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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Mol Cell Cardiol. Author manuscript; available in PMC 2011 January 1.
Published in final edited form as:
PMCID: PMC2813400

A Novel Computational Model of the Human Ventricular Action Potential and Ca Transient


We have developed a detailed mathematical model for Ca handling and ionic currents in the human ventricular myocyte. Our aims were to: 1) simulate basic excitation-contraction coupling phenomena; 2) use realistic repolarizing K current densities; 3) reach steady-state. The model relies on the framework of the rabbit myocyte model previously developed by our group, with subsarcolemmal and junctional compartments where ion channels sense higher [Ca] vs. bulk cytosol. Ion channels and transporters have been modeled on the basis of the most recent experimental data from human ventricular myocytes. Rapidly and slowly inactivating components of Ito have been formulated to differentiate between endocardial and epicardial myocytes. Transmural gradients of Ca handling proteins and Na pump were also simulated. The model has been validated against a wide set of experimental data including action potential duration (APD) adaptation and restitution, frequency-dependent increase in Ca transient peak and [Na]i. Interestingly, Na accumulation at fast heart rate is a major determinant of APD shortening, via outward shifts in Na pump and Na-Ca exchange currents. We investigated the effects of blocking K currents on APD and repolarization reserve: IKs block does not affect the former and slightly reduces the latter; IK1 blockade modestly increases APD and more strongly reduces repolarization reserve; IKr blockers significantly prolong APD, an effect exacerbated as pacing frequency is decreased, in good agreement with experimental results in human myocytes. We conclude that this model provides a useful framework to explore excitation-contraction coupling mechanisms and repolarization abnormalities at the single myocyte level.

Keywords: Human ventricular myocyte, computer model, K current block, reverse rate-dependence


In the past years, mathematical modeling has become an important tool in understanding cardiac electrophysiology and its derangements (e.g. arrhythmias). Models of excitation-contraction coupling (ECC) in several species have been developed (such as guinea pig [1], rabbit [2], mouse [3] and canine [4]) and proven useful to study the mechanisms underlying disturbances of cardiac electrophysiology due to various conditions [5] or the effects of drugs [6]. Although these animal models are commonly used to study cellular cardiac electrophysiology in a range of disease states, animal and human cardiomyocytes differ in important aspects that may influence the arrhythmogenic mechanisms, such as action potential (AP) shape, duration (APD) and restitution, range of normal heart rates, and relative contribution of ionic currents (where density and kinetics vary among species) to AP repolarization. There are recent mathematical models of electrical and ionic homeostasis in human ventricular myocytes [7-11]. Among these, the Panfilov group has comprehensively modeled the individual currents generating an AP, with APD and conduction velocity restitution properties in agreement with experimental measurements (TNNP04 and TP06) [8, 10]. Reduced versions of these models were also implemented for large-scale spatial simulations [9, 12]. Another relevant model for human ventricular myocytes was published in 2004 by Iyer et al. (IMW) [11]. This model addresses whole-cell Ca homeostasis carefully and accurately reproduces diverse aspects of ECC. The most relevant ionic currents are formulated with Markovian chains, which make this model much more complex than those previously described.

Each of the existing models has particular strengths (and weaknesses) and may be more suited for certain investigations; however, some issues unresolved in current models are: 1) the quantitative importance of individual K currents for AP repolarization; 2) the rate-dependence of AP prolongation upon K channel block, and 3) the cause of APD shortening at faster heart rates. Thus, use of these models to predict alterations of AP repolarization due to drugs or diseases should be made with caution. In addition, since the introduction of many of these models in their original form, new information regarding human myocytes electrophysiology has become available. For example, the increase in [Ca] upon Ca-induced Ca release appears to be higher just under the sarcolemma than in bulk cytosol, and this higher [Ca] is detected by Na-Ca exchanger (NCX) [13]. Here we have taken advantage of the rabbit ECC model developed by Shannon et al. [2], which includes this additional subsarcolemmal compartment (SL) and provides a detailed description of Ca handling. We also provide updated ionic currents densities and kinetics based on the most recent experimental measurements in human myocytes.

The resulting model is stable and capable of reproducing diverse behaviors measured experimentally in isolated human ventricular myocytes including: 1) AP shape of epicardial and endocardial cells; 2) Ca transient morphology and kinetics; 3) rate-dependent changes of APD, Ca transient and [Na]i; 4) APD restitution; 5) effect of blocking K currents on APD.


