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Cardiovascular Research 2002 56(3):381-392; doi:10.1016/S0008-6363(02)00598-9
© 2002 by European Society of Cardiology
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Copyright © 2002, European Society of Cardiology

Modulation of triggered activity by uncoupling in the ischemic border

A model study with phase 1b-like conditions

Andrew E Pollarda,*, Wayne E Casciob,c, Vladimir G Fasta and Stephen B Knisleyc

aDepartment of Biomedical Engineering, Cardiac Rhythm Management Laboratory, University of Alabama at Bermingham, Volker Hall B140 1670 University Blvd., Birmingham, AL 35294, USA
bDepartment of Medicine, Division of Cardiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
cDepartment of Biomedical Engineering, University of Chapel Hill at North Carolina, Chapel Hill, NC, USA

pollard{at}crml.uab.edu

* Corresponding author. Tel.: +1-205-975-4710; fax: +1-205-975-4720.

Received 12 March 2002; accepted 10 July 2002


   Abstract
Top
 Abstract
1. Introduction
 2. Methods
 3. Results
 4. Discussion
 References
 
Objective: Triggered beats during regional ischemia may depend upon the electrical source and sink charge interactions between adjacent regions of normal and ischemic cardiac tissue that are partly controlled by electrical coupling. Methods: To study these relationships, we modified parameters in the Luo–Rudy dynamic membrane equations to reflect physiologic conditions associated with phase 1b arrhythmias. Superthreshold delayed afterdepolarizations (DADs) formed after pacing. Coupling contributions were then examined using: (i) a single phase 1b myocyte connected via a variable resistance to a single normal myocyte, and (ii) a multicellular fiber with a 1-cm segment of phase 1b myocytes connected to a 1-cm normal segment having resistance changes that were confined to the ischemic segment. Integration of ionic, capacitive and coupling currents during DAD initiation allowed charge quantification. Results: In cell pairs, phase 1b myocyte DADs were suppressed at resistances where normal myocyte pacing resulted in phase 1b myocyte excitation. Coupling charge requirements limited capacitive charging in the phase 1b myocyte, which occurred in combination with diastolic hyperpolarization that shifted transmembrane potential from threshold. In multicellular fiber simulations, DADs were suppressed with strong coupling in the phase 1b segment. Moderate uncoupling of that segment allowed superthreshold DAD formation away from the border that initiated action potential propagation in the normal segment. With severe uncoupling, propagation failed at the border. Conclusions: These findings support the clinical and experimental observation that intermediate uncoupling is an important contributor to phase 1b arrhythmogenesis.

KEYWORDS Acidosis; Arrhythmia (mechanisms); Cell communication; Computer modelling; Gap junctions; Hypoxia/anoxia; Impulse formation; Ischemia

This article is referred to in the Editorial by J.R. de Groot (pages 350–352) in this issue.


   1. Introduction
Top
 Abstract
 1. Introduction
2. Methods
 3. Results
 4. Discussion
 References
 
Ventricular myocardium becomes arrhythmogenic during the phase 1b interval of ischemia [1,2]. During this interval, extracellular potassium ([K+]e) accumulation [3–5], hypoxia-induced adenosine triphosphate (ATP) depletion [6,7], intracellular and extracellular acidosis [7,8], cytosolic accumulation of Ca2+, Mg+, H+ and lipid metabolites [9], and increased tissue resistance [10–13] develop. With regional ischemia, these changes are confined to the poorly perfused tissue that is electrically coupled to normal myocardium at the ischemic border [4] where injury currents flow between regions. Border zone interactions are important to arrhythmias because the relationships between source charge generation and downstream sink charge requirements modulate membrane depolarization and repolarization, and they also dictate success or failure of action potential propagation.

Detailed theoretical models have provided insights into ischemic influences on local action potentials and on source–sink interactions during propagation. Shaw and Rudy [14] showed that modification of ionic concentrations and sarcolemmal currents in the Luo and Rudy (LRd) dynamic membrane equations [15–18] to reflect the hypoxia, hyperkalemia, and acidosis associated with phase 1a ischemia collectively influenced action potentials. Repolarization shortening was especially dependent on hypoxia. Ch’en et al. [19] integrated mathematical formulations for metabolism of high energy phosphates, glycogen metabolism and lactate transport into a ventricular myocyte model. Acid-equivalent fluxes replicated the four known sarcolemmal H+ transporters and intracellular pH (pHi) regulation was additionally considered in terms of contributions from lactate transport. Simulated pHi reductions caused intracellular sodium ([Na+]i) accumulation that promoted spontaneous Ca2+ release from the sarcoplasmic reticulum (SR). In multicellular fiber simulations that incorporated their phase 1a changes, Shaw and Rudy [15] showed conduction block induced by hyperkalemia could be reversed by increasing the L-type calcium current (ICa,L). Greater ICa,L increases were needed to offset the effects in combination with acidosis and anoxia.

