A rabbit ventricular action potential model replicating cardiac dynamics at rapid heart rates

Mathematical modeling of the cardiac action potential has proven to be a powerful tool for illuminating various aspects of cardiac function, including cardiac arrhythmias. However, no currently available detailed action potential model accurately reproduces the dynamics of the cardiac action potential and intracellular calcium (Ca_i) cycling at rapid heart rates relevant to ventricular tachycardia and fibrillation. The aim of this study was to develop such a model. Using an existing rabbit ventricular action potential model, we modified the L-type calcium (Ca) current (I_Ca,L) and Ca_i cycling formulations based on new experimental patch-clamp data obtained in isolated rabbit ventricular myocytes, using the perforated patch configuration at 35-37°C. Incorporating a minimal seven-state Markovian model of I_Ca,L that reproduced Ca- and voltage-dependent kinetics in combination with our previously published dynamic Ca_i cycling model, the new model replicates experimentally observed action potential duration and Ca_i transient alternans at rapid heart rates, and accurately reproduces experimental action potential duration restitution curves obtained by either dynamic or S1S2 pacing.     

Intracellular Ca alternans: coordinated regulation by sarcoplasmic reticulum release, uptake, and leak

Beat-to-beat alternation in the cardiac intracellular Ca (Ca_i) transient can drive action potential (AP) duration alternans, creating a highly arrhythmogenic substrate. Although a steep dependence of fractional sarcoplasmic reticulum (SR) Ca release on SR Ca load has been shown experimentally to promote Ca_i alternans, theoretical studies predict that other factors are also important. Here we present an iterated map analysis of the coordinated effects of SR Ca release, uptake, and leak on the onset of Ca_i alternans. Predictions were compared to numerical simulations using a physiologically realistic AP model as well as to AP clamp experiments in isolated patch-clamped rabbit ventricular myocytes exposed to 1), the Ca channel agonist BayK8644 (100 nM) to increase SR Ca load and release fraction, 2), overexpression of an adenoviral SERCA2a construct to increase SR Ca uptake, and 3), low-dose FK506 (20 μM) or ryanodine (1 μM) to increase SR Ca leak. Our findings show that SR Ca release, uptake, and leak all have independent direct effects that promote (release and leak) or suppress (uptake) Ca_i alternans. However, since each factor affects the other by altering SR Ca load, the net balance of their direct and indirect effects determines whether they promote or suppress alternans. Thus, BayK8644 promotes, whereas Ad-SERCA2a overexpression, ryanodine, and FK506 suppress, Ca_i alternans under AP clamp conditions.     

Targeting the late component of the cardiac L-type Ca2+ current to suppress early afterdepolarizations

Early afterdepolarizations (EADs) associated with prolongation of the cardiac action potential (AP) can create heterogeneity of repolarization and premature extrasystoles, triggering focal and reentrant arrhythmias. Because the L-type Ca²⁺ current (I_Ca,L) plays a key role in both AP prolongation and EAD formation, L-type Ca²⁺ channels (LTCCs) represent a promising therapeutic target to normalize AP duration (APD) and suppress EADs and their arrhythmogenic consequences. We used the dynamic-clamp technique to systematically explore how the biophysical properties of LTCCs could be modified to normalize APD and suppress EADs without impairing excitation–contraction coupling. Isolated rabbit ventricular myocytes were first exposed to H₂O₂ or moderate hypokalemia to induce EADs, after which their endogenous I_Ca,L was replaced by a virtual I_Ca,L with tunable parameters, in dynamic-clamp mode. We probed the sensitivity of EADs to changes in the (a) amplitude of the noninactivating pedestal current; (b) slope of voltage-dependent activation; (c) slope of voltage-dependent inactivation; (d) time constant of voltage-dependent activation; and (e) time constant of voltage-dependent inactivation. We found that reducing the amplitude of the noninactivating pedestal component of I_Ca,L effectively suppressed both H₂O₂- and hypokalemia-induced EADs and restored APD. These results, together with our previous work, demonstrate the potential of this hybrid experimental–computational approach to guide drug discovery or gene therapy strategies by identifying and targeting selective properties of LTCC.     