Model development

The ventricular AP model relies on the framework of the rabbit myocyte model developed by Shannon et al. [2] including both a cleft space (between sarcoplasmic reticulum (SR) and sarcolemmal membrane) where Ca induced Ca release occurs, and a separate SL compartment, which is a narrow space just under the rest of the cell membrane. The human myocyte model consists of a system of 38 ordinary differential equations describing the rate of change of membrane potential, gating variables describing the kinetics of ion channels, intracellular concentrations of Na and Ca ions, and the dynamics of intracellular Ca cycling processes. Model equations and parameters are given in the Online Appendix. Fitting of fast sodium and L-type calcium currents is shown in supplementary Figures S1 and S2. Here, a brief description of K current fitting is provided. The Na-Ca exchanger was formulated as described in [13] and implemented in Shannon et al. [2], as well as Na pump, Ca-activated Cl, background Na, Ca, K and Cl currents.

Slowly activating delayed rectifier K current IKs

IKs has been modeled to fit steady-state activation (Figure 1A), tail current magnitudes (Figure 1C), time constants of activation (Figure 1B and D) and deactivation (Figure 1B) obtained at physiological temperature by Virág et al. [14]. IKs conductance was set to 0.0035 mS/μF to match tail current magnitudes measured in human ventricle (Figure 1C).

Figure 1
Gating properties of IKs. Model curves (lines) and data (symbols) from Li et al. [48] and Virág et al. [14] are shown. A: Steady-state activation. B: Activation and deactivation time constants. C: Current-voltage relationship. Tail IKs was measured ...

Rapidly activating delayed rectifier K current IKr

IKr steady-state curves (not shown) reflect experimental data from Zhou et al. [15] (activation) and Johnson et al. [16] (inactivation). Time constants of activation and deactivation are derived from experiments performed by Jost et al. [17, 18] at 37°C (Figure 2A). IKr conductance was set to 0.035 mS/μF to match tail current recordings in human ventricular myocytes [19] (Figure 2B). Simulated IKr during an envelope of tails protocol is depicted in Figure 2C.

Figure 2
Gating properties of IKr and IK1. Model curves (lines) and data (symbols) from Jost et al. [17, 18], Iost et al. [19] and Magyar et al. [20] are shown. A: Activation and deactivation time constants. B: IKr current-voltage relationship. Tail IKr was measured ...

Inward rectifier K current IK1

Figure 2D shows the good agreement of our IK1 model with experimental current-voltage curves obtained by Magyar et al. [20] and Jost et al. [17, 18] at physiological temperature.

Transient outward K current Ito

Two components of Ito are found in the human ventricle: Ito,fast exhibiting fast recovery from inactivation and Ito,slow exhibiting relatively slow kinetics of recovery from inactivation. Slow and fast components were formulated based on the steady-state data (Figure 3A, B and F) from Näbauer et al. [21] and the kinetic data obtained at 37°C by Näbauer et al. [21], Wettwer et al. [22] and Varró et al. [23] (Figure 3C-E and G). In epicardial myocytes the fast component is dominant, whereas endocardial cells lack appreciable Ito,fast [21]. Accordingly, in our epicardial digital cell, Ito,fast comprises 88% of total Ito, whereas in endocardial cells the slowly recovering component accounts for most of Ito (96.4%). Figure 3G shows the agreement between the simulated and experimental (Varró et al. [23] and Näbauer et al. [21]) Ito recovery from inactivation in human epicardial and endocardial myocytes. Total Ito conductance was set to 0.13 mS/μF in epicardium and 0.04 mS/μF in endocaridum to match the experimental current-voltage relationship from Varró et al. [23] and Näbauer et al. [21] (Figure 3F). There may be additional epi- endocardial difference in ion channel/transporters that could be included, but our baseline model does not incorporate these (see online supplement).

Figure 3
Gating properties of Ito. Model curves (lines) and data (symbols) from Näbauer et al. [21], Wettwer et al. [22] and Varró et al. [23] are shown. A: Steady-state activation. B: Steady-state inactivation. C: Activation time constants of ...

Numerical implementation and simulations

Model differential equations were implemented in Matlab (Mathworks Inc., Natick, MA, U.S.A.) and solved numerically using a variable order solver (ode15s) [24]. APD was measured as the interval between AP upstroke and 90% repolarization level (APD90). APD restitution was assessed with a dynamic protocol: after establishing a steady-state at a basic cycle length of 600 ms, extrastimuli were applied at 20 cycle intervals, reducing the coupling interval in decrements of 40, 20 and 10 ms from the drive cycle length. Stimuli were also delivered at coupling intervals larger than the steady-state drive cycle length as in Morgan et al. [25].


