## 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 (*I*
_{to}) density within the theoretical fiber, composed of 80 serially arranged epicardial cells with gap junctions and then observed the P2R. The dispersion in *I*
_{to}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

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 (*I*
_{to}), having slow recovery kinetics, in this syndrome. *I*
_{to} was prominent at the RV epicardium, therefore, *I*
_{to}-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).

*I*
_{to} 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 *I*
_{to}-mediated early repolarization in the epicardium and subsequent phase 2 reentry are the potential cellular bases for VF in this syndrome (26). An*I*
_{to}-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*I*
_{to} 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*I*
_{to} 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*I*
_{to} (8). Therefore, we focused on the kinetics of L-type Ca current (*I*
_{CaL}), because self-reproductive excitation of*I*
_{CaL} must be essential to the genesis of phase 2 reentry.

Because the mathematical model of *I*
_{CaL} 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 *I*
_{CaL} at a temperature of 37°C, we measured *I*
_{CaL} by using the whole cell patch-clamp experiment at the 37°C. Furthermore, our defined mathematical model of the *I*
_{CaL} 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.

## 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 Ca^{2+}-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 CaCl_{2}, 0.5 MgCl_{2}, 5.5 d-glucose, and 5 HEPES (pH adjusted to 7.4 with NaOH). Nominally Ca^{2+}-free Tyrode solution was prepared by simply omitting CaCl_{2}. The Kraft-Brühe medium contained (in mmol/l) 50 glutamic acid-K, 10 taurin, 25 KCl, 10 KH_{2}PO_{4}, 0.5 EGTA, 3 MgCl_{2}, 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 Ca^{2+}-dependent block, Ba^{2+}was used as a charge carrier, and to obtain a better voltage clamping, the 1.8 mmol/l of Ca^{2+} were replaced with 1 mmol/l of Ba^{2+} and 0.8 mmol/l of Mg^{2+}. 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 kΩ) 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 GΩ and the series resistance of >1.5 MΩ 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 *I*
_{CaL} 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 *I*
_{CaL}. 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 *I*
_{CaL} with a gap of 3 ms for −50 mV, and then subtracted from the previous data. Remaining data were defined as the *I*
_{CaL}, 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*I*
_{CaL} 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,*I*
_{inf} is the current of the steady-state value;*I*
_{o} is the current at the onset of the test pulse; and τ is the time constant.

On the other hand, the f-gate time constant was fitted with a double-exponential function as follows
where *I*
_{inf(slow)} and*I*
_{inf(fast)} are the steady-state values of the slow and fast time constant, respectively, and*I*
_{o(slow)} and *I*
_{o(fast)} are components of slow and fast time constants; only the τ(fast) was then used for the mathematical model.

Ca^{2+} driving force was calculated by the following equation
where zCa is the valence of Ca^{2+} and equals 2; Ca_{o} is extracellular Ca^{2+} and equals 0.5 mmol/l; Ca_{i} is intracellular Ca^{2+} and equals 100 nmol/l; γCa_{i} is the activity coefficient of Ca_{i} and equals 1; γCa_{o} is the activity coefficient of Ca_{o} 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*I*
_{to}, composed by Nesterenco (8), and our model of *I*
_{CaL} 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* + dl*t*a*T*, where dl*t*a*T* 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 *I*
_{to} density to generate phase 2 reentry in the theoretical epicardial fiber. We changed the*I*
_{to} 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. *I*
_{to} 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*I*
_{CaL} 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 (APD_{90}) and maximal velocity of voltage change (*V*
_{max}) value of the upstroke of phase 2 (Ph2-*V*
_{max}) 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-*V*
_{max}.

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.

## RESULTS

#### Patch clamp.

Cell capacitance in the present study was 125 ± 4 pF (*n* = 30). Figure 1
*A, 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.1
*A*). 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. 1
*B*). 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.

#### 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.-*I*
_{CaL} kinetics (Rasmusson-*I*
_{CaL}) and an action potential with*I*
_{CaL} kinetics, as described in the present study (Miyoshi-*I*
_{CaL}). To obtain a realistic epicardial action potential, the maximal conductance of the*I*
_{CaL} was decreased by 50%, and the maximal conductance of *I*
_{to} was set to 0.55 mS/μF. Our model simulates the steepness of the slope of the upstroke of the phase 2 well.

