Re-entrant cardiac arrhythmias in computational models of long QT myocardium

Evaluating pro-arrhythmogenic effects of the T634S-hERG mutation: insights from a simulation study

A mutation to serine of a conserved threonine (T634S) in the hERG K+ channel S6 pore region has been identified as a variant of uncertain significance, showing a loss-of-function effect. However, its potential consequences for ventricular excitation and arrhythmogenesis have not been reported. This study evaluated possible functional effects of the T634S-hERG mutation on ventricular excitation and arrhythmogenesis by using multi-scale computer models of the human ventricle. A Markov chain model of the rapid delayed rectifier potassium current (IKr) was reconstructed for wild-type and T634S-hERG mutant conditions and incorporated into the ten Tusscher et al. models of human ventricles at cell and tissue (1D, 2D and 3D) levels. Possible functional impacts of the T634S-hERG mutation were evaluated by its effects on action potential durations (APDs) and their rate-dependence (APDr) at the cell level; and on the QT interval of pseudo-ECGs, tissue vulnerability to unidirectional conduction block (VW), spiral wave dynamics and repolarization dispersion at the tissue level. It was found that the T634S-hERG mutation prolonged cellular APDs, steepened APDr, prolonged the QT interval, increased VW, destablized re-entry and augmented repolarization dispersion across the ventricle. Collectively, these results imply potential pro-arrhythmic effects of the T634S-hERG mutation, consistent with LQT2.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.

A model for human action potential dynamics in vivo

Computational modeling based on experimental data remains an important component in cardiac electrophysiological research, especially because clinical data such as human action potential (AP) dynamics are scarce or limited by practical or ethical concerns. Such modeling has been used to develop and test a variety of mechanistic hypotheses, with the majority of these studies involving the rate dependence of AP duration (APD) including APD restitution and conduction velocity (CV). However, there is very little information regarding the complex dynamics at the boundary of repolarization (or refractoriness) and reexcitability. Here, we developed a "minimal" ionic model of the human AP, based on in vivo human monophasic AP (MAP) recordings obtained during clinical programmed electrical stimulation (PES) to address the progressive decrease in AP take-off potential (TOP) and associated CV slowing seen during three tightly spaced extrastimuli. Recent voltage-clamp data demonstrating the effect of intracellular calcium on sodium current availability were incorporated and were required to reproduce large (>15 mV) elevations in take-off potential and progressive encroachment. Introducing clinically observed APD gradients into the model enabled us to replicate the dynamic response to PES in patients leading to conduction block and reentry formation for the positive, but not the negative, APD gradient. Finally, we modeled the dynamics of reentry and show that spiral waves follow a meandering trajectory with a period of ~180 ms. We conclude that our model reproduces a variety of electrophysiological behavior including the response to sequential premature stimuli and provides a basis for studies of the initiation of reentry in human ventricular tissue.NEW & NOTEWORTHY This work presents a new model of the action potential of the human which reproduces the complex dynamics during premature stimulation in patients.

Systematic reduction of a detailed atrial myocyte model

Cardiac arrhythmias are a major health concern and often involve poorly understood mechanisms. Mathematical modeling is able to provide insights into these mechanisms which might result in better treatment options. A key element of this modeling is a description of the electrophysiological properties of cardiac cells. A number of electrophysiological models have been developed, ranging from highly detailed and complex models, containing numerous parameters and variables, to simplified models in which variables and parameters no longer directly correspond to electrophysiological quantities. In this study, we present a systematic reduction of the complexity of the detailed model of Koivumaki et al. using the recently developed manifold boundary approximation method. We reduce the original model, containing 42 variables and 37 parameters, to a model with only 11 variables and 5 parameters and show that this reduced model can accurately reproduce the action potential shape and restitution curve of the original model. The reduced model contains only five currents and all variables and parameters can be directly linked to electrophysiological quantities. Due to its reduction in complexity, simulation times of our model are decreased more than three-fold. Furthermore, fitting the reduced model to clinical data is much more efficient, a potentially important step towards patient-specific modeling.

Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model

Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and frequency of oscillations of the auto-rhythmic cell in WHM2D a large variety of cardiac arrhythmias can be generated including sinus tachycardia, sinus bradycardia, sinus arrhythmia, sinus pause, junctional rhythm, Wolf Parkinson White syndrome and all types of AV conduction blocks. WHM2D includes key components of the electrical conduction system of the heart like the SA (Sino atrial) node cells, fast conducting intranodal pathways, slow conducting atriovenctricular (AV) node, bundle of His cells, Purkinje network, atrial, and ventricular myocardial cells. SA nodal cells, AV nodal cells, bundle of His cells, and Purkinje cells are represented by the Fitzhugh-Nagumo (FN) model which is a reduced model of the Hodgkin-Huxley neuron model. The atrial and ventricular myocardial cells are modeled by the Aliev-Panfilov (AP) two-variable model proposed for cardiac excitation. WHM2D can prove to be a valuable clinical tool for understanding cardiac arrhythmias.

Arrhythmogenic consequences of Na+ channel mutations in the transmurally heterogeneous mammalian left ventricle: Analysis of the I1768V SCN5A mutation

BACKGROUND

Congenital mutations in the cardiac Na+ channel (encoded by SCN5A) underlie long QT syndrome type 3. The sea anemone peptide toxin ATX-II mimics the slowed inactivation kinetics characteristic of many long QT type 3 (LQT3) mutations. However, the I1768V SCN5A mutation is associated with faster recovery kinetics, for which there exists no known pharmacologic equivalent.

OBJECTIVE

The purpose of this study was to investigate the proarrhythmic consequences of the I1768V SCN5A mutation in a transmurally heterogeneous canine left ventricular wedge. We hypothesized that amplification of intrinsic electrical heterogeneities may contribute to abnormal repolarization patterns.

METHODS

We developed a multiscale computational model of the canine ventricular wedge preparation that accounts for a comprehensive set of ionic currents (including transmural heterogeneities of the voltage-dependent transient outward current I(Kv43), the late sodium current I(NaL), the slowly activating delayed rectifier current I(Ks), and the sarco[endo]plasmic reticulum Ca2+-ATPase pump SERCA) and includes mechanistic descriptions of intracellular Ca2+ cycling, the effects of ATX-II, and the I1768V mutation.

RESULTS

Experimentally observed QT intervals and rate-dependent transmural gradients in action potential duration were recapitulated in our simulations, both with and without ATX-II. With the I1768V SCN5A mutation, the model predicted endocardial early afterdepolarizations that triggered epicardial beats and R-on-T extrasystoles. Brief episodes of polymorphic, followed by sustained monomorphic, ventricular tachycardia were observed at slow pacing rates. Importantly, these arrhythmias are driven by recurring reactivation of Na+ channels localized to the endocardium.

CONCLUSION

Our findings suggest that an increase in sustained inward Na+ current arising from the I1768V SCN5A mutation leads to clinically relevant arrhythmias in the transmurally heterogeneous canine left ventricular myocardium. This novel approach for simulating transmural heterogeneity provides new insight into the development of rhythm disturbances in the mammalian left ventricle.

Modeling the Calcium Gate of Cardiac Gap Junction Channel

We addressed the question how Ca2+ transients affect gap junction conductance (Gj) during action potential (AP) propagation by constructing a dynamic gap junction model coupled with a cardiac cell model. The kinetics of the Ca2+ gate was determined based on published experimental findings that the Hill coefficient for the [Ca2+]i-Gj relationship ranges from 3 to 4, indicating multiple ion bindings. It is also suggested that the closure of the Ca2+ gate follows a single exponential time course. After adjusting the model parameters, a two-state (open-closed) model, assuming simultaneous ion bindings, well described both the single exponential decay and the [Ca2+]i-Gj relationship. Using this gap junction model, 30 cardiac cell models were electrically connected in a one-dimensional cable. However, Gj decreased in a cumulative manner by the repetitive Ca2+ transients, and a conduction block was observed. We found that a reopening of the Ca2+ gate is possible only by assuming a sequential ion binding with one rate limiting step in a multistate model. In this model, the gating time constant (T) has a bell-shaped dependence on [Ca2+]i, with a peak around the half-maximal concentration of [Ca2+]i. Here we propose a five-state model including four open states and one closed state, which allows normal AP propagation; namely, the Gj is decreased -15% by a single Ca2+ transient, but well recovers to the control level during diastole. Under the Ca(2+)-overload condition, however, the conduction velocity is indeed decreased as demonstrated experimentally. This new gap junction model may also be useful in simulations of the ventricular arrhythmia.

