INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

SUSTAINED VENTRICULAR TACHYCARDIA (VT) can be induced by electrical stimulation in the canine heart 4-5 days after ligation of the left anterior descending coronary artery, during infarct healing. Reentrant circuits causing VT are located in a thin layer of epicardial cells that survive the infarct, the epicardial border zone (EBZ) (7). Action potential measurements on multicellular preparations isolated from the EBZ showed electrical (14, 31) and structural abnormalities (31).

Action potential duration (APD) is similar in EBZ and normal myocardium, but EBZ myocardium has a longer effective refractory period (ERP) as a result of postrepolarization refractoriness (14, 17, 31). During acute myocardial ischemia, the ionic mechanism of postrepolarization refractoriness is thought to be due to delayed recovery of the sodium channel, which results from an elevated extracellular K⁺ concentration ([K⁺]_o) (29). However, during the healing phase of infarction, it is not known whether this same mechanism can explain postrepolarization refractoriness in EBZ myocardium. Modulation of ERPs by class III antiarrhythmic drugs also differs in normal and EBZ myocardium. For example, drugs that increase L-type Ca²⁺ channel current (I_CaL) or decrease the delayed rectifier currents prolong the ERP in normal myocardium but not in EBZ myocardium (5, 28). The ionic mechanism of this differential response is uncertain but is likely to play a role in how those drugs prevent VT.

Recent measurements of ionic currents in myocytes dispersed from the EBZ (IZ cells) have demonstrated that the function of several currents is modified, a process referred to as electrical remodeling (21). To better understand how changes in ion channel function affect the action potential and refractory period of cells that survive the infarct, as well as their response to antiarrhythmic agents, we formulated computer ionic models of the action potential of a normal cell (NZ) and an IZ cell based on experimental data.

Glossary

APA	Action potential amplitude
APD	Action potential duration
APD90	APD at 90% repolarization
BCL	Basic cycle length
Cm	Membrane capacitance
[Ca2+]i	Intracellular Ca2+ concentration
[Ca2+]o	Extracellular Ca2+ concentration
d	Activation gate of the L-type Ca2+ channel
d	Steady state of activation gate of the L-type Ca2+ channel
EX	Nernst potential of ion X
EBZ	Epicardial border zone
ERP	Effective refractory period
f	Fast inactivation gate of the L-type Ca2+ channel
f	Steady state of fast inactivation gate of the L-type Ca2+ channel
fCa	Ca2+-dependent inactivation gate of the L-type Ca2+ channel
fs	Slow inactivation gate of the L-type Ca2+ channel
F	Faraday's constant
gi	Maximum conductance of channel i
h	Fast inactivation gate of the Na+ channel
ICa	Ca2+ current
ICab	Background Ca2+ current
ICaL	L-type Ca2+ channel current
ICaL,Ca	Ca2+ current through the L-type Ca2+ channel
ICaL,K	K+ current through the L-type Ca2+ channel
ICaL,Na	Na+ current through the L-type Ca2+ channel
ICaT	T-type Ca2+ channel current
Iion	Total ionic current
IK1	Inward rectifier K+ current
IKp	Plateau K+ current
IKr	Rapid component of the delayed rectifier K+ current
IKs	Slow component of the delayed rectifier K+ current
Im	Total transmembrane current
INab	Background Na+ current
InsCa	Nonspecific Ca2+-activated current
INa	Na+ current
INaCa	Na+/Ca2+ exchanger current
INaK	Na+-K+ pump current
IpCa	Ca2+ pump current in the sarcolemma
Ist	Externally applied stimulus current
Ito	Transient outward K+ current
Itot	Total transmembrane current
IPI	Interpulse interval
IZ	Epicardial border zone of the infarcted heart
j	Slow inactivation gate of the Na+ channel
JSR	Junctional sarcoplasmic reticulum
kl	Steady state of the inactivation gate of IK1
KCa	Half-saturation concentration of the L-type Ca2+ channel
[K+]i	Intracellular K+ concentration
[K+]o	Extracellular K+ concentration
m	Activation gate of the Na+ channel
[Na+]i	Intracellular Na+ concentration
[Na+]o	Extracellular Na+ concentration
NSR	Nonjunctional sarcoplasmic reticulum
NZ	Epicardium from a noninfarcted area of the heart
pCa	Permeability of the L-type Ca2+ channel to Ca2+
pK	Permeability of the L-type Ca2+ channel to K+
pNa	Permeability of the L-type Ca2+ channel to Na+
R	Gas constant
riK	Time-independent inactivation gate of IKr
Ri	Intracellular resistance
RP	Resting membrane potential
Sv	Surface-to-volume ratio
t	Time
T	Absolute temperature
V0.5	50% Activation voltage
Vc	Conditioning voltage
Vm	Transmembrane potential
VT	Ventricular tachycardia
xr	Activation gate of the rapid component of IKr
xs	Activation gate of the slow component of IKs
X	Ca2+, Na+, or K+
zX	Valence of ion X
i	Opening rate constant of gate i
i	Closing rate constant of gate i
X	Activity coefficient of ion X
d	Time constant of activation gate of the L-type Ca 2+ channel
f	Time constant of the fast inactivation gate of the L-type Ca 2+ channel

