Nonlinearity between action potential alternans and restitution, which both predict ventricular arrhythmic properties in Scn5a^+/− and wild-type murine hearts

Abstract

Electrocardiographic QT- and T-wave alternans, presaging ventricular arrhythmia, reflects compromised adaptation of action potential (AP) duration (APD) to altered heart rate, classically attributed to incomplete Na_v1.5 channel recovery prior to subsequent stimulation. The restitution hypothesis suggests a function whose slope directly relates to APD alternans magnitude, predicting a critical instability condition, potentially generating arrhythmia. The present experiments directly test for such correlations among arrhythmia, APD alternans and restitution. Mice haploinsufficient in the Scn5a, cardiac Na⁺ channel gene (Scn5a^+/−), previously used to replicate Brugada syndrome, were used, owing to their established arrhythmic properties increased by flecainide and decreased by quinidine, particularly in right ventricular (RV) epicardium. Monophasic APs, obtained during pacing with progressively decrementing cycle lengths, were systematically compared at RV and left ventricular epicardial and endocardial recording sites in Langendorff-perfused Scn5a^+/− and wild-type hearts before and following flecainide (10 μM) or quinidine (5 μM) application. The extent of alternans was assessed using a novel algorithm. Scn5a^+/− hearts showed greater frequencies of arrhythmic endpoints with increased incidences of ventricular tachycardia, diminished by quinidine, and earlier onsets of ventricular fibrillation, particularly following flecainide challenge. These features correlated directly with increased refractory periods, specifically in the RV, and abnormal restitution and alternans properties in the RV epicardium. The latter variables were related by a unique, continuous higher-order function, rather than a linear relationship with an unstable threshold. These findings demonstrate a specific relationship between alternans and restitution, as well as confirming their capacity to predict arrhythmia, but implicate mechanisms additional to the voltage feedback suggested in the restitution hypothesis.

alternations in amplitude of the ECG T-wave deflection (22) and alternating QT intervals (39) have been correlated with eventual breakdown of the stable, normal pattern of electrical activity, leading to major arrhythmias (3, 17, 22, 30, 40, 48, 53, 65). Such alternans has been attributed to an inability of the action potential (AP) duration (APD) to adapt to changes in heart rate. This has classically been attributed to a reduction in the time available for voltage-gated Na⁺ channels to recover from inactivation prior to the subsequent AP, resulting in a decrease of its duration. This then lengthens the recovery period available for the following AP, leading to its prolongation and thereby restarting the cycle.

APD alternans may cause arrhythmia when a worsening concordant alternans results in progressively shortening APDs, predisposing to wavebreak, particularly when propagating in heterogeneous tissue. Alternatively, a discordant alternans could produce alternating long and short APs occurring out of phase in adjacent myocardial areas. The resulting gradient in APD between these areas will then flip on an AP-by-AP basis to produce a nodal line between them, where there is no APD alternans. This acts as a conduction barrier due to prolonged refractoriness following a long AP. Triggered activity, which may follow one of the short APs, would have both a reduced conduction velocity and be able to initiate a re-entrant excitation that propagates along the nodal line until it reaches regions that have recovered from the long APs (66). In either of these cases, the combination of a slowed AP propagation, regions of conduction block, and a unidirectional pathway preventing extinction results in re-entry.

Restitution analysis (45) has been introduced to predict the occurrence of APD alternans and hence arrhythmic tendency during variations in heart rate. This assesses the effect of variations in diastolic interval (DI) upon APD. Failure of an AP to recover fully with increasing pacing rates would then reduce the duration of the subsequent AP and produce alternans. Restitution theory hypothesizes that when the function reaches unity slope at a particular critical DI (DI_crit), there is a disproportionate decrease in APD with decreasing DI, which causes unstable waxing alternations in APD. This leads to tachyarrhythmias degenerating into ventricular fibrillation (VF) (25, 27, 28, 46, 50). Alternatively, other mechanisms, additional to those involving membrane potential restitution, have been proposed to mediate alternans. These include interactions among membrane voltage and an altered Ca²⁺ homeostasis, transient outward current contributions, and alternating occurrences of after-depolarization phenomena (13, 51).

Given the involvement of Na⁺ channel activation and inactivation in alternans, comparisons between wild-type (WT) and mice haploinsufficient in the Scn5a, cardiac Na⁺ channel gene (Scn5a^+/−), would be useful in analysis of restitution properties and the consequent arrhythmia and the relationship between them. Scn5a^+/− murine hearts have previously been used to model human Brugada syndrome (BrS) (33, 47, 57, 60), as well as other cardiac arrhythmic or conduction disorders (29, 31). This has been associated with reduced SCN5A function in 30% of cases, leading to fatal ventricular arrhythmogenesis, typically occurring in the fourth decade of life, particularly during sleep (34) and potentially during exercise (2). BrS is characterized by a type 1 ECG phenotype of ST-segment elevation and T-wave inversion in the right precordial leads (11), which may be unmasked by flecainide challenge (36, 49, 58) and alleviated by quinidine (7). Scn5a^+/− murine hearts could be tested against both of these agents, which are also known to produce contrasting effects upon cellular depolarization and recovery. Despite some differences in relative channel contributions, murine hearts have APs that show a sequence of depolarization, carried by Na⁺ and Ca²⁺ currents, followed by repolarization by K⁺ currents. Murine hearts are also sufficiently small to study as whole-organ preparations (54).

The present studies performed a novel, comparative analysis of arrhythmia, alternans, and restitution phenomena during an incremental pacing protocol, hence clarifying the relationships among them. Scn5a^+/− murine hearts were more arrhythmic than their WT counterparts. Both the magnitude of the alternans and the restitution parameters were selectively perturbed in the Scn5a^+/− right ventricular (RV) epicardium following flecainide application, demonstrating the predictive value of both alternans and restitution. There was a continuous, nonlinear relationship between alternans magnitude and the slope of the restitution curve, suggesting a contribution of nonvoltage factors in the manifestation of alternans.

METHODS

Experimental Animals

WT and Scn5a^+/− 129/sv mice, aged 3–5 mo (mean age 4.2 mo) (47), were initially bred from stock (Harlan, UK). Previous reports had suggested sex-linked differences in Scn5a^+/− mice related to increased fibrosis at >12 mo but not 3 mo (24). Such younger, male and female, mice were thus used to investigate primary electrophysiological phenotypes without confounding from age-related pathogenesis specific to the male. This also reduced the number of mice required, in keeping with UK Home Office guidelines. Mice were maintained in plastic cages at 21 ± 1°C and had free access to water, sterile chow (Rodent Maintenance Diet 3, Special Diets Services, Witham, Essex, UK), bedding, and environmental stimuli. They were subject to 12 h/day light and dark cycles. All procedures were performed in regulated premises and were approved under the UK Animals (Scientific Procedures) Act (1986) and by a university ethics review board. The experiments also conformed to the Guide for the Care and Use of Laboratory Animals, U.S. National Institutes of Health (NIH Publication No. 85-23, revised 1996).

Experimental Solutions

The Krebs-Henseleit solution comprised NaCl (119 mM), NaHCO₃ (25 mM), KCl (4 mM), MgCl₂ (1 mM), KH₂PO₄ (1.2 mM), CaCl₂ (1.8 mM), glucose (10 mM), and sodium pyruvate (1.8 mM), bubbled with 95% O₂/5% CO₂ (British Oxygen, Manchester, UK), to achieve a pH of 7.4, matching the 7.3–7.4 pH of mouse plasma. Flecainide and quinidine were made up to final concentrations of 10 μM and 5 μM, respectively, as used in previous work (7, 35, 57, 60). Experiments were performed 3–15 min following addition of either agent. Combinations or sequential additions of these agents were not studied; both are highly lipophilic, giving long washout periods of >30 min in our preparation and have class 1 Na⁺ channel-blocking activity with possible cumulative actions.

Preparation

Mice were killed under Schedule 1 [UK Animals (Scientific Procedures) Act 1986] by cervical dislocation. Hearts were obtained by bilateral sternectomy without touching the myocardial surface and placed into ice-cold Krebs-Henseleit buffer, along with excess tissue, to avoid damaging the heart and aorta. The aorta was cannulated using a modified 21-gauge cannula, precooled using ice, and attached to the cannula using an aneurysm clip (Harvard Apparatus, Edenbridge, Kent, UK) within 90 s of heart extraction. The heart was retrogradely perfused with Krebs-Henseleit solution, warmed to 37°C by a water jacket heat-exchange coil (model C-85A, Techne, Cambridge, UK) at a constant rate of 2.5 ml min⁻¹ by a peristaltic pump (model 505S, Watson-Marlow Bredel, Falmouth, Cornwall, UK) through 200 μm and 5 μm Millipore filters (Millipore, Watford, UK) on the Langendorff apparatus. Perfusion flow rate was accordingly independent of coronary vessel tone, thereby miminizing potential vasoactive pharmacological effects of the test agents. Upon warming, hearts were studied further if they resumed a healthy pink color and showed intrinsically generated activity. Ischemic hearts, identified by a gray-colored scarring on the myocardial surface and failure to capture electrical activity with stimulation, were rejected. A total of 39 WT mice were used, three of which were excluded. Of these, 16 were male and 23 were female. A total of 29 Scn5a^+/− mice were used, one of which was excluded. Of these, 15 were male and 14 were female. Both male and female Scn5a^+/− mice showed VF and VT. Fisher's exact test (FET) revealed no significant differences in arrhythmogenicity between sexes before or after addition of drug.