Suppression of ventricular arrhythmias by targeting late L-type Ca2+ current

Ventricular arrhythmias, a leading cause of sudden cardiac death, can be triggered by cardiomyocyte early afterdepolarizations (EADs). EADs can result from an abnormal late activation of L-type Ca²⁺ channels (LTCCs). Current LTCC blockers (class IV antiarrhythmics), while effective at suppressing EADs, block both early and late components of I_Ca,L, compromising inotropy. However, computational studies have recently demonstrated that selective reduction of late I_Ca,L (Ca²⁺ influx during late phases of the action potential) is sufficient to potently suppress EADs, suggesting that effective antiarrhythmic action can be achieved without blocking the early peak I_Ca,L, which is essential for proper excitation–contraction coupling. We tested this new strategy using a purine analogue, roscovitine, which reduces late I_Ca,L with minimal effect on peak current. Scaling our investigation from a human Ca_V1.2 channel clone to rabbit ventricular myocytes and rat and rabbit perfused hearts, we demonstrate that (1) roscovitine selectively reduces I_Ca,L noninactivating component in a human Ca_V1.2 channel clone and in ventricular myocytes native current, (2) the pharmacological reduction of late I_Ca,L suppresses EADs and EATs (early after Ca²⁺ transients) induced by oxidative stress and hypokalemia in isolated myocytes, largely preserving cell shortening and normal Ca²⁺ transient, and (3) late I_Ca,L reduction prevents/suppresses ventricular tachycardia/fibrillation in ex vivo rabbit and rat hearts subjected to hypokalemia and/or oxidative stress. These results support the value of an antiarrhythmic strategy based on the selective reduction of late I_Ca,L to suppress EAD-mediated arrhythmias. Antiarrhythmic therapies based on this idea would modify the gating properties of Ca_V1.2 channels rather than blocking their pore, largely preserving contractility.     

Feedback-control induced pattern formation in cardiac myocytes: A mathematical modeling study

Cardiac alternans is a dangerous rhythm disturbance of the heart, in which rapid stimulation elicits a beat-to-beat alternation in the action potential duration (APD) and calcium (Ca) transient amplitude of individual myocytes. Recently, “subcellular alternans”, in which the Ca transients of adjacent regions within individual myocytes alternate out-of-phase, has been observed. A previous theoretical study suggested that subcellular alternans may result during static pacing from a Turing-type symmetry breaking instability, but this was only predicted in a subset of cardiac myocytes (with negative Ca to voltage (Ca→V_m) coupling) and has never been directly verified experimentally. A recent experimental study, however, showed that subcellular alternans is dynamically induced in the remaining subset of myocytes during pacing with a simple feedback control algorithm (“alternans control”). Here we show that alternans control pacing changes the effective coupling between the APD and the Ca transient (V_m→Ca coupling), such that subcellular alternans is predicted to occur by a Turing instability in cells with positive Ca→V_m coupling. In addition to strengthening the understanding of the proposed mechanism for subcellular alternans formation, this work (in concert with previous theoretical and experimental results) illuminates subcellular alternans as a striking example of a biological Turing instability in which the diffusing morphogens can be clearly identified.     

Ca2+-activated chloride channel activity during Ca2+ alternans in ventricular myocytes

Cardiac alternans, defined beat-to-beat alternations in contraction, action potential (AP) morphology or cytosolic Ca transient (CaT) amplitude, is a high risk indicator for cardiac arrhythmias. We investigated mechanisms of cardiac alternans in single rabbit ventricular myocytes. CaTs were monitored simultaneously with membrane currents or APs recorded with the patch clamp technique. A strong correlation between beat-to-beat alternations of AP morphology and CaT alternans was observed. During CaT alternans application of voltage clamp protocols in form of pre-recorded APs revealed a prominent Ca²⁺-dependent membrane current consisting of a large outward component coinciding with AP phases 1 and 2, followed by an inward current during AP repolarization. Approximately 85% of the initial outward current was blocked by Cl^? channel blocker DIDS or lowering external Cl^? concentration identifying it as a Ca²⁺-activated Cl^? current (I_CaCC). The data suggest that I_CaCC plays a critical role in shaping beat-to-beat alternations in AP morphology during alternans.     

