The canine virtual ventricular wall: a platform for dissecting pharmacological effects on propagation and arrhythmogenesis

We have constructed computational models of canine ventricular cells and tissues, ultimately combining detailed tissue architecture and heterogeneous transmural electrophysiology. The heterogeneity is introduced by modifying the Hund–Rudy canine cell model in order to reproduce experimentally reported electrophysiological properties of endocardial, midmyocardial (M) and epicardial cells. These models are validated against experimental data for individual ionic current and action potential characteristics, and their rate dependencies. 1D and 3D heterogeneous virtual tissues are constructed, with detailed tissue architecture (anisotropy and orthotropy, due to fibre orientation and sheet structure) of the left ventricular wall wedge extracted from a diffusion tensor imaging data set. The models are used to study the effects of tissue heterogeneity and class III drugs on transmural propagation and tissue vulnerability to re-entry.

We have determined relationships between the transmural dispersion of action potential duration (APD) and the vulnerable window in the 1D virtual ventricular wall, and demonstrated how changes in the transmural heterogeneity, and hence tissue vulnerability, can lead to generation of re-entry in the 3D ventricular wedge. Two class III drugs with opposite qualitative effects on transmural APD heterogeneity are considered: d-sotalol that increases transmural APD dispersion, and amiodarone that decreases it. Simulations with the 1D virtual ventricular wall show that under d-sotalol conditions the vulnerable window is substantially wider compared to amiodarone conditions, primarily in the epicardial region where unidirectional conduction block persists until the adjacent M cells are fully repolarised.

Further simulations with the 3D ventricular wedge have shown that ectopic stimulation of the epicardial region results in generation of sustained re-entry under d-sotalol conditions, but not under amiodarone conditions or in control. Again, APD increase in M cells was identified as the major contributor to tissue vulnerability—re-entry was initiated primarily due to ectopic excitation propagating around the unidirectional conduction block in the M cell region. This suggests an electrophysiological mechanism for the anti- and proarrhythmic effects of the class III drugs: the relative safety of amiodarone in comparison to d-sotalol can be explained by relatively low transmural APD dispersion, and hence, a narrow vulnerable window and low probability of re-entry in the tissue.     

Increased vulnerability of human ventricle to re-entrant excitation in hERG-linked variant 1 short QT syndrome

The short QT syndrome (SQTS) is a genetically heterogeneous condition characterized by abbreviated QT intervals and an increased susceptibility to arrhythmia and sudden death. This simulation study identifies arrhythmogenic mechanisms in the rapid-delayed rectifier K(+) current (I(Kr))-linked SQT1 variant of the SQTS. Markov chain (MC) models were found to be superior to Hodgkin-Huxley (HH) models in reproducing experimental data regarding effects of the N588K mutation on KCNH2-encoded hERG. These ionic channel models were then incorporated into human ventricular action potential (AP) models and into 1D and 2D idealised and realistic transmural ventricular tissue simulations and into a 3D anatomical model. In single cell models, the N588K mutation abbreviated ventricular cell AP duration at 90% repolarization (APD(90)) and decreased the maximal transmural voltage heterogeneity (δV) during APs. This resulted in decreased transmural heterogeneity of APD(90) and of the effective refractory period (ERP): effects that are anticipated to be anti-arrhythmic rather than pro-arrhythmic. However, with consideration of transmural heterogeneity of I(Kr) density in the intact tissue model based on the ten Tusscher-Noble-Noble-Panfilov ventricular model, not only did the N588K mutation lead to QT-shortening and increases in T-wave amplitude, but δV was found to be augmented in some local regions of ventricle tissue, resulting in increased tissue vulnerability for uni-directional conduction block and predisposing to formation of re-entrant excitation waves. In 2D and 3D tissue models, the N588K mutation facilitated and maintained re-entrant excitation waves due to the reduced substrate size necessary for sustaining re-entry. Thus, in SQT1 the N588K-hERG mutation facilitates initiation and maintenance of ventricular re-entry, increasing the lifespan of re-entrant spiral waves and the stability of scroll waves in 3D tissue.     

