Inhomogeneous transmural conduction during early ischaemia in patients with coronary artery disease

Modeling and simulation of cardiac electric activity in a human cardiac tissue with multiple ischemic zones

In this work, a human ventricular model (ten Tusscher and Panfilov model) coupled with the tissue level monodomain model is used to analyze the influence of multiple myocardial ischemia on the human cardiac tissue. The existence and uniqueness of the ischemic model comprising the monodomain model with a discontinuous ionic model for the human cardiac tissue is discussed. The coupled system of partial differential equation and ordinary differential equations are solved numerically using [Formula: see text] finite elements in space and Backward Euler finite difference scheme in time. The apriori finite element error estimate for the numerical scheme has been shown to be of [Formula: see text]. Essentially, we evaluate the impact of the increasing size of the ischemic region and the presence of the multiple ischemic regions having equal or different intensities on the neighboring healthy part of the cardiac tissue. We examine both the individual and the combined influence of two types of ischemia, Hyperkalemia (with the variation of the extracellular potassium ion concentration, [Formula: see text]) and Hypoxia (with the variation of intracellular Adenosine triphosphate (ATP) concentration via parameter [Formula: see text]) on the cardiac electrical activity of cardiac tissue. We observe that with the increase in the ischemic region size by a factor five times, there is an additional almost 10% drop in the action potential duration (APD) in the neighboring healthy regions. The combined effect of Hyperkalemia and Hypoxia brings an additional 12% drop in APD in the ischemic subregions and an additional 5% drop in APD in the neighboring healthy part of the cardic tissue in comparison to the only Hyperkalemic ischemia. When the Hyperkalemic and/or Hypoxic degeneracy of a ischemic zone is non-uniform then innercore degeneracy has greater influence on resting potential and APD of outercore of variable intensity ischemic zone than the other way. Also, increasing the number of ischemic subregions from 2 to 4 leads to a 4% drop in APD.

Mechanistic investigation of Ca2+ alternans in human heart failure and its modulation by fibroblasts

Background

Heart failure (HF) is characterized, among other factors, by a progressive loss of contractile function and by the formation of an arrhythmogenic substrate, both aspects partially related to intracellular Ca²⁺ cycling disorders. In failing hearts both electrophysiological and structural remodeling, including fibroblast proliferation, contribute to changes in Ca²⁺ handling which promote the appearance of Ca²⁺ alternans (Ca-alt). Ca-alt in turn give rise to repolarization alternans, which promote dispersion of repolarization and contribute to reentrant activity. The computational analysis of the incidence of Ca²⁺ and/or repolarization alternans under HF conditions in the presence of fibroblasts could provide a better understanding of the mechanisms leading to HF arrhythmias and contractile function disorders.

Methods and findings

The goal of the present study was to investigate in silico the mechanisms leading to the formation of Ca-alt in failing human ventricular myocytes and tissues with disperse fibroblast distributions. The contribution of ionic currents variability to alternans formation at the cellular level was analyzed and the results show that in normal ventricular tissue, altered Ca²⁺ dynamics lead to Ca-alt, which precede APD alternans and can be aggravated by the presence of fibroblasts. Electrophysiological remodeling of failing tissue alone is sufficient to develop alternans. The incidence of alternans is reduced when fibroblasts are present in failing tissue due to significantly depressed Ca²⁺ transients. The analysis of the underlying ionic mechanisms suggests that Ca-alt are driven by Ca²⁺-handling protein and Ca²⁺ cycling dysfunctions in the junctional sarcoplasmic reticulum and that their contribution to alternans occurrence depends on the cardiac remodeling conditions and on myocyte-fibroblast interactions.

Conclusion

It can thus be concluded that fibroblasts modulate the formation of Ca-alt in human ventricular tissue subjected to heart failure-related electrophysiological remodeling. Pharmacological therapies should thus consider the extent of both the electrophysiological and structural remodeling present in the failing heart.

Personalized Cardiac Computational Models: From Clinical Data to Simulation of Infarct-Related Ventricular Tachycardia

