be used to
estimate the fraction of SACs that are activated by a 10% stretch of a
ventricular cell. The values for
gs expected to
effect a 12% change in ET are shown in Table 1 and range from 11.5 to
46.1 µS/µF. These values for
gs are only a
rough estimate, considering the many assumptions that have been made.
Nevertheless, the conductance values are quite low when compared with
single-channel data. Assuming a single-channel conductance on the order
of 100 pS (6, 41), channel density of
0.3/µm2 (6, 41), and specific
membrane capacitance of 1 µF/cm2, a
gs of 46.1 µS/µF corresponds to an open probability for the channels on the
order of (46.1 µS/µF)/(100 pS × 0.3/µm2) 
0.015. Therefore,
the stretch conductance activated by a 10% stretch is ~1.5% of that
expected for fully open channels, indicating that only a small fraction
of stretch channels need be opened to increase cellular excitability
significantly.
Effect of Stretch Conductance on APD
An intriguing result of our simulations is the variety of changes in the morphology of the action potential that can occur with increased stretch. For Es =50 mV, the action potential consistently shortens with
increasing stretch for both membrane models (Fig. 2). However, for
Es = 20
mV, the FV model shows APD shortening whereas the GPV model shows APD
lengthening as gs
increases (Fig. 3). This action potential lengthening in the GPV model
is accompanied by a crossover during repolarization and can ultimately
lead to formation of an EAD (Fig. 3A,
trace d). Thus our modeling results
indicate that differences in
Es (as reported
for different subtypes of SACs; Refs. 21 and 41) can modulate
stretch-induced changes in APD.
To determine whether other factors can modulate the APD response to
stretch, additional simulations were performed in which the relative
levels of the ionic currents or ionic concentrations were varied. The
possibility that calcium may be a modulator of stretch has been
described by Gannier and co-workers (16). Their results show that a
stretch-induced increase in intracellular calcium depends on
extracellular calcium rather than on intracellular stores and seems to
be caused by calcium influx through L-type calcium channels (16), which
have been found to be mechanically sensitive (29). We found that in the
FV model, the magnitude of
ICa plays a
crucial role in the behavior of the action potential with stretch. Our
simulation of Fig. 3C was executed
with a [Ca]o of 1 mM,
and action potential shortening was observed. However, if
[Ca]o were raised to 4 mM, or if the magnitude of
ICa were increased (analogous to upregulation of the channel), action potential lengthening could be induced (Fig.
7A). Augmentation of this current contributes to the creation of a small, negative region of the current-voltage relation during the plateau phase that is not present
in the FV model under normal calcium conditions (Fig. 1B). Therefore, a quasi-stable
potential is created at approximately 10 mV, leading to the
observed lengthening in the action potential.
Taken together, these action potential simulations show that the stretch response of APD may be highly sensitive to a few ionic currents or ionic conditions, leading either to shortening or lengthening of APD from its normal value. Also, activation of a stretch channel does not imply that the point of crossover of action potentials with increasing stretch is necessarily equal to Es, contrary to the assertions of some previous studies (43). The crossover point may be either positive (Fig. 7) or negative (Fig. 3A) (55) to Es. Also, a crossover need not always occur (Fig. 3B).
Clinical Implications for Arrhythmogenesis
Both the depolarization in Vrest and the decrease in ET seen in this study may be sufficient to produce an action potential without external electrical stimulation, as was seen in model simulations at high stretch conductances (Fig. 6). Stretch-induced depolarizations have been observed to induce extrasystoles experimentally (3, 19, 25). Pulsatile volume increases in rabbit whole heart preparations induce corresponding Vrest depolarizations such that increasing the magnitude of these volume pulses leads to progressively increased depolarizations and eventually to triggered extrasystoles (15). Transient stretch of frog ventricular tissue will also consistently trigger tissue activation that can be detected both mechanically and electrically (11).The altered durations of the plateau and repolarization phases of the action potential also have proarrhythmic tendencies. An extended plateau can create a conditional phase (22) when the cell is vulnerable to EADs. Once formed, an EAD may trigger a premature upstroke, resulting in an extrasystole. EADs were seen in simulations of the GPV model (Fig. 3A, trace c) and were capable of triggering a regenerative upstroke (Fig. 3A, trace d).