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Single Cell Model

Na+ current. I_Na was formulated from whole cell voltage-clamp measurements of Na⁺ current reported by Pu and Boyden (24) using one activation gate (m) and two inactivation gates (h and j), similar to the formulation used in the Luo-Rudy model. To estimate the magnitude of the shift of steady-state inactivation relations with temperature (19), we used measurements of I_Na availability obtained from action potential dV/dt_max performed on single cells at 37°C (17). The three main differences measured experimentally between I_Na in NZ and IZ cells are reproduced in the model. First, steady-state inactivation of I_Na is shifted between 5 and 10 mV in the hyperpolarizing direction for IZs (in the model, V_0.5 is 59 mV in NZ and 66 mV in IZ cells; Fig. 1A). Second, I_Na recovery from inactivation is not only slower in IZ cells but also exhibits a lag before the onset of recovery (Fig. 1B) (17, 24). To reproduce the lag, the slow inactivation gate (j) was raised to the second power in IZs (see the APPENDIX). There are no differences in I_Na activation between NZ and IZ cells. Third, measured I_Na density is reduced in IZs. The hyperpolarizing shift of the IZ steady-state inactivation curve results in a reduction in current density in IZs that is similar to the reduction that has been measured experimentally (see RESULTS). Therefore, we used the same maximum g_Na of 20 mS/cm² for both NZ and IZ cell models.

View larger version (11K): [in this window] [in a new window]   Fig. 1.   A: steady-state inactivation of INa (h) versus conditioning voltage (Vc) in the NZ and IZ models. Note that the curve is shifted in IZ cells in the hyperpolarizing direction. B: recovery from inactivation of INa in the NZ and IZ models. The amplitude of INa at each IPI was normalized to value at IPI = 200 ms. The pulse protocol is shown in the inset. Calculations were performed at 37°C, with [Na+]o = 140 mM and [Na+]i = 10 mM. See Glossary for abbreviations.

Ca²+ currents. I_CaL was formulated using the constant-field equation, the same approach used by Luo and Rudy (18). Voltage dependence of activation and inactivation were formulated from voltage-clamp measurements reported by Aggarwal and Boyden (1, 2). The three main differences measured experimentally between the I_CaL in NZ and IZ cells are reproduced in the model using similar voltage-clamp protocols. First, peak I_CaL density is reduced by ~50% in IZs compared with NZs, and this reduction is not associated with changes in steady-state activation or deactivation and may indicate a decrease in the number of functional channels (1, 2). Consequently, the maximum conductance of the L-type Ca²⁺ channel (and corresponding permeabilities) was reduced by 50% in the IZ model (Fig. 2A). Second, the decay of peak I_Ca,L is faster in IZs versus in NZs. Therefore, _f in the IZ model was one-half the value in the NZ model (Fig. 2B). Third, experimental results suggest a slowed recovery from inactivation of the L-type Ca²⁺ channel in IZ cells (1). The time constant of recovery was 50% larger in IZs than in NZs, although, due to variability, this difference was not significant. Furthermore, a significant frequency-dependent reduction of the I_CaL peak was measured in IZ cells. Therefore, we used a slow inactivation gate (f_s) to implement the slower recovery from inactivation measured in IZ cells. Finally, because no information is available on calcium-induced inactivation of the channel, we used the implementation proposed by Luo and Rudy (18) for both IZ and NZ cells.