In the chronic stage of myocardial infarction, a significant number of patients develop life-threatening ventricular tachycardias (VT) due to the arrhythmogenic nature of the remodeled myocardium. Radiofrequency ablation (RFA) is a common procedure to isolate reentry pathways across the infarct scar that are responsible for VT. Unfortunately, this strategy show relatively low success rates; up to 50% of patients experience recurrent VT after the procedure. In the last decade, intensive research in the field of computational cardiac electrophysiology (EP) has demonstrated the ability of three-dimensional (3D) cardiac computational models to perform in-silico EP studies. However, the personalization and modeling of certain key components remain challenging, particularly in the case of the infarct border zone (BZ). In this study, we used a clinical dataset from a patient with a history of infarct-related VT to build an image-based 3D ventricular model aimed at computational simulation of cardiac EP, including detailed patient-specific cardiac anatomy and infarct scar geometry. We modeled the BZ in eight different ways by combining the presence or absence of electrical remodeling with four different levels of image-based patchy fibrosis (0, 10, 20, and 30%). A 3D torso model was also constructed to compute the ECG. Patient-specific sinus activation patterns were simulated and validated against the patient's ECG. Subsequently, the pacing protocol used to induce reentrant VTs in the EP laboratory was reproduced in-silico. The clinical VT was induced with different versions of the model and from different pacing points, thus identifying the slow conducting channel responsible for such VT. Finally, the real patient's ECG recorded during VT episodes was used to validate our simulation results and to assess different strategies to model the BZ. Our study showed that reduced conduction velocities and heterogeneity in action potential duration in the BZ are the main factors in promoting reentrant activity. Either electrical remodeling or fibrosis in a degree of at least 30% in the BZ were required to initiate VT. Moreover, this proof-of-concept study confirms the feasibility of developing 3D computational models for cardiac EP able to reproduce cardiac activation in sinus rhythm and during VT, using exclusively non-invasive clinical data.

Effects of Heart Rate and Ventricular Wall Thickness on Non-invasive Mapping: An in silico Study

Background: Non-invasive cardiac mapping—also known as Electrocardiographic imaging (ECGi)—is a novel, painless and relatively economic method to map the electrical activation and repolarization patterns of the heart, providing a valuable tool for early identification and diagnosis of conduction abnormalities and arrhythmias. Moreover, the ability to obtain information on cardiac electrical activity non-invasively using ECGi provides the potential for a priori information to guide invasive surgical procedures, improving success rates, and reducing procedure time.

Previous studies have shown the influence of clinical variables, such as heart rate, heart size, endocardial wall, and body composition on surface electrocardiogram (ECG) measurements. The influence of clinical variables on the ECG variability has provided information on cardiovascular control and its abnormalities in various pathologies. However, the effects of such clinical variables on the Body Surface Potential (BSP) and ECGi maps have yet to be systematically investigated.

Methods: In this study we investigated the effects of heart size, intracardiac thickness, and heart rate on BSP and ECGi maps using a previously-developed 3D electrophysiologically-detailed ventricles-torso model. The inverse solution was solved using the three different Tikhonov regularization methods.

Results: Through comparison of multiple measures of error/accuracy on the ECGi reconstructions, our results showed that using different heart geometries to solve the forward and inverse problems produced a larger estimated focal excitation location. An increase of ~2 mm in the Euclidean distance error was observed for an increase in the heart size. However, the estimation of the location of focal activity was still able to be obtained. Similarly, a Euclidean distance increase was observed when the order of regularization was reduced.

For the case of activation maps reconstructed at the same ectopic focus location but different heart rates, an increase in the errors and Euclidean distance was observed when the heart rate was increased.

Conclusions: Non-invasive cardiac mapping can still provide useful information about cardiac activation patterns for the cases when a different geometry is used for the inverse problem compared to the one used for the forward solution; rapid pacing rates can induce order-dependent errors in the accuracy of reconstruction.

Optimization of Lead Placement in the Right Ventricle During Cardiac Resynchronization Therapy. A Simulation Study

Patients suffering from heart failure and left bundle branch block show electrical ventricular dyssynchrony causing an abnormal blood pumping. Cardiac resynchronization therapy (CRT) is recommended for these patients. Patients with positive therapy response normally present QRS shortening and an increased left ventricle (LV) ejection fraction. However, around one third do not respond favorably. Therefore, optimal location of pacing leads, timing delays between leads and/or choosing related biomarkers is crucial to achieve the best possible degree of ventricular synchrony during CRT application. In this study, computational modeling is used to predict the optimal location and delay of pacing leads to improve CRT response. We use a 3D electrophysiological computational model of the heart and torso to get insight into the changes in the activation patterns obtained when the heart is paced from different regions and for different atrioventricular and interventricular delays. The model represents a heart with left bundle branch block and heart failure, and allows a detailed and accurate analysis of the electrical changes observed simultaneously in the myocardium and in the QRS complex computed in the precordial leads. Computational simulations were performed using a modified version of the O'Hara et al. action potential model, the most recent mathematical model developed for human ventricular electrophysiology. The optimal location for the pacing leads was determined by QRS maximal reduction. Additionally, the influence of Purkinje system on CRT response was assessed and correlation analysis between several parameters of the QRS was made. Simulation results showed that the right ventricle (RV) upper septum near the outflow tract is an alternative location to the RV apical lead. Furthermore, LV endocardial pacing provided better results as compared to epicardial stimulation. Finally, the time to reach the 90% of the QRS area was a good predictor of the instant at which 90% of the ventricular tissue was activated. Thus, the time to reach the 90% of the QRS area is suggested as an additional index to assess CRT effectiveness to improve biventricular synchrony.