Effects of transmural electrical heterogeneities and electrotonic interactions on the dispersion of cardiac repolarization and action potential duration: A simulation study

It has been shown in the literature that myocytes isolated from the ventricular walls at various intramural depths have different action potential durations (APDs). When these myocytes are embedded in the ventricular wall, their inhomogeneous properties affect the sequence of repolarization and the actual distribution of the APDs in the entire wall. In this article, we implement a mathematical model to simulate the combined effect of (a) the non-homogeneous intrinsic membrane properties (in particular the non-homogeneous APDs) and (b) the electrotonic currents that modulate the APDs when the myocytes are embedded in the ventricular myocardium. In particular, we study the effect of (a) and (b) on the excitation and repolarization sequences and on the distribution of APDs in the ventricles. We implement a Monodomain tissue representation that includes orthotropic anisotropy, transmural fiber rotation and homogeneous or heterogeneous transmural intrinsic membrane properties, modeled according to the phase I Luo-Rudy membrane ionic model. Three-dimensional simulations are performed in a cartesian slab with a parallel finite element solver employing structured isoparametric trilinear finite elements in space and a semi-implicit adaptive method in time. Simulations of excitation and repolarization sequences elicited by epicardial or endocardial pacing show that in a homogeneous slab the repolarization pathways approximately follow the activation sequence. Conversely, in the heterogeneous cases considered in this study, we observed two repolarization wavefronts that started from the epi and the endocardial faces respectively and collided in the thickness of the wall and in one case an additional repolarization wave starting from an intramural site. Introducing the heterogeneities along the transmural epi-endocardial direction affected both the repolarization sequence and the APD dispersion, but these effects were clearly discernible only in transmural planes. By contrast, in planes parallel to epi- and endocardium the APD distribution remained remarkably similar to that observed in the homogeneous model. Therefore, the patterns of the repolarization sequence and APD dispersion on the epicardial surface (or any other intramural surface parallel to it) do not reveal the uniform transmural heterogeneity.     

Effect of activation sequence on transmural patterns of repolarization and action potential duration in rabbit ventricular myocardium

Although transmural heterogeneity of action potential duration (APD) is established in single cells isolated from different tissue layers, the extent to which it produces transmural gradients of repolarization in electrotonically coupled ventricular myocardium remains controversial. The purpose of this study was to examine the relative contribution of intrinsic cellular gradients of APD and electrotonic influences to transmural repolarization in rabbit ventricular myocardium. Transmural optical mapping was performed in left ventricular wedge preparations from eight rabbits. Transmural patterns of activation, repolarization, and APD were recorded during endocardial and epicardial stimulation. Experimental results were compared with modeled data during variations in electrotonic coupling. A transmural gradient of APD was evident during endocardial stimulation, which reflected differences previously seen in isolated cells, with the longest APD at the endocardium and the shortest at the epicardium (endo: 165 ± 5 vs. epi: 147 ± 4 ms; P < 0.05). During epicardial stimulation, this gradient reversed (epi: 162 ± 4 vs. endo: 148 ± 6 ms; P < 0.05). In both activation sequences, transmural repolarization followed activation and APD shortened along the activation path such that significant transmural gradients of repolarization did not occur. This correlation between transmural activation time and APD was recapitulated in simulations and varied with changes in intercellular coupling, confirming that it is mediated by electrotonic current flow between cells. These data suggest that electrotonic influences are important in determining the transmural repolarization sequence in rabbit ventricular myocardium and that they are sufficient to overcome intrinsic differences in the electrophysiological properties of the cells across the ventricular wall.     

