Role of IKur in Controlling Action Potential Shape and Contractility in the Human Atrium
Influence of Chronic Atrial Fibrillation
Background— The ultrarapid outward current IKur is a major repolarizing current in human atrium and a potential target for treating atrial arrhythmias. The effects of selective block of IKur by low concentrations of 4-aminopyridine or the biphenyl derivative AVE 0118 were investigated on right atrial action potentials (APs) in trabeculae from patients in sinus rhythm (SR) or chronic atrial fibrillation (AF).
Methods and Results— AP duration at 90% repolarization (APD90) was shorter in AF than in SR (300±16 ms, n=6, versus 414±10 ms, n=15), whereas APD20 was longer (35±9 ms in AF versus 5±2 ms in SR, P<0.05). 4-Aminopyridine (5 μmol/L) elevated the plateau to more positive potentials from −21±3 to −6±3 mV in SR and 0±3 to +12±3 mV in AF. 4-Aminopyridine reversibly shortened APD90 from 414±10 to 350±10 ms in SR but prolonged APD90 from 300±16 to 320±13 ms in AF. Similar results were obtained with AVE 0118 (6 μmol/L). Computer simulations of IKur block in human atrial APs predicted secondary increases in ICa,L and in the outward rectifiers IKr and IKs, with smaller changes in AF than SR. The indirect increase in ICa,L was supported by a positive inotropic effect of 4-aminopyridine without direct effects on ICa,L in atrial but not ventricular preparations. In accordance with the model predictions, block of IKr with E-4031 converted APD shortening effects of IKur block in SR into AP prolongation.
Conclusions— Whether inhibition of IKur prolongs or shortens APD depends on the disease status of the atria and is determined by the level of electrical remodeling.
Received November 4, 2003; de novo received April 5, 2004; revision received May 17, 2004; accepted May 21, 2004.
The cardiac repolarization process is regulated by several outward currents, of which the ultrarapid delayed rectifier potassium current (IKur) is thought to play a major role. This current is absent in the ventricles and hence represents a suitable target for selectively modulating action potentials (APs) in the atria.1–3 The selective blocker of IKur 4-aminopyridine in low micromolar concentrations is expected to prolong the AP duration (APD). However, experimental results in human atrial preparations from patients with sinus rhythm (SR) are inconsistent with shortening of APD in multicellular trabeculae4 and prolongation of APD in isolated atrial myocytes.1 Although block of IKur and the subsequent prolongation of the APD are expected to be beneficial in chronic atrial fibrillation (AF), the experimental proof is still lacking. Furthermore, AF itself induces shortening of APD and effective refractory period, known as electrical remodeling, that is associated with changes in expression and activity of the involved ion channels.5 Human IKur was found to be reduced by ≈50%, whereas other groups reported no changes.5
To predict the AP alterations associated with IKur block during chronic AF, Courtemanche et al2 simulated these changes in a model of human APs in AF and demonstrated that the reduction of IKur was associated with prolongation of APD. However, this article only predicted the changes without experimental verification.
Here, we studied the effects of IKur block with 4-aminopyridine and with the new IKur blocker, the biphenyl derivative AVE 0118, on APs in trabeculae from SR and AF patients. The impact of IKur block on other atrial currents was predicted by simulating APs in a modified Luo-Rudy model, and the predictions were tested experimentally by recording APs or force of contraction (Fc) in trabeculae or by measuring membrane currents in isolated atrial myocytes.
Human Tissue Samples and Patient Characteristics
The study was approved by the ethics committee of the Dresden University of Technology (No. EK790799). Each patient gave written, informed consent.
Right atrial appendages were obtained from 34 patients with SR and 18 patients with chronic AF (AF >6 months, Table 1). Significant differences between the 2 groups were found for underlying heart disease and pulmonary hypertension. AF patients more often received digitalis and diuretics, and β-blockers and lipid-lowering drugs were prescribed more frequently in SR patients. Ventricular trabeculae (n=10) originated from left and right ventricles from 2 explanted end-stage failing hearts.