AP and Ca transient characteristics

In Figure 4A a steady-state epicardial AP simulated at 1 Hz pacing rate is depicted. The AP shows the characteristic spike notch dome morphology found for epicardial cells. APD is 283 ms, resting potential is −81.3 mV, maximum plateau potential is 25 mV, all in agreement with experimental data [26-28]. Model AP amplitude is 124 mV, which is in the midrange of experimental measurements (100 mV [29], 132 mV [27], and 135 mV [21]). Model maximal upstroke velocity is 372 V/s (experimental measurements range from 228±20 V/s [26] to 446±46 V/s [30]). The rise in free junctional cleft [Ca] (Figure 4C) resulting from L-type Ca current (Figure 4F) initiates Ca-induced Ca release from the SR (total Ca load ~95 μmol/L cytosol). Calcium in the cleft peaks very rapidly at a high value before diffusing through the SL to the cytosol. Also the SL Ca transient (Figure 4D) rises higher than the cytosolic [Ca] (as estimated by Weber et al. [31]) and decreases as Ca diffuses into the bulk cytosol. The cytosolic [Ca] (Figure 4B) rises from a diastolic level of 89 nM to a peak value of 0.4 μM and declines with a time constant of 175 ms, comparable to values experimentally obtained by Piacentino at el. [28] at 37°C. Figure 4 also shows the major ionic currents generating and shaping the AP, which agree in amplitude and time course with those measured experimentally.

Figure 4
Steady-state epicardial AP, calcium transient, and major ionic currents simulated at 1-Hz pacing rate. A: Action potential. B: Cytosolic [Ca]. C: Junctional [Ca]. D: SL [Ca]. E: Fast sodium current. F: L-type calcium current. G: Rapidly activating delayed ...

Response to frequency

Steady-state APs last 364 and 385 ms at 0.25 Hz in epicardial and endocardial cells respectively. APD90 decreases to 219 and 236 ms as the pacing rate is increased to 3 Hz (Figure 5A). The predicted APD shortening is in the range of experimental variability (Figure 5B), as is the duration of the AP [27, 29, 32, 33]. The APD restitution curve for a single endocardial cell is shown in Figure 5C (dashed line) and approximates the experimental curve (circles) found by Morgan et al. [25] with a similar protocol (see Methods).

Figure 5
A: Simulated APD adaptation curves. Steady-state APD of human epicardial (solid line) and endocardial (dashed line) ventricular cell models shortened as pacing rate was made faster. B: Fractional APD90 changes on increasing pacing frequency from 0.5 to ...

Figure 6A shows the change in cytosolic calcium transient peak when increasing the pacing frequency in a stepwise fashion between 0.25 and 3 Hz. In our epicardial and endocardial cell models (solid and dashed lines) cytosolic [Ca] peaks at ~250 nM at the slowest rate and increases substantially as the pacing frequency increases. Model predictions are in agreement with [Ca] measurements (aequorin light emission) in ventricular muscle strips [32] and isolated trabeculae [34]. In Figure 6B the corresponding percentage increase in [Na]i with increasing frequency is shown (being [Na]i~7.25 mM at 0.25 Hz). The relative changes in [Na]i are similar to those measured in human myocardium [35], although a possible overestimation of absolute [Na]i was acknowledged [35].

Figure 6
A: Fractional changes in peak [Ca]i and B: [Na]i at increasing pacing frequencies in the human epicardial (solid lines) and endocardial (dashed lines) ventricular myocyte models. Experimental results (symbols) are from references [32, 34] and [35]. C ...