Calcium-activated chloride current contributes to action potential alternations in left ventricular hypertrophy rabbit

T-wave alternans, characterized by a beat-to-beat change in T-wave morphology, amplitude, and/or polarity on the ECG, often heralds the development of lethal ventricular arrhythmias in patients with left ventricular hypertrophy (LVH). The aim of our study was to examine the ionic basis for a beat-to-beat change in ventricular repolarization in the setting of LVH. Transmembrane action potentials (APs) from epicardium and endocardium were recorded simultaneously, together with transmural ECG and contraction force, in arterially perfused rabbit left ventricular wedge preparation. APs and Ca(2+)-activated chloride current (I(Cl,Ca)) were recorded from left ventricular myocytes isolated from normal rabbits and those with renovascular LVH using the standard microelectrode and whole cell patch-clamping techniques, respectively. In the LVH rabbits, a significant beat-to-beat change in endocardial AP duration (APD) created beat-to-beat alteration in transmural voltage gradient that manifested as T-wave alternans on the ECG. Interestingly, contraction force alternated in an opposite phase ("out of phase") with APD. In the single myocytes of LVH rabbits, a significant beat-to-beat change in APD was also observed in both left ventricular endocardial and epicardial myocytes at various pacing rates. APD alternans was suppressed by adding 1 microM ryanodine, 100 microM 4,4'-diisothiocyanostilbene-2,2'-disulfonic acid (DIDS), and 100 microM 4-acetamido-4'-isothiocyanostilbene-2,2'-disulfonic acid (SITS). The density of the Ca(2+)-activated chloride currents (I(Cl,Ca)) in left ventricular myocytes was significantly greater in the LVH rabbits than in the normal group. Our data indicate that abnormal intracellular Ca(2+) fluctuation may exert a strong feedback on the membrane I(Cl,Ca), leading to a beat-to-beat change in the net repolarizing current that manifests as T-wave alternans on the ECG.     

Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations

Heterogeneities in the densities of membrane ionic currents of myocytes cause regional variations in action potential duration (APD) at various intramural depths and along the apico-basal and circumferential directions in the left ventricle. This work extends our previous study of cartesian slabs to ventricular walls shaped as an ellipsoidal volume and including both transmural and apex-to-base APD heterogeneities. Our 3D simulation study investigates the combined effect on repolarization sequences and APD distributions of: (a) the intrinsic APD heterogeneity across the wall and along the apex-to-base direction, and (b) the electrotonic currents that modulate the APDs when myocytes are embedded in a ventricular wall with fiber rotation and orthotropic anisotropy. Our findings show that: (i) the transmural and apex-to-base heterogeneities have only a weak influence on the repolarization patterns on myocardial layers parallel to the epicardium; (ii) the patterns of APD distribution on the epicardial surface are mostly affected by the apex-to-base heterogeneities and do not reveal the APD transmural heterogeneity; (iii) the transmural heterogeneity is clearly discernible in both repolarization and APD patterns only on transmural sections; (iv) the apex-to-base heterogeneity is clearly discernible only in APD patterns on layers parallel to the epicardium. Thus, in our orthotropic ellipsoidal wall, the complex 3D electrotonic modulation of APDs does not fully mix the effects of the transmural and apex-to-base heterogeneity. The intrinsic spatial heterogeneity of the APDs is unmasked in the modulated APD patterns only in the appropriate transmural or intramural sections. These findings are independent of the stimulus location (epicardial, endocardial) and of Purkinje involvement.     

Transmural and apicobasal gradients in repolarization contribute to T-wave genesis in human surface ECG

The cellular basis of the T-wave morphology of surface ECG remains controversial in clinical cardiology. We examined the effect of action potential duration (APD) distribution on T-wave morphology using a realistic model of the human ventricle and torso. We developed a finite-element model of the ventricle consisting of ～26 million elements, including the conduction system, each implemented with the ion current model of cardiomyocytes. This model was embedded in a torso model with distinct organ structures to obtain the standard ECG leads. The APD distribution was changed in the transmural direction by locating the M cells in either the endocardial or epicardial region. We also introduced apicobasal gradients by modifying the ion channel parameters. Both the transmural gradient (with M cells on the endocardial side) and the apicobasal gradient produced positive T waves, although a very large gradient was required for the apicobasal gradient. By contrast, T waves obtained with the transmural gradient were highly symmetric and, therefore, did not represent the true physiological state. Only combination of the transmural and the moderate apicobasal gradients produced physiological T waves in surface ECG. Positive T waves in surface ECG mainly originated from the transmural distribution of APD with M cells on the endocardial side, although the apicobasal gradient was also required to attain the physiological waveform.     