Atrial APs were recorded with conventional intracellular microelectrodes in right atrial trabeculae (microelectrode tip resistance, 10 to 25 MΩ; 1-ms stimulus, 25% above threshold intensity). The bath solution contained (in mmol/L): NaCl 127, KCl 4.5, MgCl2 1.5, CaCl2 1.8, glucose 10, NaHCO3 22, and NaH2PO4 0.42, equilibrated with O2/CO2 (95:5) at 35±2°C, pH 7.4. A computer-aided system (developed at the University of Szeged, Hungary) was used for generating stimuli and data acquisition of various AP parameters. After equilibration for 1 hour, control APs were recorded for 20 minutes before 4-aminopyridine or AVE 0118 was cumulatively added, with 20 minutes of recording between concentration increments.
Human myocytes were isolated from atrial appendages as previously described.6 ICa,L and IK1 were measured with conventional voltage-clamp technique as previously described.6,7 Mean cell capacitance was 101±6.5 pF (n=29).
Measurement of Fc
Pairs of right atrial or ventricular trabeculae were mounted in organ baths filled with 50 mL of buffer (composition in mmol/L: NaCl 126.7, KCl 5.4, CaCl2 1.8, MgCl2 1.05, NaHCO3 22.0, NaH2PO4 0.42, EDTA 0.04, and glucose 5.0, equilibrated with O2/CO2 [95:5] at 37°C, pH 7.4).8 The bath solution contained 200 nmol/L (−)-propranolol to exclude effects mediated through β-adrenoceptors. The preparations were paced (0.5 Hz, 5-ms stimulus, 10% above threshold intensity) and were stretched to 80% of the length associated with maximum developed force. After an equilibration period of 30 minutes, the effects of 4-aminopyridine or AVE 0118 on Fc were determined by cumulatively increasing concentrations every 20 minutes.
Action Potential Simulations
For simulating the shapes of human atrial APs, we modified mathematical models described in the literature.9–11 The incorporated membrane currents and transporters and factors controlling intracellular ion concentrations are listed in the Appendix (see online-only Data Supplement), which also contains specific kinetic parameters, constants of ion currents, and the equations used for current calculations. Maximum current conductances of ICa,L, Ito,f, IKur, IK1, and INaCaX were adapted to simulate the characteristic AP shapes. For AP simulation in chronic AF, original current data were taken from the literature and, when not available, amplitudes were extrapolated from changes in channel expression.
As an approximation, APs were assumed to be spatially uniform, ie, conduction within the preparation was neglected. Changes of membrane potential were calculated for space-clamp conditions as follows: d(Vm)/dt = −(Iion,total+Istim)/Cm, with Iion,total = INa+ICa,T+ ICa,L+Ito,f+IKur+IKr+IKs+IK1+IK,Ach+IK,Ca+Ib,Na+Ib,Ca+Ib,Cl+ INa,Kpump+ INaCaE and Istim = stimulus current of −90 μA/μF applied 0.5 ms at beginning of each cycle, and Cm = membrane capacitance (specific Cm assumed to be 1 μF/cm2).
Numerical integration of d(Vm)/dt was performed according to a modified Euler method suggested by Rush and Larsen.12 The length of the time steps was varied between 0.02 and 20 ms, depending on the extent of resultant voltage changes. Momentary values of gating variables were calculated from analytical solution of the related first-order differential equations9–11,13: x(Vm, tj) = xSS(Vm)−[xSS(Vm)− xSS(Vm, ti)] × exp[−dti/τ(Vm)], with dti = ith timestep (ie, tj = ti+dti) and xSS (Vm) = voltage-dependent steady-state value, τ (Vm) = voltage-dependent time constant.
Simulated APs, currents, and ionic concentrations were allowed to stabilize for at least 200 cycles. The model was implemented in Turbo Pascal 6.0. For further details of the model, see Appendix.
Differences between continuous data were compared by unpaired Student t test or 1-way ANOVA. Frequency data were analyzed with χ2 statistics. Data are mean±SEM. A value of P<0.05 was considered statistically significant.
Effect of 4-Aminopyridine on AP Configuration in SR and AF
Resting membrane potentials were −75±1 mV in SR (n=15) and significantly more negative in AF (−80±3 mV, n=6, P<0.05). In accordance with our previous results,14 APD at 20% of repolarization (APD20) was shorter in SR (5±2 ms) than in AF (35±9 ms, P<0.05), whereas APD90 was longer in SR (414±10 ms) compared with AF (300±16 ms, P<0.05).
