Vol. 284, Issue 4, H1285-H1294, April 2003
A mathematical model of phase 2 reentry: role of L-type Ca
current
Shunichiro
Miyoshi1,
Hideo
Mitamura2,
Kana
Fujikura2,
Yukiko
Fukuda2,
Kojiro
Tanimoto2,
Yoko
Hagiwara2,
Makoto
Ita3, and
Satoshi
Ogawa2
1 Department of Physiology and
2 Cardiopulmonary Division, Keio University School
of Medicine, and 3 Pharmacia Laboratory, Tokyo, 160-8582 Japan
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ABSTRACT |
Phase 2 reentry (P2R) is known to be
one of the mechanisms of malignant ventricular arrhythmias, especially
those associated with Brugada syndrome. However, little is known about
the underlying mechanism for P2R. Our aim in this study was to simulate
P2R in a mathematical model to enable us to understand its mechanism and identify a potential therapeutic target. A mathematical model of
the L-type Ca current was composed according to whole cell current data
from guinea pig ventricular myocytes recorded at 37°C. Our
mathematical model was incorporated into the modified Luo-Rudy phase 2 model. We set a dispersion in transient outward current
(Ito) density within the theoretical fiber,
composed of 80 serially arranged epicardial cells with gap junctions
and then observed the P2R. The dispersion in Ito
density within an only 0.8-cm epicardial theoretical fiber generated
P2R with our Ca channel but not with the original model. When the P2R
developed in the theoretical fiber, the calculated extracellular field
potential showed coved-type ST segment elevation. We succeeded in
generating P2R in our model for the first time. The local epicardial
P2R may contribute the genesis of coved-type ST segment elevation in
the Brugada syndrome.
ventricular fibrillation; computer simulation; patch clamp; electrocardiogram; Brugada syndrome
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INTRODUCTION |
BRUGADA SYNDROME is
characterized by ST segment elevation in the right precordial leads and
sudden cardiac death in the absence of obvious organic heart disease
(3). Although prophylactic drug therapy to prevent
ventricular fibrillation (VF) and sudden cardiac death is essential to
the proper management of this syndrome, no therapy is yet been
identified. Because a correlation between increased ST segment
elevation and the occurrence of premature ventricular complexes (PVC)
originating in the right ventricles (RV) and VF has been reported
(18, 23), the RV must play a pivotal role in the genesis
of VF in this syndrome. The mechanism of the VF, however, is still
undetermined. Bradycardia-dependent increase in the ST segment
elevation in previous reports (1, 17) suggested the
importance of the transient outward current (Ito), having slow recovery kinetics, in this
syndrome. Ito was prominent at the RV
epicardium, therefore, Ito-mediated early repolarization of the action potential was observed preferentially at
the RV epicardium (6, 12), which elevated the ST segment via increasing transmural gradient of membrane potential
(26), and was believed to be one of the potential cellular
mechanisms for ST segment elevation in this syndrome (18,
26). This dispersion of repolarization in the RV is known to
cause phase 2 reentry and subsequent circus movement reentry (11,
14, 26).
Ito must play a pivotal role in the phase 2 reentry, because this reentry was only observed in the epicardial
ventricular muscle and was blocked by 4-aminopyridine (11, 14,
26). Thus Ito-mediated early
repolarization in the epicardium and subsequent phase 2 reentry are the
potential cellular bases for VF in this syndrome (26). An
Ito-mediated marked outward shift of the current in phase 1 causes loss of the dome and early repolarization, which is
capable of precipitating reentry but does not always do so. Despite the
delicate balance between the outward and inward currents in the phase 1 having been believed to be important in the genesis of this reentry
(11, 14), the precise underlying mechanisms have not been
elucidated. There is cell-to-cell dispersion in Ito density not only within the transmural wall
(12, 13) but also within the epicardium (6,
7), which is believed to cause dispersion in the repolarization
within the epicardium and consequently phase 2 reentry. Many studies
(18, 26) have attempted to ascertain the mechanism of the
ST segment elevation and the phase 2 reentry in this syndrome, but
there is limitation in the experimental models.