Extracellular proton depression of peak and late Na⁺ current in the canine left ventricle

Cardiac ischemia reduces excitability in ventricular tissue. Acidosis (one component of ischemia) affects a number of ion currents. We examined the effects of extracellular acidosis (pH 6.6) on peak and late Na(+) current (I(Na)) in canine ventricular cells. Epicardial and endocardial myocytes were isolated, and patch-clamp techniques were used to record I(Na). Action potential recordings from left ventricular wedges exposed to acidic Tyrode solution showed a widening of the QRS complex, indicating slowing of transmural conduction. In myocytes, exposure to acidic conditions resulted in a 17.3 ± 0.9% reduction in upstroke velocity. Analysis of fast I(Na) showed that current density was similar in epicardial and endocardial cells at normal pH (68.1 ± 7.0 vs. 63.2 ± 7.1 pA/pF, respectively). Extracellular acidosis reduced the fast I(Na) magnitude by 22.7% in epicardial cells and 23.1% in endocardial cells. In addition, a significant slowing of the decay (time constant) of fast I(Na) was observed at pH 6.6. Acidosis did not affect steady-state inactivation of I(Na) or recovery from inactivation. Analysis of late I(Na) during a 500-ms pulse showed that the acidosis significantly reduced late I(Na) at 250 and 500 ms into the pulse. Using action potential clamp techniques, application of an epicardial waveform resulted in a larger late I(Na) compared with when an endocardial waveform was applied to the same cell. Acidosis caused a greater decrease in late I(Na) when an epicardial waveform was applied. These results suggest acidosis reduces both peak and late I(Na) in both cell types and contributes to the depression in cardiac excitability observed under ischemic conditions.     

Repolarisation and vulnerability to re-entry in the human heart with short QT syndrome arising from KCNQ1 mutation--a simulation study

Idiopathic short QT syndrome (SQTS) is a recently identified, genetically heterogeneous condition characterised by abbreviated QT intervals and an increased susceptibility to arrhythmia and sudden death. This simulation study identifies mechanisms by which cellular electrophysiological changes in the SQT2 (slow delayed rectifier, I_Ks, -linked) SQTS variant increases arrhythmia risk. The channel kinetics of the V307L mutation of the KCNQ1 subunit of the I_Ks channel were incorporated into human ventricular action potential (AP) models and into 1D and 2D transmural tissue simulations. Incorporating the V307L mutation into simulations reproduced defining features of the SQTS: abbreviation of the QT interval, and increases in T wave amplitude and T_peak–T_end duration. In the single-cell model, the V307L mutation abbreviated ventricular cell AP duration at 90% repolarisation (APD₉₀) and increased the maximal transmural voltage heterogeneity (δV) during APs; this resulted in augmented transmural heterogeneity of APD₉₀ and of the effective refractory period (ERP). In the intact tissue model, the vulnerable window for unidirectional conduction block was also increased. In 2D tissue the V307L mutation facilitated and maintained reentrant excitation. Thus, in SQT2 increases in transmural heterogeneity of APD, δV, ERP and an increased vulnerable window for unidirectional conduction block generate an electrical substrate favourable to reentrant arrhythmia.     