The present study focused on source–sink relationships under physiologic conditions attendant to phase 1b. We modified LRd ionic concentrations, sarcolemmal currents and SR Ca2+ uptake (Iup) and release (Irel) processes to levels that promoted spontaneous Irel. That Irel triggered transient inward current (Iti) and initiated superthreshold delayed afterdepolarizations (DADs) in isolated myocytes. Electrical coupling of phase 1b myocytes to normal myocytes then allowed determination of source–sink interactions that suppressed and facilitated triggered activity.


   2. Methods
Top
 Abstract
 1. Introduction
 2. Methods
3. Results
 4. Discussion
 References
 
2.1 LRd membrane equations
Integrated LRd components included those documented in Refs. [15–18] with the exception that the sodium-dependent potassium current (IK,Na) was not included because of its limited contribution to the action potential [18]. Parameters modified to reflect phase 1b conditions are summarized in Table 1.


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  		Table 1 Modified LRd parameters

 
2.2 Phase 1b characteristics
Parameter modifications were based on the degrees of hypoxia, hyperkalemia and acidosis reported for the 15–25-min interval. During this interval, the extent of hypoxia changes with a triphasic fall in the total cytosolic free-energy for hydrolysis of ATP. In comparing free-energy measurements from perfused rat hearts exposed to varying extents of global ischemia, Fiolet et al. [6] showed an early rapid fall from 55 kJ/mol (0 min) to 46 kJ/mol (4 min) that was followed by a plateau (15–20 min). At 15–25 min, specifically, free energy measured between {approx}45 and {approx}40 kJ/mol. During this same interval, [K+]e changes little. As described by Hill and Gettes [3], [K+]e rises over a triphasic time course. Rapid early accumulation (0–5 min) is followed by a long plateau (5–25 min) before continued elevation (25–60 min). Significant acidosis is also associated with the 15–25-min interval. Koretsune and Marban [7] measured pHi reductions from 7.2 (control) to between 6.8 and 6.6 at 15 and 25 min, respectively, in ferret hearts. Owens et al. [8] measured comparable extracellular pH (pHe) reductions from 7.4 (control) to between 6.4 and 6.0 at 15 and 25 min, respectively, in rabbit hearts.

2.3 Modification of ionic concentrations
2.3.1 Extracellular potassium ([K+]e)
Hill and Gettes [3] observed [K+]e levels that were maintained between 8 and 10 mM during most of phase 1b. To reflect phase 1b conditions, [K+]e was therefore fixed at 9 mM.

2.3.2 Intracellular sodium ([Na+]i)
Hypoxia and acidosis cause a rise in [Na+]i that is secondary to Na+–H+ exchange and Na+–K+ pump inhibition. That rise occurs throughout phase 1b, as evidenced by studies using 23Na NMR spectroscopy of rat hearts subjected to no-flow ischemia. Increases to 154, 178 and 238% of control were reported at 10, 21, and 30 min, respectively, by van Echteld et al. [20], Pike et al. [21] and Malloy et al. [22] [Na+]i was therefore fixed at 200% of control.

2.4 Modification of sarcolemmal currents
2.4.1 L-type calcium current (ICa,L)
Acidosis inhibits ICa,L. Prod’hom et al. [23] showed I–V curves with consistent shapes at pHe of 7.5 and 6.5 in whole cell voltage clamps of guinea pig ventricular myocytes, with the main difference being peak ICa,L at the lower pH measured 40–60% of control. Similarly, Kaibara and Kameyama [24] showed half maximal inhibition of ICa,L activity following pHi reductions to 6.6. Both observations are consistent with guinea pig ventricular myocyte experiments in which exposure to ischemia-like solutions caused peak ICa,L reduction to 51% of control [25]. Peak ICa,L was therefore reduced to 50% of control.