View larger version (12K): [in this window] [in a new window]   Fig. 2.   Simulated ICa calculated by removing calcium-induced inactivation (fCa = 1) to show voltage-dependent activation and inactivation of ICaL. A: ICaL in the absence of calcium-induced inactivation in the NZ and IZ models. B: same ICaL as in A normalized to the peak to illustrate different time constants of decay. The pulse protocol is shown in the inset. Calculations were performed at 37°C, and [Ca2+]o = 2 mM. See Glossary for abbreviations.

Transient outward K+ current. Several computer models of I_to have been proposed (8, 9, 22, 34). Because the model of I_to proposed by Priebe and Beuckelmann (22) for human ventricular cells fits well the experimental measurements of I_to in canine epicardium (17), we adopted their formulation to model I_to in the NZ model. Most IZ cells lack I_to (17); therefore, I_to was not included in the IZ model.

Delayed rectifier K+ currents. I_Kr and I_Ks were formulated from measurements of cells from normal canine epicardium by Liu and Antzelevitch (16) and Jiang et al. (12). The formulation is similar to the one used by Sanguinetti and Jurkiewicz (27) and Priebe and Beuckelmann (22). The three main differences measured experimentally between the delayed rectifier currents in NZ and IZ cells (12) are reproduced in the model using similar voltage-clamp protocols. First, the current density of I_Kr is reduced in IZ cells to 30% of the value in NZ cells, and the current density of I_Ks is reduced in IZ cells to 20% of the value in NZ cells. Second, there is an acceleration of I_Kr activation in IZ cells compared with NZ cells. Third, there is an acceleration of I_Ks deactivation in IZs compared with NZs.

Inward rectifier K+ current. To model I_K1 in NZ cells, we used the formulation proposed by Winslow et al. (34), which is based on canine midmyocardial myocytes and fits well with experimental measurements in epicardial myocytes (21). To simulate I_K1 in the IZ cell model, the rectification of the channel was modified to simulate the reduced total membrane current measured in IZ cells either during ramp or clamp protocols (17, 21). Rectification is controlled by the parameter kl in the equations to model I_K1 (see the APPENDIX). As a result, I_K1 density is smaller in IZ cells than in IZ cells. In NZ cells at 60 mV, I_K1 density is ~2.5 pA/pF, whereas in IZ cells it is ~1.5 pA/pF.

Na+/Ca²⁺ exchanger current. We use the same formulation proposed by Luo and Rudy (18) because that formulation reproduces the experimental results obtained in NZ cells (25). The formulation of the Na⁺/Ca²⁺ exchanger in IZ cells was identical to that used for NZ cells because no differences were found experimentally even under different [Na⁺]_i loads (25).

Intracellular calcium handling. Simulation of intracellular calcium handling in NZ cells is identical to the formulation by Luo and Rudy (18). In the IZ cell model, the value of the time constant for the translocation between the NSR and JSR was increased to 300 ms (from 180 ms in NZ cells). With these values, the first intracellular calcium transient after a 3-s rest is potentiated in IZ cells to a larger extent than in NZ cells, as was measured experimentally by Licata et al. (15).

Propagation Model

1

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Action Potentials of NZ and IZ Cells: the Effects of [K+]_o

View larger version (13K): [in this window] [in a new window]   Fig. 3.   Simulated action potential of a single cell in the NZ and IZ models at BCL = 1,000 ms. A: [K+]o = 4 mM; B: [K+]o = 5.4 mM.

APD₉₀ measured in multicellular preparations isolated from the EBZ are considerably smaller than those reported in isolated cells (21, 31). Also, APD₉₀ in IZ cells is similar or even shorter than APD₉₀ in NZ cells (21, 31). To investigate whether a higher [K⁺]_o in the multicellular preparations explains the experimental differences, we calculated the action potentials in NZs and IZs when [K⁺]_o = 5.4 mM and BCL = 1,000 ms (Fig. 3B). APD₉₀ of NZs and IZs is shorter at [K⁺]_o= 5.4 mM than at [K⁺]_o = 4 mM, and their differences are reduced (Table 1). The results of Fig. 3 suggest that the [K⁺]_o in multicellular preparations is higher than 4 mM. Because we are interested in characterizing the model to simulate what is most likely to occur in multicellular preparations, we used a [K⁺]_o = 5.4 mM for all the following simulations.