Arrhythmogenic substrate and its modification by nicorandil in a murine model of long QT type 3 syndrome

The gain-of-function Scn5a+/ΔKPQ mutation in the cardiac Na⁺ channel causes human long QT type 3 syndrome (LQT3) associated with ventricular arrhythmogenesis. The K_ATP channel-opener nicorandil (20 μM) significantly reduced arrhythmic incidence in Langendorff-perfused Scn5a+/Δ hearts during programmed electrical stimulation; wild-types (WTs) showed a total absence of arrhythmogenicity. These observations precisely correlated with alterations in recently established criteria for re-entrant excitation reflected in: (1) shortened left-ventricular epicardial but not endocardial monophasic action potential durations at 90% repolarization (APD₉₀) that (2) restored transmural repolarization gradients, ΔAPD₉₀. Scn5a+/Δ hearts showed longer epicardial but not endocardial APD₉₀s, giving shorter ΔAPD₉₀s than WT hearts. Nicorandil reduced epicardial APD₉₀ in both Scn5a+/Δ and WT hearts thereby increasing ΔAPD₉₀. (3) Reduced epicardial critical intervals for re-excitation; Scn5a+/Δ hearts showed greater differences between APD₉₀ and ventricular effective refractory period than WT hearts that were reduced by nicorandil. (4) Reduced APD₉₀ alternans. Scn5a+/Δ hearts showed greater epicardial and endocardial alternans than WTs, which increased with pacing rate. Nicorandil reduced these in Scn5a+/Δ hearts to levels indistinguishable from untreated WTs. (5) Flattened restitution curves. Scn5a+/Δ hearts showed larger epicardial and endocardial critical diastolic intervals than WT hearts. Nicorandil decreased these in Scn5a+/Δ and WT hearts. The presence or absence of arrhythmogenesis in Scn5a+/Δ and WT hearts thus agreed with previously established criteria for re-entrant excitation, and alterations in these precisely correlated with the corresponding antiarrhythmic effects of nicorandil. Together these findings implicate spatial and temporal re-entrant mechanisms in arrhythmogenesis in LQT3 and their reversal by nicorandil.     

Electrical remodeling of the epicardial border zone in the canine infarcted heart: a computational analysis

The density and kinetics of several ionic currents of cells isolated from the epicardial border zone of the infarcted heart (IZs) are markedly different from cells from the noninfarcted canine epicardium (NZs). To understand how these changes in channel function affect the action potential of the IZ cell as well as its response to antiarrhythmic agents, we developed a new ionic model of the action potential of a cell that survives in the infarct (IZ) and one of a normal epicardial cell (NZ) using formulations based on experimental measurements. The difference in action potential duration (APD) between NZ and IZ cells during steady-state stimulation (basic cycle length = 250 ms) was 6 ms (156 ms in NZ and 162 ms in IZ). However, because IZs exhibit postrepolarization refractoriness, the difference in the effective refractory period (ERP), calculated using a propagation model of a single fiber of 100 cells, was 43 ms (156 ms in NZ and 199 ms in IZ). Either an increase in L-type Ca(2+) current (to simulate the effects of BAY Y5959) or a decrease of both or either delayed rectifier currents (e.g., to simulate the effects of azimilide, sotalol, and chromanol) had significant effects on NZ ERP. In contrast, the effects of these agents in IZs were minor, in agreement with measurements in the in situ canine infarcted heart. Therefore 1) because IZs exhibit postrepolarization refractoriness, conclusions drawn from APD measurements cannot be extrapolated directly to ERPs; 2) ionic currents that are the major determinants of APD and the ERP in NZs are less important in IZs; and 3) differential effects of either BAY Y5959 or azimilide in NZs versus IZs are predicted to decrease ERP dispersion and in so doing prevent initiation of arrhythmias in a substrate of inhomogeneous APD/ERPs.     

Transmural reentry during acute global ischemia and reperfusion in canine ventricular muscle

Coronary occlusion and reperfusion produce tachyarrhythmias. We tested the hypothesis that variations in transmural activation after global ischemia and reperfusion were responsible for arrhythmias. We arterially perfused 36 isolated transmural wedges from canine left ventricular free walls. After > or =100 min of stabilization, the artery was occluded for 25 min, followed by reperfusion at various flow rates. We recorded 256 channels of fluorescent action potentials on transmural surfaces from preocclusion to >15 min after reperfusion. During endocardial pacing at 300 ms, ischemia of > or =570 +/- 165 s (n = 34) produced 1:1 endocardial conduction and then 2:1 and 4:1 block as the wave fronts conducted toward epicardium. Transmural reentry appeared after 535 +/- 146 s of ischemia (n = 31). Further ischemia caused epicardial inactivation and eliminated reentry (n = 24). During reperfusion, tissues progressed through sequences of epicardial inactivation and reappearance of activation with 1:1, 2:1, and 4:1 conduction; both sustained and nonsustained reentry occurred. We conclude that heterogeneous activation responses to endocardial pacing during acute ischemia provide the substrate for initiating reentry, suppressed reentry during further ischemia, and caused reentry during reperfusion.     