A somewhat surprising emergent property was that [Na]i accumulation contributes significantly to APD90 shortening at faster pacing rates. In fact, changes in INaK (from 0.2 to 0.3 to 0.4 A/F) are the most significant increase in outward current during the initial phase of the AP plateau when increasing the pacing rate from 0.25 to 1 Hz to 2 Hz (Figure S3, A). In addition, the increased [Na]i causes Na-Ca exchange current to shift in the outward direction (Figure S3, B), thus contributing to APD shortening. We have tested this further by pacing the epicardial cell at high frequency (2 Hz), but setting [Na]i to the steady-state level predicted at 0.5 Hz ([Na]i=7.65 mM, Figure 5A, ○). Under these conditions, APD does not adapt to frequency and lasts ~330 ms (as when pacing at 0.5 Hz). When the cell is stimulated at 0.5 Hz but [Na]i is set to the steady-state level predicted at 2-Hz stimulation (9.1 mM), APD is short (~240 ms), just like when the cell is paced at 2 Hz (Figure 5A, ●). Furthermore, if the increased [Na]i is only sensed by INaK, APD is decreased from 330 to 265 ms, but if only sensed by INaCa, APD shortens to only 283 ms. If both sense the increased [Na]i then APD shortens to 240 ms. This indicates that INaK is dominant ~2:1 over INaCa in this effect. Moreover, our results suggest that fast INa and background Na current do not contribute to APD adaptation per se, but do contribute to Na accumulation at fast pacing rates (not shown). In Figure 6C we show the changes in APD90 predicted by our epicardial cell model at 1 Hz when clamping [Na]i at various levels. Simulation of partial Na pump blockade (50%) shows a biphasic impact on APD: repolarization prolongs instantaneously (due to the reduction in an outward current), and then shortens as Na starts accumulating intracellularly reaching a new shorter steady APD (Figure 6D).

Effect of K current block

Next we assessed the contribution of IKs and IKr to ventricular repolarization by analyzing the effect of their complete block on APD. The model predicts no changes in AP duration or morphology when IKs is silenced (Figure 7B, ▲ vs. ●), in agreement with experimental results in isolated ventricular myocytes ([18, 36], Figure 7A). This does not mean that IKs is irrelevant, but is consistent with the idea that in normal human ventricle it is only functionally important upon β-adrenergic stimulation to decrease APD in the fight or flight response.

Figure 7
Contribution of IKs and IKr to ventricular repolarization and repolarization reserve. A: Effects of IKs (HMR-1556), IKr (dofetilide), and combined (IKs+IKr) block on APD in isolated human myocytes. Redrawn from [18]. B: Simulations predicted a large effect ...

On the other hand, IKr blockade significantly prolongs APD in human ventricular myocytes (Figure 7A [36]) and in our model (Figure 7B, [diamond] vs. ●). Furthermore, IKr block-induced AP prolongation is more prominent in our endocardial myocyte model, and both cell types show reverse frequency-dependence, i.e. block-induced prolongation was more pronounced at lower pacing frequencies (Figure 7D, solid and dashed lines), as measured in canine cardiac muscle preparations and human ventricular myocytes (Figure 7, C and D, symbols) [36, 37].

It now seems established that IKs block in absence of sympathetic stimulation plays little role in increasing normal human (and large mammal) ventricular APD. However, when the repolarization reserve is attenuated (e.g., by drugs or diseases that reduce other repolarizing currents), IKs may become increasingly important in limiting AP prolongation [36]. Our simulations predict that IKr block increases APD by 27% when IKs is present (Figure 7B, [diamond] vs. ●), vs. 33% with IKs block (Figure 7B, ■ vs. ▲), that is an increase of 22% attributable to the loss of IKs contribution to repolarization reserve. A more modest increase (16%) was observed in the experimental work of Jost et al. [18] (Figure 7A), with a greater APD prolongation upon IKr block (~56%).

Silva and Rudy [38] have identified a Markov model of IKs from human data. Used in their guinea pig AP model, this IKs formulation generated AP shortening at fast rates, but a very large maximal conductance was required for normal AP repolarization. We have used their formulation of human IKs in our AP model (with a moderate maximal conductance of 0.0065 mS/μF, Ca-independent). Figure S4, A shows IKs traces when pacing the digital cell at 1 and 3 Hz. At fast rate we observe an increase in open-state accumulation, responsible for the initial current increase, and closed-state accumulation in states that activate rapidly, creating a reserve that allows an increase in the peak current [39]. However, this increase has negligible effects on APD adaptation, which is entirely due to increase in [Na]i (e.g., no adaptation occurs when [Na] is clamped at low values, as already discussed). When IKr is blocked, IKs increase is slightly enhanced at high frequencies (Figure S4, B), but shortening is hardly affected (26% vs. 22% APD shortening when going from 1 to 3 Hz pacing rate), and the reverse rate-dependence is similar to that obtained with our IKs model (not shown).