In the presence of 4-aminopyridine (5 μmol/L), the potentials of the notch and dome (SR) and of the plateau shoulder (AF) were shifted to more positive values, leading to a significant increase in APD20 from 5±2 to 12±5 ms in SR (P=0.05) and from 35±9 to 78±5 ms in AF (P=0.002, Figure 1, A and B). The final repolarization phase was accelerated in both groups; however, APD90 was shortened from 414±10 to 350±10 ms in SR (P<0.0001) but was prolonged from 300±16 to 320±13 ms in AF (P=0.006; Figure 1, C and D), suggesting that the directions of APD90 changes are different in SR and AF. The effects of 4-aminopyridine were reversible on washout.
In SR preparations, the mean notch potential, ie, the minimum potential after the initial rapid repolarization phase, was shifted by 4-aminopyridine (5 μmol/L) from −32±4 to −22±5 mV (P<0.003), and the mean dome potential, ie, the most positive plateau potential before final repolarization, was shifted from −28±4 to −13±6 mV (P=0.001). Because APs in AF did not exhibit the typical notch as in SR, we introduced the parameter “plateau potential” for analysis of changes in this potential range. Plateau potential is defined as the mean amplitude within the time window of 20 to 80 ms after the upstroke of the AP (Figure 1, A and B). In SR, the plateau potential was shifted by 4-aminopyridine (5 μmol/L) from −21±3 to −6±3 mV (P<0.0001, Figure 1E). In AF, the plateau potential was more positive (0±3 mV, P=0.0001 versus SR) and was shifted by 4-aminopyridine to +12±3 mV (P=0.0012, Figure 1F).
The effect of 4-aminopyridine on the shift in notch-and-dome potentials was concentration-dependent (0.3 to 100 μmol/L, Figure 2, A and B). In SR, the notch potential became less negative and shifted from −23±2 to −4±2 mV with 100 μmol/L 4-aminopyridine (Figure 2, A and C, n=5, P<0.001), and the respective dome potential was changed from −18±1 to 0±2 mV (P<0.001). Nonlinear curve fitting resulted in EC50 values of 15 μmol/L 4-aminopyridine for elevation of notch potential and 14 μmol/L for elevation of dome potential (Figure 2C). In AF, the effect of 4-aminopyridine on the plateau potential was also concentration-dependent, with an EC50 value of 28 μmol/L in 1 experiment (Figure 2, B and D).
Model Simulations of APs in SR and AF: Block of IKur
Inserting experimentally estimated parameters into the mathematical model of human atrial APs (see Appendix) provided the spike-and-dome shape typical for tissue from SR patients (compare Figures 1A and 3⇓). Selective inhibition of IKur by 4-aminopyridine was simulated by setting the current to 20% of its regular value in SR (see Table 2). The model reproduced the observed shifts of notch-and-dome potentials to more positive values (Figure 3) and shortened APD90. Block of IKur induced a series of indirect effects on other currents because of their voltage and time dependence during the course of a free-running action potential. The model predicted peak ICa,L to increase by 37% at the elevated plateau potential (Figure 3) and increases in the outward potassium currents IKr and IKs by 80% and 50%, respectively.
The characteristic triangular shape of APs in AF was reproduced by setting conductances of IK1, ICa,L, Ito,f, IKur, and INaCaX to values of reported ion current densities or channel expression (Figures 1B and 3⇑; see Reference 5 and Table 2). The effect of 4-aminopyridine was simulated by setting the maximum conductance of IKur to 20% of the AF control value and computing membrane currents in the course of the resulting AP. The simulation produced a shift of the plateau potential and an overall prolongation of APD20 and APD90 (Figure 3). The accompanying indirect changes of other currents were qualitatively similar to those in SR but were substantially smaller in size.
Experimental Verification of Model Predictions (ICa,L, IKr)
The model predicted an increase of ICa,L by block of IKur. 4-Aminopyridine did not modulate ICa,L in atrial myocytes (peak current density during clamp steps from −80 to +10 mV: 5.5±1.3 pA/pF before and 5.1±1.0 pA/pF after 100 μmol/L 4-aminopyridine, n=8 cells from 6 SR patients; P=NS). Similar results, although at lower basal ICa,L, were obtained in atrial myocytes from AF patients (data not shown). 4-Aminopyridine (100 μmol/L) had no effect on IK1 (data not shown).