In contrast, shortening of the action potential does not have any inherently arrhythmogenic effects at the cellular level. However, at the tissue or whole heart level, APD shortening will lead to a reduction in wavelength, known to predispose cardiac tissue to arrhythmia. In addition, regional APD shortening will increase the dispersion of refractoriness and repolarization, also commonly believed to be substrates for arrhythmia formation (18, 24). Such a dispersion of refractoriness would be augmented further if regional lengthening were also to occur in other parts of the heart. Spatially heterogeneous refractoriness and repolarization have been reported in the isolated pig heart when subjected to increased loading by aortic clamping (8), and a significant increase of regional dispersion of repolarization was shown to result from sustained stretch in isolated rabbit hearts (56). This modeling study reinforces these experimental findings and suggests that local variations in stretch levels and ionic conditions may act synergistically, leading to simultaneous action potential shortening and lengthening in different cardiac regions, thereby increasing the dispersion of APD throughout the heart.
The concept that ionic conditions play a role in the modulation of APD under stretch conditions implies that pathological conditions may augment or alter the baseline electrophysiological effects of stretch. During ischemia and reperfusion, membrane currents are modified as a result of altered ionic composition of intracellular and extracellular fluids and the buildup of metabolic byproducts (4). Ischemia leads to an accumulation of extracellular potassium, caused at least partially by an ATP-sensitive potassium channel activated by a decrease in cellular ATP levels (2). There is also considerable evidence for abnormal calcium cycling in heart failure, resulting in altered calcium transients (5). Both ischemia and heart failure, although generally viewed as mechanical disorders, are associated with an increased risk of sudden death by arrhythmia (36, 57). The pathological ionic conditions associated with these diseases may compound the stretch-induced effects on APD, thereby contributing to an increased dispersion of refractoriness throughout the heart.
In addition to heterogeneity of the magnitude of stretch or of ionic
conditions, a heterogeneity of stretch channel types throughout the
heart may also increase the dispersion of repolarization. Cells may
contain multiple stretch channel subtypes, each having a characteristic
Es and
distribution pattern (21, 41). In chick heart cells, for example, two
populations of SAC have been identified, having
Es of 70
and 2 mV (21). The effective
Es of the total
stretch-induced current will lie between these two Es and will be
determined by the relative conductances contributed by each channel
type. If the channels are nonuniformly distributed throughout the
heart, so that different channel types dominate regionally, the
effective Es of
the stretch-induced current will also vary from region to region. We
have shown that in guinea pig cells, stretch can cause either action
potential shortening or lengthening depending on the exact value of
Es (Figs.
2A and 3A).
Early Afterdepolarizations
EADs were seen in simulations using the GPV model but not in those using the FV model (Figs. 3, 6). Because SR has a much greater functional role in the mammal compared with the frog (10, 31), we expected that the more complex calcium dynamics of the guinea pig might explain why the GPV model shows a tendency towards EAD formation. However, we found that Irel was zero during the EAD, indicating that some other current must be involved in EAD formation.In a modeling study by Zeng and Rudy in a guinea pig ventricular cell
model (59), the critical factors for drug-induced EAD formation were
determined to be a prolonged action potential plateau and reactivation
of L-type calcium channels. These two factors are related, because the
extended plateau phase provides time for
ICa to recover
from inactivation, a necessary precursor to its reactivation. In our
experiments using the GPV model, the action potential plateau was
lengthened by addition of a stretch current with
Es = 20 mV
(Fig. 3A). A conditioning phase
developed at approximately 30 mV, the same as observed by Zeng
and Rudy (59). This potential is sufficiently negative to
permit significant (~40%) recovery of inactivation and the
subsequent reactivation of
ICa (Fig. 4). In
the FV model, a prolonged plateau appeared during stretch only under
varied extracellular ionic conditions (Fig. 7). However, this plateau
level was 0 to 10 mV, much more positive than that seen for GPV
action potentials. At this membrane potential, little recovery from
inactivation is possible, and reactivation of the L-type calcium
channels does not occur. Because the characteristics of the activation
and inactivation gates are nearly identical in the GPV and FV models,
the level of the plateau potential may therefore be critical to whether
reactivation of ICa and formation
of EADs result from stretch.