I(NaCa) contributes to electrical heterogeneity within the canine ventricle

This study examines the amplitude of sodium-calcium exchange current (I(NaCa)) in epicardial, midmyocardial, and endocardial canine ventricular myocytes. Whole cell currents were recorded at 37( degrees )C using standard or perforated-patch voltage-clamp techniques in the absence of potassium, calcium-activated chloride, and sodium-pump currents. I(NaCa) was triggered by release of calcium from the sarcoplasmic reticulum or by rapid removal of external sodium. I(NaCa) was large in midmyocardial myocytes and significantly smaller in endocardial myocytes, regardless of the method used to activate I(NaCa). I(NaCa) at -80 mV was -0.316 +/- 0. 013, -0.293 +/- 0.016, and -0.210 +/- 0.007 pC/pF, respectively, in midmyocardial, epicardial, and endocardial myocytes when activated by the calcium transient. When triggered by sodium removal, peak I(NaCa) was 0.74 +/- 0.04, 0.57 +/- 0.04, and 0.50 +/- 0.03 pA/pF, respectively, in midmyocardial, epicardial, and endocardial myocytes. Epicardial I(NaCa) was smaller than midmyocardial I(NaCa) when activated by removal of external sodium but was comparable to epicardial and midmyocardial I(NaCa) when activated by the normal calcium transient, implying possible transmural differences in excitation-contraction coupling. Our results suggest that I(NaCa) differences contribute to transmural electrical heterogeneity under normal and pathological states. A large midmyocardial I(NaCa) may contribute to the prolonged action potential of these cells as well as to the development of triggered activity under calcium-loading conditions.     

Altered connexin43 expression produces arrhythmia substrate in heart failure

Recently, we found that repolarization heterogeneities between subepicardial and midmyocardial cells can form a substrate for reentrant ventricular arrhythmias in failing myocardium. We hypothesized that the mechanism responsible for maintaining transmural action potential duration heterogeneities in heart failure is related to intercellular uncoupling from downregulation of cardiac gap junction protein connexin43 (Cx43). With the use of the canine model of pacing-induced heart failure, left ventricles were sectioned to expose the transmural surface (n = 5). To determine whether heterogeneous Cx43 expression influenced electrophysiological function, high-resolution transmural optical mapping of the arterially perfused canine wedge preparation was used to measure conduction velocity (theta(TM)), effective transmural space constant (lambda(TM)), and transmural gradients of action potential duration (APD). Absolute Cx43 expression in failing myocardium, quantified by confocal immunofluorescence, was uniformly reduced (by 40 +/- 3%, P < 0.01) compared with control. Relative Cx43 expression was heterogeneously distributed and lower (by 32 +/- 18%, P < 0.05) in the subepicardium compared with deeper layers. Reduced Cx43 expression in heart failure was associated with significant reductions in intercellular coupling between transmural muscle layers, as evidenced by reduced theta(TM) (by 18.9 +/- 4.9%) and lambda(TM) (by 17.2 +/- 1.4%; P < 0.01) compared with control. Heterogeneous transmural distribution of Cx43 in failing myocardium was associated with lower subepicardial theta(TM) (by 12 +/- 10%) and lambda(TM) (by 13 +/- 7%), compared with deeper transmural layers (P < 0.05). APD dispersion was greatest in failing myocardium, and the largest transmural APD gradients were consistently found in regions exhibiting lowest relative Cx43 expression. These data demonstrate that reduced Cx43 expression produces uncoupling between transmural muscle layers leading to slowed conduction and marked dispersion of repolarization between epicardial and deeper myocardial layers. Therefore, Cx43 expression patterns can potentially contribute to an arrhythmic substrate in failing myocardium.     