Electrophysiological Measurements

LV and RV epicardial MAPs were recorded by placing a MAP electrode (Hugo Sachs Elektronik-Harvard Apparatus) on the epicardial surface, with the heart opposed to a custom-made, nonmetallic mechanical support. Endocardial MAP recordings used a modified MAP electrode, constructed by intertwining two pieces of high-grade, Teflon-coated silver wire, whose ends were stripped for 1 mm, galvanically chlorided, and splayed. This electrode was then placed on the LV endocardium by cutting a small window on the left side of the heart, close to the apex, to minimize disruption to the left anterior-descending artery. The RV endocardial electrode was placed by cutting a small window one-half of the way down the RV myocardium, due to the smaller size of this ventricle. Electrode positioning within the correct ventricle was checked at the end of each experiment by staining with methylene blue, followed by cross-sectioning. Epicardial and endocardial recordings were not obtained simultaneously due to the potential effects of surgical interference on the epicardial surface. MAP recordings were obtained, amplified (NeuroLog NL100 preamplifier, NL104 amplifier, Digitimer, Welwyn Garden City, Hertfordshire, UK), band-pass filtered (NL125 filter; 0.5 Hz–1.0 kHz), and sampled at 5 kHz (Micro1401 interface, Cambridge Electronic Design, Cambridge, UK) for display using Spike2 software (Cambridge Electronic Design).

APD₉₀ was calculated on an AP-by-AP basis. This involved automatic detection of the peak and baseline of the AP, followed by the determination of 90% repolarization given these boundaries. This method is necessary as MAP recordings do not give absolute voltage recordings but relative changes, and also compensates for any rate-dependent change in peak amplitude. The corresponding DIs were calculated from the BCL and APD₉₀ values using the relationship DI = BCL − APD₉₀.

Stimulation Protocol

The heart was artificially paced using a pair of platinum-coated, stimulating electrodes, placed on the ventricular septum, connected to a DS2A Mk.II stimulator (Digitimer), consistently adjusted with each recording to deliver twice the threshold voltage. Stimulation protocols were computer controlled using Spike2.

Hearts were stimulated initially at a BCL of 134 ms during preliminary explorations for optimal recording positions, which yielded stable MAP recordings. The MAPs met established criteria of stable baselines, triangular waveforms with rapid upstroke phases, and smooth recoveries to baseline (26). An incremental pacing protocol first paced the heart at a BCL of 134 ms for 100 beats for steady-state activity to be reached. The BCL was then decremented by 5 ms and the pacing sequence repeated.

This process was continued until hearts showed either entry into a 2:1 block or arrhythmogenesis. A 2:1 block was taken as the steady-state relative refractory period at twice threshold stimulation. When arrhythmia occurred, the pacing was removed, followed by application of an 8-Hz continuous pacing protocol, which frequently cardioverted the heart to sinus rhythm. If the heart remained in arrhythmia, cold buffer was applied. All hearts responded to this cardioversion procedure. The heart was then paced at 8 Hz to re-establish viable MAP appearances (26) and to allow the heart to recover from the cold buffer application. Wider ranges of BCLs were investigated than on earlier occasions, which stopped before this endpoint.

Following each run, the heart was checked for the continued presence of intrinsic activity, healthy coloration, capacity to be paced at 8 Hz, and MAP waveforms that corresponded to those at the beginning of the run, implying continued viability and stability of the preparation. This also confirmed recovery of the tissue from the high-stress condition of rapid pacing, where ATP and Ca²⁺ levels may become disturbed. Such controls were also performed following endocardial electrode insertion.

Detection and Quantification of Alternans

An algorithm for the detection of alternans on an AP-by-AP basis was previously used to detect the presence of alternans (35). This algorithm used a set of logical operators to determine whether a string of 10 APs showed sequential alternations in APD >0.2 ms. However, such an algorithm was limited to finding the presence of a transient or sustained alternans and could not assess its severity, which is likely to be the defining mechanistic parameter in alternans-generated arrhythmia. This necessitated substantial additions to this algorithm. Firstly, the 0.2-ms margin for significant alternans was removed, as this could potentially confound measures of the time intervals over which alternans occurred. This permitted direct counting of alternans to a resolution of ≥10 APs. Secondly, once the alternans was identified, a novel set of logical operators determined the magnitude of the alternans as the modulus of the difference in APDs between successive APs on an AP-by-AP basis. This was stored and the mean and SE found during the 100-beat run of each BCL.

Once quantified, all data were plotted and processed, then displayed for individual hearts in each group whose parameterizations were closest to the group medians. This avoided inappropriate linearization of the original curved data, owing to averaging of slightly shifted functions. The number of APs displaying alternans and the magnitude of these alternans were plotted against DI (OriginPro 8, OriginLab, Northampton, MA). The progression of both of these phenomena could be described by an exponential decay function of the form

$$y=y_0+A{\text{e}}^{\frac{-x}{\tau }}$$ (1)

where y represents alternans occurrence or magnitude, x represents the DI, and τ, A, and y₀ are fitting constants. The constant τ represents the decay in y with increasing x to 1/e of its maximum value at x = 0, giving an index of the slope of the function. Thus for the occurrence of alternans, Eq. 1 is applied as

$$\text{count}=y_{0\text{c}}+{\text{A}}_{\text{c}}{e}^{\frac{-\text{DI}}{{\tau }_{\text{c}}}}$$ (2)

and parameters for magnitude of alternans are applied according to

$$\text{mag}=y_{0\text{m}}+{\text{A}}_{\text{m}}{e}^{\frac{-\text{DI}}{{\tau }_{\text{m}}}}$$ (3)

These analytical functions were also used to determine the inflection points, DI_count and DI_mag, from the tangents of the alternans occurrence and magnitude curves at the DI_ERP, assuming linear piece-wise fitting by finding its horizontal axis intercept. It also yielded the maximum values, count_max and mag_max, for the occurrence and magnitude of alternans, respectively.

Construction and Analysis of Restitution Curves

Restitution curves plotting the APD₉₀ against DI values were then constructed using OriginPro 8 (OriginLab) and approximated by a simple, monoexponential decaying growth function (46)

$$y=y_0+\text{A}\left(1-e^{\frac{-\text{X}}{\tau }}\right)$$ (4)

Here, y represents APD₉₀, x represents DI, and y₀, A, and τ are constants obtained by least-squares fitting; hence

$${\text{APD}}_{90}=y_{0\text{r}}+{\text{A}}_{\text{r}}\left(1-e^{\frac{-\text{DI}}{{\tau }_{\text{r}}}}\right)$$ (5)

The corresponding gradient, m, is then given by

$$\frac{\text{dy}}{\text{dx}}=\text{m}=\frac{{\text{A}}_{\text{r}}}{{\tau }_{\text{r}}}{e}^{\frac{-\text{DI}}{{\tau }_{\text{r}}}}$$ (6)

This assumes its maximum value, m_max, at the DI where capture is lost, DI_ERP

$${\text{m}}_{\text{max}}=\frac{{\text{A}}_{\text{r}}}{{\tau }_{\text{r}}}{e}^{\frac{-{\text{DI}}_{\text{ERP}}}{{\tau }_{\text{r}}}}$$ (7)

The DI_crit is the DI at which the gradient is equal to 1 and is hence, calculated as follows

$${\text{DI}}_{\text{crit}}=-{\tau }_{\text{r}}\ln \frac{{\tau }_{\text{r}}}{{\text{A}}_{\text{r}}}$$ (8)

Furthermore, the novel variable DI_limit is the x-axis intercept of the monoexponential function. It occurs when APD₉₀ is equal to zero and is calculated by

$${\text{DI}}_{\text{limit}}=-{\tau }_{\text{r}}\ln \left(1+\frac{y_{\text{0r}}}{{\text{A}}_{\text{r}}}\right)$$ (9)

This is also equivalent to the BCL_limit due to the relationship, BCL = APD + DI, where APD is zero and may hence be considered as the absolute refractory period.

Calculation of the Intersection Between Functions Describing Alternans Magnitude and Restitution

The DI at the point of intersection, DI_χ, between the magnitude of alternans and the restitution curves, describes the situation predicting the 2:1 block due to alternans. This prediction could then be compared with experimental values of DI_ERP. DI_χ was obtained by equating the right-hand sides of Eqs. 3 and 5 and solving the resulting transcendental function [f(x) = 0] by Newton's method. This involved giving a reasonable estimate of x = a, for which, f(x) = 0, then obtaining the resulting value of f(a)/f′(a) for use in subsequent iterations in which x = [a − f(a)/f′(a)] until the result of the computation altered by <10⁻¹⁵ ms.