The loss of plateau during the IZ action potential is in part (see Repolarizing Currents During the Action Potential in NZ and IZ Cells: Importance of I_K1 and I_NaCa in IZ Cells) due to decreased I_CaL in IZ cells (Fig. 4A). The peak of the calcium transient during the action potential is reduced in IZs with respect to NZs. Calcium transients decay more slowly from their peak to the diastolic value in IZs, in agreement with experimental measurements (Fig. 4B) (25).

View larger version (9K): [in this window] [in a new window]   Fig. 4.   A: ICaL during the action potentials of Fig. 3B in the NZ and IZ models. B: [Ca2+]i transient during the action potential in the NZ and IZ model. BCL = 1,000 ms. Arrows indicate the time of repolarization to APD90. [K+]o = 5.4 mM. (Note that at BCL = 1,000 ms, APD90 is about the same in the NZ and IZ models; see Fig. 7.) See Glossary for abbreviations.

Repolarizing Currents During the Action Potential in NZ and IZ Cells: Importance of I_K1 and I_NaCa in IZ Cells

View larger version (17K): [in this window] [in a new window]   Fig. 5.   Repolarizing currents in the NZ and IZ models during the action potentials of Fig. 3B. A: IKr; B: IKs; C: IK1; D: INaCa. BCL = 1,000 ms. Arrows indicate the time of repolarization to APD90. [K+]o = 5.4 mM. See Glossary for abbreviations.

Not all ionic currents are reduced in IZs. In contrast to delayed rectifier currents, I_K1 and I_NaCa are not dramatically altered in IZs (Fig. 5, C and D) (21, 25). However, note that despite having an identical formulation for NZ and IZ cells (25), during the first 50 ms of the action potential, I_NaCa is larger in IZ cells than in NZ cells (Fig. 5D). This is a consequence of the dynamic voltage changes occurring during the action potential. Because the delayed rectifier currents are reduced in IZ cells and I_K1 and I_NaCa are not, it is expected that these latter currents gain in importance during the time course of repolarization of the action potential in IZs.

To further illustrate the relative contribution of the different repolarizing currents in IZ and NZ cells, Fig. 6 shows I_to, I_Kr, I_Ks, I_K1, I_Kp, and I_NaCa in the same plot. In NZs (Fig. 6A), during the first 50 ms of the action potential, repolarization is dominated by I_to, which is orders of magnitude larger than other repolarizing currents. After the first 50 ms, repolarizing currents are of similar magnitude and, therefore, all play a significant role in action potential repolarization. In IZs (Fig. 6B), during the first 100 ms of the action potential, I_Kp and I_NaCa are large relative to the delayed rectifier currents (note that I_to is absent in IZs) and dominate repolarization. Earlier, we discussed that the loss of plateau in IZ cells is caused in part by the diminished I_CaL (Fig. 4B). From Fig. 6B it is now evident that a large I_NaCa (repolarizing) current during the first 100 ms of the action potential also contributes significantly to the time course of early repolarization and the subsequent loss of the plateau phase in the action potential of IZ cells.

View larger version (17K): [in this window] [in a new window]   Fig. 6.   Relative magnitudes of repolarizing currents during the first 100 ms of action potentials of Fig. 3B. A: NZ model; B: IZ model. BCL = 1,000 ms. [K+]o = 5.4 mM. See Glossary for abbreviations.

In summary, currents that are critical to the repolarization of NZ action potentials, like the delayed rectifier currents, are not as critical to the repolarization of IZs. Because delayed rectifier currents are diminished by both disease and action potential dynamics, time-independent currents (I_Kp, I_K1, and I_NaCa) gain importance in the repolarization process of IZs.