A response surface optimization approach to adjust ionic current conductances of cardiac electrophysiological models. Application to the study of potassium level changes

Cardiac electrophysiological computational models are often developed from previously published models. The new models may incorporate additional features to adapt the model to a different species or may upgrade a specific ionic formulation based on newly available experimental data. A relevant challenge in the development of a new model is the estimation of certain ionic current conductances that cannot be reliably identified from experiments. A common strategy to estimate those conductances is by means of constrained non-linear least-squares optimization. In this work, a novel methodology is proposed for estimation of ionic current conductances of cardiac electrophysiological models by using a response surface approximation-based constrained optimization with trust region management. Polynomial response surfaces of a number of electrophysiological markers were built using statistical sampling methods. These markers included action potential duration (APD), triangulation, diastolic and systolic intracellular calcium concentration, and time constants of APD rate adaptation. The proposed methodology was applied to update the Carro et al. human ventricular action potential model after incorporation of intracellular potassium ([K⁺]_i) dynamics. While the Carro et al. model was well suited for investigation of arrhythmogenesis, it did not allow simulation of [K⁺]_i changes. With the methodology proposed in this study, the updated Carro et al. human ventricular model could be used to simulate [K⁺]_i changes in response to varying extracellular potassium ([K⁺]_o) levels. Additionally, it rendered values of evaluated electrophysiological markers within physiologically plausible ranges. The optimal values of ionic current conductances in the updated model were found in a notably shorter time than with previously proposed methodologies. As a conclusion, the response surface optimization-based approach proposed in this study allows estimating ionic current conductances of cardiac electrophysiological computational models while guaranteeing replication of key electrophysiological features and with an important reduction in computational cost with respect to previously published approaches. The updated Carro et al. model developed in this study is thus suitable for the investigation of arrhythmic risk-related conditions, including those involving large changes in potassium concentration.

Ventricular repolarization wave variations during the amiodarone treatment course

The aim of this study was to assess ventricular repolarization wave variations during the amiodarone treatment course for patients with ventricular arrhythmias and atrial fibrillation.Sixty-nine patients with ventricular arrhythmias and 9 patients with persistent atrial fibrillation were treated with intravenous injection of a 150 mg loading dose of amiodarone, followed by 1 mg/minute for 6 hours and 0.5 mg/minute for 48 hours. After the initial 24 hours of intravenous injection, amiodarone was also administered orally at a dose of 0.2 g tid for 1 week; followed by 0.2 g bid for 1 week and 0.2 g qd for maintenance. During the procedure, the heart rate, QT, QTc, QTd, QTcd TpTe, TpTe-c, TpTe-d, TpTe/QT, and QTp were measured on days 1, 3, 7, 10, 14, 17, and 20 of amiodarone treatment.The control rate of arrhythmias was 91.0% (71/78). The heart rate dropped significantly on the 7th day after treatment initiation and reached the minimal value on day 14. The QT interval was prolonged from day 3; TpTe was prolonged from day 7 to day 14; QTp was prolonged from day 1 to day 20. The longest QT interval (441.2 ± 33.9 ms) and TpTe (95.0 ± 18.0 ms) occurred on day 14. QTc, QTd, QTcd, TpTe-c, TpTe-d, and TpTe/QT showed no significant changes throughout the treatment.Amiodarone lowers the heart rate, prolongs QT and QTp intervals, and transiently prolongs TpTe. However, it has no effects on QTc, QTd, QTcd, TpTe-c, TpTe-d or TpTe/QT. Amiodarone prolongs QT interval evenly, showing no effects on repolarization dispersion. TpTe/QT is a better indicator of ventricular transmural repolarization dispersion compared with TpTe.

Effects of island-distribution of mid-cardiomyocytes on ventricular electrical excitation associated with the KCNQ1-linked short QT syndrome

AIMS

Short QT syndrome (SQTS) is a new genetic disorder of the electrical system of the heart. To date, there are six gene mutations in ion channels underlying SQTS. However, functional effects of spatial heterogeneities, such as island-distribution of mid-cardiomyocytes (M island) on ventricular electrical excitation in SQTS condition are poorly understood or even not understood at all. Therefore, this study used computational modelling to investigate such possible effects.

METHODS

The spatial heterogeneities of ventricular tissue was studied by using ten Tusscher et al.