Relating the Magnitude of APD Alternans to Restitution

The classical restitution hypothesis (45) related the slope of the restitution function to the occurrence of APD alternans. This possible relationship was now explored by assuming the exponential functions shown in Eqs. 3 and 6, relating these quantities through the DI. This permitted mag to be plotted against m through the following analytical solution

$$\text{mag}={\text{A}}_{\text{m}}{\left(\frac{{\tau }_{\text{r}}}{{\text{A}}_{\text{r}}}\right)}^{\frac{{\tau }_{\text{r}}}{{\tau }_{\text{m}}}}{\text{m}}^{\frac{{\tau }_{\text{r}}}{{\tau }_{\text{m}}}}+y_{0\text{m}}$$ (10)

The function describes a smooth dependence of the form

$$\text{mag}={\text{qm}}^{\text{s}}+\text{c}$$ (11)

A power of s = 1, corresponding to τ_r ≈ τ_m, would predict a direct linear 1:1 relationship between alternans and the restitution slope. A power s > 1, resulting from the condition τ_r > τ_m, would predict a nonlinear, steeper dependence of alternans magnitude upon restitution curve slope. A nonzero value of c would be consistent with alternans occurrence without changes in restitution slope.

Statistical Testing

Discrete incidences of VT or VF, expressed relative to the total number of hearts studied under each specific condition, were compared for Scn5a^+/− and WT hearts, with and without either flecainide or quinidine administration. These incidences were compared using FETs. The corresponding BCL values at which these events took place, represented normally distributed data and were accordingly significance tested using adjusted Bonferroni corrected two-tailed heteroscedastic Student's t-tests. At this stage, comparisons were not made between RV and LV, epicardial or endocardial recording sites, as it was not possible to implicate particular recording sites in the origins of established arrhythmias.

Parameters describing detailed, local electrophysiological properties could be distinguished between different recording sites. It was thus possible to compare properties of the RV and LV, epicardium and endocardium, within and between groups consisting of Scn5a^+/− and WT. These comparisons were extended to hearts before and following pharmacological challenge. These parameters were derived from nonlinear least-squares optimizations to data from individual hearts and did not reflect normal distributions (Shapiro-Wilks test: P = 0.0165). Such data were expressed accordingly as medians and interquartile ranges (IQRs). These data were compared between 1) different WT and Scn5a^+/− genotypes, 2) at distinct LV and RV, 3) at epicardial and endocardial recording sites, and 4) both with and without administration of either 5) flecainide or 6) quinidine.

Such data were treated as unpaired, as they involved comparing separate Scn5a^+/− and WT hearts. Furthermore, within any given group, it was not always possible to obtain endocardial and epicardial recordings in every chamber in the same heart due to the invasive procedures that preceded endocardial recording. Furthermore, the experimental procedure involved making recordings at different sites in sequence rather than simultaneously, although all recordings were made at a constant distance from the site of stimulation. Both of these limitations applied whether studies were being made with or without introduction of a pharmacological agent. Finally, hearts were exposed to either flecainide or quinidine, resulting in different hearts being used in control and test data sets.

Statistical testing was performed using SPSS (IBM, Somers, NY) for significant differences between different experimental groups using nonparametric methods. Kruskal-Wallis tests were first applied to the entire data set obtained from the WT and Scn5a^+/− hearts, with and without introduction of flecainide or quinidine, at their LV and RV epicardial and endocardial recording sites. This determined the presence of significant differences, suggesting a requirement for more specific analysis, hence allowing statistical focus on physiological comparisons. Significant P values for Kruskal-Wallis testing are shown in the results.

Specific testing for physiologically significant comparisons applied Mann-Whitney U-tests, where indicated by the Kruskal-Wallis tests. For each WT or Scn5a^+/− genotype, they first compared the results of varying the RV or LV, epicardial or endocardial recording site, under each pharmacological condition. They then compared the results obtained at each site for any given genotype, with and without flecainide or quinidine treatment. They also compared findings between the WT and the Scn5a^+/− at any given recording site for each pharmacological condition. Finally, they compared the actions of flecainide against quinidine at each site for each genotype. All significance thresholds were recalculated using an adjusted-Bonferroni correction to P ≤ 0.05 (23). All P values indicated in results are adjusted in this way. This corrected for type 1 error, while minimizing type 2 error. Significant P values for Mann-Whitney U-testing are shown in results.

Correlations were also explored between the resulting indices of refractoriness (DI_ERP, DI_limit), inflection points (DI_count, DI_mag), unity gradient measures of the functions (DI_crit, DI_Γ), and their intersection points (DI_χ) and measures of maximum gradient (m_max and ∂_max). These were assessed by calculating values of Spearman's rho (ρ) and the associated P for any given number of data. This then considered correlations that were significant (P < 0.05). Such correlations were then interpreted using their ρ values in which ρ > 0.75 was taken to suggest strong agreement, 0.5 < ρ < 0.75 as agreement, and 0.25 < ρ < 0.5 as weak agreement; ρ < 0.25 was excluded. Correlations with significant P values and ρ > 0.25 are displayed in results.

The outcome of this testing is provided at each relevant point in results. This includes the test statistic (Student's t, Kruskal-Wallis χ², Mann-Whitney U, or Spearman's ρ), the value of P, and the degrees of freedom (d.f.), number (n), or effect size (r)—the latter calculated as the ratio between the z-value and the square root of n.

RESULTS

AP Waveforms at Varying Pacing Rates

Figure 1 illustrates typical APs from the RV of WT hearts. Pacing rates up to double normal resting values did not affect either stimulus capture or cause arrhythmic episodes in either epicardium (Fig. 1A, a–e) or endocardium (Fig. 1B, a–e). Flecainide often increased the RV epicardial APDs and produced alternans (Fig. 1A, a–c) at the lower and VF at the higher heart rates (Fig. 1A, d). In contrast, RV endocardial AP generation appeared relatively unaffected (Fig. 1B, a–d). Quinidine produced a 2:1 block at lower heart rates in the RV epicardium (Fig. 1A, d) than in the RV endocardium (Fig. 1A, d and e). Scn5a^+/− hearts (Fig. 2, A and B, a–e) could also be paced at high rates. However, flecainide (10 μM) markedly decreased these permitted pacing rates compared with WT, giving rise to alternans (Fig. 2A, a). Progressively greater pacing rates resulted in a transition into VF (Fig. 2A, b–e). Quinidine (5 μM) left relatively normal AP waveforms in both RV epicardium and endocardium, apart from some loss of stimulus capture at the highest stimulus frequency (Fig. 2, A and B, e).

Fig. 1.

Typical MAP traces obtained from the WT RV myocardium in the absence of pharmacological intervention (left column) or the presence of flecainide (center column) or quinidine (right column). A and B: traces in the epicardial and endocardial regions, respectively, at BCLs of 124 (a), 99 (b), 84 (c), 74 (d), and 54 ms (e). This corresponds to a wide range of physiological heart rates of 483, 606, 714, 810, and 1,111 beats/min (bpm), respectively. Thus 483–606 bpm falls within the range of typical resting and 606–810 bpm of exercising, and 1,111 bpm approaches twice the normal heart rate in the laboratory mouse. Traces are displayed along a common horizontal timescale. The vertical scale was normalized to a standard AP deflection at a BCL of 134 ms. Protocol Completed, runs obtained at the highest BCLs, which were terminated due to attainment of arrhythmic or capture loss endpoints.

Fig. 2.

Typical MAP traces obtained from the Scn5a^+/− RV myocardium in the absence of pharmacological intervention (left column) or the presence of flecainide (center column) or quinidine (right column). A and B: traces in the epicardial and endocardial regions, respectively, at BCLs of 124 (a), 99 (b), 84 (c), 74 (d), and 54 ms (e). Traces are displayed along a common horizontal timescale. The vertical scale was normalized to a standard AP deflection at a BCL of 134 ms.

Refractory and Arrhythmic Endpoints of the Incremental Pacing Procedures

The incremental pacing procedures ended with either refractoriness, detected as a 2:1 block, or arrhythmia in the form of either VF or VT (Fig. 3). Table 1 summarizes the refractory properties. Significant differences existed in BCL_ERP among experimental subgroups in the LV epicardium (χ² = 21.2, P = 0.001, d.f. = 5), RV epicardium (χ² = 19.0, P = 0.002, d.f. = 5), and RV endocardium (χ² = 19.9, P = 0.001, d.f. = 5). Furthermore, there were differences in DI_ERP in RV epicardium (χ² = 20.5, P = 0.001, d.f. = 5) and RV endocardium (χ² = 14.9, P = 0.011, d.f. = 5) only.

Fig. 3.

Typical arrhythmic phenotypes recorded from the RV epicardium of Scn5a^+/- hearts during the steady-state incremental pacing protocol. All panels are shown as voltage, normalized to that achieved during steady-state pacing at a BCL of 134 ms, against the absolute time during the protocol. Triangular markers indicate imposed pacing. A: a nonsustained VT in the RV epicardium at a BCL of 134 ms. B: the initiation of a sustained polymorphic VT in the RV epicardium at a BCL of 124 ms. C: alternans waveform degenerating into VF in the RV epicardium at BCL of 44 ms. D: a mixed picture of VT degenerating into VF in the RV epicardium at a BCL of 84 ms.

Table 1.