There has been some debate as to whether experimental findings of stretch-induced EADs in frog (25) and mammalian (33) tissue are real or artifactual. Our results suggest that EAD formation, at least in guinea pig, is indeed a real effect of stretch.
Comparison to Previous SAC Modeling Studies
Our model for Is is similar to the SAC implemented in previous modeling by Sachs (42) and Zabel et al. (55) for guinea pig ventricle using the Oxsoft HEART program. In those simulations, the stretch conductance was explicitly assumed to be a function of sarcomere length, in the form gs =
(L), where is
single-channel conductance, is channel density,
(L) is a nonlinear
length-dependent factor that defines channel open probability, and
L is sarcomere length. According to
their model, (L) asymptotically
approaches zero at short lengths and is 1% activated at a sarcomere
length of 1.9 µm, the slack length for guinea pig ventricular
myocytes (17). We have made no assumptions regarding the relationship between channel open probability and sarcomere length in our
formulation, because this relationship is not currently known.
The previous modeling studies using this SAC formulation illustrated that some stretch-induced action potential and Vrest changes reported by experimental studies could be successfully modeled by implementing a linear, time-independent SAC with a negative Es (42, 55). The current study shows that stretch of cardiac tissue produces more than just a change in the duration of the action potential. The APD change has a significant impact on arrhythmogenicity and excitability of cardiac tissue. Changes in APD, especially when regionally distributed, can become arrhythmogenic through mechanisms such as EADs, wavelength shortening, and increased dispersion of repolarization. Stretch also depolarizes Vrest and increases the excitability of individual cardiac cells.
Limitations of Study
The SAC has been assumed to be linear and time-independent, on the basis of findings from numerous experimental studies. Other modeling studies have made the same assumptions with respect to SAC properties (42, 55). However, although experimental studies have confirmed the existence of linear, time-independent SACs in guinea pig (44), direct experimental data have not yet been obtained to show their existence in the frog ventricle. In addition, there may be a slow time-dependent inactivation of SACs, on the order of seconds (21) or minutes (44, 50), that has not been accounted for in this study.Other ionic effects of stretch have been described for cardiac muscle. First, several of the fundamental time-dependent channels typically found in cardiac cells, including the L-type calcium, delayed rectifier potassium, and ATP-sensitive potassium channels (29, 51, 53), have been shown to be modified by stretch. Second, currents have been identified in frog and guinea pig ventricle that are mechanosensitive but not necessarily stretch sensitive, including the swelling-sensitive chloride current (39, 52). This current is not activated under isotonic conditions, and therefore is not expected to alter the results of the current study. Third, it is known that the binding of calcium to troponin C is stretch sensitive (7). The effects of stretch on these other mechanisms have not been considered in the current study.
In conclusion, these results confirm experimental observations that stretch of cardiac tissue can be arrhythmogenic. Stretch leads to Vrest depolarization and increased cellular excitability. The diversity of APD changes induced by stretch may lead to an increased dispersion of repolarization, a potentially arrhythmogenic situation in cardiac tissue. EADs and premature action potentials can be elicited by a stretch current and may initiate extrasystoles in the whole heart.
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APPENDIX. FV Model |
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Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
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The FV model simulates the electrophysiological properties of frog
ventricular cardiac membrane. The simulation equations for this model
are based largely on the model formulated by Rasmusson et al. (35) for
the frog atrium (FA model). The FV model assumes a "standard"
cell with a capacitance of
104 µF, the convention
used in the FA model. Conductances are expressed in microsiemens,
membrane potential in millivolts, and membrane currents in nanoamperes.
The diffusion-limited cleft space in the FA model was eliminated.
Changes from the FA membrane equations were implemented as necessary to
match simulations to whole cell voltage-clamp and action potential data
obtained from single frog ventricular myocytes. A putative
stretch-activated current was also included in the model.