When blocking IK1 (50% to reproduce experimental block with 10 μM BaCl2), APD is moderately increased as observed experimentally (Figure 8, ▲ vs. ●), and the extent of AP prolongation (~10% vs. 5% in experiments) is independent of the pacing rate. IKr block increases APD by 27% when IK1 is present (Figure 8B, [diamond] vs. ●), vs. 35% in presence of IK1 block (Figure 8B, ■ vs. ▲), suggesting a 30% increase in IKr blocking effect when IK1 is partially inhibited, similar to that observed experimentally by Jost et al. [18] (~34%, Figure 8A).

Figure 8
Contribution of IK1 to ventricular repolarization and repolarization reserve. A: Effect of IK1 (BaCl2), IKr (dofetilide) and combined (IK1+IKr) block on APD in isolated human myocytes. Redrawn from [18]. B: Simulated results predict a modest AP prolongation ...

Epicardial vs. endocardial cells

Changes in Ito current densities and ratios between Ito,fast and Ito,slow (as measured by Näbauer et al. [21]) allowed differentiating endocardial and epicardial myocyte models. No difference has been reported in IKs density between the two cell types [30]. In epicardial myocytes, Ito has larger conductance and recovers more rapidly from inactivation. This confers the typical AP shape, with a pronounced notch in the early repolarization phase (Figure 4A). In endocardial myocytes, the smaller Ito leads to absence of AP notch (Figure 7B), longer APD (296 ms vs. 283 ms at 1 Hz pacing rate, Figure 5A) and higher sensitivity to IKr block (Figure 7D). APD adaptation does not differ between epicardial and endocardial digital cells (Figure 5A), as also reported experimentally [26, 27].

Transmural heterogeneity in Ca handling proteins has been described in canine ventricular myocytes. Xiong et al. [40] reported a greater NCX current and mRNA and protein levels, and Laurita et al. [41] reported significantly more SR Ca-ATPase (SERCA) expression and function in epicardial vs. endocardial myocytes. In failing human ventricle, Prestle et al. [42] showed lower SERCA2 and phospholamban protein levels in endocardium vs. epicardium, but similar NCX mRNA levels. In nonfailing hearts there was only a trend (non-significant) toward lower SERCA2a and phospholamban in endo- vs. epicardium and no NCX mRNA difference [42]. To explore the impact of these possible changes, we simulated increases of SERCA and NCX by 20 and 10% at the epicardium and reducing by the same percent at the endocardium (i.e. gradients of ~40% and 20% for SERCA and NCX). This resulted in slightly larger Ca transient amplitude, delayed time to peak and rate of [Ca]i decline in endocardium (Figure S5). The slowed Ca transient decay was also reported in dog heart transmural wedges [41]. Frequency-dependent changes in APD, Ca transient amplitude and [Na]i are only slightly altered in both cell types (Figure S6 vs. Figures 5A-B and 6A-B), but none of our conclusions are altered (e.g. the [Na]i effect on APD adaptation).

In canine myocardium, INaK decreases from epicardium to endocardium [43]. Further incorporating a Na pump transmural gradient (+/-20% in epicardium/endocardium), causes a consequent transmural [Na]i gradient, but the fractional increase in Ca and Na and decrease of APD with frequency were not appreciably altered vs. Figure S6B-D (not shown). However, APD in endocardial cells became shorter than in epicardial cells (277 vs. 296 ms at 1 Hz) due to greater [Na]i(8.8 vs. 7.8 mM at 1 Hz).


Here we propose an improved computational model of the human epicardial and endocardial myocytes, based on some of the best features from different prior models combined with newer data. We have validated the model against experimental results not included in the fitting process. The model predicts experimental properties characteristic of human myocytes, including: 1) APD shortening as a function of pacing frequency (adaptation); 2) Ca transient morphology and kinetics; 3), monotonic increase of the intracellular Ca transient peak as a function of pacing frequency; 4) monotonic increase of [Na]i as a function of pacing frequency; 5) effects of IKs, IKr, and IK1 blockade on APD and its rate-dependence.