Refractory periods following incremental pacing

		BCLERP (ms)		DIERP (ms)
	n	Median	IQR	Median	IQR
WT LV Epi	20	64.00	7.50	36.60	13.28
WT RV Epi	19	64.00	15.00	39.74	13.24
WT LV Endo	7	64.00	21.25	31.63	14.86
WT RV Endo	8	59.00	36.25	34.10	24.93
WT LV Epi Flec	8	74.00	25.00	51.73	18.08
WT RV Epi Flec	6	89.00	30.00	60.01	25.46
WT LV Endo Flec	8	64.00	3.75	42.06	10.18
WT RV Endo Flec	11	59.00	22.50	33.77	22.30
WT LV Epi Quin	10	79.00	12.50	52.98	33.05
WT RV Epi Quin	7	54.00	25.00	39.31	15.35
WT LV Endo Quin	10	69.00	25.00	46.97	17.76
WT RV Endo Quin	7	74.00	5.00	57.44	14.54
Scn5a+/− LV Epi	17	56.50	23.75	37.28	12.28
Scn5a+/− RV Epi	22	56.50	15.00	37.73	10.74
Scn5a+/− LV Endo	8	49.00	6.25	42.49	17.14
Scn5a+/− RV Endo	8	49.00	15.00	29.18	13.54
Scn5a+/− LV Epi Flec	9	74.00	50.00	50.61	21.58
Scn5a+/− RV Epi Flec	8	71.50	17.50	48.85	10.88
Scn5a+/− LV Endo Flec	5	64.00	25.00	53.37	10.80
Scn5a+/− RV Endo Flec	7	69.00	31.11	50.08	28.67
Scn5a+/− LV Epi Quin	8	71.50	21.25	46.23	17.21
Scn5a+/− RV Epi Quin	6	76.50	28.25	49.58	16.51
Scn5a+/− LV Endo Quin	6	69.00	17.50	55.63	23.48
Scn5a+/− RV Endo Quin	11	81.50	31.25	48.71	38.04

Data are shown as medians and interquartile ranges (IQRs). Epi, epicardial; Endo, endocardial; Flec, flecainide addition; Quin, quinidine addition.

BCL_ERP values from WT and Scn5a^+/− were similar in all areas before drug. However, both flecainide (U = 20.5, P = 0.004, r = 0.613) and quinidine (U = 56.0, P = 0.024, r = 0.391) increased BCL_ERP values in the Scn5a^+/− RV epicardium. Flecainide (U = 35.0, P = 0.034, r = 0.478) but not quinidine exerted similar actions on WT RV epicardium. Both agents (flecainide, U = 13.0, P = 0.009, r = 0.650; quinidine, U = 12.5, P = 0.004, r = 0.691) increased BCL_ERP in the RV endocardium of Scn5a^+/− but not WT. In contrast, both flecainide (U = 20.0, P = 0.015, r = 0.558) and quinidine (U = 12.5, P < 0.0001, r = 0.753) increased BCL_ERP in the WT but not the Scn5a^+/− LV epicardium. The DI_ERP values from WT and Scn5a^+/− were similar in all areas before drug. However, both flecainide (U = 15.5, P = 0.002, r = 0.652) and quinidine (U = 49.0, P = 0.023, r = 0.489) then increased DI_ERP in the Scn5a^+/− RV epicardium. Flecainide also increased the DI_ERP in the Scn5a^+/− RV endocardium (U = 22.0, P = 0.034, r = 0.539) but not in WT. Flecainide (U = 32.0, P = 0.034, r = 0.497) but not quinidine exerted similar actions on WT RV epicardium.

The alternative outcome of frank arrhythmia appeared in greater proportions of the Scn5a^+/− compared with the WT. VF occurred in 22.86% of WT hearts, but it took place at a BCL (44.3 ± 2.73 ms) substantially lower than normal physiological values during maximal exercise (15). Nonsustained VT occurred in 2.86% of WT hearts, at a BCL of 134 ms. VF occurred in a similar proportion (20.69%) of Scn5a^+/− hearts as WT but did so at a higher BCL (64 ± 8.13 ms), only just above maximum exercise limits. VT occurred in a larger proportion of Scn5a^+/− hearts (27.59%), doing so at lower BCLs (104.9 ± 14.9 ms). Whereas localization of major arrhythmias is limited, as they may involve many cardiac areas once established, 63.6% of the VT in the Scn5a^+/− was recorded in the RV epicardium.

Flecainide increased the proportion of hearts entering VF in both WT (53.85%) and Scn5a^+/− (57.14%) at BCLs (78.75 ± 6.55 ms and 86.18 ± 5.84 ms, respectively), falling within normal exercising heart rates. However, flecainide reduced the incidence of VT in both WT (0%) and Scn5a^+/− (7.14%; BCL 89 ms). Quinidine increased VF in both WT (63.64%) and Scn5a^+/− (50%), doing so at BCLs of 80.88 ± 8.76 ms and 72.25 ± 8.25 ms, respectively. It increased the proportion of WT hearts, demonstrating VT (9.09%; BCL 98 ms), but decreased the proportion of Scn5a^+/− hearts to 0%.

There were significant increases in the incidence of VF under two particular conditions: introduction of quinidine to the WT (P = 0.024, FET) and introduction of flecainide to the Scn5a^+/− (P = 0.035, FET). Furthermore, Scn5a^+/− hearts showed significantly greater incidences of VT than in WT before pharmacological treatment (P = 0.0084, FET). VF began at significantly shorter BCLs and therefore, later in the pacing procedure in the WT than Scn5a^+/− (t = 2.08, P = 0.048, d.f. = 24). Flecainide similarly resulted in earlier onsets of VF in both WT (t = 4.25, P = 0.00021, d.f. = 28) and Scn5a^+/− (t = 2.21, P = 0.042, d.f. = 17). Quinidine significantly increased the BCL at which VF began in the WT (t = 3.22, P = 0.0036, d.f. = 24) but not the Scn5a^+/−. VT was rare in both WT as well as in Scn5a^+/− during pharmacological interventions. In Scn5a^+/−, before pharmacological intervention, there were significant differences in BCLs, at which VF and VT occurred (t = 3.37, P = 0.0036, d.f. = 17).

These results together demonstrate similar and homogeneous regional distributions of refractory periods in WT and Scn5a^+/−, which are increased by the pharmacological maneuvers. This results in heterogeneous alterations in refractory properties, particularly in the RV and in turn, preferentially in the Scn5a^+/−. Furthermore, Scn5a^+/− hearts are more arrhythmic than WT, particularly due to increased incidences of VT at high BCLs. This correlates with the increased incidence of polymorphic VT reported in BrS during sleep (11). Flecainide is a pro-VF agent in both genotypes, causing an earlier onset of VF in the WT and an earlier onset and increased incidence of VF in the Scn5a^+/−. However, flecainide appears to exert anti-VT effects in both genotypes. Quinidine is a strong pro-VF agent in WT but not in Scn5a^+/−. In contrast, quinidine-treated hearts show no VT in any of the Scn5a^+/− traces.

Occurrence of APD Alternans During Incremental Pacing

Periods of alternans occurred in all traces but to different extents during incremental pacing. These periods were quantified by counting the number of APs, showing this pattern out of a possible 100 recorded APs obtained at each BCL (Fig. 4). The count obtained under each condition increased with decreasing DI along an approximately exponential curve. Its curvature could be defined by a time constant, τ_c, its maximal extent at refractoriness, count_max, and its position by the DI at its turning point, DI_count (Table 2). There were no significant differences in count_max. However, τ_c showed significant differences within the Scn5a^+/− (χ² = 24.5, P = 0.011, d.f. = 11), RV (χ² = 21.5, P = 0.028, d.f. = 11), endocardial (χ² = 21.6, P = 0.027, d.f. = 11), and RV endocardial (χ² = 12.5, P = 0.028, d.f. = 5) subgroups. DI_count showed significant differences within the Scn5a^+/− (χ² = 29.7, P = 0.002, d.f. = 11), untreated hearts (χ² = 15.9, P = 0.026, d.f. = 7), RV (χ² = 25.4, P = 0.008, d.f. = 11), endocardial (χ² = 20.2, P = 0.043, d.f. = 11), and RV endocardial (χ² = 11.4, P = 0.043, d.f. = 5) subgroups. The Mann-Whitney U-tests then demonstrated no significant physiological differences in τ_c. DI_count was greater in the Scn5a^+/− RV epicardium than endocardium (U = 23.0, P = 0.011, r = 0.589). This would give rise to transmural heterogeneities in the occurrence of alternans, potentially leading to discordance in the RV. Quinidine increased DI_count in the Scn5a^+/− RV endocardium (U = 7.0, P = 0.025, r = 0.663). Due to the inherent existence of transmural heterogeneities in the Scn5a^+/−, this would potentially normalize these heterogeneities, giving earlier but concordant onsets of alternans.

Fig. 4.

Typical plots of the number of alternans (out of 100 measured over any given BCL) against DI at 90% repolarization (DI₉₀) for WT (left) and Scn5a^+/− (right) genotypes in each cardiac area. Plots follow approximately monoexponential progressions. Thick, solid lines with open circle points represent no pharmacological addition; dashed lines with filled triangle points show flecainide; and thin, solid lines with filled square points represent quinidine addition. Epi, epicardial; Endo, endocardial. Each trace represents n = 1 data for the heart closest to the median parameters in the data set. This avoids inappropriate linearization from averaged curve data. Points shown are means for a given BCL with their corresponding SE.

Table 2.