A mathematical model might facilitate one to understand the genesis of
phase 2 reentry in this syndrome. Thus the aim of the present study was
to simulate phase 2 reentry in the one-dimensional epicardial fiber
model and to calculate the extracellular field potential to determine
how the phase 2 reentry can be observed in the ECG. In the present
study, we were unable to generate phase 2 reentry by means of
Ito density dispersion within a physiological range in a theoretical fiber model of the modified Luo-Rudy phase 2 model (15, 16), including a mathematical model of
Ito (8). Therefore, we
focused on the kinetics of L-type Ca current
(ICaL), because self-reproductive excitation of
ICaL must be essential to the genesis of phase 2 reentry.
Because the mathematical model of ICaL defined
by Rasmusson et al. (21), which is utilized in the
Luo-Rudy phase 2 model (15, 16), might not represent the
kinetics of mammalian ICaL at a temperature of
37°C, we measured ICaL by using the whole cell
patch-clamp experiment at the 37°C. Furthermore, our defined mathematical model of the ICaL was applied to
the Luo-Rudy phase 2 model. Finally, we devised a theoretical fiber
with multiple epicardial cells connected via gap junctions
(22) and observed phase 2 reentry in this mathematical
one-dimensional model and the extracellular field potential.
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METHODS |
Cell preparation.
Ventricular myocytes from adult guinea pigs were isolated according to
procedures described previously (19). Briefly, adult guinea pigs weighing 150-300 g were intraperitoneally injected with heparin (1,000 units) and pentobarbital sodium (30 mg/kg). Hearts
were retrogradely perfused with nominally Ca2+-free Tyrode
solution for 3 min and with the same solution containing 0.5 g/l of
type II collagenase (Worthington Biochemical) for 18-20 min at the
temperature of 37°C. The left ventricles were dissected and agitated
in high-K+ medium (KB medium) to retrieve the ventricular
myocytes. All experiments were approved by the ethics committee
of Keio University School of Medicine.
Solutions and chemicals.
The Tyrode solution contained (in mmol/l) 143 NaCl, 4 KCl, 1.8 CaCl2, 0.5 MgCl2, 5.5 D-glucose,
and 5 HEPES (pH adjusted to 7.4 with NaOH). Nominally
Ca2+-free Tyrode solution was prepared by simply omitting
CaCl2. The Kraft-Brühe medium contained (in mmol/l)
50 glutamic acid-K, 10 taurin, 25 KCl, 10 KH2PO4, 0.5 EGTA, 3 MgCl2, 27.8 glucose, and 10 HEPES (pH adjusted to 7.4 with KOH).
The pipette solution for whole cell recording contained (in mmol/l) 110 CsCl, 20 TEA-Cl, 3 Mg-ATP, 0.4 Tris-GTP, 10 BAPTA, and 5 HEPES (pH
adjusted to 7.2 with CsOH). To prevent contamination by other
monovalent cation currents and the Na/Ca exchanger current, the
external Na+ and K+ in the bath solution were
replaced with equimolar choline. To analyze gating precisely,
independently of the Ca2+-dependent block, Ba2+
was used as a charge carrier, and to obtain a better voltage clamping,
the 1.8 mmol/l of Ca2+ were replaced with 1 mmol/l of
Ba2+ and 0.8 mmol/l of Mg2+. Most reagents were
purchased from Sigma (St. Louis, MO).
Electrophysiology.
Cardiomyocytes were transferred into a thermocontrolled perfusion
chamber (37-37.5°C), mounted on the stage of an inverted microscope (IX-70, Olympus; Tokyo, Japan), and superfused with Tyrode
solution. Superfusates were applied via a gravity-fed, thermocontrolled
Y tube with a diameter of ~120 µm. Its opening was positioned
~150 µm from the cell. The bath temperature and heater temperature
of the Y tube were monitored with a digital thermistor (model 2455, Iuchi; Osaka, Japan).