To test for indirect effects of block of IKur on Ca2+ entry via ICa,L, we measured Fc as an indirect indicator of ICa,L activity (Figure 4A). In SR trabeculae, 4-aminopyridine (100 μmol/L) enhanced Fc from 4.5±0.7 to 7.3±1.1 mN (n=8/6 [trabeculae/patients], P<0.05). The EC50 for 4-aminopyridine obtained by curve fitting was 52 μmol/L (Figure 4B). With 1 mmol/L 4-aminopyridine, Fc increased maximally (8.8±1.3 mN), corresponding to 58±3% of the Fc developed by 8 mmol/L CaCl2 (14.9±1.6 mN). As expected, basal Fc was lower (1.3±0.4 mN, n=9/5, P<0.001) and the effect of 4-aminopyridine on Fc was smaller in AF than in SR. Fc increased at 1 mmol/L 4-aminopyridine to 2.9±0.9 mN, corresponding to 28±8% of that obtained by 8 mmol/L CaCl2 (10.9±1.6 mN, P=NS versus SR). The EC50 value was 36 μmol/L. The positive inotropic effects were not affected by (−)-propranolol and hence were independent of enhanced neurotransmitter release.8 If the effect of 4-aminopyridine on Fc was a result of the blockade of IKur, it should be absent in ventricular preparations, in which IKur cannot be measured.15 Indeed, 4-aminopyridine (0.3 μmol/L to 1 mmol/L) did not affect Fc in ventricular trabeculae (Figure 4, C and D), excluding a direct effect of 4-aminopyridine on Ca2+ release or contractile machinery.
According to the model prediction in SR, the shortening of APD90 by block of IKur is expected to be induced by an increase in IKr. Block of IKr with E-4031 (1 μmol/L) prolonged APD90, although the effect did not reach the level of statistical significance (P=0.3661, n=5); Figure 5, A and C). In the presence of E-4031, 4-aminopyridine (25 μmol/L) no longer shortened but rather prolonged APD90 from 412±43 to 483±33 ms (n=5, P=0.2217; versus control, P=0.0249) and significantly elevated the notch and plateau potentials from −30±2 to −19±3 mV (n=5, P<0.05) and from −27±2 to −14±3 mV (n=5, P<0.001), respectively. These effects were reproduced in the model simulation by reducing the conductance of IKr by 95% and that of IKur by 90% (Figure 5B).
Effect of the IKur Blocker AVE 0118 on AP in SR and AF
The effects of IKur inhibition were verified with the new IKur blocker AVE 0118 (6 μmol/L). AVE 0118 revealed the typical changes in AP shape as found with low concentrations of 4-aminopyridine (5 μmol/L), ie, elevation of the plateau potential from −16.3±4.1 to −6.7±4.2 mV (n=9, P<0.01) in the presence of 6 μmol/L AVE 0118, and shortening of ADP90 from 343±14 to 328±17 ms (P=0.066) in SR. In AF, the plateau amplitude increased from −2.4±3.6 to 8.8±3.6 mV (n=6, P<0.001), and APD90 increased from 260±14 to 280±13 ms (P<0.05; Figure 6).
The concept of block of IKur as a therapeutic target in AF is widely accepted,3 despite inconsistent experimental and theoretical evidence for changes in APD. Here, we report that selective block of IKur shortens APD of human atrial trabeculae from SR but prolongs APD in AF. Changes in APD in SR and AF were consistent with secondary current changes as predicted by a modified Luo-Rudy model and were verified experimentally.