Data values for the occurrence of alternans presented as medians and IQRs

	y0c		Ac		τc (ms)		countmax (ms)		DIcount (ms)
	Median	IQR	Median	IQR	Median	IQR	Median	IQR	Median	IQR
WT LV Epi	−16.31	28.35	1,082.77	2.44 × 104	21.96	25.91	229.70	975.33	62.73	14.84
WT RV Epi	−4.79	16.01	205,176.41	1.04 × 109	9.23	11.00	423.78	13,577.02	44.16	18.87
WT LV Endo	−1.78	9.74	2,569.27	2.44 × 104	12.15	13.12	110.07	67.39	46.57	13.74
WT RV Endo	−11.77	30.27	3,465.66	7.61 × 103	17.85	9.24	193.60	931.87	39.26	38.28
WT LV Epi Flec	−1.89	10.25	1,070,640.00	3.02 × 1011	7.26	4.80	4,250.70	4,398.00	61.79	19.32
WT RV Epi Flec	0.05	14.79	6,0364,200.00	2.60 × 1016	5.14	4.13	117.66	66.77	61.63	19.13
WT LV Endo Flec	0.11	14.68	289,681.60	1.14 × 106	8.30	1.92	826.83	2,463.06	52.12	9.50
WT RV Endo Flec	−5.75	40.48	970.66	1.02 × 103	19.64	32.14	94.29	77.40	43.84	23.50
WT LV Epi Quin	−3.76	30.99	29,320.71	1.49 × 105	19.86	23.33	103.00	204.07	59.86	20.62
WT RV Epi Quin	−0.19	13.72	14,354.56	2.73 × 1010	10.08	23.64	654.65	706.37	66.84	17.60
WT LV Endo Quin	−25.78	35.82	4,010.27	3.68 × 105	16.27	17.70	101.15	172.01	63.15	15.38
WT RV Endo Quin	4.81	10.02	7,710,379.79	1.83 × 107	4.88	6.88	84.05	58.82	58.23	8.48
Scn5a+/− LV Epi	−2.23	39.66	1,579.41	6.23 × 106	12.41	13.14	193.94	253.72	52.24	10.03
Scn5a+/− RV Epi	−7.88	35.63	5,029.88	1.33 × 104	15.79	15.27	208.31	440.83	55.96	12.05
Scn5a+/− LV Endo	−0.54	16.82	6,097,600.00	3.52 × 109	6.63	4.73	326.14	8,131.81	55.95	15.41
Scn5a+/− RV Endo	−0.92	6.51	1,349.70	6.22 × 104	10.75	10.34	119.36	231.04	41.10	10.16
Scn5a+/− LV Epi Flec	−1.92	3.01	143,778.41	4.33 × 106	7.34	10.83	362.90	169.51	47.18	12.77
Scn5a+/− RV Epi Flec	−6.07	33.33	2,371.20	1.49 × 105	14.49	22.03	65.30	53.94	57.62	8.77
Scn5a+/− LV Endo Flec	−2.70	11.99	3,582.83	1.46 × 107	16.28	12.07	166.04	121.54	74.42	20.28
Scn5a+/− RV Endo Flec	0.78	3.72	2,321,180.00	2.60 × 1014	3.79	2.10	5,868.29	2,052.91	36.93	14.42
Scn5a+/− LV Epi Quin	1.24	34.35	52,845.82	9.23 × 1011	5.93	10.74	293.69	370.36	49.21	5.32
Scn5a+/− RV Epi Quin	−9.95	43.38	142,261.43	9.56 × 107	13.78	21.86	122.03	89.45	69.62	15.65
Scn5a+/− LV Endo Quin	−0.80	7.50	386,415,000.00	3.02 × 1011	3.35	2.28	99.14	217.38	53.82	19.76
Scn5a+/− RV Endo Quin	3.83	3.57	33,186,100.00	1.00 × 1018	3.81	8.53	93.79	193.16	60.58	20.58

Quantitation of the Magnitude of APD Alternans

The magnitude of the APD alternans was then evaluated from APD₉₀ differences between consecutive APs in the portions of the traces where such alternans occurred. Figure 5 shows that this increased with decreasing DI along approximately exponential curves in tandem with their occurrence. It was thus possible to characterize their maximum extents, mag_max, gradients, ∂_max, at refractoriness, their position by the DIs at their turning points, DI_mag, and the DI at which their slopes assumed negative unity value, DI_Γ. The latter could be compared with the DI_crit. These values are shown in Table 3. There were significant differences in mag_max in the RV (χ² = 28.9, P = 0.002, d.f. = 11), τ_m in the LV epicardium (χ² = 14.1, P = 0.015, d.f. = 5), DI_Γ in the RV epicardium (χ² = 20.1, P = 0.001, d.f. = 5), DI_mag in the RV endocardium (χ² = 15.6, P = 0.008, d.f. = 5) and ∂_max in the RV (χ² = 25.5, P = 0.008, d.f. = 11). The Mann-Whitney U-tests demonstrated that flecainide increased the DI_Γ (U = 0.0, P = 0.001, r = 0.735), mag_max (U = 16.0, P = 0.014, r = 0.572), DI_mag (U = 17.0, P = 0.021, r = 0.557), and ∂_max (U = 18.0, P = 0.020, r = 0.550) in the Scn5a^+/− RV epicardium. In addition, DI_mag in the WT RV endocardium was greater following quinidine administration (U = 1.0, P = 0.042, r = 0.771). The value of τ_m in the LV epicardium was smaller in Scn5a^+/− than in WT (U = 49.0, P = 0.033, r = 0.474). Finally, there was a significant, although relatively weak (ρ=0.490, P < 0.0001, n = 200), correlation between the DI_Γ and the DI_ERP values. The DI_count correlated well with the DI_mag (ρ = 0.619, P < 0.0001, n = 138).

Fig. 5.

Typical plots of the magnitude of alternans against DI₉₀ for WT (left) and Scn5a^+/− (right) genotypes in each cardiac area. Plots follow approximately monoexponential progressions. Thick, solid lines with open circle points represent no pharmacological addition; dashed lines with filled triangle points show flecainide; and thin, solid lines with filled square points represent quinidine addition. Each trace represents n = 1 data for the heart closest to the median parameters in the data set. This avoids inappropriate linearization from averaged curve data. Flecainide shows marked perturbation of the Scn5a^+/− RV epicardial relationship. Points shown are means for a given BCL with their corresponding SE.

Table 3.

Data values for the magnitude of alternans presented as medians and IQRs

	y0m (ms)		Am (ms)		τm (ms)		DIΓ (ms)		∂max		magmax (ms)		DImag (ms)
	Median	IQR	Median	IQR	Median	IQR	Median	IQR	Median	IQR	Median	IQR	Median	IQR
WT LV Epi	−0.46	6.44	47.86	63.56	22.12	29.12	16.52	17.16	−0.35	0.40	3.65	16.72	51.03	18.87
WT RV Epi	0.09	0.23	89.27	1,001.59	7.63	11.77	22.45	27.37	−0.26	0.48	2.98	3.93	46.79	25.83
WT LV Endo	0.81	1.32	46.58	1,162.75	12.73	27.15	16.73	70.31	−0.32	1.12	4.87	1.46	50.20	36.33
WT RV Endo	0.46	0.87	10,407.66	927,247.59	3.89	4.70	36.61	9.76	−5.76	4.04	36.30	28.81	30.30	10.84
WT LV Epi Flec	−0.17	0.60	338.78	1,857.53	10.84	3.73	38.53	5.86	−0.59	0.74	6.45	5.28	62.72	12.37
WT RV Epi Flec	0.09	0.10	116,800.50	890,448.10	5.82	1.80	52.45	21.06	−0.16	0.65	1.60	3.07	68.14	19.66
WT LV Endo Flec	0.32	3.60	78.93	6,842.03	12.49	41.32	23.03	42.05	−0.30	2.06	10.00	9.77	66.09	40.00
WT RV Endo Flec	0.64	0.24	72,996.40	1,730,870.55	6.19	9.56	31.15	32.81	−0.84	2.18	6.56	6.94	49.93	19.85
WT LV Epi Quin	0.35	0.65	2,516.83	557,343,892.18	9.69	11.55	53.03	27.10	−0.96	0.99	6.01	6.36	64.89	12.40
WT RV Epi Quin	0.51	0.74	492.67	359,868.62	8.13	8.49	35.44	25.77	−0.86	24.59	10.03	58.32	53.88	10.18
WT LV Endo Quin	0.72	1.01	36,648.41	127,297,123.32	6.37	6.30	55.84	17.14	−0.60	2.36	5.87	24.48	60.78	16.65
WT RV Endo Quin	2.01	3.33	8.13 × 109	5.29 × 1019	4.57	10.84	43.94	46.60	−0.29	1.83	5.14	4.79	75.43	22.76
Scn5a+/− LV Epi	0.07	0.29	11,049.60	2,882,169.91	5.68	8.62	31.92	26.22	−0.55	1.08	2.71	5.43	42.07	17.24
Scn5a+/− RV Epi	0.09	0.10	469.99	1,493.95	7.95	6.01	26.14	17.33	−0.15	0.46	0.96	4.67	49.21	14.42
Scn5a+/− LV Endo	0.31	0.46	352.84	4,102.21	10.18	11.45	27.77	35.81	−0.21	0.39	2.63	0.94	54.93	23.86
Scn5a+/− RV Endo	0.58	0.67	21.75	16,039.65	8.21	9.50	7.16	33.54	−0.35	0.31	2.28	2.47	35.74	9.00
Scn5a+/− LV Epi Flec	0.11	0.04	170.75	27,875,121.31	6.49	4.53	26.50	25.39	−0.15	0.59	0.93	5.36	51.02	20.48
Scn5a+/− RV Epi Flec	0.51	0.68	1,089,642.07	79,936,670.14	9.37	7.98	57.45	33.67	−2.09	996.90	17.40	5,080.02	60.31	17.35
Scn5a+/− LV Endo Flec	0.21	0.49	2,700.34	990,058.67	8.82	7.05	37.50	26.51	−0.56	0.74	2.17	4.69	71.35	35.99
Scn5a+/− RV Endo Flec	0.46	1.94	10,441.65	69,305,524.18	8.18	11.19	54.84	34.00	−1.79	1.46	16.28	19.45	59.18	32.56
Scn5a+/− LV Epi Quin	0.45	0.92	25,776.47	8,023,840.86	8.24	18.53	35.63	54.11	−0.42	3.00	6.71	8.84	57.03	13.81
Scn5a+/− RV Epi Quin	0.17	0.61	1,331.22	1,804.64	9.24	11.18	32.75	28.88	−0.25	0.26	2.47	2.23	49.60	23.47
Scn5a+/− LV Endo Quin	0.55	0.71	270,404.10	36,225,145.07	5.87	5.22	42.92	10.79	−0.35	0.49	2.32	2.21	60.22	33.53
Scn5a+/− RV Endo Quin	0.51	0.64	325.38	50,105.47	9.12	6.57	30.36	13.04	−0.20	0.42	2.54	0.87	62.81	36.88