Data were obtained by using patch-clamp procedures in the conventional
whole cell configuration. The resistance of pipettes filled with
internal solution was of low range (700-900 k
) to allow quick
clamping of the membrane voltage and evaluate gating kinetics
accurately, and the pipettes were coupled via an Ag-AgCl wire to an
amplifier. The liquid junction potential at the recording pipette and
the ground electrode was 
1 to 2 mV. The seal resistance of <2 G
and the series resistance of >1.5 M were discarded from the
analysis. Membrane voltages were computer controlled (pCLAMP8 software,
Axon Instruments). The currents were amplified and then filtered with a
built-in four-pole Bessel filter set at 10 kHz (Axopatch-200B, Axon
Instruments). Data were sampled with an analog-to-digital converter
(DigiData-1321A, Axon Instruments) at a frequency of 100 kHz and stored
in an AT/T computer. Recording was started 3 min after the patch
membrane was ruptured to allow the contents of the pipette and the
cytoplasm to equilibrate.
The voltage-dependent kinetics of ICaL at a
membrane potential of more than 30 mV were recorded using a
depolarizing step-pulse protocol. We held cells at a potential of 80
mV before evoking a 500-ms conditioning pulse for 50 mV to inactivate
the T-type Ca current, and a 1-s test pulse from 45 to +50 mV with
5-mV increment was then applied. We set the sweep-to-sweep interval at
30 s to ensure complete recovery of ICaL.
The inward current at the test potential was completely blocked by 10 µmol/l of nifedipine (n = 3, data not shown).
Capacitance current and other background currents were elicited by the
same step-test pulse protocol, followed by the conditioning step pulse
of 1 s for 0 mV to inactivate ICaL with a
gap of 3 ms for 50 mV, and then subtracted from the previous data.
Remaining data were defined as the ICaL, and the
time constants of the activation gate (d-gate) and the inactivation
gate (f-gate) were calculated. The steady-state value of the d-gate at
each membrane potential was calculated from the amplitude of the peak inward current. The voltage-dependent kinetics of
ICaL at a membrane potential below 30 mV was
calculated by the following way. The time constant of the d-gate was
measured from the tail current. The cell was held at a potential of
80 mV before evoking a 500-ms conditioning pulse for 50 mV and then
3 ms for 0 mV, subsequently repolarizing the test pulse to 30 to 90
mV with application of a 5-mV increment. The capacitance and other
background currents were elicited by the same step-test pulse protocol
followed by the conditioning pulse of 1 s for 0 mV and then
subtracted from the previous data. On the other hand, the f-gate time
constant was measured using a twin-pulse protocol. Initially, a
conditioning pulse of 0 mV was applied for 1 s from the holding
potentials of 30, 40, 50, 60, or 80 mV to inactivate the
channel, and the membrane potentials then returned to the holding
potential for variable intervals to allow for recovery from
inactivation before application of the test pulse to 0 mV. The
steady-state value of the f-gate was calculated from the steady-state
inactivation protocol. We held the potential in the same way with a 1-s
depolarizing conditioning pulse from 50 to +50 mV with a 5-mV
increment, and the test depolarizing pulse subsequently went to 0 mV
with a gap of 3 ms for 50 mV.
To achieve better curve fitting, the d-gate time constant was fitted by
the chi-square method with a function of
where t is the time from the onset of the test pulse,
Iinf is the current of the steady-state value;
Io is the current at the onset of the test
pulse; and 
is the time constant.
On the other hand, the f-gate time constant was fitted with a
double-exponential function as follows
where Iinf(slow) and
Iinf(fast) are the steady-state values of the
slow and fast time constant, respectively, and
Io(slow) and Io(fast) are
components of slow and fast time constants; only the (fast) was then
used for the mathematical model.
Ca2+ driving force was calculated by the following
equation
where zCa is the valence of Ca2+ and equals 2;
Cao is extracellular Ca2+ and equals 0.5 mmol/l; Cai is intracellular Ca2+ and equals
100 nmol/l; 
Cai is the activity coefficient of
Cai and equals 1; Cao is the activity
coefficient of Cao and equals 0.341; V is the
membrane potential; F is the Faraday constant (96,500 C/mol); R is the gas constant (1.987 calories · mol · K
1);
and T is the absolute temperature (in K).
Fitting was done on the commercial software Igor Pro 4 (Wavemetrics; Lake Oswego, OR) on a personal computer.
Mathematical model.