Model Equations
Sodium current. The kinetic equations used to describe the fast sodium current (INa) are based on the data of Seyama and Yamaoka (45) for bullfrog ventricular cells. The rate constants were scaled by 5.2 to account for an apparent Q10 of 2.5 in these cells (1) and the 18°C temperature difference between experimental (4°C) and model (22°C) conditions. This value of Q10 was calculated by comparing the activation time constant data at 4°C (45) with the activation time constant reported for 25°C (1). However, this value of Q10 did not account for the difference in the inactivation time constant between these two sets of data (1, 45). To adjust for this discrepancy, the inactivation time constant was increased by a factor of 1.7. The maximum conductance was set to a value of 0.66 µS.
Calcium current. ICa was the FA calcium current for frog atrial cells scaled by a factor of 2.125 as reported in a current density comparison between frog atrial and ventricular cells (20).
Delayed rectifier potassium current. IK was the FA current scaled by a factor of 0.25 to match the 400-ms isochronal current-voltage relation at positive transmembrane potentials obtained experimentally in frog ventricular cells, as shown in Fig. 1B.
Inward rectifier potassium current.
The mathematical formulation for
IK1 in the FA
model had too few free parameters to match our experimental data for
frog ventricular cells. Instead, a modified version of the Luo-Rudy
IK1 current (28)
was used, with parameters altered to match the 400-ms isochronal current-voltage relation for transmembrane potentials negative to 20 mV (Fig. 1B). The
current was defined by the following equations
|
(A1) |
![<IT>g</IT><SUB>K1</SUB> = 0.101486<FR><NU><IT>a</IT><SUB>K1</SUB><IT>c</IT><SUB>K1</SUB><RAD><RCD>[K]<SUB>o</SUB></RCD></RAD></NU><DE><IT>a</IT><SUB>K1</SUB> + <IT>b</IT><SUB>K1</SUB></DE></FR>](/content/vol275/issue2/fulltext/H431/img003.gif)
|
(A2) |
![<IT>a</IT><SUB>K1</SUB> = <FR><NU>2.04</NU><DE>1 + exp [0.07155(<IT>V</IT><SUB>m</SUB> − <IT>E</IT><SUB>K</SUB> − 54.215)]</DE></FR>](/content/vol275/issue2/fulltext/H431/img004.gif)
|
(A3) |
![<IT>c</IT><SUB>K1</SUB> = 1 − <FR><NU>0.9</NU><DE>1 + exp [0.11925 (<IT>V</IT><SUB>m</SUB> − <IT>E</IT><SUB>K</SUB> − 99.215)]</DE></FR>](/content/vol275/issue2/fulltext/H431/img005.gif)
|
(A4) |
![<IT>b</IT><SUB>K1</SUB> = <FR><NU><FENCE><AR><R><C>0.49124 exp [0.05783(<IT>V</IT><SUB>m</SUB> − <IT>E</IT><SUB>K</SUB> − 13.524)]</C></R><R><C> + exp [0.06175(<IT>V</IT><SUB>m</SUB> − <IT>E</IT><SUB>K</SUB> − 584.31)]<SUB> </SUB></C></R></AR></FENCE></NU><DE>1 + exp [−0.5143(<IT>V</IT><SUB>m</SUB> − <IT>E</IT><SUB>K</SUB> + 14.753)]</DE></FR>](/content/vol275/issue2/fulltext/H431/img006.gif)
|
(A5) |
Background currents. The calcium background current and the sodium background current were identical to those in the FA model.
Stretch-activated current.
The putative Is
used in the FV model was assumed to have a time-independent, linear
current-voltage relation, with
Es in the range
of 50 to 20 mV and a
gs that increased
with stretch (Eq. 1).
Pump and exchanger currents. The sodium-calcium exchanger current (INaCa) and the sarcolemmal calcium pump current were identical to those in the FA model. The sodium-potassium pump current (INaK) was scaled by a factor of 0.5 from that of the FA model.
Corrections to the FA Model. On the basis of discussions with R. Rasmusson, corrections were made to three published equations of the FA model (35). These equations, including corrections, are also part of the FV model.