Responses to frequency

Model results suggest that increase of intracellular [Na] at fast rates is the major mechanism responsible for APD adaptation. When accumulation of [Na]i at high frequencies was prevented by clamping [Na]i at the constant level predicted at slow rates, APD shortening did not occur and APD was comparable to that obtained at low frequency. Thus, changes in INaK and INaCa produced by changes in [Na]i at different pacing frequencies have significant effects on APD90. In fact, experiments in failing human myocytes have shown that [Na]i can influence APD [44]. Our model predictions reveal a potential direct role for [Na]i (other than its involvement in the regulation of [Ca]i via Na-Ca exchanger) that could be tested experimentally. Indeed, a biphasic effect of INaK inhibition on APD (as in Figure 6D) has been reported in guinea pig ventricular myocytes [45] and human atrial fibers [46]. Our model suggests that gradual AP shortening following instantaneous prolongation is due to Na accumulation over several beats. We also speculate that the increased [Na]i in heart failure may limit AP prolongation caused by reduced K channel conductance and increased late Na current. An effect of [Na]i accumulation to shorten APD has been shown previously in guinea pig (but considered more modest) [1] and human [11] models.

Our model provides an accurate description of Ca handling in the human ventricular myocyte. Experimentally, in nonfailing human myocardium, [Ca]i and twitch force increase monotonically with frequency over a wide range of pacing rates (from 0.25 to 3 Hz) [32]. This behavior is predicted by our model and IMW, whereas in TP06 the Ca transient peak increases by 2, 7 and 12 fold when pacing frequency is increased from 0.25 to 0.5, 1 and 2 Hz respectively (e.g., much more than experimentally observed and reported in Figure 6A). TNNP04 response to changes in frequency more closely resembles experimental results, however, the model falls short in certain aspects (e.g., post rest behavior, repolarization failure when SERCA is inhibited). In our model the increased Ca transient amplitude (Figure 6A) at faster pacing rates is due to increased SR Ca load, causing larger release events and thus larger Ca transients. A small contribution is also due to [Na]i accumulation at higher frequencies, which increases the reverse mode INaCa which flows for a short time early in the AP and leads to greater Ca influx during systole. Some controversy exists as to whether NCX works in forward or reverse mode during the AP plateau. Weber et al. [13] have provided direct evidence in nonfailing human myocytes (using AP clamp) that NCX extrudes Ca for most of the AP (although in failing human myocytes Ca influx via NCX was prominent during the plateau). Accordingly, INaCa is normally inward over most of the plateau phase in our model (unlike previous human myocyte models). In failing myocytes, reduced subsarcolemmal Ca, increased Na, and prolonged AP may contribute to a substantial outward current during the plateau [13].

Effects of K current block

A profound difference has been reported in the effects of IKs and IKr blockers on human ventricular APs. Iost et al. [19] did not detect IKs in human ventricle at 35°C. Subsequently the same group [18, 36] has shown that the IKs blockers chromanol 293B and HMR do not significantly lengthen APD (<3.2%) over a broad range of pacing cycle lengths (300-5,000 ms). Our model predicts ~1 and 2.7% prolongation of APD at 1 and 0.2-Hz pacing rates respectively. The effect of blocking IKs is quite different in other human ventricular cell models. At 1 Hz, blocking IKs lengthened APD in TNNP04 and TP06 greatly (+38% and 74%) [10] and mildly in IMW (+8%) [11], as reviewed in [9]. Thus, TNNP04 and TP06 seem to overestimate the contribution of IKs to basal AP repolarization, whereas in IMW its importance more closely resembles experiments and our model. In fact, IKs has nearly the same density as in IMW and our model, whereas in the ten Tusscher models [8, 10] IKs density was set higher to reproduce results from Bosch et al. [47] showing 35% prolongation upon chromanol 293B administration in left ventricular midmyocardial cells from one patient with dilated cardiomyopathy.

At 1 Hz, Li et al. [48] reported an APD prolongation of 26% upon full IKr block with E-4031, whereas Jost et al. reported an APD prolongation of ~40 and 70 ms when IKr is blocked either with sotalol or E-4031 [36] and 56% prolongation with dofetilide [18]. IKr current block leads to ~17% APD prolongation in the ten Tusscher models and ~31% in IMW (paced at 1 Hz). The results from the ten Tusscher and Iyer models thus are in the lower range of the experimental results, as are our model predictions (19% shortening in epicardial and 27% in endocardial myocytes).

Most importantly, in the paper by Jost et al. [36] it is shown that over the entire range of frequencies explored, d-sotalol and E-4041 markedly lengthened the AP in a reverse frequency-dependent manner [36] (Figure 7C and D). This behavior is reproduced by both our endocardial and epicardial cell models, but not by the other existing human ventricular cell models. Indeed, in TNNP04, TP06 and IMW models increased pacing frequency caused greater predicted AP prolongation upon IKr block (direct rate-dependence) (Figure S7).