MODEL

The model was modified to simulate changes to IKs based on experimental observations of KCNQ1 V307L mutation in SQT2 condition. Cell models were coupled to construct a strand tissue, among which 35% were mid-cardiomyocytes, either distributed in island form or in band form, 25% were endocardial (ENDO), and the rest part were epicardial (EPI) cells.

RESULTS

In simulations, the QT interval was shortened due to the KCNQ1 V307L mutation. The model with M band form failed to reproduce a markedly increase in the T-wave height. However, the model with M island form was able to produce a markedly increased T-wave height with the V307L mutation, matching the major features of SQT clinical ECGs.

CONCLUSIONS

This study substantiates a causal link between the M island and T-wave amplitude in the KCNQ1-linked short QT syndrome.

Effect of Transmural Differences in Excitation-Contraction Delay and Contraction Velocity on Left Ventricle Isovolumic Contraction: A Simulation Study

Recent studies have shown that left ventricle (LV) exhibits considerable transmural differences in active mechanical properties induced by transmural differences in electrical activity, excitation-contraction coupling, and contractile properties of individual myocytes. It was shown that the time between electrical and mechanical activation of myocytes (electromechanical delay: EMD) decreases from subendocardium to subepicardium and, on the contrary, the myocyte shortening velocity (MSV) increases in the same direction. To investigate the physiological importance of this inhomogeneity, we developed a new finite element model of LV incorporating the observed transmural gradients in EMD and MSV. Comparative simulations with the model showed that when EMD or MSV or both were set constant across the LV wall, the LV contractility during isovolumic contraction (IVC) decreased significantly ((dp/dt)max⁡  was reduced by 2 to 38% and IVC was prolonged by 18 to 73%). This was accompanied by an increase of transmural differences in wall stress. These results suggest that the transmural differences in EMD and MSV play an important role in physiological contractility of LV by synchronising the contraction of individual layers of ventricular wall during the systole. Reduction or enhancement of these differences may therefore impair the function of LV and contribute to heart failure.

Coupling Langevin Dynamics With Continuum Mechanics: Exposing the Role of Sarcomere Stretch Activation Mechanisms to Cardiac Function

High-performance computing approaches that combine molecular-scale and macroscale continuum mechanics have long been anticipated in various fields. Such approaches may enrich our understanding of the links between microscale molecular mechanisms and macroscopic properties in the continuum. However, there have been few successful examples to date owing to various difficulties associated with overcoming the large spatial (from 1 nm to 10 cm) and temporal (from 1 ns to 1 ms) gaps between the two scales. In this paper, we propose an efficient parallel scheme to couple a microscopic model using Langevin dynamics for a protein motor with a finite element continuum model of a beating heart. The proposed scheme allows us to use a macroscale time step that is an order of magnitude longer than the microscale time step of the Langevin model, without loss of stability or accuracy. This reduces the overhead required by the imbalanced loads of the microscale computations and the communication required when switching between scales. An example of the Langevin dynamics model that demonstrates the usefulness of the coupling approach is the molecular mechanism of the actomyosin system, in which the stretch-activation phenomenon can be successfully reproduced. This microscopic Langevin model is coupled with a macroscopic finite element ventricle model. In the numerical simulations, the Langevin dynamics model reveals that a single sarcomere can undergo spontaneous oscillation (15 Hz) accompanied by quick lengthening due to cooperative movements of the myosin molecules pulling on the common Z-line. Also, the coupled simulations using the ventricle model show that the stretch-activation mechanism contributes to the synchronization of the quick lengthening of the sarcomeres at the end of the systolic phase. By comparing the simulation results given by the molecular model with and without the stretch-activation mechanism, we see that this synchronization contributes to maintaining the systolic blood pressure by providing sufficient blood volume without slowing the diastolic process.

Arrhythmogenicity of fibro-fatty infiltrations

The onset of cardiac arrhythmias depends on electrophysiological and structural properties of cardiac tissue. One of the most important changes leading to arrhythmias is characterised by the presence of a large number of non-excitable cells in the heart, of which the most well-known example is fibrosis. Recently, adipose tissue was put forward as another similar factor contributing to cardiac arrhythmias. Adipocytes infiltrate into cardiac tissue and produce in-excitable obstacles that interfere with myocardial conduction. However, adipose infiltrates have a different spatial texture than fibrosis. Over the course of time, adipose tissue also remodels into fibrotic tissue. In this paper we investigate the arrhythmogenic mechanisms resulting from the presence of adipose tissue in the heart using computer modelling. We use the TP06 model for human ventricular cells and study how the size and percentage of adipose infiltrates affects basic properties of wave propagation and the onset of arrhythmias under high frequency pacing in a 2D model for cardiac tissue. We show that although presence of adipose infiltrates can result in the onset of cardiac arrhythmias, its impact is less than that of fibrosis. We quantify this process and discuss how the remodelling of adipose infiltrates affects arrhythmia onset.

Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles

Early Afterdepolarizations, EADs, are defined as the reversal of the action potential before completion of the repolarization phase, which can result in ectopic beats. However, the series of mechanisms of EADs leading to these ectopic beats and related cardiac arrhythmias are not well understood. Therefore, we aimed to investigate the influence of this single cell behavior on the whole heart level. For this study we used a modified version of the Ten Tusscher-Panfilov model of human ventricular cells (TP06) which we implemented in a 3D ventricle model including realistic fiber orientations. To increase the likelihood of EAD formation at the single cell level, we reduced the repolarization reserve (RR) by reducing the rapid delayed rectifier Potassium current and raising the L-type Calcium current. Varying these parameters defined a 2D parametric space where different excitation patterns could be classified. Depending on the initial conditions, by either exciting the ventricles with a spiral formation or burst pacing protocol, we found multiple different spatio-temporal excitation patterns. The spiral formation protocol resulted in the categorization of a stable spiral (S), a meandering spiral (MS), a spiral break-up regime (SB), spiral fibrillation type B (B), spiral fibrillation type A (A) and an oscillatory excitation type (O). The last three patterns are a 3D generalization of previously found patterns in 2D. First, the spiral fibrillation type B showed waves determined by a chaotic bi-excitable regime, i.e. mediated by both Sodium and Calcium waves at the same time and in same tissue settings. In the parameter region governed by the B pattern, single cells were able to repolarize completely and different (spiral) waves chaotically burst into each other without finishing a 360 degree rotation. Second, spiral fibrillation type A patterns consisted of multiple small rotating spirals. Single cells failed to repolarize to the resting membrane potential hence prohibiting the Sodium channel gates to recover. Accordingly, we found that Calcium waves mediated these patterns. Third, a further reduction of the RR resulted in a more exotic parameter regime whereby the individual cells behaved independently as oscillators. The patterns arose due to a phase-shift of different oscillators as disconnection of the cells resulted in continuation of the patterns. For all patterns, we computed realistic 9 lead ECGs by including a torso model. The B and A type pattern exposed the behavior of Ventricular Tachycardia (VT). We conclude that EADs at the single cell level can result in different types of cardiac fibrillation at the tissue and 3D ventricle level.

Modelling the effects of chloroquine on KCNJ2-linked short QT syndrome

A gain-of-function KCNJ2 D172N mutation in KCNJ2-encoded Kir2.1 channels underlies one form of short QT syndrome (SQT3), which is associated with increased susceptibility to arrhythmias and sudden death. Anti-malarial drug chloroquine was reported as an effective inhibitor of Kir2.1 channels. Using biophysically-detailed human ventricle computer models, this study assessed the effects of chloroquine on SQT3. The ten Tusscher et al. model of human ventricular cell action potential was modified to recapitulate functional changes in the inward rectifier K⁺ current (I_K1) due to heterozygous and homozygous forms of the D172N mutation. Mutant formulations were incorporated into multi-scale models. The blocking effects of chloroquine on ionic currents were modelled using IC₅₀ and Hill coefficient values from literatures. Effects of chloroquine on action potential duration (APD), effective refractory period (ERP) and pseudo-ECGs were quantified. It was shown that chloroquine caused a dose-dependent reduction in I_K1, prolonged APD, and decreased the maximum voltage heterogeneity. Chloroquine prolonged QT interval and declined the T-wave amplitude. Although chloroquine reduced tissue’s temporal vulnerability, it increased the minimum substrate size necessary for sustaining re-entry. The actions of chloroquine decreased arrhythmia risk, due to the reduced tissue vulnerability, prolonged ERP and wavelength of re-entrant excitation waves, which in combination prevented and terminated re-entry in the tissue models. In conclusion, the results of this study provide new evidence that the anti-arrhythmic effects of chloroquine on SQT3 and, by extension, to the possibility that chloroquine may be a potential therapeutic agent for SQT3 treatment.