A computational model of pig ventricular cardiomyocyte electrophysiology and calcium handling: Translation from pig to human electrophysiology

The pig is commonly used as an experimental model of human heart disease, including for the study of mechanisms of arrhythmia. However, there exist differences between human and porcine cellular electrophysiology: The pig action potential (AP) has a deeper phase-1 notch, a longer duration at 50% repolarization, and higher plateau potentials than human. Ionic differences underlying the AP include larger rapid delayed-rectifier and smaller inward-rectifier K⁺-currents (I_Kr and I_K1 respectively) in humans. AP steady-state rate-dependence and restitution is steeper in pigs. Porcine Ca²⁺ transients can have two components, unlike human. Although a reliable computational model for human ventricular myocytes exists, one for pigs is lacking. This hampers translation from results obtained in pigs to human myocardium. Here, we developed a computational model of the pig ventricular cardiomyocyte AP using experimental datasets of the relevant ionic currents, Ca²⁺-handling, AP shape, AP duration restitution, and inducibility of triggered activity and alternans. To properly capture porcine Ca²⁺ transients, we introduced a two-step process with a faster release in the t-tubular region, followed by a slower diffusion-induced release from a non t-tubular subcellular region. The pig model behavior was compared with that of a human ventricular cardiomyocyte (O’Hara-Rudy) model. The pig, but not the human model, developed early afterdepolarizations (EADs) under block of I_K1, while I_Kr block led to EADs in the human but not in the pig model. At fast rates (pacing cycle length = 400 ms), the human cell model was more susceptible to spontaneous Ca²⁺ release-mediated delayed afterdepolarizations (DADs) and triggered activity than pig. Fast pacing led to alternans in human but not pig. Developing species-specific models incorporating electrophysiology and Ca^2+-handling provides a tool to aid translating antiarrhythmic and arrhythmogenic assessment from the bench to the clinic.     

Spatially Discordant Alternans and Arrhythmias in Tachypacing-Induced Cardiac Myopathy in Transgenic LQT1 Rabbits: The Importance of IKs and Ca2+ Cycling

BackgroundRemodeling of cardiac repolarizing currents, such as the downregulation of slowly activating K⁺ channels (I_Ks), could underlie ventricular fibrillation (VF) in heart failure (HF). We evaluated the role of I_ks remodeling in VF susceptibility using a tachypacing HF model of transgenic rabbits with Long QT Type 1 (LQT1) syndrome.ConclusionsCompared with LMC-TICM, LQT1-TICM rabbits exhibit steepened APD restitution and complex DA modulated by Ca²⁺. Our results strongly support the contention that the downregulation of I_Ks in HF increases Ca²⁺ dependent alternans and thereby the risk of VF.     

Distinct Patterns of Constitutive Phosphodiesterase Activity in Mouse Sinoatrial Node and Atrial Myocardium

Phosphodiesterases (PDEs) are critical regulators of cyclic nucleotides in the heart. In ventricular myocytes, the L-type Ca²⁺ current (I_Ca,L) is a major target of regulation by PDEs, particularly members of the PDE2, PDE3 and PDE4 families. Conversely, much less is known about the roles of PDE2, PDE3 and PDE4 in the regulation of action potential (AP) properties and I_Ca,L in the sinoatrial node (SAN) and the atrial myocardium, especially in mice. Thus, the purpose of our study was to measure the effects of global PDE inhibition with Isobutyl-1-methylxanthine (IBMX) and selective inhibitors of PDE2, PDE3 and PDE4 on AP properties in isolated mouse SAN and right atrial myocytes. We also measured the effects of these inhibitors on I_Ca,L in SAN and atrial myocytes in comparison to ventricular myocytes. Our data demonstrate that IBMX markedly increases spontaneous AP frequency in SAN myocytes and AP duration in atrial myocytes. Spontaneous AP firing in SAN myocytes was also increased by the PDE2 inhibitor erythro-9-[2-hydroxy-3-nonyl] adenine (EHNA), the PDE3 inhibitor milrinone (Mil) and the PDE4 inhibitor rolipram (Rol). In contrast, atrial AP duration was increased by EHNA and Rol, but not by Mil. IBMX also potently, and similarly, increased I_Ca,L in SAN, atrial and ventricular myocytes; however, important differences emerged in terms of which inhibitors could modulate I_Ca,L in each myocyte type. Consistent with our AP measurements, EHNA, Mil and Rol each increased I_Ca,L in SAN myocytes. Also, EHNA and Rol, but not Mil, increased atrial I_Ca,L. In complete contrast, no selective PDE inhibitors increased I_Ca,L in ventricular myocytes when given alone. Thus, our data show that the effects of selective PDE2, PDE3 and PDE4 inhibitors are distinct in the different regions of the myocardium indicating important differences in how each PDE family constitutively regulates ion channel function in the SAN, atrial and ventricular myocardium.     