2.4.2 Sodium–calcium exchange (NCX)
Acidosis inhibits NCX. Using guinea pig ventricular myocyte patches, Doerring and Lederer [26] showed a pHi reduction from 7.2 to 6.4 was accompanied by peak NCX reduction to 60% of control. NCX inhibition by extracellular acidosis was demonstrated by Egger and Niggli [27] in whole-cell voltage-clamps of guinea pig ventricular myocytes, with pHe lowered from 7.6 to 6.0 decreasing peak NCX to 30% of control. To reflect pHi and pHe reductions, peak NCX was therefore reduced to 20% of control.

2.4.3 Background calcium current (ICa,B)
Metabolic inhibition augments ICa,B. Wang et al. [28] exposed neonatal rat ventricular myocyte cultures to free radicals and measured a 10-fold increase in the open probability for individual ICa,B channels. The extent to which such a large open probability change influences total ICa,B under phase 1b conditions is unclear. Recognizing some enhancement is likely, peak ICa,B was increased to 130% of control.

2.4.4 Calcium-sensitive nonselective cation current (Ins,Ca)
Elevated diastolic [Ca2+]i and metabolic inhibition both enhance Ins,Ca. Albert and Large [29] measured unitary conductance in rabbit portal vein myocytes and showed a 77% increase from control following Ca2+ elevation to 3 µM. Jabr and Cole [30] showed enhancements in quasi-steady state current in guinea pig ventricular myocytes exposed to oxygen-derived free radicals that increased Ins,Ca independent of [Ca2+]i changes. To reflect these measurements in a qualitative sense, Ins,Ca conductance was increased to 170% of control.

2.4.5 ATP-dependent potassium current (IK,ATP)
IK,ATP activates under hypoxic and anoxic conditions. The LRd [15] formulation depends, primarily, on [ATP]i, with half-maximal saturation for control IK,ATP at 0.114 mM. [ATP]i measures under phase 1b conditions vary. In ischemic pig hearts, Schaefer et al. [31] measured flow reductions to 20% of control that were accompanied by [ATP]i reductions to 60% of control. With such [ATP]i maintenance, IK,ATP contributes relatively little to the LRd action potential. By comparison, in rat hearts subjected to no-flow ischemia, Murphy et al. [32] showed full [ATP]i depletion within 15 min. To insure IK,ATP activation without full [ATP]i depletion, [ATP]i was set to 0.15 mM to simulate phase 1b conditions.

2.4.6 Na+–K+ pump
The extent to which hypoxia and acidosis inhibit the Na+–K+ pump under phase 1b conditions is uncertain. Preservation of [K+]e at plateau levels throughout phase 1b supports partial pump maintenance [5], consistent with relatively high [ATP]i levels. [Na+]i accumulation supports pump inhibition. Using purified rabbit sarcolemmal vesicles, Bersohn [33] found increased binding sites (126% of control) and reduction of initial pump velocity (46% of control) accompanying ischemia. In cultured chick ventricular myocytes exposed to metabolic inhibition, Ikenouchi et al. [34] found decreased pump density (46% of control). For consistency with these observations and with our selected [ATP]i and [Na+]i values, peak Na+–K+ pump was reduced to 30% of control to simulate phase 1b conditions.

2.5 Modification of SR calcium handling
2.5.1 SR calcium release (Irel)
Hypoxia and acidosis inhibit Irel. Using voltage-clamped purified cardiac Ca2+ release channels, Xu et al. [35] showed that open channel probabilities reduced with ATP depletion, Mg+ accumulation and pH reduction. That probability fell to 75% of control during ATP depletion from 1.0 to 0.0 mM, 28% of control during Mg+ exposure up to 7 mM in the presence of 5 mM [ATP]i, and 22% of control during Mg+ exposure with no ATP. Adjustments in pH from 7.4 to 6.5 and 6.3 reduced probabilities further. Irel inhibition under phase 1b conditions is also supported by whole cell Ca2+ fluorescence [36] and confocal Ca2+ spark imaging during metabolic inhibition [37] and pHi reduction [38] in rat ventricular myocytes. This collective data was represented by modifying LRd parameters, including a reduced Irel to 5% of control during SR Ca2+ induced Ca2+ release (CICR) and a reduced Irel during spontaneous release in response to calsequestrin buffer overload to 65% of control. The reduction during CICR was introduced because it led to [Ca2+]i transients that were comparable in magnitude to those under control conditions, despite the end-diastolic [Ca2+]i elevation that accompanied the phase 1b modifications to sarcolemmal currents and ionic concentrations. Less reduction during spontaneous Irel was included because the control magnitude for steady-state conductance under overload conditions is considerably less than that magnitude during CICR. Both changes were intended to reflect indo-1 fluorescence measurements in rabbit hearts subjected to no-flow ischemia by Mohabir et al. [39], who showed peak-systolic [Ca2+]i increases that accompanied end-diastolic [Ca2+]i elevation.