Effects of Block of IKur on Shapes of Atrial APs in SR and AF
In low concentrations, 4-aminopyridine is a selective blocker of IKur. In earlier work, we found that 4-aminopyridine blocks IKur and Ito,f in human atrial myocytes with IC50 values of 8 μmol/L and 1 mmol/L, respectively.15 Similar values were published by others (ie, 49 μmol/L for IKur and 1.9 mmol/L for Ito,f).1
Block of repolarizing outward current is expected to prolong APD; however, we observed shortening in SR preparations instead. In the literature, shortening,4 prolongation,1 and even no effect at all have been reported.2 How can these inconsistencies be reconciled? The shape of the cardiac AP is the result of the balanced activity of several ion currents. Provided that 4-aminopyridine at the concentrations used is in fact selective for IKur block, APD shortening in SR must be associated with alterations in additional currents. In this context, the pronounced elevation of the action potential plateau may provide an important clue because enhanced amplitude of ICa,L at more positive potentials could activate repolarizing outward currents that would shorten APD.4
In AF, block of IKur resulted in the expected APD prolongation. The characteristic triangular AP shape in AF compared with the spike-and-dome configuration in SR is a result of electrical remodeling that comprises changes in several ion conductances. The densities of ICa,L and Ito,f are reduced by ≈70%16,17 and ≈60%,16,18,19 respectively, and inward rectifier IK1 is increased by ≈100%.14,16,18,20 From these considerations, it follows that selective block of IKur (or any other current) will perturb the balance of ion channel activation differently in AF and SR and may result in different patterns of secondary effects.
Computer Simulations: Indirect Effects of 4-Aminopyridine on ICa,L
To predict individual current changes secondary to selective block of IKur, we used a computer model of AP simulation. For this purpose, ion conductances in the Luo-Rudy model9 were set to the experimentally observed values reported recently for human AF. The model simulated the characteristic AP shapes. For selective block of IKur in SR APs, the model produced a more pronounced spike-and-dome configuration. The shift of the plateau to more positive potentials was associated with enhanced ICa,L activation in the model (although 4-aminopyridine had no direct effects on ICa,L) and is expected to increase systolic Ca2+ influx during a free-running AP. Indeed, 4-aminopyridine significantly increased Fc in atrial trabeculae in a concentration-dependent manner (see Figure 4) in SR and AF, respectively. Although the positive inotropic effect was much smaller in AF, it is considered to be clinically interesting, because atrial contractility is already impaired in AF21 and all other drugs currently used in the treatment of AF, eg, β-adrenoceptor blockers or calcium channel blockers, have a negative inotropic effect.
Computer Simulations: Indirect Effects of 4-Aminopyridine on IKr
Secondary enhancement of outward currents as an explanation for APD shortening in SR by block of IKur was also predicted by the model. As the likely candidates, the model identified IKr and IKs. Because of its slow activation kinetics, IKs will not play a major role in the course of the short atrial APs. Conversely, the impact of IKr was examined experimentally: pharmacological block of IKr in trabeculae from SR unmasks the APD-prolonging effect of IKur block (see Figure 5). Therefore, we speculate that 4-aminopyridine prolongs APD in atrial myocytes, because IKr may be absent because of the enzymatic isolation procedure, as was shown for canine atrial myocytes.22
The model simulation of the human atrial SR AP reproduces the experimentally observed APD shortening that is induced by IKur block. However, this experimental finding is reproduced only when IKr is set to sufficiently high values (Table 2). If low values are used (see, for instance, Nygren et al23), APD either is prolonged23 or remains unaffected.2 Although the large conductance of IKr assumed in our model was not proved with current measurements, the APD-prolonging effect of IKr block by E-4031 (Figure 5) points to a prominent role of this current in atrial repolarization, supported also by current measurements of IKr in human atrium.24 In the presence of IKr block, IKur inhibition further prolonged APD. We therefore assume that in multicellular trabeculae, IKr was fully available for repolarization. In conscious dogs, the IKr blocker ibutilide prolonged atrial monophasic APs and effective refractory period,25 providing evidence for a prominent IKr contribution.
Because ICa,L is reduced in AF, block of IKur cannot produce much indirect increase in ICa,L, and therefore the plateau is only slightly elevated. Because of enhanced IK1 in AF, rapid and strong induction of the repolarization process abbreviates the time window for activation of IKr and thus reduces its repolarizing potency. All interacting factors together will produce an AP-prolonging effect of IKur block, which possibly represents the antiarrhythmic potency of putative IKur blockers.
The majority of patients donating tissue samples suffered from coronary artery disease. Therefore, AP measurements from SR trabeculae may not be considered to be fully representative of APs from trabeculae of a healthy population. In addition, the patients’ medications may have additional effects. The large variability in action potential shapes may represent this inhomogeneity of the material.