Dynamical and cellular electrophysiological mechanisms of ECG changes during ischaemia

The interpretation of normal and pathological electrocardiographic (ECG) patterns in terms of the underlying cellular and tissue electrophysiology is rudimentary, as the existing theories rely on geometrical aspects. We relate effects of sub-endocardial ischaemia on the ST-segment depression in ECG to patterns of transmural action potential propagation in a one-dimensional virtual ventricular wall. Our computational study exposes two electrophysiological mechanisms of ST depression: dynamic-predominantly positive spatial gradients in the membrane potential during abnormal repolarization of the wall, produced by action potential duration changes in the ischaemic region; and static-a negative spatial gradient of the resting membrane potential between the normal and ischaemic regions. Hyperkalaemia is the major contributor to both these mechanisms at the cellular level. These results complement simulations of the effects of cardiac geometry on the ECG, and dissect spatio-temporal and cellular electrophysiological mechanisms of ST depression seen in sub-endocardial ischaemia.

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome.

Enhanced self-termination of re-entrant arrhythmias as a pharmacological strategy for antiarrhythmic action

Ventricular tachycardia and fibrillation are potentially lethal cardiac arrhythmias generated by high frequency, irregular spatio-temporal electrical activity. Re-entrant propagation has been demonstrated as a mechanism generating these arrhythmias in computational and in vitro animal models of these arrhythmias. Re-entry can be idealised in homogenous isotropic virtual cardiac tissues as spiral and scroll wave solutions of reaction-diffusion equations. A spiral wave in a bounded medium can be terminated if its core reaches a boundary. Ventricular tachyarrhythmias in patients are sometimes observed to spontaneously self-terminate. One possible mechanism for self-termination of a spiral wave is meander of its core to an inexcitable boundary. We have previously proposed the hypothesis that the spatial extent of meander of a re-entrant wave in the heart can be directly related to its probability of self-termination, and so inversely related to its lethality. Meander in two-dimensional virtual ventricular tissues based on the Oxsoft family of cell models, with membrane excitation parameters simulating the inherited long Q-T syndromes has been shown to be consistent with this hypothesis: the largest meander is seen in the syndrome with the lowest probability of death per arrhythmic episode. Here we extend our previous results to virtual tissues based on the Luo-Rudy family of models. Consistent with our hypothesis, for both families of models, whose different ionic mechanisms produce different patterns of meander, the LQT virtual tissue with the larger meander simulates the syndrome with the lower probability of death per episode. Further, we search the parameter space of the repolarizing currents to find their conductance parameter values that give increased meander of spiral waves. These parameters may provide targets for antiarrhythmic drugs designed to act by increasing the likelihood of self-termination of re-entrant arrhythmias. (c) 2002 American Institute of Physics.

Inherited Brugada and long QT-3 syndrome mutations of a single residue of the cardiac sodium channel confer distinct channel and clinical phenotypes

Defects of the SCN5A gene encoding the cardiac sodium channel alpha-subunit are associated with both the long QT-3 (LQT-3) subtype of long-QT syndrome and Brugada syndrome (BrS). One previously described SCN5A mutation (1795insD) in the C terminus results in a clinical phenotype combining QT prolongation and ST segment elevation, indicating a close interrelationship between the two disorders. Here we provide additional evidence that these two disorders are closely related. We report the analysis of two novel mutations on the same codon, Y1795C (LQT-3) and Y1795H (BrS), expressed in HEK 293 cells and characterized using whole-cell patch clamp procedures. We find marked and opposing effects on channel gating consistent with activity associated with the cellular basis of each clinical disorder. Y1795H speeds and Y1795C slows the onset of inactivation. The Y1795H, but not the Y1795C, mutation causes a marked negative shift in the voltage dependence of inactivation, and neither mutation affects the kinetics of the recovery from inactivation. Interestingly, both mutations increase the expression of sustained Na+ channel activity compared with wild type (WT) channels, although this effect is most pronounced for the Y1795C mutation, and both mutations promote entrance into an intermediate or a slowly developing inactivated state. These data confirm the key role of the C-terminal tail of the cardiac Na+ channel in the control of channel gating, illustrate how subtle changes in channel biophysics can have significant and distinct effects in human disease, and, additionally, provide further evidence of the close interrelationship between BrS and LQT-3 at the molecular level.

Computational models of normal and abnormal action potential propagation in cardiac tissue: linking experimental and clinical cardiology

Computational models have the potential to make a huge impact on our understanding of normal and abnormal cardiac function. The aim of this article is to review tools that have been developed to simulate the electrophysiology of cardiac cells and tissue, and to show how computational models have been used to gain insight into normal and abnormal action potential propagation. Some of the practical problems experienced in the development and application of these models are described, and examples are given.