Influence of LVAD function on mechanical unloading and electromechanical delay: a simulation study

This study hypothesized that a left ventricular assist device (LVAD) shortens the electromechanical delay (EMD) by mechanical unloading. The goal of this study is to examine, by computational modeling, the influence of LVAD on EMD for four heart failure (HF) cases ranging from mild HF to severe HF. We constructed an integrated model of an LVAD-implanted cardiovascular system, then we altered the Ca²⁺ transient magnitude, with scaling factors 1, 0.9, 0.8, and 0.7 representing HF1, HF2, HF3, and HF4, respectively, in order of increasing HF severity. The four HF conditions are classified into two groups. Group one is the four HF conditions without LVAD, and group two is the conditions treated with continuous LVAD pump. The single-cell mechanical responses showed that EMD was prolonged with the higher load. The findings indicated that in group one, the HF-induced Ca2 + transient remodeling prolonged the mechanical activation time (MAT) and decreased the contractile tension, which reduced the left ventricle (LV) pressure, and increased the end-diastolic strain. In group two, LVAD shortened MAT of the ventricles. Furthermore, LVAD reduced the contractile tension, and end-diastolic strain, but increased the aortic pressure. The computational study demonstrated that LVAD shortens EMD by mechanical unloading of the ventricle.

Modelling the effects of quinidine, disopyramide, and E-4031 on short QT syndrome variant 3 in the human ventricles

OBJECTIVE

Short QT syndrome (SQTS) is an inherited cardiac channelopathy, but at present little information is available on its pharmacological treatment. SQT3 variant (linked to the inward rectifier potassium current I _K1) of SQTS, results from a gain-of-function mutation (Kir2.1 D172N) in the KCNJ2-encoded channels, which is associated with ventricular fibrillation (VF). Using biophysically-detailed human ventricular computer models, this study investigated the potential effects of quinidine, disopyramide, and E-4031 on SQT3.

APPROACH

The ten Tusscher et al model of human ventricular myocyte action potential (AP) was modified to recapitulate the changes in I _K1 due to heterozygous and homozygous forms of the D172N mutation. Wild-type (WT) and mutant WT-D172N and D172N formulations were incorporated into one-dimensional (1D) and 2D tissue models with transmural heterogeneities. Effects of drugs on channel-blocking activity were modelled using half-maximal inhibitory concentration (IC₅₀) and Hill coefficient (nH) values. Effects of drugs on AP duration (APD), effective refractory period (ERP) and QT interval of pseudo-ECGs were quantified, and both temporal and spatial vulnerability to re-entry was measured. Re-entry was simulated in the 2D ventricular tissue.

MAIN RESULTS

At the single cell level, the drugs quinidine, disopyramide, and E-4031 prolonged APD at 90% repolarization (APD₉₀), and decreased maximal transmural voltage heterogeneity (δV); this caused the decreased transmural dispersion of APD₉₀. Quinidine prolonged the QT interval and decreased the T-wave amplitude. Furthermore, quinidine increased ERP and reduced temporal vulnerability and increased spatial vulnerability, resulting in a reduced susceptibility to arrhythmogenesis in SQT3. In the 2D tissue, quinidine was effective in terminating and preventing re-entry associated with the heterozygous D172N condition. Quinidine exhibited significantly better therapeutic effects on SQT3 than disopyramide and E-4031.

SIGNIFICANCE

This study substantiates a causal link between quinidine and QT interval prolongation in SQT3 Kir2.1 mutations and highlights possible pharmacological agent quinidine for treating SQT3 patients.

Ventricular action potential adaptation to regular exercise: role of β-adrenergic and KATP channel function

Regular exercise training is known to affect the action potential duration (APD) and improve heart function, but involvement of β-adrenergic receptor (β-AR) subtypes and/or the ATP-sensitive K+ (KATP) channel is unknown. To address this, female and male Sprague-Dawley rats were randomly assigned to voluntary wheel-running or control groups; they were anesthetized after 6–8 wk of training, and myocytes were isolated. Exercise training significantly increased APD of apex and base myocytes at 1 Hz and decreased APD at 10 Hz. Ca2+ transient durations reflected the changes in APD, while Ca2+ transient amplitudes were unaffected by wheel running. The nonselective β-AR agonist isoproterenol shortened the myocyte APD, an effect reduced by wheel running. The isoproterenol-induced shortening of APD was largely reversed by the selective β1-AR blocker atenolol, but not the β2-AR blocker ICI 118,551, providing evidence that wheel running reduced the sensitivity of the β1-AR. At 10 Hz, the KATP channel inhibitor glibenclamide prolonged the myocyte APD more in exercise-trained than control rats, implicating a role for this channel in the exercise-induced APD shortening at 10 Hz. A novel finding of this work was the dual importance of altered β1-AR responsiveness and KATP channel function in the training-induced regulation of APD. Of physiological importance to the beating heart, the reduced response to adrenergic agonists would enhance cardiac contractility at resting rates, where sympathetic drive is low, by prolonging APD and Ca2+ influx; during exercise, an increase in KATP channel activity would shorten APD and, thus, protect the heart against Ca2+ overload or inadequate filling.