These findings thus strongly implicate the Scn5a^+/− RV epicardium as showing greater increases in magnitude of APD alternans following provocation using flecainide. This itself could potentially lead to wavebreak within the RV epicardium. Furthermore, in the absence of the corresponding change in the RV endocardium, this finding would predict an increased transmural gradient in the dependence of alternans upon DI. Together, these findings parallel the greater arrhythmic tendency of the RV. The WT RV endocardium has greater tendency to APD alternans following challenge by quinidine. This is also in keeping with the higher degree of arrhythmia demonstrated under these conditions. Furthermore, there was correlation between increasing alternans and the onset of refractoriness, implying that alternans may play a significant role in determining this endpoint.

Restitution Analysis of APD Values

Restitution curves were next obtained by plotting the APD₉₀ against the corresponding DI. Typical results from hearts whose parameters were close to the median values in the subsequent statistical analysis are displayed before and following flecainide and quinidine administration (Fig. 6). Table 4 summarizes the restitution data. Statistical significances were indicated in each variable in the RV epicardium (τ_r: χ² = 11.2, P = 0.047, d.f. = 5; DI_crit: χ² = 18.8, P = 0.002, d.f. = 5; DI_limit: χ² = 17.2, P = 0.004, d.f. = 5) apart from m_max (χ² = 10.0, P = 0.075, d.f. = 5), which consistently just exceeded unity, giving an average of 1.3 over all conditions. This suggests a common point on the restitution function that cannot be exceeded with regular activity but taking place at a slightly greater value than predicted by the restitution hypothesis.

Fig. 6.

Typical restitution plots of the APD₉₀ against DI₉₀ for WT (left) and Scn5a^+/− (right) genotypes in each cardiac area. Plots follow approximately monoexponential trends, mirroring the alternans progression. Thick, solid lines with open circle points represent no pharmacological addition; dashed lines with filled triangle points show flecainide; and thin, solid lines with filled square points represent quinidine addition. Each trace represents n = 1 data for the heart closest to the median parameters in the data set. This avoids inappropriate linearization from averaged curve data. Points shown are means for a given BCL with their corresponding SE.

Table 4.

Data values for the restitution properties presented as medians and IQRs

	y0r (ms)		Ar (ms)		τr (ms)		DIcrit (ms)		mmax		DIlimit (ms)
	Median	IQR	Median	IQR	Median	IQR	Median	IQR	Median	IQR	Median	IQR
WT LV Epi	−78.35	192.04	129.73	207.96	18.98	19.31	34.40	16.12	0.90	0.98	22.88	11.93
WT RV Epi	−48.60	99.06	93.26	109.86	22.51	15.46	32.55	23.96	0.74	0.46	19.50	13.89
WT LV Endo	−179.21	410.07	240.18	378.40	22.63	13.42	42.38	21.21	1.48	1.50	23.01	24.64
WT RV Endo	−107.23	824.38	151.94	829.63	28.34	21.33	34.78	33.66	1.58	1.63	21.64	15.65
WT LV Epi Flec	−353.31	678.97	402.19	661.70	13.91	14.32	46.77	16.58	1.24	0.87	29.04	11.36
WT RV Epi Flec	−3,239,460.00	7,354,238.48	3,239,500.00	7,354,249.05	5.38	11.63	60.60	20.22	1.85	2.04	39.70	18.15
WT LV Endo Flec	−11.68	86.94	72.39	128.49	52.46	22.58	11.89	70.52	0.59	1.52	19.97	39.93
WT RV Endo Flec	−131.11	395.67	179.81	393.73	16.56	13.25	38.03	20.11	1.52	1.02	28.15	21.81
WT LV Epi Quin	−284.79	1,740.15	325.46	1,737.08	18.47	16.93	43.29	26.84	0.95	0.83	33.53	26.76
WT RV Epi Quin	−317.59	1,364.34	356.25	1,363.31	16.28	10.09	44.39	17.05	1.62	0.77	30.50	18.31
WT LV Endo Quin	−360.36	829,147.80	408.14	829,122.92	14.88	13.50	54.09	27.51	1.06	2.47	36.84	28.00
WT RV Endo Quin	−25,944.25	1,231,342.97	26,001.78	1,231,384.47	8.21	10.65	54.18	19.15	2.32	2.01	40.62	17.08
Scn5a+/− LV Epi	−88.02	146.47	126.29	128.31	17.90	9.66	36.85	12.80	1.26	0.77	18.61	14.48
Scn5a+/− RV Epi	−513.26	3,041.57	553.94	3,028.85	12.49	12.87	41.17	12.44	1.43	2.18	27.25	13.88
Scn5a+/− LV Endo	−107.62	1,951.35	251.64	1,954.27	36.56	68.85	61.79	67.07	1.27	1.97	45.89	35.91
Scn5a+/− RV Endo	−231.93	482.16	306.65	468.96	14.94	9.13	41.84	11.37	2.58	1.79	20.57	20.53
Scn5a+/− LV Epi Flec	−2,184.24	31,701,018.83	2,229.50	31,700,962.23	9.95	19.16	53.83	23.94	1.38	3.02	25.88	25.50
Scn5a+/− RV Epi Flec	−379.87	708.40	443.04	698.27	18.19	12.73	54.82	14.02	1.85	1.86	35.28	12.67
Scn5a+/− LV Endo Flec	−140.45	184.74	295.57	182.38	27.36	63.20	52.61	34.68	1.27	2.49	40.54	19.05
Scn5a+/− RV Endo Flec	−6,635.23	3,788,653.33	6,673.57	3,788,692.72	7.55	8.42	51.24	16.67	2.15	2.28	40.17	11.37
Scn5a+/− LV Epi Quin	−328.40	1,258.66	377.62	1,283.49	17.69	8.76	48.30	19.82	1.36	2.09	33.56	17.09
Scn5a+/− RV Epi Quin	−552.03	560.09	638.27	501.29	14.62	16.94	46.48	36.28	1.21	1.38	35.20	20.24
Scn5a+/− LV Endo Quin	−9,535.82	41,789.62	9,617.12	41,765.33	11.59	14.84	71.43	20.53	3.56	4.47	50.70	18.43
Scn5a+/− RV Endo Quin	−339.05	1,117,421.03	371.68	1,117,430.50	13.33	18.52	50.82	21.54	0.93	0.64	28.35	17.49

However, more specific testing then demonstrated significant physiological differences, which largely involved the RV epicardium. Before pharmacological intervention, the DI_crit and DI_limit values were similar in the Scn5a^+/− and WT. However, τ_r was significantly smaller in the Scn5a^+/− compared with the WT (U = 90.0, P = 0.034, r = 0.427), suggesting a steeper restitution function. Flecainide significantly increased DI_crit in the Scn5a^+/− RV epicardium only (U = 15.0, P = 0.009, r = 0.586). However, flecainide did not significantly alter RV epicardial τ_r in either WT or Scn5a^+/−. τ_r was also greater in the flecainide-treated WT LV endocardium, as opposed to epicardium (U = 6.0, P = 0.040, r = 0.621). This implies that flecainide may protect the WT LV endocardium from voltage instabilities but may increase the risk of transmural re-entry problems to the WT LV epicardium. Finally, there were significant correlations with strong agreement between DI_crit and DI_limit (ρ = 0.852, P < 0.0001, n = 239), agreement between DI_ERP and DI_limit (ρ = 0.603, P < 0.0001, n = 239), as well as weak agreement between DI_crit and DI_ERP (ρ = 0.487, P < 0.0001, n = 247).

Overall, the restitution analysis thus demonstrates a destabilization produced by flecainide, specifically in the Scn5a^+/− RV epicardium. Furthermore, restitution is related to incomplete recovery through its relationship to both effective and absolute refractory periods.