Rate Adaptation of APD: Importance of I_CaL

View larger version (15K): [in this window] [in a new window]   Fig. 7.   Rate adaptation of the APD. A: superimposed action potentials at BCLs = 1,000, 500, and 200 ms in the NZ model. B: superimposed action potentials at BCLs = 1,000, 500, and 200 ms in the IZ model. C: APD90 at different cycle lengths (BCL) in the NZ () and IZ () models. [K+]o = 5.4 mM. See Glossary for abbreviations.

The mechanism of APD rate adaptation differs in NZ and IZ cells. Figure 8A shows I_Ks (left), I_CaL (middle), and I_Kr (right) of an NZ cell when stimulated at a BCL = 500 (dotted lines) or 200 ms (solid lines). Note that in NZs, I_Ks increases with a decrease in BCL particularly during the initial 100 ms of the action potential (Fig. 8A, left). A larger repolarizing current at shorter cycle lengths suggests an important role of I_Ks in APD rate adaptation. At shorter BCLs, I_Ks is incompletely deactivated, resulting in an abrupt increase in I_Ks when the NZ cell is next depolarized (I_Ks "accumulation"). However, I_Ks is not the only current that plays a role in APD rate adaptation in NZ cells. In the NZ model, peak as well as sustained I_CaL decreases at short BCLs (Fig. 8A, middle) because the channel has only partially recovered from inactivation between stimuli. Thus a decreased I_CaL contributes to the decrease in APD at short BCLs in NZ cells. Finally, I_Kr is larger during the initial 100 ms of the action potential at shorter BCL (Fig. 8A, right) and therefore also contributes to APD rate adaptation in NZs. The decrease in depolarizing I_CaL at the shorter BCL outweighs the increase in repolarizing delayed rectifier currents, and, therefore, I_CaL is largely responsible for APD rate adaptation in NZs.

View larger version (17K): [in this window] [in a new window]   Fig. 8.   Ionic currents during the action potential at BCL = 500 and 200 ms. A: IKs (left), ICaL (middle), and IKr (right) at BCL = 200 and 500 ms in the NZ model. B: IKs (left), ICaL (middle), and IKr (right) at BCL = 200 and 500 ms in the IZ model. The two arrows indicate the time of repolarization to APD90 at the two different BCLs. [K+]o = 5.4 mM. See text for more details. (Note different y-axis scales.)

The mechanism of APD rate adaptation in IZs differs markedly. Figure 8B shows I_Ks (left), I_CaL (middle), and I_Kr (right) when an IZ cell is stimulated with BCL = 500 (dotted lines) and 200 ms (solid lines). Note that unlike NZs, I_Ks is smaller at the shorter BCLs in IZs. A small I_Ks would tend to increase APD at faster rates, and, therefore, it seems does not play a role in IZ APD rate adaptation (as seen in Fig. 7C). I_Ks has no accumulation in IZs at short BCLs due to the acceleration of deactivation kinetics in IZs (12). On the other hand, except for the initial 10 ms, I_CaL is decreased at short BCLs (Fig. 8B, middle) because the channel has only partially recovered from inactivation between stimuli. Finally, somewhat similar to NZs, I_Kr is large during the initial 100 ms of the action potential at shorter BCL in IZs (Fig. 8B, right) and therefore contributes to APD rate adaptation. However, overall and as it occurred in NZs, the decrease in a depolarizing current outweighs the increase in I_Kr, and, therefore, I_CaL plays an important role in rate adaptation of APD in IZ cells.

In summary, while in NZ cells, I_Ks, I_Kr, and I_CaL all contribute to shortening of the action potential at short cycle lengths; only a weak I_Kr and I_CaL are responsible for modest shortening in IZ cells.

Conduction Velocity in NZ and IZ Cells in Steady-State Conditions

Increased ERP due to Postrepolarization Refractoriness in IZ Cells

View larger version (18K): [in this window] [in a new window]   Fig. 9.   ERPs in a propagation model of NZ (A) and IZ (B) cells (S1S1 = 250 ms). Top: premature impulse at coupling interval S1S2 that does not propagate; bottom: premature impulse at the S1S2 interval that propagates along the fiber. Action potentials were initiated by electrical stimulation at one end of the fiber. Action potentials were calculated at the stimulation site (a), 2.5 mm from the stimulation site (b), and 5 mm away from the stimulation site (c). [K+]o = 5.4 mM. See text for more details.