NEW & NOTEWORTHY Our data demonstrated that regular exercise prolonged the action potential and Ca2+ transient durations in myocytes isolated from apex and base regions at 1-Hz and shortened both at 10-Hz stimulation. Novel findings were that wheel running shifted the β-adrenergic receptor agonist dose-response curve rightward compared with controls by reducing β1-adrenergic receptor responsiveness and that, at the high activation rate, myocytes from trained animals showed higher KATP channel function.

In silico assessment of the effects of quinidine, disopyramide and E-4031 on short QT syndrome variant 1 in the human ventricles

Aims

Short QT syndrome (SQTS) is an inherited disorder associated with abnormally abbreviated QT intervals and an increased incidence of atrial and ventricular arrhythmias. SQT1 variant (linked to the rapid delayed rectifier potassium channel current, I_Kr) of SQTS, results from an inactivation-attenuated, gain-of-function mutation (N588K) in the KCNH2-encoded potassium channels. Pro-arrhythmogenic effects of SQT1 have been well characterized, but less is known about the possible pharmacological antiarrhythmic treatment of SQT1. Therefore, this study aimed to assess the potential effects of E-4031, disopyramide and quinidine on SQT1 using a mathematical model of human ventricular electrophysiology.

Methods

The ten Tusscher et al. biophysically detailed model of the human ventricular action potential (AP) was modified to incorporate I_Kr Markov chain (MC) formulations based on experimental data of the kinetics of the N588K mutation of the KCNH2-encoded subunit of the I_Kr channels. The modified ventricular cell model was then integrated into one-dimensional (1D) strand, 2D regular and realistic tissues with transmural heterogeneities. The channel-blocking effect of the drugs on ion currents in healthy and SQT1 cells was modeled using half-maximal inhibitory concentration (IC₅₀) and Hill coefficient (nH) values from literatures. Effects of drugs on cell AP duration (APD), effective refractory period (ERP) and pseudo-ECG traces were calculated. Effects of drugs on the ventricular temporal and spatial vulnerability to re-entrant excitation waves were measured. Re-entry was simulated in both 2D regular and realistic ventricular tissue.

Results

At the single cell level, the drugs E-4031 and disopyramide had hardly noticeable effects on the ventricular cell APD at 90% repolarization (APD₉₀), whereas quinidine caused a significant prolongation of APD₉₀. Quinidine prolonged and decreased the maximal transmural AP heterogeneity (δV); this led to the decreased transmural heterogeneity of APD across the 1D strand. Quinidine caused QT prolongation and a decrease in the T-wave amplitude, and increased ERP and decreased temporal susceptibility of the tissue to the initiation of re-entry and increased the minimum substrate size necessary to prevent re-entry in the 2D regular model, and further terminated re-entrant waves in the 2D realistic model. Quinidine exhibited significantly better therapeutic effects on SQT1 than E-4031 and disopyramide.

Conclusions

The simulated pharmacological actions of quinidine exhibited antiarrhythmic effects on SQT1. This study substantiates a causal link between quinidine and QT interval prolongation in SQT1 and suggests that quinidine may be a potential pharmacological agent for treating SQT1 patients.

Effects of amiodarone on short QT syndrome variant 3 in human ventricles: a simulation study

Background

Short QT syndrome (SQTS) is a newly identified clinical disorder associated with atrial and/or ventricular arrhythmias and increased risk of sudden cardiac death (SCD). The SQTS variant 3 is linked to D172N mutation to the KCNJ2 gene that causes a gain-of-function to the inward rectifier potassium channel current (I_K1), which shortens the ventricular action potential duration (APD) and effective refractory period (ERP). Pro-arrhythmogenic effects of SQTS have been characterized, but less is known about the possible pharmacological treatment of SQTS. Therefore, in this study, we used computational modeling to assess the effects of amiodarone, class III anti-arrhythmic agent, on human ventricular electrophysiology in SQT3.

Methods

The ten Tusscher et al. model for the human ventricular action potentials (APs) was modified to incorporate I_K1 formulations based on experimental data of Kir2.1 channels (including WT, WT-D172N and D172N conditions). The modified cell model was then implemented to construct one-dimensional (1D) and 2D tissue models. The blocking effects of amiodarone on ionic currents were modeled using IC₅₀ and Hill coefficient values from literatures. Effects of amiodarone on APD, ERP and pseudo-ECG traces were computed. Effects of the drug on the temporal and spatial vulnerability of ventricular tissue to genesis and maintenance of re-entry were measured, as well as on the dynamic behavior of re-entry.