An action potential model of a modified version of the Luo-Rudy phase 2 model was used (15, 16). The model of
Ito, composed by Nesterenco (8),
and our model of ICaL were incorporated into the
Luo-Rudy model to simulate epicardial fiber. The theoretical fiber is
composed of 80 serially arranged ventricular cells (total fiber length
of 0.8 cm) with gap junctions (22). Differential equations
were solved numerically by using the Crank-Nicholson method
(5) (the average of the second central difference at time t and t + dltaT,
where dltaT is the time step). The time derivative was set to 10 µs, and the space derivative was set to 0.1 mm (22).
We set dispersion in the Ito density to generate
phase 2 reentry in the theoretical epicardial fiber. We changed the
Ito density in the right 50 cells from that in
the left 30 cells and applied pacing to a cell at the end of the left
side (to observe phase 2 reentry, we practically split the cells in
this proportion). It is believed that in the ventricular myocardium,
impulses propagate along the transmural axis from the endocardium
toward the epicardium, because the rapid conduction of Purkinje fibers
overcomes the conduction of ordinary cardiac muscle along the axis of
the epicardial surface. Therefore, in some experiments, we applied
pacing to each cell in the whole fiber and stimulated them
simultaneously. Ito densities were changed from
0.5 to 2 mS/µF incrementally by 0.09375, and the phase 2 reentry was
observed. Phase 2 reentry was set to the following criteria. Two action
potentials, separated by full repolarization of less than 80 mV, are
generated by a single ventricular pacing. Because the current through
the membrane of the cell at both dead ends of the fiber must be
overestimated, the generated phase 2 reentry data from the three cells
at both ends of the fiber were discarded. Maximal
ICaL conductance was decreased to 50% of the
original Luo-Rudy phase 2 model value (8) in every experiment.
The action potential durations at 90% repolarization
(APD90) and maximal velocity of voltage change
(Vmax) value of the upstroke of phase 2 (Ph2-Vmax) were measured. The phase 1 duration
(Ph1-duration) was defined as the duration from the onset of phase 0 until the timing of the Ph2-Vmax.
A pseudo-ECG was calculated as an extracellular field potential
(20) along the axis of our theoretical fiber and 4 cm from the right end of the fiber.
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RESULTS |
Patch clamp.
Cell capacitance in the present study was 125 ± 4 pF
(n = 30). Figure 1A,
top, shows a hemilog plot of the
representative current traces and superimposed fitted curves at each
membrane potential. The measured time constant of the d-gate was
averaged and plotted against the membrane potential (Fig.
1A). The data were fitted by the function in the Fig. 1,
inset, and superimposed. Interestingly, the time constant of
the d-gate is considerably faster than that previously described
(21). Averaged data from steady-state activation,
normalized to the maximal inward current, were plotted against the
membrane potential (Fig. 1B). The first measured time
constant of the f-gate and data from steady-state inactivation are
shown in Fig. 2. In our experiment on the
physiological range of membrane potential, the depolarization-induced
activation of the f-gate is modest compared with the previous model.
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Fig. 1.
Measured activation gate (d-gate). A: measured
time constant () of the activation gate was averaged and plotted
against the test potential, and the fitted curve was superimposed.
Function of curve is depicted along side. Left
inset, recorded kinetics below a membrane potential of 35
mV; right inset, recorded kinetics above 30 mV.
Top, representative current data at each membrane potential
and fitted curve was superimposed. B: peak inward current
was normalized to the maximal inward current and then averaged and
plotted against test potential. Data were fitted by the function beside
it and superimposed in the same figure. Extracellular Ba2+
was used as a current carrier. V, membrane potential. See
text for details.
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Fig. 2.
Measured inactivation gate (f-gate). A:
measured fast component of time constant of the activation gate was
averaged and plotted against the test potential. Data were fitted by
the function along side and superimposed in same figure. Left
inset, recorded kinetics at a membrane potential below 30 mV;
right inset, recorded kinetics above 30 mV. B:
data from steady-state inactivation protocol (inset) were
normalized to the maximal inward current and then averaged and plotted
against the test potential. Data were fitted by the function along side
and superimposed in the same figure. Extracellular Ba2+ was
used as a current carrier.
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Mathematical model of action potentials.