2.5.2 SR calcium uptake (Iup)
Hypoxia and acidosis inhibit Iup. Kaplan et al. [40] measured Ca2+ uptake rates in homogenized ventricular muscle SR vesicles from control and ischemic hearts and found a decrease to 74% of control after 15 min of global ischemia. Using skinned rat papillary muscles in which caffeine-induced contractures were measured after SR Ca2+ loading during exposure to normal and hypoxic solutions, Zhu et al. [41] measured comparable reductions. Iup inhibition by acidosis is supported by Hulme and Orchard [42], who showed pHi reductions to 6.5 prolonged the relaxation time constant for caffeine-induced [Ca2+]i transients. Because we expect less overall inhibition under phase 1b conditions, peak Iup was reduced to only 90% of control.

2.6 Multicellular simulations
2.6.1 Cell pairs
Border zone interactions were first evaluated using the coupled myocyte approach [43]. The simulation procedure followed Zaniboni et al. [44] with:


Formula (1)


Formula (2)

solved for the ionic current density (Iion, µA/µF) and for the transmembrane potential (Vm, mV). Subscripts norm and 1b represent normal and phase 1b myocyte contributions, respectively. Rj was the junctional resistance in M{Omega}. Sm was the membrane surface area for each myocyte (1.534x10–4 cm2), which was set in recognition of the specified myocyte radius (a = 11 µm) and length ({Delta}x = 100 µm) upon which the LRd membrane equations are based. Cm was the specific membrane capacitance (1.0 µF/cm2). Lower bound time steps were 0.004 ms. They were maintained from the time of stimulation or spontaneous Irel throughout the upstrokes and early plateaus. Time steps were automatically adjusted to an upper bound of 0.064 ms for calculations during the late plateaus, downstrokes, and diastole [45]. Stimuli were 2 ms duration square pulses of 18.5 and 35.0 µA/µF for the isolated myocyte and cell pair simulations, respectively.

2.6.2 Multicellular fibers
Fiber simulations were completed to represent uncoupling between segments containing normal and phase 1b myocytes over a spatial scale consistent with regional ischemia in tissue preparations. The fiber included a 100 myocyte (1 cm) normal segment with control LRd membrane properties. That segment was coupled to an additional 100 myocyte (1 cm) segment with phase 1b modifications. As in Shaw and Rudy [15], the equation:


Formula (3)

was solved numerically with Ri the axial resistance per unit length (k{Omega}·cm) composed of myoplasmic (Rmyo=150 {Omega}·cm) and gap junctional (Rg=4 {Omega}·cm2) components, i.e. Ri=Rmyo+Rg/dx. This Rg was sufficient to establish a conduction velocity near 50 cm/s, and corresponded to a total Rj=Rg/(3.80x10–6 cm2) of 1.05 M{Omega} incorporating the membrane surface area for cell ends. This Rj is below reports of 1.7 and 5.7 M{Omega} for rat [46] and rabbit [47] ventricular cell pairs, respectively. The resistance between myocytes coupled in tissue is likely lower than that reported for cell pairs because of the disaggregation process. Increments in Rg reflected ischemic uncoupling and were therefore confined to the phase 1b segment. Stimuli were 2-ms duration square pulses of 200 µA/µF applied to the normal segment's end.

2.6.3 Charge measurements
Source–sink interactions were quantified with charge (Q) measurements achieved by temporal integration of Iion, the capacitive current (Icap=Cm dVm/dt>) and coupling currents (Ic). Because our focus was on the ability of spontaneous Irel to trigger superthreshold DADs, Qion, Qcap and Qc were determined over a 12-ms interval following that release.