The Relationship Between APD Alternans and APD Restitution

Table 5 shows DI_χ values, which correspond to the situation in which alternate APs assume zero duration, resulting in a 2:1 block. Significant differences were indicated, specifically within the RV epicardial (χ² = 15.587, P = 0.008, d.f. = 5) data in the DI_χ. These were found in the DI_χ in the Scn5a^+/− RV epicardium following introduction of flecainide (U = 8.0, P = 0.020, r = 0.573). This suggests that flecainide may increase the refractory period in this area by increasing alternans to equal the APD. The DI_χ in turn strongly correlated with the DI_limit (ρ = 0.822, P < 0.0001, n = 183) and the DI_ERP (ρ = 0.646, P < 0.0001, n = 186). This demonstrates a role for alternans in determining effective refractory properties in addition to stimulation thresholds.

Table 5.

Data showing parameters defining the relationship between alternans and restitution as medians and IQRs

	DIχ (ms)		s		q (ms)
	Median	IQR	Median	IQR	Median	IQR
WT LV Epi	30.31	16.57	0.85	0.64	8.24	24.37
WT RV Epi	27.06	10.02	2.24	3.58	7.61	14.15
WT LV Endo	29.17	11.22	1.50	3.61	4.72	7.61
WT RV Endo	41.91	4.87	6.22	3.42	7.25	4,631.57
WT LV Epi Flec	34.53	9.57	1.66	1.50	14.28	42.18
WT RV Epi Flec	49.54	23.40	2.13	2.23	1.22	1.38
WT LV Endo Flec	41.15	15.94	4.30	4.68	79.31	123.65
WT RV Endo Flec	38.70	14.36	1.89	1.86	2.18	0.87
WT LV Epi Quin	43.21	19.62	1.84	2.10	3.36	12.98
WT RV Epi Quin	34.08	9.20	3.13	3.72	4.10	11.34
WT LV Endo Quin	51.34	6.06	3.42	4.44	33.17	62.13
WT RV Endo Quin	36.89	11.38	3.12	3.09	0.32	15.71
Scn5a+/− LV Epi	26.06	23.24	2.34	2.33	3.05	5.27
Scn5a+/− RV Epi	30.10	13.41	1.98	1.67	2.33	9.63
Scn5a+/− LV Endo	38.38	26.21	1.46	2.53	7.14	41.45
Scn5a+/− RV Endo	29.55	15.54	1.78	2.51	0.39	0.22
Scn5a+/− LV Epi Flec	35.05	37.68	2.11	2.33	0.60	1.64
Scn5a+/− RV Epi Flec	49.29	12.58	3.46	1.97	5.19	4.79
Scn5a+/− LV Endo Flec	44.52	9.87	6.63	3.76	5.26	174.85
Scn5a+/− RV Endo Flec	42.15	34.02	1.16	1.47	22.52	91.59
Scn5a+/− LV Epi Quin	38.66	16.80	1.66	3.82	7.11	7.84
Scn5a+/− RV Epi Quin	45.23	19.44	2.16	3.07	1.86	57.78
Scn5a+/− LV Endo Quin	45.94	20.07	1.51	1.26	0.63	0.65
Scn5a+/− RV Endo Quin	38.02	7.69	2.21	4.00	2.51	2.85

The analysis of both alternans and restitution demonstrated common effects involving the Scn5a^+/− RV epicardium following introduction of flecainide, both paralleling the comparisons of arrhythmic tendency. The DI_Γ weakly correlated with the DI_crit of the restitution curves (ρ = 0.421, P < 0.0001, n = 187).

This led to closer comparisons of the coefficient q and power s in Eq. 10 under different experimental conditions. Significant differences were indicated in s in the untreated (χ² = 17.3, P = 0.016, d.f. = 7) as well as q in the LV endocardial (χ² = 13.5, P = 0.019, d.f. = 5) and the WT (χ² = 21.6, P = 0.028, d.f. = 11) experimental groups. Further tests demonstrated that q was constant through all of the pharmacological conditions, genetic background, and the site of recording at a median value of ∼4.1, apart from significant increases in q in the WT LV endocardium following flecainide (U = 2.0, P = 0.034, r = 0.731). The power n, also assumed similar values in all of the experimental cases and was ∼2.1 apart from a single comparison between the WT LV epicardium and the Scn5a^+/− LV epicardium (U = 50.0, P = 0.038, r = 0.466), where n took the value of 0.85 in the WT. Finally, all values of c were relatively consistent at ∼0.2. However, c was significantly lower in the WT LV epicardium than in the WT LV epicardium following introduction of quinidine (U = 25.0, P = 0.012, r = 0.563), the WT RV epicardium compared with the WT RV endocardium (U = 7.0, P = 0.022, r = 0.593), and the Scn5a^+/− RV epicardium than the Scn5a^+/− RV endocardium (U = 23.0, P = 0.048, r = 0.493).

This consistency in m, s, and c suggests a unique dependence of alternans upon the slope of the restitution curves under virtually all conditions studied. There is thus a greater stability than expected for a linear relationship between the magnitude of alternans and the slope of the restitution relationship when slopes were <1. However, they predict an increasingly greater magnitude of alternans as slopes reached and exceeded unity value, owing to the smooth, second-power relationship between alternans magnitude and restitution curve slope.

Such findings imply a continuous dependence of alternans magnitude upon restitution curve slope, of the form mag = 4m² + 0.2, in contrast to the original predictions for an abrupt development of a regenerative pattern of APD oscillation leading directly to arrhythmia beyond the DI_crit. However, both analyses predict a critical condition concerning the amplitude of alternans at unity restitution slope, potentially explaining the value of restitution suggested by previous studies.

DISCUSSION

Alternans is thought to result from a failure of APD to adapt to changes in heart rate. This reduces the DI available for Na⁺ channel recovery from inactivation, thereby decreasing the depolarization and duration of the subsequent AP. This results in a persistent pattern of alternating APDs presaging breakdown of cardiac electrical activity into major ventricular arrhythmias (3, 17, 22, 30, 40, 48, 53, 65). Alternans has been mechanistically described by restitution theory (45), relating APD to DI at different BCLs. This proposes a condition in which unity slope of the function at a DI_crit leads to persistent and unstable alternans, potentially causing arrhythmia. This simple and elegant condition has been used extensively in tests for arrhythmic tendency (38, 43).

This paper describes direct experimental tests for this suggested correlation among arrhythmia, alternans, and restitution for the first time. A comparative analysis first assessed for the presence or absence of an arrhythmic phenotype under different recording conditions. This was then related to the specific occurrence and magnitude of alternans and the latter, in turn, to the results of a restitution analysis, all in the same heart. Use of murine hearts (54) permitted genetic manipulation to achieve a defined arrhythmic tendency, thereby avoiding invasive surgical and pharmacological intervention (67). Mice share significant genetic homology with humans and have been previously used to study myocardial electrical properties and arrhythmogenesis (33, 35, 55, 57, 60), as they show many different types of clinically relevant arrhythmia (61). Bundle branch architecture is similar in mouse and human hearts with consequent similarities in activation pattern (37). Regional expression of Scn5a mRNA and Na_v1.5 protein in atrioventricular bundle, bundle branches, and Purkinje fibers in murine hearts precisely replicates distributions in nondiseased human hearts (20, 52). However, murine conducting bundles may assume a less prominent role in propagating the impulse than in humans (63, 64). This could be related to discontinuities in a thin sheet of connective tissue, isolating the common bundle from septal working myocardium (62). However, there is a considerably smaller myocardial mass requiring effective Purkinje system excitation in mouse compared with human heart. In any case, the arrhythmic tendency in Scn5a^+/− and BrS likely reflects altered electrical properties in myocardium, to which the present paper is directed, rather than the Purkinje system.

The studies were accordingly performed in an established murine system with a demonstrable arrhythmic phenotype. This used a Na⁺ channel haploinsufficient, Scn5a^+/−, model due to its likely effects on depolarizing properties (47) and therefore, on recovery and alternans. Humans and murine ventricular APs share inward, depolarizing, Na_v1.5-mediated upstroke processes (21) ended by outward K⁺ currents, as well as electrotonic processes spreading initiated AP waves from excited to quiescent tissue (44). Transmural gradients in Scn5a RNA, Na_v1.5, and functional Na⁺ channel availability in murine hearts closely parallel epicardial and endocardial tissue patterns in human hearts (20, 52). However, murine and human myocardia show some differences in their K⁺ channel phenotypes. Human AP late repolarization largely results from the rapid and slow K⁺ currents, I_Kr and I_Ks, respectively. This contrasts with the early repolarization, resulting from the fast and slow transient outward K⁺ currents, I_to,f and I_to,s, respectively, as well as the late steady-state and slow, I_Kslow murine repolarizing K⁺ currents in mice (9, 10, 14, 54). I_Kslow performs the role of the human I_Kr and I_Ks in mouse APs. Furthermore, recent evidence suggests that murine hearts do express I_Kr and I_Ks (5, 6, 16) and that ATP-dependent and cardiac inward rectifier K⁺ currents, I_KATP and I_K1, are important during repolarization and electrical diastole in both species (41, 42). Mouse myocardium additionally shows smaller contributions from L-type Ca²⁺ channel currents, I_Ca,L. These result in different AP time courses, reflected in their ECG morphology but which are nevertheless appropriate to greater murine heart rates. Mouse hearts are therefore useful in studying physiological consequences of Scn5a mutations, particularly concerning the balances between inward and early outward currents, as occurs in BrS.