The conductance of *I*
_{to} or*I*
_{CaL} is variable in both models and shape of the action potential is observed in Fig. 4. Measured Ph2-*V*
_{max} and Ph1 duration versus phase 1 amplitude are summarized in Fig. 5,*A* and *B*. Measured APD_{90} versus *I*
_{to} or*I*
_{CaL} density are summarized in Fig. 5,*C* and *D*. In both models, as a function of the increase in *I*
_{to} density, prolongations of phase 1 duration and action potential duration are observed (Fig. 4,*A* and *C*, and Fig. 5
*D*). Compared with the Rasmusson-*I*
_{CaL}, the degree of accentuation of the phase 1 dip and also Ph2-*V*
_{max} are marked in the Miyoshi-*I*
_{CaL} with the same*I*
_{to} density. A further increase in the*I*
_{to} density results in the loss of dome and early repolarization in both models. The degree of action potential shortening is marked in Miyoshi-*I*
_{CaL} (Fig.5
*D*). On the other hand, as a function of the increase in the*I*
_{CaL} density, the action potential duration was prolonged to some extent and then paradoxically shortened after this prolongation (Fig. 4, *B* and *D*, and Fig.5
*C*). The degree of prolongation is obvious and is observed early after depolarization in the Rasmusson-*I*
_{CaL}. The threshold of the phase 1 amplitude needed to generate a phase 2 dome is almost the same in the two models (Fig. 5
*A*). As a function of hyperpolarization in the phase 1 amplitude, Ph2-*V*
_{max} was increased (Fig. 5
*A*) and emergence of the phase 2 dome was delayed in both models (Fig. 5
*B*). The degree of the increase in Ph2-*V*
_{max} was marked in Miyoshi-*I*
_{CaL}.

The mathematically calculated intracellular Ca concentration ([Ca]_{i}) and current through *I*
_{CaL}by the models are shown in Fig. 6. With the *I*
_{to}-mediated phase 1 dip,*I*
_{CaL} during phase 1 increased and the timing of the rise in [Ca]_{i} was earlier (Fig. 6
*C*), and the amplitude of [Ca]_{i} was increased in both models. The clear double peak (*) inward current in Miyoshi-*I*
_{CaL} suggests that there is still a large amount of available channel for phase 2, despite the marked deactivation of *I*
_{CaL} at the end of phase 1.

#### Theoretical fiber model with epicardial myocytes.

Spatial dispersion in *I*
_{to} density generates phase 2 reentry in the model with Miyoshi-*I*
_{CaL}(Fig. 7) but not in the Rasmusson-*I*
_{CaL} model (data not shown). The axis of the matrix shows *I*
_{to} 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 *I*
_{to} 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*I*
_{to} 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 *I*
_{to} 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 *I*
_{CaL} 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 *I*
_{CaL} density.

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. 8
*A*. The phase 2 reentry was initiated at 190.2 ms after pacing (*). Action potentials from each numbered cell are shown in Fig. 8
*B*. In the lower three traces, there are two distinct action potentials generated by a single stimulus.

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 *I*
_{CaL} density was set at 40%, the QT segment of the pseudo-ECG was shortened. When the *I*
_{CaL}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 *I*
_{CaL}density (*I*
_{CaL} = 51%) shortened the QT interval and caused the onset of phase 2 reentry (*) to occur earlier. A further increase in *I*
_{CaL} density returned the elevated ST segment, large negative T wave, and prolonged QT interval to normal.

## DISCUSSION

#### Model of I_{CaL}.

Our model simulates phase 2 reentry, whereas the Rasmusson-*I*
_{CaL} does not. The mathematical model of *I*
_{CaL}, 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 *I*
_{CaL} 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 MΩ, 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*I*
_{CaL} at 37°C with a low pipette resistance of 700–800 kΩ. The sweep with increased series resistance, which was continuously monitored immediately before each sweep, exceeding 1.5 MΩ was discarded from the analysis.

The fast d-gate kinetics of *I*
_{CaL} 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)*I*
_{CaL} such that a large amount of*I*
_{CaL} is still available until the onset of phase 2 (Fig. 6) and consequently increases Ph2-*V*
_{max}. Because the *V*
_{max} in phase 0 correlates well with the conduction velocity and the safety factor for conduction, Ph2-*V*
_{max} 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-*V*
_{max} (Fig. 5
*A*) in Miyoshi-*I*
_{CaL} might contribute to the genesis of phase 2 reentry in the Miyoshi-*I*
_{CaL} model but not in the Rasmusson-*I*
_{CaL} 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*I*
_{to} and *I*
_{CaL} densities. Our model clearly showed that only 0.8-cm epicardial fibers with spatial dispersion of *I*
_{to} 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 *I*
_{CaL} 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*I*
_{to} 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*I*
_{CaL} 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 *I*
_{CaL} = 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 I_{to}-mediated phase 1 dip.

We should also mention the physiological role of*I*
_{to}. *I*
_{to} increases Ca^{2+} influx via *I*
_{CaL} 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.

## Acknowledgments

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

- Copyright © 2003 the American Physiological Society