Delayed rectifier current
|
(A6) |
![<IT>I</IT><SUB>NaK</SUB> = 0.0725 ⋅ <FENCE><FR><NU>[Na]<SUB>i</SUB></NU><DE>[Na]<SUB>i</SUB> + 5.46</DE></FR></FENCE><SUP>3</SUP> <FENCE><FR><NU>[K]<SUB>o</SUB></NU><DE>[K]<SUB>o</SUB> + 0.621</DE></FR></FENCE><SUP>2</SUP> <FENCE><FR><NU><IT>V</IT><SUB>m</SUB> + 150</NU><DE><IT>V</IT><SUB>m</SUB> + 200</DE></FR></FENCE>](/content/vol275/issue2/fulltext/H431/img008.gif)
|
(A7) |
![<IT>I</IT><SUB>NaCa</SUB> = 1.5 × 10<SUP>−6</SUP> ⋅ <FR><NU><FENCE><AR><R><C>[Na]<SUP>3</SUP><SUB>i</SUB>[Ca]<SUB>o</SUB> exp (0.0195<IT>V</IT><SUB>m</SUB>)</C></R><R><C> − [Na]<SUP>3</SUP><SUB>o</SUB>[Ca]<SUB>i</SUB> exp (−0.0195<IT>V</IT><SUB>m</SUB>)</C></R></AR></FENCE></NU><DE>1 + 0.0001([Na]<SUP>3</SUP><SUB>o</SUB>[Ca]<SUB>i</SUB> + [Na]<SUP>3</SUP><SUB>i</SUB>[Ca]<SUB>o</SUB>)</DE></FR>](/content/vol275/issue2/fulltext/H431/img009.gif)
|
(A8) |
Field Excitation
To determine cellular excitation threshold under experimental conditions of field stimulation, the model was modified further in a manner similar to that developed previously (49). Unlike the previous field model in which cells were stimulated by longitudinally oriented fields, here we consider the case of transverse stimulation because this configuration allows a clear separation of membrane channel versus geometric effects, as will become apparent. Assuming a prolate spheroid shape for the cell, the extracellular surface potential (Ve) resulting from the applied field (Eoy) can be determined analytically and is a linear function of distance (y) (23)
|
(A9) |
), defined as
, where a and
b are the semimajor and semiminor
axes, respectively. For simplicity in our model, we have
assumed the limiting case of a cylindrical geometry with radius
(b) for the cell, in which case
a 
, 1, A 2, and
Ve assumes the
well-known cosine dependence if y is
expressed in terms of polar angle (i.e.,
y = b
cos 
).
The membrane was divided circumferentially into 11 segments over which
Ve (varying from
2Eoyb
to
+2Eoyb) was partitioned into 11 equal ranges. The potential drop over one-half
of the cell
(Eoyb),
termed the half-cell-length potential (HCLP), was used to define ET.
The biophysical properties of each membrane patch were represented by
the model equations described by the FV model or the GPV model, and the
relative sizes of the membrane patches were calculated as previously
described (49). To reduce the simulation times, intracellular and
extracellular resistances were omitted, which resulted in a slight but
systematic overestimation of ET.
In the interpretation of our simulation results, it is necessary to
take into account changes in the cell geometry with stretch. If a
constant cell volume is assumed, an increment of
L/L
in cell length will decrease cell diameter by
, thereby decreasing
the sensitivity of the cell to the extracellular field and raising
the stimulus threshold. A 10% longitudinal stretch will result in a
4.65% decrease in cell diameter, resulting in an effective increase in
ET by a factor of 100/(100 4.65) = 1.05 from geometric effects
alone. In previous experiments from our laboratory, the ET for
cross-shock field stimuli in single frog ventricular myocytes was found
to decrease on the order of 0.8% per 1% stretch
(n = 10; Ref. 50).
Accounting for the expected geometric changes, the ET for a 10%
increase in cell length can be calculated to be (100 8)/1.05 = 87.7% of the prestretch value, i.e., a decrease of ~12%. This 12%
decrease in ET resulting from a 10% cell stretch is used as a
characteristic measure of the stretch effect.
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ACKNOWLEDGEMENTS |
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This work was supported by National Institutes of Health Grant R01 HL-50610. T. Riemer was a recipient of a Whitaker Foundation Graduate Fellowship in Biomedical Engineering.
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FOOTNOTES |
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Address for reprint requests: L. Tung, Dept. of Biomedical Engineering, Johns Hopkins Univ., 720 Rutland Ave., Baltimore, MD 21205.
Received 20 November 1997; accepted in final form 20 April 1998.
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Appendix
References
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