   3. Results
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
4. Discussion
 References
 
3.1 Isolated myocytes
Phase 1b modifications caused sustained triggered activity. Fig. 1A shows Vm and [Ca2+]i recorded during the pacing protocol that established superthreshold DADs. Here, a 15-s pause allowed LRd variables to adjust to the collective phase 1b modifications. That settling period was followed by 5 s of pacing at a 400-ms cycle length to elevate SR Ca2+ content. Then, when pacing was terminated, persistent spontaneous Irel caused multiple [Ca2+]i transients. Fig. 1B shows Vm recorded under control conditions for all LRd variables during 400 ms pacing, with phase 1b modifications during 400 ms pacing, and with phase 1b modifications during a triggered response. The phase 1b changes depolarized resting Vm and shortened action potential duration, shown here as the time between the maximum temporal derivative and repolarization to 80% of action potential amplitude. Fig. 1C shows the accompanying changes to [Ca2+]i. Relative to control, the phase 1b modifications elevated end-diastolic [Ca2+]i 3.4-fold, although the rises in [Ca2+]i during CICR were comparable during 400 ms pacing. DADs resulted from spontaneous Irel, as evidenced by the [Ca2+]i transient that preceded the upstroke in the triggered traces.


Figure 1
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  		Fig. 1 (A) Pacing protocol used to study superthreshold DADs in a myocyte with phase 1b modifications. The top train shows action potentials. The bottom train shows [Ca2+]i transients. Stimulus times are marked below the action potentials. (B) Action potentials and (C) [Ca2+]i transients in response to pacing under control conditions, pacing of a phase 1b myocyte, and spontaneous Irel release in a phase 1b myocyte. Pacing was at a 400-ms cycle length. The paced phase 1b and triggered phase 1b records in B and C are from the responses marked in A.

 
Parameter modifications contributed to DAD formation to varying extents. To quantify those extents, we completed a set of simulations in which each modified parameter was adjusted over a range that included phase 1b and control conditions while all other parameters were set to phase 1b conditions. Fig. 2 shows the latency between the last paced response and the first spontaneous Irel following these adjustments. Graphs shown in Fig. 2A include parameters that had a marked influence on that latency. These included [Na+]i, NCX, ICa,B, Iup and Irel (during CICR). Of these parameters, the [Na+]i accumulation's influence was most pronounced. Graphs shown in Fig. 2B are for parameters whose influences on latency were more modest. These included [K+]e, [ATP]i, the Na+–K+ pump, ICa,L and Ins,Ca. Note differences in the vertical axes between Fig. 2A (0–20 s) and Fig. 2B (0–4 s).


Figure 2
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  		Fig. 2 Time between last stimulus and first spontaneous Irel in response to selective changes in the indicated model parameters. The filled arrow in each panel shows the control parameter value. The open arrow in each panel shows the phase 1b parameter value. All percentages are relative to the control LRd values. Graphs shown in A use a 0–20-s scale for latency. Graphs shown in B use a 0–4-s scale for latency.

 
Superthreshold DADs were established because Iti induced capacitive charging that brought the phase 1b myocyte to threshold. Fig. 3A shows Vm after spontaneous Irel in the first superthreshold response of the pause. After 12 ms, membrane depolarization to near the threshold Vm of –53.4 mV occurred. Fig. 3B shows Iion and Icap over this interval. Spontaneous Irel generated Qcap=Qion=2.14 pC. Fig. 3C shows the sarcolemmal currents that contributed to DAD formation. With these phase 1b modifications, Iti was {approx}10% NCX and {approx}90% Ins,Ca. For reference, the main outward currents opposing Iti are shown.


Figure 3
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  		Fig. 3 (A) Transmembrane potential, (B) capacitive and total ionic currents, and (C) Ins,Ca, NCX, IK,ATP and inward rectifier potassium (IK1) currents during spontaneous Irel in the phase 1b myocyte.

 
3.2 DAD suppression in cell pairs
Coupling of a single phase 1b myocyte to a normal myocyte suppressed DAD formation. This occurred because the Ic limited Qcap during spontaneous Irel and it hyperpolarized resting Vm in the phase 1b myocyte away from threshold. Fig. 4A shows Vm from the normal and phase 1b myocytes alongside Icap, Iion and Ic from the phase 1b myocyte during the first spontaneous Irel when the cells were coupled at Rj=8 M{Omega}. Only the normal myocyte was paced. Just before spontaneous Irel, outward Ic just balanced inward Iion at 2.05 µA/µF. After that release occurred, Qion measured 7.35 pC in the phase 1b myocyte. Of that charge, Qc of 5.92 pC was supplied to the normal myocyte, allowing Qcap of only 1.44 pC in the phase 1b myocyte. Fig. 4B shows these traces when Rj was raised to 145 M{Omega}, which was the critical value above which normal myocyte pacing failed to establish phase 1b myocyte excitation. With higher Rj, less of Qion from the phase 1b myocyte (3.79 pC) was supplied to the normal myocyte via coupling (Qc of 1.70 pC), which allowed Qcap of 2.09 pC in the phase 1b myocyte. Vm remained below threshold, however.