The three action potentials in Fig. 3 are
a typical canine action potential recorded from the RV epicardium by
using a standard microelectrode, an action potential generated by the
modified Luo-Rudy phase 2 model with the Rasmusson et
al.-ICaL kinetics (Rasmusson-ICaL) and an action potential with
ICaL kinetics, as described in the present study
(Miyoshi-ICaL). To obtain a realistic epicardial
action potential, the maximal conductance of the
ICaL was decreased by 50%, and the maximal
conductance of Ito was set to 0.55 mS/µF. Our
model simulates the steepness of the slope of the upstroke of the phase
2 well.
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Fig. 3.
A: typical canine action potential recorded
from the right ventricular epicardium by standard microelectrode
experiment. B: action potential generated in the modified
Luo-Rudy phase 2 model has original L-type Ca2+ current
(ICaL) kinetics
(Rasmusson-ICaL). C: action potential
with ICaL kinetics described in the present
study (Miyoshi-ICaL). Maximal conductance of the
ICaL was decreased by 50%, and the maximal
conductance of Ito was set to 0.55 mS/µF. Our
model simulates the steepness of the slope of the upstroke of phase 2 well. Horizontal bar represents 100 ms, vertical bar represents 50 mV.
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The conductance of Ito or
ICaL is variable in both models and shape of the
action potential is observed in Fig. 4.
Measured Ph2-Vmax and Ph1 duration versus phase
1 amplitude are summarized in Fig. 5,
A and B. Measured
APD90 versus Ito or
ICaL density are summarized in Fig. 5,
C and D. In both models, as a function of the
increase in Ito density, prolongations of phase
1 duration and action potential duration are observed (Fig. 4,
A and C, and Fig. 5D). Compared with
the Rasmusson-ICaL, the degree of accentuation of the phase 1 dip and also Ph2-Vmax are marked
in the Miyoshi-ICaL with the same
Ito density. A further increase in the
Ito density results in the loss of dome and
early repolarization in both models. The degree of action potential
shortening is marked in Miyoshi-ICaL (Fig.
5D). On the other hand, as a function of the increase in the
ICaL density, the action potential duration was
prolonged to some extent and then paradoxically shortened after this
prolongation (Fig. 4, B and D, and Fig.
5C). The degree of prolongation is obvious and is observed
early after depolarization in the
Rasmusson-ICaL. The threshold of the phase 1 amplitude needed to generate a phase 2 dome is almost the same in the
two models (Fig. 5A). As a function of hyperpolarization in
the phase 1 amplitude, Ph2-Vmax was increased (Fig. 5A) and emergence of the phase 2 dome was delayed in
both models (Fig. 5B). The degree of the increase in
Ph2-Vmax was marked in
Miyoshi-ICaL.
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Fig. 4.
Action potential shapes with various transient outward current
(Ito) and ICaL densities.
A and B: action potential shapes with
Rasmusson-ICaL. A: action potential
with a variable Ito density; B:
action potential shape with a variable ICaL
density. As a function of the increase in ICaL
density, the early after depolarization is generated. C and
D: action potential shapes with
Miyoshi-ICaL. C: action potential
with a variable Ito density; D:
action potential shape with a variable ICaL
density. See text for details.
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Fig. 5.
Summarization of measured action potential parameters. Measured
maximal velocity (Vmax) value of the upstroke of
phase 2 (Ph2-Vmax, A) and phase 1 duration (Ph1 duration, B) are plotted against phase 1 amplitude. Repolarization in phase 1 will increases
Ph2-Vmax and delays the emergence of the phase 2 dome. Measured action potential duration at 90% repolarization point
(APD90) is plotted against ICaL
(C) and Ito (D) density.
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The mathematically calculated intracellular Ca concentration
([Ca]i) and current through ICaL
by the models are shown in Fig. 6. With
the Ito-mediated phase 1 dip,
ICaL during phase 1 increased and the timing of
the rise in [Ca]i was earlier (Fig. 6C), and the amplitude of [Ca]i was increased in both models. The
clear double peak (*) inward current in
Miyoshi-ICaL suggests that there is still a
large amount of available channel for phase 2, despite the marked
deactivation of ICaL at the end of phase 1.
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Fig. 6.