Figure 9A shows the last beat of a train of 10 stimuli at BCL = 250 ms (S₁)- and premature impulse (S₂)-initiated action potentials calculated at the stimulation site (site a) and sites 2.5 (site b) and 5 mm (site c) away in the NZ fiber. Note that at S₁S₂ = 156 ms, no action potential propagated (Fig. 9A, top). However, a propagated response was initiated with S₁S₂ = 157 ms, indicating an ERP of 156 ms (Figs. 9A, bottom). Figure 9B shows a similar experiment in IZs. Here, a propagated response was initiated only when S₁S₂  200 ms, well after the end of APD repolarization, indicating an ERP of 199 ms.

To understand the ionic mechanism of postrepolarization refractoriness in the IZ fiber, we determined a "membrane responsiveness" curve in NZs and IZs by applying an S₂ at different times after repolarization to 70 mV that coincides with APD₉₀ (Fig. 10A). In the NZ fiber, a propagated S₂ action potential was initiated when the peak I_Na reached 66 pA/pF and occurred within 1 ms after the fiber had repolarized to 70 mV (arrow in Fig. 10A). In the IZ fiber, the first propagating action potential occurred when the peak I_Na had reached 50 pA/pF. However, this occurred 40 ms after repolarization (arrow in Fig. 10A). Even though the I_Na necessary to initiate a propagated response is smaller in IZs versus NZs, it took a longer time in the IZ fiber to reach that value. This may be due to I_Na slowed recovery from inactivation in IZ cells (Fig. 1B) (17, 24).

View larger version (15K): [in this window] [in a new window]   Fig. 10.   Ionic mechanism of postrepolarization refractoriness. A: INa of the cell at the stimulation site (site a in Fig. 9) in a NZ and IZ fiber at different times after repolarization to 70 mV. (Time 0 represents the time at which the cell has repolarized to 70 mV.) Arrows indicate the INa necessary to initiate the first propagated action potential. B: availability of INa of a cell at the stimulation site (solid line) during stimulation at the shortest S1S2 interval that initiates a propagating action potential (dashed line) in the NZ (top) and IZ (bottom) fiber. See text for more details.

To further understand the mechanism of postrepolarization refractoriness, we plotted changes in I_Na availability (solid line) during a propagated action potential (dashed line) initiated with a S₁S₂ just above the ERP in an NZ fiber (Fig. 10B, top) and IZ fiber (Fig. 10B, bottom). Availability was calculated as hj in NZs and as hj² in IZs. Note that to initiate a propagated action potential in the IZ fiber, availability had to reach a higher value than that in the NZ fiber, indicating that in IZs a larger percentage of the Na⁺ channels must be recovered from inactivation before propagation. Also, the time necessary for that to happen is longer in the IZ fiber than in the NZ fiber.

Differential Response of the Refractory Period of NZ and IZ Cells to Antiarrhythmic Drugs

Therefore, we simulated the effects of a 50% increase of I_CaL [to simulate the effects of the calcium agonist BAY Y5959 (3, 26)] or 100% block of delayed rectifier currents [simulating the effects of azimilide (4)] in an NZ and IZ fiber. In our simulations, both agents prolong the ERP in the NZ fiber by ~15% (Table 2). In contrast, the prolongation of the ERP in the IZ fiber was only 5%. These results of the computer simulations are in agreement with experimental measurements in the in situ canine infarcted heart, which showed that refractory periods are prolonged to a larger extent in normal myocardium than in the EBZ (5, 28). The relative contribution of each of the two components of the delayed rectifier current, I_Kr and I_Ks, to the prolongation of the ERP also differs in NZs and IZs. The effects of 100% block of I_Kr (to simulate the effects of sotalol or E4031) and 100% block of I_Ks (to simulate the effects of chromanol) are shown in Table 2. Whereas the contribution of I_Ks and I_Kr to ERP prolongation is about the same in NZs, in IZs the contribution of blocking I_Ks to ERP prolongation is almost negligible. In the simulations, the effects of these drugs on APD₉₀ are similar to the effects observed for ERP (Table 3).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Repolarizing Currents in NZ Cells