Figure 4
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  		Fig. 4 Transmembrane potentials from the normal and phase 1b myocytes (left side) alongside coupling, capacitive and total ionic currents (right side) from cell pair simulations with coupling at (A) Rj=8 M{Omega} and (B) Rj=145 M{Omega}. Marks below each transmembrane potential train show stimulus times.

 
Fig. 5A shows Qion in the phase 1b myocyte, Qc supplied to the normal myocyte and Qcap in the phase 1b myocyte for Rj values between those in Fig. 4. As Rj increased, Qion and Qc both decreased, but at slightly different rates. Because Qc decreased more rapidly than Qion, Qcap increased, although its magnitude remained well below that achieved in the isolated myocyte. Fig. 5B shows the resting Vm in the phase 1b and normal myocytes. For comparison, values for the isolated myocytes are shown. Coupling hyperpolarized resting Vm away from threshold in the phase 1b myocyte at all Rj studied.


Figure 5
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  		Fig. 5 (A) Charge measurements for coupling, capacitive and transient inward currents over the 12 ms following spontaneous SR Ca2+ release in the phase 1b myocyte over a range of coupling resistances in cell pair simulations. (B) Resting potentials from the normal and phase 1b myocytes from cell pair simulations.

 
3.3 Multicellular fiber simulations
Moderate uncoupling in the phase 1b segment of the multicellular fiber allowed sustained superthreshold DAD formation, as DADs were suppressed when all nodes were strongly coupled and propagation across the border failed with severe uncoupling. These different responses were directly related to Qc requirements at different myocytes on the fiber. For example, with Rj=1.05 M{Omega} on the normal and phase 1b segments, DAD suppression was graded, being most pronounced at the border. Fig. 6A (left side) shows Vm from the normal segment's center, the border and the phase 1b segment's center. The 5-s pacing interval and the first 10-s of the pause are shown. At the border, Qc of 27.8 pC was supplied to the normal segment and Qc of 14.6 pC was received from the phase 1b segment as compared to 13.9 and 14.8 pC for the same charge measurements in the phase 1b segment's center. This mismatch depended primarily on spatial differences in resting Vm. Fig. 6A (right side) shows Vm during spontaneous Irel from sites located at 1-mm steps between the border and the phase 1b segment's center. Note that increases in resting Vm corresponded with increased DAD magnitude.


Figure 6
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  		Fig. 6 (A) The left side shows transmembrane potentials from sites in the multicellular fiber model with Rj=1.05 M{Omega} between all nodes. The right side shows transmembrane potentials at sites equally distributed between the border and the phase 1b segment's center during spontaneous Irel. Panels B and C show the same records for simulations with uncoupling of the phase 1b segment to Rj=3.22 M{Omega} and Rj=9.25 M{Omega} between phase 1b myocytes. The arrow marks the direction for propagation in the phase 1b segment in B.

 
As phase 1b myocytes were uncoupled from one another and from the normal segment, DADs continued to be suppressed near the border but became superthreshold on the phase 1b segment's center. Fig. 6B shows Vm during pacing and the pause alongside waveforms recorded between the border and the phase 1b segment's center during first spontaneous Irel with Rj=3.22 M{Omega}. Superthreshold DADs triggered action potentials that propagated into the normal segment. Spontaneous Irel failed to establish superthreshold DADs at the border because coupling charge requirements remained high at this site, despite the moderate uncoupling.

With more severe uncoupling, further reduction of Qc mismatches that occurred closer to the border led to superthreshold DADs that triggered action potential propagation through the phase 1b segment. Fig. 6C shows Vm during pacing and the pause alongside waveforms recorded between the border and the phase 1b segment's center during first spontaneous Irel with Rj=9.5 M{Omega} at the border and on the phase 1b segment. The resulting source charge generated by those myocytes was not effectively supplied to the normal segment because of the severe uncoupling. Propagation failed at the border.