Contribution of Ito to the
mathematically calculated current through ICaL
and intracellular Ca concentration ([Ca]i) change in the
two models. A and B: Ito
increased the peak amplitude of the [Ca]i rise and the
peak amplitude of early Ca2+ influx via
ICaL. However, in the
Rasmusson-ICaL (A), the current
decrease in phase 1 is modest compared with the
Miyoshi-ICaL (B) and the second
influx peak, which corresponds to the timing of the upstroke of phase
2, is smaller. C: time course of the [Ca]i
rise with the Miyoshi-ICaL is magnified on the
time scale. Ito increased not only the peak
amplitude of [Ca]i but also the rapid rise in
[Ca]i. Ito densities were set to
0.05 and 0.55 mS/µF.
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Theoretical fiber model with epicardial myocytes.
Spatial dispersion in Ito density generates
phase 2 reentry in the model with Miyoshi-ICaL
(Fig. 7) but not in the
Rasmusson-ICaL model (data not shown). The axis
of the matrix shows Ito density at the left
(vertical axis) and right (horizontal axis) side of the cells. The
white area shows that no cell on the fiber caused early repolarization,
and the black area shows that some cells on the fiber caused early
repolarization but did not cause phase 2 reentry. The area of phase 2 reentry is shown in gray. When the Ito density
on the left side is smaller than that on the right side, the direction
of impulses of phase 0 and phase 2 reentry is the same from the left to
right (orthodromic). On the other hand, when the
Ito density on the left side is larger than that on the right side, the direction is the opposite (antidromic). In
orthodromic phase 2 reentry, the gray area is located in the border
zone between the black and white areas. In contrast, antidromic phase 2 seems to be dependent on the Ito density of the
right side. Simultaneous pacing of all epicardial cells can cause
orthodromic and antidromic phase 2 reentry. As a function of the
increase in ICaL density, the area of phase 2 reentry increased and gradually shifted to the upper right side,
suggesting that the occurrence of phase 2 reentry can be modified by
changing ICaL density.
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Fig. 7.
Occurrences of the phase 2 reentry by dispersion at an
Ito density under various
ICaL concentration and different forms of
pacing. Vertical axis of the matrix represents the
Ito density of the 30 cells on the left side,
and the horizontal axis represents the Ito
density of the 50 cells on the right side in the theoretical fiber.
Axis corresponds to the gray area in the matrix, showing the
Ito density balance, which generates phase 2 reentry in the fiber. White indicates that there is no cell with early
repolarization in the fiber, and black indicates there are cells in the
fiber with action potentials of early repolarization. B: in
simulation, every cell on the fiber is simultaneously paced and in
another simulation in this figure, one cell on the left end
(cell-00) is paced. Density of the
ICaL is denoted at the top of each panel. See
the text for details.
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A representative phase 2 reentry generated in our model is shown in
Fig. 8. Membrane potentials in the fiber
at the each time from the onset of pacing (noted in each trace) are
shown in Fig. 8A. The phase 2 reentry was initiated at 190.2 ms after pacing (*). Action potentials from each numbered cell are
shown in Fig. 8B. In the lower three traces, there are two
distinct action potentials generated by a single stimulus.
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Fig. 8.
Representative trace of phase 2 reentry in the
mathematical model. A: membrane potentials in fiber at the
each time point. Horizontal axis shows distance of cell from left end
of the fiber; vertical axis is the membrane potential. Each line
represents membrane potential at each time point from onset of pacing
(denoted along side). Top bar depicts distribution of cells with each
Ito density, shown within the bar. * Phase 2 dome conducted from the left side to the right side and generated
another action potential. B: calculated action potentials.
Clear phase 2 reentry can be seen in this model.
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The pseudo-ECGs showed a large positive deflection at the beginning
that corresponded to the phase 0 impulse conduction along the fiber
(Fig. 9). Because all of the epicardial
action potentials showed loss of the dome and early repolarization when
the ICaL density was set at 40%, the QT segment
of the pseudo-ECG was shortened. When the ICaL
density was set at 50%, the pseudo-ECG showed ST segment elevation, a
large negative T wave, and prolongation of the QT interval. A negative
spike (Fig. 9, **) in the trace corresponded to the time to initiation
of the phase 2 reentry. A 1% increase in ICaL
density (ICaL = 51%) shortened the QT
interval and caused the onset of phase 2 reentry (*) to occur earlier.