Cardiac alternans in embryonic mouse ventricles

T-wave alternans, an important arrhythmogenic factor, has recently been described in human fetuses. Here we sought to determine whether alternans can be induced in the embryonic mouse hearts, despite its underdeveloped sarcoplasmic reticulum (SR) and, if so, to analyze the response to pharmacological and autonomic interventions. Immunohistochemistry confirmed minimal sarcoplasmic-endoplasmic reticulum Ca-ATPase 2a expression in embryonic mouse hearts at embryonic day (E) 10.5 to E12.5, compared with neonatal or adult mouse hearts. We optically mapped voltage and/or intracellular Ca (Ca(i)) in 99 embryonic mouse hearts (dual mapping in 64 hearts) at these ages. Under control conditions, ventricular action potential duration (APD) and Ca(i) transient alternans occurred during rapid pacing at an average cycle length of 212 +/- 34 ms in 57% (n = 15/26) of E10.5-E12.5 hearts. Maximum APD restitution slope was steeper in hearts developing alternans than those that did not (2.2 +/- 0.6 vs. 0.8 +/- 0.4; P < 0.001). Disabling SR Ca(i) cycling with thapsigargin plus ryanodine did not significantly reduce alternans incidence (44%, n = 8/18, P = 0.5), whereas isoproterenol (n = 14) increased the incidence to 100% (P < 0.05), coincident with steepening APD restitution slope. Verapamil abolished Ca(i) transients (n = 9). Thapsigargin plus ryanodine had no major effects on Ca(i)-transient amplitude or its half time of recovery in E10.5 hearts, but significantly depressed Ca(i)-transient amplitude (by 47 +/- 8%) and prolonged its half time of recovery (by 18 +/- 3%) in E11.5 and older hearts. Embryonic mouse ventricles can develop cardiac alternans, which generally is well correlated with APD restitution slope and does not depend on fully functional SR Ca(i) cycling.     

Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation

Cellular electrophysiology experiments, important for understanding cardiac arrhythmia mechanisms, are usually performed with channels expressed in non myocytes, or with non-human myocytes. Differences between cell types and species affect results. Thus, an accurate model for the undiseased human ventricular action potential (AP) which reproduces a broad range of physiological behaviors is needed. Such a model requires extensive experimental data, but essential elements have been unavailable. Here, we develop a human ventricular AP model using new undiseased human ventricular data: Ca(2+) versus voltage dependent inactivation of L-type Ca(2+) current (I(CaL)); kinetics for the transient outward, rapid delayed rectifier (I(Kr)), Na(+)/Ca(2+) exchange (I(NaCa)), and inward rectifier currents; AP recordings at all physiological cycle lengths; and rate dependence and restitution of AP duration (APD) with and without a variety of specific channel blockers. Simulated APs reproduced the experimental AP morphology, APD rate dependence, and restitution. Using undiseased human mRNA and protein data, models for different transmural cell types were developed. Experiments for rate dependence of Ca(2+) (including peak and decay) and intracellular sodium ([Na(+)](i)) in undiseased human myocytes were quantitatively reproduced by the model. Early afterdepolarizations were induced by I(Kr) block during slow pacing, and AP and Ca(2+) alternans appeared at rates >200 bpm, as observed in the nonfailing human ventricle. Ca(2+)/calmodulin-dependent protein kinase II (CaMK) modulated rate dependence of Ca(2+) cycling. I(NaCa) linked Ca(2+) alternation to AP alternans. CaMK suppression or SERCA upregulation eliminated alternans. Steady state APD rate dependence was caused primarily by changes in [Na(+)](i), via its modulation of the electrogenic Na(+)/K(+) ATPase current. At fast pacing rates, late Na(+) current and I(CaL) were also contributors. APD shortening during restitution was primarily dependent on reduced late Na(+) and I(CaL) currents due to inactivation at short diastolic intervals, with additional contribution from elevated I(Kr) due to incomplete deactivation.     