Transmural action potential and ionic current remodeling in ventricles of failing canine hearts

Heart failure (HF) produces important alterations in currents underlying cardiac repolarization, but the transmural distribution of such changes is unknown. We therefore recorded action potentials and ionic currents in cells isolated from the endocardium, midmyocardium, and epicardium of the left ventricle from dogs with and without tachypacing-induced HF. HF greatly increased action potential duration (APD) but attenuated APD heterogeneity in the three regions. Early afterdepolarizations (EADs) were observed in all cell types of failing hearts but not in controls. Inward rectifier K(+) current (I(K1)) was homogeneously reduced by approximately 41% (at -60 mV) in the three cell types. Transient outward K(+) current (I(to1)) was decreased by 43-45% at +30 mV, and the slow component of the delayed rectifier K(+) current (I(Ks)) was significantly downregulated by 57%, 49%, and 58%, respectively, in epicardial, midmyocardial, and endocardial cells, whereas the rapid component of the delayed rectifier K(+) current was not altered. The results indicate that HF remodels electrophysiology in all layers of the left ventricle, and the downregulation of I(K1), I(to1), and I(Ks) increases APD and favors occurrence of EADs.     

In silico study of action potential and QT interval shortening due to loss of inactivation of the cardiac rapid delayed rectifier potassium current

The rapid delayed rectifier K(+) current, I(Kr), plays a key role in repolarisation of cardiac ventricular action potentials (APs). In recent years, a novel clinical condition denoted the short QT syndrome (SQTS) has been identified and, very recently, gain in function mutations in the gene encoding the pore-forming sub-unit of the I(Kr) channel have been proposed to underlie SQTS in some patients. Here, computer simulations were used to investigate the effects of the selective loss of voltage-dependent inactivation of I(Kr) upon ventricular APs and on the QT interval of the electrocardiogram. I(Kr) and inactivation-deficient I(Kr) were incorporated into Luo-Rudy ventricular AP models. Inactivation-deficient I(Kr) produced AP shortening that was heterogeneous between endocardial, mid-myocardial, and epicardial ventricular cell models, irrespective of whether heterogeneity between these sub-regions was incorporated of slow delayed rectifier K(+) current (I(Ks)) alone, or of I(Ks) together with that of transient outward K(+) current. The selective loss of rectification of I(Kr) did not augment transmural dispersion of AP repolarisation, as AP shortening was greater in mid-myocardial than in endo- or epicardial cell models. Simulated conduction through a 1 D transmural ventricular strand was altered by incorporation of inactivation-deficient I(Kr) and the reconstructed QT interval was shortened. Collectively, these results substantiate the notion that selective loss of I(Kr) inactivation produces a gain in I(Kr) function that causes QT interval shortening.     

Torsion of the human left ventricle: experimental analysis and computational modeling

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.     

Electrotonic influences on action potential duration dispersion in small hearts: a simulation study

Intrinsic spatial variations in repolarization currents in the heart can produce spatial gradients in action potential duration (APD) that serve as possible sites for conduction block and the initiation of reentrant activity. In well-coupled myocardium, however, electrotonic influences at the stimulus site and wavefront collision sites act to modulate any intrinsic heterogeneity in APD. These effects alter APD gradients over an extent larger than that suggested by the length constant associated with propagation and, thus, are hypothesized to play a greater role in smaller hearts used as experimental models of human disease. This study uses computer simulation to investigate how heart size, tissue properties, and the spatial assignment of cell types affect functional APD dispersion. Simulations were carried out using the murine ventricular myocyte model of Pandit et al. or the Luo-Rudy mammalian model in three-dimensional models of mouse and rabbit ventricular geometries. Results show that the spatial extent of the APD dispersion is related to the dynamic changes in transmembrane resistance during recovery. Also, because of the small dimensions of the mouse heart, electrotonic effects on APD primarily determine the functional dispersion of refractoriness, even in the presence of large intrinsic cellular heterogeneity and reduced coupling. APD dispersion, however, is found to increase significantly when the heart size increases to the size of a rabbit heart, unmasking intrinsic cell types.     