A further increase in ICaL density returned the
elevated ST segment, large negative T wave, and prolonged QT interval
to normal.
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Fig. 9.
Effect of change in ICaL density
on calculated extracellular field potential (Pseudo-ECG) from
theoretical epicardial fiber. Ito density of the
30 cells on the left side was set at 1.015625 mS/µF as opposed to
1.34375 mS/µF on the right side with a ICaL
density of between 40% and 100% (noted beside the trace) of the
original Luo-Rudy model. Pseudo-ECG were calculated and superimposed.
Only when the ICaL density was set at 50% and
51% of the original Luo-Rudy model did the pseudo-ECG show ST segment
elevataion, a large negative T wave, and prolongation of the QT
interval. Negative spike in the pseudo-ECG (* and **) corresponds to
the onset of the occurrence of phase 2 reentry in the fiber. See the
text for details.
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DISCUSSION |
Model of ICaL.
Our model simulates phase 2 reentry, whereas the
Rasmusson-ICaL does not. The mathematical model
of ICaL, utilized in the Luo-Rudy model, was
described in the 1980s by Rasmusson et al. (21) as being
based on recorded data from the bullfrog atrial cell at room
temperature. In the Luo-Rudy model, the maximal conductance of the
current was simply multiplied by a Q10 of 2.96, as measured by Cavalie
et al. (4), to a normal body temperature of 37°C, whereas the time constant of the voltage-dependent kinetics was unchanged. Therefore, our first aim in this study was to describe the
voltage-dependent kinetics of ICaL precisely at
a normal body temperature. Furthermore, in our preliminary study, the
calculated time constant of the d-gate recorded, using pipettes with a
relatively high resistance of 1.2-1.8 M, showed a slow time
constant of ~2-3 ms at the test potential of 20 mV. This is
almost the same as in Rasmusson et al.'s model, in which the membrane
potential may not have been quickly clamped membrane potential voltage. Therefore, in the present study, we measured
ICaL at 37°C with a low pipette resistance of
700-800 k. The sweep with increased series resistance, which
was continuously monitored immediately before each sweep, exceeding 1.5 M was discarded from the analysis.
The fast d-gate kinetics of ICaL allow rapid
deactivation during the phase 1 dip in the epicardial action potential,
which repolarizes phase 1 amplitude in a positive feedback manner. A deep phase 1 dip will not inactivate (f-gate)
ICaL such that a large amount of
ICaL is still available until the onset of phase 2 (Fig. 6) and consequently increases Ph2-Vmax.
Because the Vmax in phase 0 correlates well with
the conduction velocity and the safety factor for conduction,
Ph2-Vmax corresponds to a rich current source
for depolarizing cells to the regenerating dome in the cell that has an
action potential with early repolariztion, consequently acting as a
trigger for phase 2 reentry. The greater
Ph2-Vmax (Fig. 5A) in
Miyoshi-ICaL might contribute to the genesis of
phase 2 reentry in the Miyoshi-ICaL model but
not in the Rasmusson-ICaL model.
Clinical contribution.
Our second aim in this study was to simulate phase 2 reentry in the
mathematical model and determine how it can be affected by changes in
Ito and ICaL densities.
Our model clearly showed that only 0.8-cm epicardial fibers with
spatial dispersion of Ito density could generate
phase 2 reentry. When the impulse of the reentry spreads over the
entire ventricle, it is observed as a PVC with very short coupling, as
reported previously (25). Such a short coupling of PVC
might result in the functional block and subsequent VF. Further
extension of this model will facilitate understanding the genesis of
phase 2 reentry in the Brugada syndrome and selection of appropriate
prophylactic drug therapy for VF in the Brugada syndrome.
An increase in ICaL density, i.e., a change in
autonomic tone or administration of isoproterenol, increases the size
of the area in the matrix shown in Fig. 7 that can cause phase 2 reentry. However, extremely enlarged
Ito conductance requires the genesis of phase 2 reentry, which consequently blocks the occurrence of ventricular
arrhythmia, in accordance with clinical observations in this syndrome
(10, 18, 24). On the other hand, a decrease in
ICaL density, which might increase the area of
early repolarization (black area) that results in ST segment elevation
(9, 26), however, will decrease the area of phase 2 reentry (gray area).