Systematic characterization of the ionic basis of rabbit cellular electrophysiology using two ventricular models

Several mathematical models of rabbit ventricular action potential (AP) have been proposed to investigate mechanisms of arrhythmias and excitation-contraction coupling. Our study aims at systematically characterizing how ionic current properties modulate the main cellular biomarkers of arrhythmic risk using two widely-used rabbit ventricular models, and comparing simulation results using the two models with experimental data available for rabbit. A sensitivity analysis of AP properties, Ca²⁺ and Na⁺ dynamics, and their rate dependence to variations (±15% and ±30%) in the main transmembrane current conductances and kinetics was performed using the Shannon et al. (2004) and the [Mahajan et?al., 2008a] and [Mahajan et?al., 2008b] AP rabbit models. The effects of severe transmembrane current blocks (up to 100%) on steady-state AP and calcium transients, and AP duration (APD) restitution curves were also simulated using both models. Our simulations show that, in both virtual rabbit cardiomyocytes, APD is significantly modified by most repolarization currents, AP triangulation is regulated mostly by the inward rectifier K⁺ current (I_K1) whereas APD rate adaptation as well as [Na⁺]_i rate dependence is influenced by the Na⁺/K⁺ pump current (I_NaK). In addition, steady-state [Ca²⁺]_i levels, APD restitution properties and [Ca²⁺]_i rate dependence are strongly dependent on I_NaK, the L-Type Ca²⁺ current (I_CaL) and the Na⁺/Ca²⁺ exchanger current (I_NaCa), although the relative role of these currents is markedly model dependent. Furthermore, our results show that simulations using both models agree with many experimentally-reported electrophysiological characteristics. However, our study shows that the Shannon et al. model mimics rabbit electrophysiology more accurately at normal pacing rates, whereas Mahajan et al. model behaves more appropriately at faster rates. Our results reinforce the usefulness of sensitivity analysis for further understanding of cellular electrophysiology and validation of cardiac AP models.     

Lysophosphatidic Acid Increases the Electrophysiological Instability of Adult Rabbit Ventricular Myocardium by Augmenting L-Type Calcium Current

Lysophosphatidic acid (LPA) has diverse actions on the cardiovascular system and is widely reported to modulate multiple ion currents in some cell types. However, little is known about its electrophysiological effects on cardiac myocytes. This study investigated whether LPA has electrophysiological effects on isolated rabbit myocardial preparations. The results indicate that LPA prolongs action potential duration at 90% repolarization (APD₉₀) in a concentration- and frequency-dependent manner in isolated rabbit ventricular myocytes. The application of extracellular LPA significantly increases the coefficient of APD₉₀ variability. LPA increased L-type calcium current (I_Ca,L) density without altering its activation or deactivation properties. In contrast, LPA has no effect on two other ventricular repolarizing currents, the transient outward potassium current (I_to) and the delayed rectifier potassium current (I_K). In arterially perfused rabbit left ventricular wedge preparations, the monophasic action potential duration, QT interval, and Tpeak-end are prolonged by LPA. LPA treatment also significantly increases the incidence of ventricular tachycardia induced by S₁S₂ stimulation. Notably, the effects of LPA on action potentials and I_Ca,L are PTX-sensitive, suggesting LPA action requires a G_i-type G protein. In conclusion, LPA prolongs APD and increases electrophysiological instability in isolated rabbit myocardial preparations by increasing I_Ca,L in a G_i protein-dependent manner.     

β3-Adrenergic Regulation of L-Type Ca2+ Current and Force of Contraction in Human Ventricle

β₃-Adrenergic receptor (β₃-AR) is expressed in human atrial and ventricular tissues. Recently, we have demonstrated that it was involved in the activation of L-type Ca²⁺ current (I _Ca,L) in human atrial myocytes and the force of contraction of human atrial trabeculae. In the present study, we examined the effect of β₃-AR agonist CGP12177 which also is a β₁-AR/β₂-AR antagonist on I _Ca,L in human ventricular myocytes (HVMs) and the force of contraction of human ventricular trabeculae. CGP12177 stimulated I _Ca,L in HVMs with high potency but much lower efficacy than isoprenaline. The β₃-AR antagonist L-748,337 inhibited the effect of CGP12177. CGP12177 and L748,337 competed selectively on β₃-ARs because L748,337 had no effect on isoprenaline-induced stimulation of I _Ca,L, while CGP12177 completely blocked the effect of isoprenaline. The activation of β₃-ARs by CGP12177 does not involve the activation of G_i proteins because CGP12177 had no effect on forskolin-induced stimulation of I _Ca,L. CGP12177 had no effect on the force of contraction of human ventricular trabeculae. L-NMMA, an inhibitor of NO synthase, and IBMX, a nonselective inhibitor of phosphodiesterases, did not potentiate the effect of CGP12177 either on contraction of human ventricular trabeculae or on I _Ca,L in HVMs. We conclude that in human ventricles β₃-AR activation has no inotropic effect, while it slightly increases I _Ca,L. In contrast to human atrium, the activation of β₃-ARs in human ventricle is not accompanied by increased activity of phosphodiesterases.     