A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes.

Mathematical models were developed to reconstruct the action potentials (AP) recorded in epicardial and endocardial myocytes isolated from the adult rat left ventricle. The main goal was to obtain additional insight into the ionic mechanisms responsible for the transmural AP heterogeneity. The simulation results support the hypothesis that the smaller density and the slower reactivation kinetics of the Ca(2+)-independent transient outward K(+) current (I(t)) in the endocardial myocytes can account for the longer action potential duration (APD), and more prominent rate dependence in that cell type. The larger density of the Na(+) current (I(Na)) in the endocardial myocytes results in a faster upstroke (dV/dt(max)). This, in addition to the smaller magnitude of I(t), is responsible for the larger peak overshoot of the simulated endocardial AP. The prolonged APD in the endocardial cell also leads to an enhanced amplitude of the sustained K(+) current (I(ss)), and a larger influx of Ca(2+) ions via the L-type Ca(2+) current (I(CaL)). The latter results in an increased sarcoplasmic reticulum (SR) load, which is mainly responsible for the higher peak systolic value of the Ca(2+) transient [Ca(2+)](i), and the resultant increase in the Na(+)-Ca(2+) exchanger (I(NaCa)) activity, associated with the simulated endocardial AP. In combination, these calculations provide novel, quantitative insights into the repolarization process and its naturally occurring transmural variations in the rat left ventricle.     

Atrial proarrhythmia due to increased inward rectifier current (IK1) arising from KCNJ2 mutation – A simulation study

Atrial fibrillation (AF) has been linked to increased inward rectifier potassium current, I_K1, either due to AF-induced electrical remodelling, or from functional changes due to the Kir2.1 V93I mutation. The aim of this simulation study was to identify at cell and tissue levels' mechanisms by which increased I_K1 facilitates and perpetuates AF. The Courtemanche et al. human atrial cell action potential (AP) model was modified to incorporate reported changes in I_K1 induced by the Kir2.1 V93I mutation in both heterozygous (Het) and homozygous (Hom) mutant forms. The modified models for wild type (WT), Het and Hom conditions were incorporated into homogeneous 1D, 2D and 3D tissue models. Restitution curves of AP duration (APD), effective refractory period (ERP) and conduction velocity (CV) were computed and both the temporal and the spatial vulnerability of atrial tissue to re-entry were measured. The lifespan and tip meandering pattern of re-entry were also characterised. For comparison, parallel simulations were performed by incorporating into the Courtmanche et al. model a linear increase in maximal I_K1 conductance. It was found that the gain-in-function of V93I ‘mutant’ I_K1 led to abbreviated atrial APs and flattened APD, ERP and CV restitution curves. It also hyperpolarised atrial resting membrane potential and slowed down intra-atrial conduction. V93I ‘mutant’ I_K1 reduced the tissue's temporal vulnerability but increased spatial vulnerability to initiate and sustain re-entry, resulting in an increased overall susceptibility of atrial tissue to arrhythmogenesis. In the 2D model, spiral waves self-terminated for WT (lifespan < 3.3 s) tissue, but persisted in Het and Hom tissues for the whole simulation period (lifespan > 10 s). The tip of the spiral wave meandered more in WT tissue than in Het and Hom tissues. Increased I_K1 due to augmented maximal conductance produced similar results to those of Het and Hom Kir2.1 V93I mutant conditions. In the 3D model the dynamic behaviour of scroll waves was stabilized by increased I_K1. In conclusion, increased I_K1 current, either by the Kir2.1 V93I mutation or by augmented maximal conductance, increases atrial susceptibility to arrhythmia by increasing the lifespan of re-entrant spiral waves and the stability of scroll waves in 3D tissue, thereby facilitating initiation and maintenance of re-entrant circuits.