Reverse rate-dependence of IKr block was first explained by an increase in IKs during rapid heart rates in guinea pig myocytes [49]. IKs accumulation was due to the relatively slow kinetics of this current, which does not permit complete deactivation during short diastolic intervals. However, deactivation kinetics of IKs in guinea pig myocytes are very slow (deactivation τ~756 ms) compared to those of dog (τ ~89 ms), rabbit (τ ~157 ms) and human (τ~122 ms) (all at −40 mV) [50]. Thus, the role of IKs in reverse rate-dependence does not necessarily apply to species with rapid IKs deactivation kinetics, where little IKs accumulation occurs at physiological rapid rates (as shown by our simulations). Even when incorporating a Markov IKs model [38], which predicts increases of the instantaneous and time-dependent component of IKs at fast rates [39] (Figure S4), the smaller IKs density compared to guinea pig makes this explanation unsatisfactory for human myocytes. In fact, reverse rate-dependence is still predicted by our model when IKr is silenced in the presence of IKs blockade (not shown).

We have further explored this mechanism. Figure S8 shows simulated IKr traces obtained by pacing the cell at 0.5 and 2 Hz. Despite the initial spikelike increase (only at fast rates), the current peak amplitude does not change appreciably with frequency (~7% larger at 0.5 vs. 2 Hz). Accordingly, experiments from guinea pig [39], dog and human myocytes [51] did not reveal rate-dependent changes in peak IKr. If anything, the changes suggest that IKr becomes more important at high frequency, and do not explain the reverse rate-dependence. Our results are not completely IKr model-independent, since when we use the ten Tusscher formulation of the current (with our conductance value) in our comprehensive AP description, the reverse-rate dependency is maintained, but reduced. An explanation for the reverse rate-dependence was recently suggested by Zaza [52] who stated that when the AP repolarization is slower (meaning smaller net repolarizing current) a larger APD change would be expected from any change in the total membrane current. As a proof of concept, we have taken the same approach and simulated the injection of a constant inward current Ii = -0.05 A/F. The effect of this small inward current on APD is remarkably larger when pacing the cell at low frequency (Figure S9, A) vs. fast pacing rate (Figure S9, B). To avoid any rate-dependent effect we simulated APs with different durations by clamping [Na]i at low (Figure S9, C) vs. high (Figure S9, D) levels. Similarly, APD prolongation is more marked for the longer initial AP, supporting the view that the same inward Ii may prolong long APs more than short APs.

In human ventricular muscle selective inhibition of IK1 with 10 μM BaCl2 elicited only marginal AP prolongation (~5%), which is slightly overestimated by our model, where AP prolongs by about 10% upon 50% IK1 block. At 1-Hz pacing rate, TNNP04 and TP06 predict ~9% and 4% AP prolongation respectively, whereas a much stronger AP prolongation (~90%) is predicted by IMW. Interestingly, when assessing the contribution of IK1 to repolarization reserve (by comparing the APD change due to IKr block alone and combined IK1+IKr suppression) we obtained a 30% increase in the APD attributable to the loss of IK1 contribution, which is comparable to recent experimental observations [18]. Similarly, we estimated a lesser contribution of IKs to repolarization reserve with IKr block (22%), slightly higher than the experimental estimate (16%) [18].

We conclude that our new human ventricular myocyte model is a significant advance over previously existing models and provides a useful framework to explore ECC mechanisms and repolarization abnormalities at the single cell level. Due to its low computational cost the model may be integrated into multi-scale models of tissue and/or heart.

Supplementary Material



We thank Drs. András Varró and Norbert Jost for providing us with recent data, Drs. Stefano Severi, Antonio Zaza, Eckard Picht and Kenneth Ginsburg for valuable comments. Supported by NIH R37-HL30077, P01-HL80101, a grant from the Fondation Leducq (to D.M.B) and the Max Schaldach Fellowship in Cardiac Pacing and Electrophysiology from the Heart Rhythm Society (to E.G.).


Action Potential
Action Potential Duration
Excitation-Contraction Coupling
Sarcoplasmic Reticulum
SR Ca-ATPase
Na-Ca exchanger
ten Tusscher-Noble-Noble-Panfilov model
ten Tusscher-Panfilov model
Iyer-Mazhari-Winslow model


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