Effect of beta-adrenergic blockade on dynamic electrical restitution in vivo

The slope of the action potential duration (APD) restitution curve may be a significant determinant of the propensity to develop ventricular fibrillation, with steeper slopes associated with a more arrhythmogenic substrate. We hypothesized that one mechanism by which beta-blockers reduce sudden cardiac death is by flattening the APD restitution curve. Therefore, we investigated whether infusion of esmolol modulates the APD restitution curve in vivo. In 10 Yorkshire pigs, dynamic APD restitution curves were determined from measurements of APD at 90% repolarization with a monophasic action potential catheter positioned against the right ventricular septum during right ventricular apical pacing in the basal state and during infusion of esmolol. APD restitution curves were fitted to the three-parameter (a, b, c) exponential equation, APD = a.[1 - e((-b.DI))] + c, where DI is the diastolic interval. Esmolol decreased the maximal APD slope, 0.68 +/- 0.14 vs. 0.94 +/- 0.24 (baseline), P = 0.002, and flattened the APD restitution curve at shorter DIs, 75 and 100 ms (P < 0.05). To compare the slopes of the APD restitution curves at similar steady states, slopes were also computed at points of intersection between the restitution curve and the lines representing pacing at a fixed cycle length (CL) of 200, 225, 250, 275, and 300 ms using the relationship CL = APD + DI. Esmolol decreased APD restitution slopes at CLs 200-275 ms (P < 0.05). Esmolol flattens the cardiac APD restitution curve in vivo, particularly at shorter CLs and DIs. This may represent a novel mechanism by which beta-blockers prevent sudden cardiac death.     

L-type calcium current in right ventricular outflow tract myocytes of rabbit heart

The mechanism of idiopathic ventricular tachycardia originating from the right ventricular outflow tract (RVOT) is not clear. Many clinical reports have suggested a mechanism of triggered activity. However, there are few studies investigating this because of the technical difficulties associated with examining this theory. The L-type calcium current (I _Ca-L), an important inward current of the action potential (AP), plays an important role in arrhythmogenesis. The aim of this study was to explore differences in the APs of right ventricular (RV) and RVOT cardiomyocytes, and differences in electrophysiological characteristics of the ICa-L in these myocytes. Rabbit RVOT and RV myocytes were isolated and their AP and I _Ca-L were investigated using the patch-clamp technique. RVOT cardiomyocytes had a wider range of AP duration (APD) than RV cardiomyocytes, with some markedly prolonged APDs and markedly shortened APDs. The markedly shortened APDs in RVOT myocytes were abolished by treatment with 4-AP, an inhibitor of the transient outward potassium current, but the markedly prolonged APDs remained, with some myocytes with a long AP plateau not repolarizing to resting potential. In addition, early afterdepolarization (EAD) and second plateau responses were seen in RVOT myocytes but not in RV myocytes. RVOT myocytes had a higher current density for I _Ca-L than RV myocytes (RVOT (13.16±0.87) pA pF⁻¹, RV (8.59±1.97) pA pF⁻¹; P<0.05). The I _Ca-L and the prolonged APD were reduced, and the EAD and second plateau response disappeared, after treatment with nifedipine (10 μmol L⁻¹), which blocks the I _Ca-L. In conclusion, there was a wider range of APDs in RVOT myocytes than in RV myocytes, which is one of the basic factors involved in arrhythmogenesis. The higher current density for I _Ca-L is one of the factors causing prolongation of the APD in RVOT myocytes. The combination of EAD with prolonged APD may be one of the mechanisms of RVOT-VT generation.     