Gintant (10) and Varro et al. (32) reported I_Kr peak values of 0.25-0.5 pA/pF during action potential-clamp protocols in normal canine ventricular myocytes. The I_Kr peak value during a NZ action potential in the computer model is 0.2 pA/pF (Fig. 5), similar to the lower end of reported experimental values. Varro et al. (32) also found that the I_Kr peak value is several times greater than the I_Ks peak. In the NZ action potential, I_Kr is about two times larger than I_Ks (Fig. 5). Therefore, in NZs, I_Kr plays a more prominent role than I_Ks in initiation of repolarization (32). This is in contrast with findings in other species, like the guinea pig, where I_Ks has a large magnitude and consequently plays a dominant role in initiation of repolarization (27).

Gintant (10) measured a I_K1 peak value of 1.5 pA/pF during an action potential clamp, whereas the I_K1 peak value in our NZ model is 2 pA/pF. It is usually thought that repolarization during the phase 2 plateau results from the activation of the delayed rectifier K⁺ channels and that I_K1 contributes only to late (phase 3) repolarization. However, our simulations show that I_K1 and I_Kr are of similar magnitude during the phase 2 plateau. Therefore, we suggest that I_K1 plays an important role in both the early and late phases of repolarization in NZs. Indeed, complete block of both delayed rectifier currents in the NZ model does not prevent repolarization of the NZ; it causes only a 15% prolongation of APD (see azimilide in Table 3). Similarly, experimental studies have shown that complete block of I_Kr with E4031 in isolated cells prolongs APD by only 20%, whereas block of I_Ks has a minimal effect on APD (32).

Repolarizing Currents in IZ Cells

This finding has important consequences for the development of antiarrhythmic agents aimed at the prevention of postinfarction VTs. Currently, most class III antiarrhythmic drugs are thought to prolong APD by blocking I_Ks and/or I_Kr. But this categorization appears to hold true for cells from normal myocardium. If the therapeutic goal is to prolong APD in IZ cells to prevent arrhythmias, the results of our computer simulations show that blocking delayed rectifier currents together or separately will not produce the desired effects. Rather, on the basis of our results, we suggest that agents aimed at increasing I_NaCa and/or reducing I_K1 would be effective in prolonging APD in IZs.

Propagation in IZ Cells

Electrical mapping studies of the EBZ have shown that there are areas where conduction velocity is almost normal, whereas in other areas conduction velocity is very slow (<5 cm/s) (5). The values of conduction velocity calculated in a fiber of IZ cells are consistent with measurements in the in situ heart in the areas that show reasonably normal conduction velocities in the EBZ (5). Previous computer simulations (30) have shown that a reduction in peak I_Na, similar to the reduction observed in IZ cells, is not sufficient to cause very slow conduction. Therefore, the very slow conduction occurring in certain areas of the EBZ may be the result of other factors like gap junction remodeling (20) in addition to remodeling of the I_Na channel.

Effect of Drugs on ERPs and Initiation of VT

Still, despite a negligible effect on the ERPs of EBZ myocardium, BAY Y5959 and azimilide have been shown to prevent initiation of VT in the canine infarcted heart (5, 28). It is possible that the differential effect of drug action in IZs vs. NZs and a subsequent decrease in the dispersion of refractory periods in the EBZ contributed to prevention of VT in the experimental studies. However, in some experiments, prevention of VT during infusion of BAY Y5959 was secondary to an effect on cell-to-cell coupling, possibly as a result of increased intracellular calcium. The latter resulted in conduction block in areas of the EBZ that were crucial for initiation of VT (5).

Limitations of the Model

Furthermore, cell populations are not uniform. For example, some IZs cells have a small but measurable I_CaT (1, 2) and/or I_to (17), but most of them do not. Because the goal of this paper is to model a "typical" IZ cell, we did not included these currents in the IZ model. Therefore, the propagation model described here treats all cells as having homogenous electrophysiological properties, which may not simulate well the intact myocardium. Also, we have not included gap junction remodeling (20) in the IZ fiber model because it is unknown at this time what is the functional effect of such a remodeling. The gap junctions in the propagation model are modeled as pure resistors, and consequently possible effects of drugs on gap junctions (5) have not been incorporated in the model. Future studies are needed to determine the effects of all these factors on the results and conclusions presented here.