Our third aim was to investigate how this phase 2 reentry in the
epicardium affects the wave morphology recorded in the body surface
ECG. No typical saddleback-type ST segment elevation was observed in
the present study because our model does not simulate a transmural axis
of the myocardium. The early repolarization in the epicardial cell
(trace of ICaL = 0.4 in Fig. 9) should increase the voltage gradient along the transmural axis, which is
observed as ST segment elevation in the form of a saddleback in the
body surface ECG (9, 26), although no phase 2 reentry was
observed. On the other hand, when the phase 2 reentry occurred in the
epicardial fiber, the pseudo-ECG showed prolongation of the QT
interval, marked ST segment elevation, and a large negative T wave,
which closely resemble the coved-type ST segment elevation observed in
patients with Brugada syndrome. The impulse of the phase 2 reentry in
the epicardial fiber may have been blocked by the refractoriness of the
myocardium enclosing this fiber and may have been unable to spread over
the entire ventricle. Such localized phase 2 reentry cannot generate
PVC and may be observed as coved-type ST segment elevation in the body
surface ECG. In another words, coved-type ST segment elevation might in
some part reflect epicardial localized phase 2 reentry. This may be why coved-type ST segment elevation is known to be an omen of future sudden
death in the Brugada syndrome compared with the saddleback type ST
segment elevation (2).
The orthodromic and antidromic conductions of the phase 2 reentry were
distinguishable in the present study. Experimentally it has been
difficult to distinguish antidromic reentry from reflection of the
conduction at the dead end of the experimental tissue, such that phase
2 reentry might be described only as occurring in an orthodromic manner
(11, 14).
Physiological role of Ito-mediated phase 1 dip.
We should also mention the physiological role of
Ito. Ito increases
Ca2+ influx via ICaL and therefore
must act as a positive inotrophic factor. In the normal ventricle,
there is a conduction delay from the endocardium to the epicardium in
propagating the impulse (27). Therefore, the rapid rise in
the [Ca]i in epicardum compared with the endocardium aids
simultaneous contraction along the transmural ventricular wall,
possibly also acting as a positive inotrophic factor.
| |
ACKNOWLEDGEMENTS |
We greatly appreciate to Prof. Akimichi Kaneko for the useful
comment and experimental support.
| |
FOOTNOTES |
This work was supported by Research Grant for Cardiovascular Diseases
13-1 from the Ministry of Health, Labor and Welfare Japan and The
Suntory Fund for Advanced Cardiac Therapeutics Keio University School
of Medicine.
Address for reprint requests and other correspondence: S. Miyoshi, Keio Univ. School of Medicine, 35-Shinanomachi
Shinjuku-ku Tokyo, 160-8582 Japan (E-mail:
smiyoshi{at}cpnet.med.keio.ac.jp).
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.
First published December 12, 2002;10.1152/ajpheart.00849.2002
Received 27 September 2002; accepted in final form 10 December
2002.
| |
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Am J Physiol Heart Circ Physiol 284(4):H1285-H1294
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TOP
ABSTRACT
INTRODUCTION
![I = (1 − ratio) × <FENCE><IT>I</IT><SUB>inf(slow)</SUB> + [<IT>I</IT><SUB>o(slow)</SUB> − <IT>I</IT><SUB>inf(slow)</SUB>] × <IT>e</IT><SUP>−<FR><NU><IT>t</IT></NU><DE>&tgr;(slow)</DE></FR></SUP></FENCE>](/content/vol284/issue4/fulltext/H1285/img002.gif)
![+ ratio × <FENCE><IT>I</IT><SUB>inf(fast)</SUB> + [<IT>I</IT><SUB>o(fast)</SUB> − <IT>I</IT><SUB>inf(fast)</SUB>] × <IT>e</IT><SUP>−<FR><NU><IT>t</IT></NU><DE>&tgr;(fast)</DE></FR></SUP> (0 < ratio < 1)</FENCE>](/content/vol284/issue4/fulltext/H1285/img003.gif)