The Transfer Functions of Cardiac Tissue during Stochastic Pacing

The restitution properties of cardiac action potential duration (APD) and conduction velocity (CV) are important factors in arrhythmogenesis. They determine alternans, wavebreak, and the patterns of reentrant arrhythmias. We developed a novel approach to characterize restitution using transfer functions. Transfer functions relate an input and an output quantity in terms of gain and phase shift in the complex frequency domain. We derived an analytical expression for the transfer function of interbeat intervals (IBIs) during conduction from one site (input) to another site downstream (output). Transfer functions can be efficiently obtained using a stochastic pacing protocol. Using simulations of conduction and extracellular mapping of strands of neonatal rat ventricular myocytes, we show that transfer functions permit the quantification of APD and CV restitution slopes when it is difficult to measure APD directly. We find that the normally positive CV restitution slope attenuates IBI variations. In contrast, a negative CV restitution slope (induced by decreasing extracellular [K⁺]) amplifies IBI variations with a maximum at the frequency of alternans. Hence, it potentiates alternans and renders conduction unstable, even in the absence of APD restitution. Thus, stochastic pacing and transfer function analysis represent a powerful strategy to evaluate restitution and the stability of conduction.     

Dynamic origin of spatially discordant alternans in cardiac tissue

Alternans, a condition in which there is a beat-to-beat alternation in the electromechanical response of a periodically stimulated cardiac cell, has been linked to the genesis of life-threatening ventricular arrhythmias. Optical mapping of membrane voltage (V_m) and intracellular calcium (Ca_i) on the surface of animal hearts reveals complex spatial patterns of alternans. In particular, spatially discordant alternans has been observed in which regions with a large-small-large action potential duration (APD) alternate out-of-phase adjacent to regions of small-large-small APD. However, the underlying mechanisms that lead to the initiation of discordant alternans and govern its spatiotemporal properties are not well understood. Using mathematical modeling, we show that dynamic changes in the spatial distribution of discordant alternans can be used to pinpoint the underlying mechanisms. Optical mapping of V_m and Ca_i in paced rabbit hearts revealed that spatially discordant alternans induced by rapid pacing exhibits properties consistent with a purely dynamical mechanism as shown in theoretical studies. Our results support the viewpoint that spatially discordant alternans in the heart can be formed via a dynamical pattern formation process which does not require tissue heterogeneity.     

Effects of [K(+)](o) on electrical restitution and activation dynamics during ventricular fibrillation

To test whether hyperkalemia suppresses ventricular fibrillation (VF) by reducing the slope of the action potential duration (APD) restitution relation, we determined the effects of the extracellular K(+) concentration ([K(+)](o)) ([KCl] = 2.7-12 mM) on the restitution of APD and maximum upstroke velocity (V(max)) the magnitude of APD alternans and spatiotemporal organization during VF in isolated canine ventricle. As [KCl] was increased incrementally from 2.7 to 12 mM, V(max) was reduced progressively. Increasing [KCl] from 2.7 to 10 mM decreased the slope of the APD restitution relation at long, but not short, diastolic intervals (DI), decreased the range of DI over which the slope was >/=1, and reduced the maximum amplitude of APD alternans. At [KCl] = 12 mM, the range of DI over which the APD restitution slope was >/=1 increased, and the maximum amplitude of APD alternans increased. For [KCl] = 4-8 mM, the persistence of APD alternans at short DI was associated with maintenance of VF. For [KCl] = 10-12 mM, the spontaneous frequency during VF was reduced, and activation occurred predominantly at longer DI. The lack of APD alternans at longer DI was associated with conversion of VF to a periodic rhythm. These results provide additional evidence for the importance of APD restitution kinetics in the development of VF.     

Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects

We examine the utility of the action potential (AP) duration (APD) restitution curve slope in predicting the onset of electrical alternans when electrotonic and memory effects are considered. We develop and use two ionic cell models without memory that have the same restitution curve with slope >1 but different AP shapes and, therefore, different electrotonic effects. We also study a third cell model that incorporates short-term memory of previous cycle lengths, so that it has a family of S1-S2 restitution curves as well as a dynamic restitution curve with slope >1. Our results indicate that both electrotonic and memory effects can suppress alternans, even when the APD restitution curve is steep. In the absence of memory, electrotonic currents related to the shape of the AP, as well as conduction velocity restitution, can affect how alternans develops in tissue and, in some cases, can prevent its induction entirely, even when isolated cells exhibit alternans. When short-term memory is included, alternans may not occur in isolated cells, despite a steep APD restitution curve, and may or may not occur in tissue, depending on conduction velocity restitution. We show for the first time that electrotonic and memory effects can prevent conduction blocks and stabilize reentrant waves in two and three dimensions. Thus we find that the slope of the APD restitution curve alone does not always well predict the onset of alternans and that incorporating electrotonic and memory effects may provide a more useful alternans criterion.