Scn5a^+/− hearts have been thought to show arrhythmic properties greatest in the RV epicardium, which are specifically accentuated and alleviated by flecainide and quinidine, respectively (57, 60). This system has been used to model human BrS, where the best-characterized and most-commonly associated single genetic defect involves a loss-of-function mutation in the Na_v1.5 channel α-subunit (1). BrS is phenotypically characterized by a type 1 ECG pattern of ST-segment elevation and negative T-wave in the right precordial leads, V1–V3 (11), in keeping with experimental findings in the murine system (32). The type 1 ECG pattern can be unmasked by the class 1c Na⁺ channel blocker flecainide, used clinically in a diagnostic stress test (49). In contrast, quinidine has been suggested to be antiarrhythmic, owing to its effects on the transient outward current, I_to, thereby balancing inward and outward currents early in the AP (7). Clinical reports also describe abnormal electrical properties both during sleep (34) and exercise (2).

The experiments used a wide range of heart rates provided by artificially imposed incremental pacing. MAPs were recorded at epicardial and endocardial sites in both RV and LV to examine for arrhythmic substrate and its variation with steady-state heart rate in WT and Scn5a^+/− hearts. Such an approach represented the only means of recording waveform morphology, amplitude, and repolarization times, which experimentally reproduced corresponding features of transmembrane APs with high fidelity (18, 26) over the entire duration of the incremental pacing procedures. Recent theoretical modeling studies have demonstrated close correlations between recovery time courses in reference transmembrane AP and MAP recordings in an anisotropic, bidomain myocardial surface (19). Indeed, MAP recordings have been used extensively in recent clinical and experimental studies (4, 12, 43). Thus whereas not reflecting absolute amplitudes or upstroke velocities of transmembrane APs, MAP recordings accurately represent APD and configuration. They also permit regional assessments of electrophysiological events without myocardial disruption (68). The traces in the present experiments contained stable baselines from which MAPs with rapid, smooth upstrokes and monotonic recoveries could be clearly delineated (26), at least up to the pacing rates at which the hearts entered a 2:1 block, over which restitution curves were constructed. Although Langendorff-perfused preparations do not fully recapitulate conditions in in situ hearts, they are well established (8, 59) as stable platforms containing intact conducting and myocardial tissue. Furthermore, the hearts are isolated from autonomic and humoral interference and are amenable to controlled pacing. They are thus appropriate for investigating pathophysiological processes and the effects of pharmacological agents primarily involving the myocardium itself.

Recordings were obtained before and following flecainide (10 μM) or quinidine (5 μM) challenge (33, 35, 57, 60). The incremental pacing procedure culminated in either arrhythmic or refractory endpoints. VF typically occurred at high pacing rates and was the most common arrhythmia in WT. Such VF also occurred in Scn5a^+/− at slower pacing rates. VT occurred with markedly higher incidences in the Scn5a^+/− than WT, in accord with clinical findings of polymorphic VT (11). Class 1 antiarrhythmic agents, characterized by their increasing refractory period, appeared to prevent VT but not VF in Scn5a^+/−. Thus flecainide prevents VT but increases the incidence of VF, whereas quinidine reduces VT without increasing the incidence of VF in Scn5a^+/−. Refractory properties reflected in DI_ERP values were indistinguishable in corresponding recording sites in WT and Scn5a^+/−, before pharmacological manipulations. In the Scn5a^+/−, both flecainide and quinidine increased both RV epicardial and RV endocardial DI_ERP. In WT, flecainide also did so only in the RV epicardium, and quinidine did so only in the RV endocardium. Thus class 1 drugs heterogeneously increased the refractory periods, particularly in the RV, potentially producing pockets of functional conduction block leading to re-entry.

These findings prompted further investigation of APD alternans. All hearts showed alternans when stressed with increased heart rate, regardless of condition or recording site. The occurrence of alternans achieved significant proportions of the recording durations, implying steady-state oscillation was reached, permitting analysis of alternans amplitude. Furthermore, the Scn5a^+/− RV epicardium began significant alternans at longer BCLs than did the Scn5a^+/− RV endocardium, giving rise to transmural heterogeneities with a potential for discordance. Alternans magnitude was increased and began at lower BCLs following addition of flecainide, specifically in the Scn5a^+/− RV epicardium. These features were not observed in the Scn5a^+/− LV or the WT, thus demonstrating a spatially distributed temporal heterogeneity involving the RV of the Scn5a^+/−.

Restitution studies then showed that the DI_crit at any given recording site was indistinguishable between WT and Scn5a^+/−. Flecainide then specifically increased DI_crit in Scn5a^+/− RV epicardium, whereas quinidine specifically increased DI_crit in the WT RV epicardium. In the Scn5a^+/− RV epicardium, τ_r, reflecting the function curvature, was significantly smaller than its WT counterpart.

Both alternans analysis and restitution thus independently implicated the Scn5a^+/− RV epicardium as the site at which electrical phenotype is perturbed. This parallels the arrhythmic phenotype in the Scn5a^+/− upon addition of flecainide. A direct correlation of the parameters emerging from these different analyses demonstrated a statistically significant, albeit relatively weak, agreement between them. This prompted an analytical comparison of the magnitude of alternans and the slope of the restitution curve. The present findings demonstrate a unique, continuous relationship of higher power order 2, with coefficient term close to 4 and constant of 0.2. This implicates altered intracellular calcium homeostasis and its interaction with membrane voltage, known to occur under tachycardic conditions. This would be in addition to electrical restitution, reflecting ion channel recovery, which by itself, would predict a direct linear correlation with abrupt threshold for instability, originally suggested by Nolasco and Dahlen (45). The remaining possible mechanisms suggested for alternans phenomena involving transient outward currents and early after-depolarizations occur under bradycardic rather than tachycardic conditions (51, 66).

In conclusion, the present findings associate both restitution and alternans with the onset and site of arrhythmia in a well-defined system for the first time. It emerges with a unique and empirical but nonlinear and continuous relationship between the magnitude of alternans and the slope of the restitution function, implicating nonelectrophysiological contributions to this relationship. Such phenomena bear on fundamental adaptations of AP characteristics in response to altered heart rate, as may also occur in normal physiological events, such as exercise, and the extent to which these might affect cardiac electrophysiological stability.

GRANTS

Support for this study was provided by the British Heart Foundation, Wellcome Trust, Medical Research Council, and Biotechnology and Biological Sciences Research Council.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

Author contributions: G.D.K.M. and C.L-H.H. conception and design of research; G.D.K.M. performed experiments; G.D.K.M. analyzed data; G.D.K.M. and C.L-H.H. interpreted results of experiments; G.D.K.M. prepared figures; G.D.K.M. and C.L-H.H. drafted manuscript; G.D.K.M., L.G., A.G., and C.L-H.H. edited and revised manuscript; G.D.K.M., L.G., A.G., and C.L-H.H. approved final version of manuscript.

Glossary

A

Amplitude of a given exponential function

A_c

Amplitude of the alternans count function

A_m

Amplitude of the alternans magnitude function

AP

Action potential

APD

Action potential duration

APD₉₀

Action potential duration at 90% repolarization

A_r

Amplitude of the restitution function

BCL

Basic cycle length

BCL_ERP

The first BCL at which 2:1 block occurred during the incremental pacing procedure, giving a comparable index of refractoriness, as is used in S1S2 studies

BrS

Brugada syndrome

c

y-Axis intercept in the relationship between restitution and alternans

count_max

Maximum predicted number of action potentials in alternans at the DI_ERP; values >100 represent extrapolations

DI

Diastolic interval

DI₉₀

Diastolic interval at 90% repolarization

DI_count

The inflection point of the alternans count function as determined by linear piece-wise fitting

DI_crit

Critical diastolic interval (slope of the restitution function = 1)

DI_ERP

The mean final diastolic interval permitted before capture loss at the BCL_ERP

DI_limit

The diastolic interval at which the restitution function has zero APD value, regardless of stimulation properties; DI_limit is used as an index of absolute refractoriness

DI_mag

The inflection point of the alternans magnitude function, as determined by linear piece-wise fitting

DI_Γ

The diastolic interval at which the magnitude of alternans plot reached a gradient of −1 for comparison with the DI_crit, which is at a gradient of +1

DI_χ

The diastolic interval at which the restitution function and magnitude of the alternans function intersect

LV

Left ventricle/ventricular

mag

Magnitude of alternans at any given DI

mag_max

Experimentally determined maximum magnitude of alternans at the DI_ERP

MAP

Monophasic action potential

m_max

The maximum gradient of the restitution function

q

Coefficient in the relationship between restitution and alternans

RV

Right ventricle/ventricular

s

Exponent in the relationship between restitution and alternans

Scn5a^+/−

Mice haploinsufficient in the Scn5a, cardiac Na⁺ channel gene

VF

Ventricular fibrillation

VT

Ventricular tachycardia

WT

Wild-type

y₀

Offset of a given exponential function

y_0c

Offset of the alternans count function

y_0m

Offset of the alternans magnitude function

y_0r

Offset of the restitution function

∂_max

The maximum gradient of the magnitude of alternans plot, which occurs at the DI_ERP

τ

Tau; time constant of a given exponential function

τ_c

Tau; time constant of the alternans count function

τ_m

Tau; time constant of the alternans magnitude function

τ_r

Tau; time constant of the restitution function