   4. Discussion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
References
 
Specific LRd parameters were adjusted to levels representing the physiologic changes attendant to phase 1b. These modifications promoted [Ca2+]i elevation and spontaneous Irel under conditions where sufficient Iti was generated to achieve superthreshold DADs in isolated myocyte simulations. The ability of such DADs to trigger excitation of adjacent normal myocardium, which must occur for phase 1b arrhythmias to be initiated by this mechanism, was then analyzed in cell pair and multicellular fiber simulations. Coupling charge requirements imposed by connected normal myocytes limited capacitive charging in response to Iti in phase 1b myocytes, causing DAD suppression at the border. However, superthreshold DAD formation distant from the border did occur. It triggered action potential propagation into normal myocytes when there was moderate uncoupling. This observation is consistent with reports that phase 1b arrhythmias occur during an interval of ischemic uncoupling, and suggests one possible mechanism for the trigger of such arrhythmias.

4.1 [Ca2+]i elevation, Iti enhancement and superthreshold DADs
Superthreshold DADs resulted because of the collective modifications. The ability of those changes to cause [Ca2+]i elevation was essential, as that elevation promoted the SR Ca2+ sequestration that gave rise to spontaneous Irel. While scrutiny of individual changes is appropriate given the integration of data for our selections from different species, cell types and experimental conditions, it is important to note that most of the changes had limited impact on the latency to first spontaneous Irel (Fig. 2). Furthermore, the magnitude of diastolic [Ca2+]i elevation (3.4-fold) was comparable to the indo-1 fluorescence elevation ({approx}3-fold) shown by Dekker et al. [12] in the 15–25-min period of no-flow ischemia with oxygen removal in their perfused rabbit papillary muscle experiments. That elevation was caused, primarily, by increased [Na+]i, increased ICa,B and reduced NCX in our simulations. The [Na+]i and NCX contributions were especially important in that they highlight Na+ overload as a potential contributor to phase 1b arrhythmias. Na+ overload resulting from Na+–H+ exchange and Na+–K+ pump inhibition that causes a secondary rise in [Ca2+]i that is mediated through NCX is an established mechanism for triggered arrhythmias [48]. In this regard, we note similarities between our findings and those of Ch’en et al. [19] support the overall changes we introduced to the phase 1b myocytes.

In our simulations, superthreshold DADs depended significantly upon Ins,Ca enhancement to provide sufficient Iti. Such enhancement is likely in the presence of free radicals [30]. Nevertheless, it is important to recognize potential inconsistencies between this enhancement and experimental reports. Iti is thought to be a combination of NCX, Ins,Ca and calcium activated chloride current (ICl(Ca)). Kass et al. [49] studied Iti in calf Purkinje fibers exposed to acetylstrophanthidin and concluded NCX and Ins,Ca contributed comparably. More recent experiments with isolated canine mid-myocardial myocytes exposed to isoproterenol and ouabain [50] and with isolated sheep Purkinje and ventricular myocytes exposed to norepinephrine [51] include estimates for Iti at {approx}60% NCX/{approx}40% ICl(Ca) and {approx}80% NCX/{approx}20% ICl(Ca), respectively. Our phase 1b modifications resulted in Iti of {approx}10% NCX/{approx}90% Ins,Ca. Although we believe the lack of an ICl(Ca) formulation for the LRd membrane equations and the experimental analyses of Iti contributions under conditions that differ from phase 1b support the large Ins,Ca contribution included here, we do recognize that inconsistency with these reports likely impacted our quantitative findings.

4.2 DAD suppression at the ischemic border
The finding that DADs were suppressed at the border in the cell pair and fiber simulations demonstrates the importance of source–sink relationships for triggered activity to initiate phase 1b arrhythmias. With the selected parameter modifications, source charge generation, reflected as Qion, was insufficient to overcome sink charge requirements, reflected as Qc. This response is consistent with the concept that membrane resistance is the primary determinant for the common Vm time course during strong coupling in cell pairs with intrinsic inhomogeneities. Using isolated rabbit ventricular myocytes with intrinsically low membrane resistance coupled to atrioventricular node cells with intrinsically high membrane resistance, Spitzer et al. [52] showed the common resting Vm at ventricular myocyte levels. Here, comparable membrane resistances between the normal and phase 1b myocytes led to an intermediate Vm (Fig. 5). Hyperpolarization of resting Vm away from threshold was an important component of this response.