Early repolarization is controlled not only by IKur but also by Ito,f. Although low concentrations of 4-aminopyridine are selective for block of IKur, a contribution of Ito,f block cannot be excluded at larger concentrations. In the absence of selective blockers for Ito,f, model simulations are useful for estimating the consequences of Ito,f block on atrial AP. Like IKur block, reduced basal conductance of Ito,f shifted the notch potential to more positive values and abbreviated APD90 in SR and only slightly prolonged APD90 in AF. In contrast to IKur block, selective block of Ito,f did not elevate the dome potential or enhance the spike-and-dome configuration (data not shown). The rapid Ito,f inactivation most likely limits indirect enhancement of IKr if Ito,f is blocked.
We hypothesize that IKur is a major determinant in controlling action potential shape and therefore also contractility in the human atrium. The antiarrhythmic potency of IKur inhibitors is determined largely by the level of electrical remodeling of the diseased atrium. Although the antiarrhythmic effectiveness of IKr blockers is significantly attenuated in chronic AF,26 selective IKur blockers may be more potent in prolonging atrial refractory period in chronic AF than in SR and may therefore be more efficient in terminating AF than in maintaining SR.
This work was supported by the Sächsisches Staatsministerium für Wissenschaft und Kunst (Az 4-7531.50-04-0370-01/2, -02/4, and -03/8) and by the Bundesministerium für Bildung und Forschung (Atrial Fibrillation Network, No 01GI0204). We acknowledge the donation of AVE 0118 by Aventis Pharma AG, Frankfurt, Germany, and thank Prof Dr H. Gögelein from Aventis Pharma AG for valuable comments on the manuscript.
↵*The first 2 authors contributed equally to this work.
The online-only Data Supplement, which contains an Appendix, is available with this article at http://www.circulationaha.org.
Wang Z, Fermini B, Nattel S. Sustained depolarization-induced outward current in human atrial myocytes: evidence for a novel delayed rectifier K+ current similar to Kv1.5 cloned channels currents. Circ Res. 1993; 73: 1061–1076.
Courtemanche M, Ramirez RJ, Nattel S. Ionic targets for drug therapy and atrial fibrillation-induced electrical remodeling: insights from a mathematical model. Cardiovasc Res. 1999; 42: 477–489.
Dobrev D, Wettwer E, Himmel HM, et al. G-protein β3-subunit allele is associated with enhanced human atrial rectifier potassium currents. Circulation. 2000; 102: 692–697.
Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential, I: simulations of ionic currents and concentration changes. Circ Res. 1994a; 74: 1071–1096.
Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential, II: afterdepolarizations, triggered activity and potentiation. Circ Res. 1994b; 74: 1097–1113.
Ramirez JR, Nattel S, Courtemanche M. Mathematical analysis of canine action potentials: rate, regional factors and electrical remodelling. Am J Physiol. 2000; 279: H1767–H1785.
Dobrev D, Graf E, Wettwer E, et al. Molecular basis of downregulation of G-protein–coupled inward rectifying K+ current IK,ACh in chronic human atrial fibrillation: decrease in GIRK4 mRNA correlates with reduced IK,ACh and muscarinic receptor–mediated shortening of action potentials. Circulation. 2001; 104: 2551–2557.
Bosch RF, Zeng X, Grammer JB, et al. Ionic mechanisms of electrical remodeling in human atrial fibrillation. Cardiovasc Res. 1999; 44: 121–131.
Van Wagoner DR, Pond AL, Lamorgese M, et al. Atrial L-type Ca2+ currents and human atrial fibrillation. Circ Res. 1999; 85: 428–436.
Van Wagoner DR, Pond AL, McCarthy PM, et al. Outward K+ current densities and Kv1.5 expression are reduced in chronic human atrial fibrillation. Circ Res. 1997; 80: 772–781.
Workman AJ, Kane KA, Rankin AC. The contribution of ionic currents to changes in refractoriness of human atrial myocytes associated with chronic atrial fibrillation. Cardiovasc Res. 2001; 52: 226–235.
Dobrev D, Wettwer E, Kortner A, et al. Human inward rectifier potassium channels in chronic and postoperative atrial fibrillation. Cardiovasc Res. 2002; 54: 397–404.
Schotten U, Greiser M, Benke D, et al. Atrial fibrillation-induced atrial contractile dysfunction: a tachycardiomyopathy of a different sort. Cardiovasc Res. 2002; 53: 192–201.
Nygren A, Fiset C, Clark JW, et al. Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. Circ Res. 1998; 82: 63–81.