The suppression of triggered activity that we observed during weak coupling differed, in a qualitative sense, from a number of experimental reports. In considering this behavior, it is important to recognize that resting Vm depolarization resulted from the selection of [K+]e at 9 mM to reflect measurements by Hill and Gettes [3] during the phase 1b interval. That [K+]e depolarized resting Vm to {approx}–75 mV. Much higher resting Vm was used to study triggered activity in isolated myocytes weakly coupled to passive RC circuits representing inexcitable and ischemic tissue [43]. For example, Kumar and Joyner [53] showed guinea pig ventricular myocytes exposed to isoproterenol, forskolin and Bay K8644 required injury current from the RC circuit with resting Vm near 0 mV and showed early afterdepolarizations (EADs) that only formed during weak coupling. Injury current that flowed from the circuit to the myocyte likely prolonged action potentials by a sufficient magnitude to allow recovery from inactivation of ICa,L. Huelsing et al. [54] showed rabbit Purkinje cell aggregates exposed to isoproterenol developed spontaneous activity during coupling to an RC circuit with resting Vm depolarization to –50 or –60 mV, and Verkerk et al. [55] showed sheep Purkinje and ventricular myocytes exposed to norepinephrine developed sustained superthreshold DADs during coupling to an RC circuit with Vm at –33 mV and above. Injury current supplied to the myocytes likely altered Vm time course to promote SR Ca2+ sequestration under these conditions. However, a major consequence of studying DAD formation with circuit coupling at such high resting Vm is that Qc adds to Qion to provide sufficient Qcap to raise the myocyte to threshold, which is a response that is less likely to occur at the [K+]e levels we associated with the phase 1b interval.

4.3 Triggered activity in multicellular fibers
The circumstances under which sustained triggered activity was established in the multicellular fiber simulations are illustrative in that they demonstrate initiation that occurred distant from the border required moderate uncoupling. Such uncoupling is closely associated with phase 1b arrhythmias in regionally ischemic hearts [1,2,11]. In fact, a recent intramural mapping investigation by de Groot et al. [13] showed that phase 1b arrhythmia induction by programmed pacing of regionally ischemic pig hearts was most pronounced as tissue resistance increased. Arrhythmias were reentrant, with slim lines of functional block in circuits that were largely confined to the subepicardium. They suggested depression of excitability in the subepicardium through residual coupling to depolarized midmyocardium formed an arrhythmia substrate that differed from the substrate associated with depressed excitability caused by hypoxia, hyperkalemia and acidosis. Our finding is potentially complimentary, in that it shows how phase 1b conditions that promote [Ca2+]i elevation [10,12] and cellular uncoupling [2,11], spatially modulate source–sink interactions imposed by the border. Under these conditions, uncoupling is an important component for the arrhythmia trigger as well as the arrythmia substrate.

4.4 Limitations
It is important to recognize certain additional limitations in the methodology in interpreting the overall results. (1) Parameter selections generally promoted SR Ca2+ sequestration by facilitating [Ca2+]i elevation with modest Iup inhibition. More severe Iup inhibition would necessarily have limited spontaneous Irel, with prevention of that Irel occurring below {approx}70% of control. (2) Elevated [Na+]i was achieved by setting initial conditions to reflect accumulation at 200% of control, based on data from rat experiments. Control [Na+]i in the LRd membrane equations is 10 mM, which is a relatively high value specific to guinea pig ventricular myocytes. Elevation to 20 mM to reflect the percentage increase may potentially have overestimated the magnitude of the [Na+]i increase that occurs under phase 1b conditions in guinea pig. (3) Simulations included a 15-s pause in advance of pacing to allow the LRd variable to achieve steady-state in response to the phase 1b modifications. That approach potentially introduced instabilities that facilitated spontaneous Irel. (4) Analyses were necessarily influenced by the pacing protocol. Pacing of the normal region was halted to monitor DAD development, and to analyze whether DADs were superthreshold. The important issue of whether triggered responses continued with normal segment pacing was not addressed. (5) Simulations were confined to one-dimensional representations of tissue structure. Modulation of source–sink interactions based on the geometry of the border between normal and phase 1b myocytes in a two- or three-dimensional setting would therefore be expected to alter our quantitative findings.

Time for primary review 28 days.


   Acknowledgements
 
This work was supported by National Science Foundation Award BES-9903466, American Heart Association Southeast Affiliate Award 0051196B and National Award 9740173N and National Heart, Lung and Blood Institute Awards HL67961, HL67728, HL52003 and HL27430.


   References
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 References
 

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