Results

Amiodarone prolonged the ventricular cell APD and decreased the maximal voltage heterogeneity (δV) among three difference cells types across transmural ventricular wall, leading to a decreased transmural heterogeneity of APD along a 1D model of ventricular transmural strand. Amiodarone increased cellular ERP, prolonged QT interval and decreased the T-wave amplitude. It reduced tissue’s temporal susceptibility to the initiation of re-entry and increased the minimum substrate size necessary to sustain re-entry in the 2D tissue.

Conclusions

At the therapeutic-relevant concentration of amiodarone, the APD and ERP at the single cell level were increased significantly. The QT interval in pseudo-ECG was prolonged and the re-entry in tissue was prevented. This study provides further evidence that amiodarone may be a potential pharmacological agent for preventing arrhythmogenesis for SQT3 patients.

Electronic supplementary material

The online version of this article (doi:10.1186/s12938-017-0369-0) contains supplementary material, which is available to authorized users.

Naturally Engineered Maturation of Cardiomyocytes

Ischemic heart disease remains one of the most prominent causes of mortalities worldwide with heart transplantation being the gold-standard treatment option. However, due to the major limitations associated with heart transplants, such as an inadequate supply and heart rejection, there remains a significant clinical need for a viable cardiac regenerative therapy to restore native myocardial function. Over the course of the previous several decades, researchers have made prominent advances in the field of cardiac regeneration with the creation of in vitro human pluripotent stem cell-derived cardiomyocyte tissue engineered constructs. However, these engineered constructs exhibit a functionally immature, disorganized, fetal-like phenotype that is not equivalent physiologically to native adult cardiac tissue. Due to this major limitation, many recent studies have investigated approaches to improve pluripotent stem cell-derived cardiomyocyte maturation to close this large functionality gap between engineered and native cardiac tissue. This review integrates the natural developmental mechanisms of cardiomyocyte structural and functional maturation. The variety of ways researchers have attempted to improve cardiomyocyte maturation in vitro by mimicking natural development, known as natural engineering, is readily discussed. The main focus of this review involves the synergistic role of electrical and mechanical stimulation, extracellular matrix interactions, and non-cardiomyocyte interactions in facilitating cardiomyocyte maturation. Overall, even with these current natural engineering approaches, pluripotent stem cell-derived cardiomyocytes within three-dimensional engineered heart tissue still remain mostly within the early to late fetal stages of cardiomyocyte maturity. Therefore, although the end goal is to achieve adult phenotypic maturity, more emphasis must be placed on elucidating how the in vivo fetal microenvironment drives cardiomyocyte maturation. This information can then be utilized to develop natural engineering approaches that can emulate this fetal microenvironment and thus make prominent progress in pluripotent stem cell-derived maturity toward a more clinically relevant model for cardiac regeneration.

Mechanisms Underlying the Emergence of Post-acidosis Arrhythmia at the Tissue Level: A Theoretical Study

Acidosis has complex electrophysiological effects, which are associated with a high recurrence of ventricular arrhythmias. Through multi-scale cardiac computer modeling, this study investigated the mechanisms underlying the emergence of post-acidosis arrhythmia at the tissue level. In simulations, ten Tusscher-Panfilov ventricular model was modified to incorporate various data on acidosis-induced alterations of cellular electrophysiology and intercellular electrical coupling. The single cell models were incorporated into multicellular one-dimensional (1D) fiber and 2D sheet tissue models. Electrophysiological effects were quantified as changes of action potential profile, sink-source interactions of fiber tissue, and the vulnerability of tissue to the genesis of unidirectional conduction that led to initiation of re-entry. It was shown that acidosis-induced sarcoplasmic reticulum (SR) calcium load contributed to delayed afterdepolarizations (DADs) in single cells. These DADs may be synchronized to overcome the source-sink mismatch arising from intercellular electrotonic coupling, and produce a premature ventricular complex (PVC) at the tissue level. The PVC conduction can be unidirectionally blocked in the transmural ventricular wall with altered electrical heterogeneity, resulting in the genesis of re-entry. In conclusion, altered source-sink interactions and electrical heterogeneity due to acidosis-induced cellular electrophysiological alterations may increase susceptibility to post-acidosis ventricular arrhythmias.

Electrophysiological properties of computational human ventricular cell action potential models under acute ischemic conditions

Acute myocardial ischemia is one of the main causes of sudden cardiac death. The mechanisms have been investigated primarily in experimental and computational studies using different animal species, but human studies remain scarce. In this study, we assess the ability of four human ventricular action potential models (ten Tusscher and Panfilov, 2006; Grandi et al., 2010; Carro et al., 2011; O'Hara et al., 2011) to simulate key electrophysiological consequences of acute myocardial ischemia in single cell and tissue simulations. We specifically focus on evaluating the effect of extracellular potassium concentration and activation of the ATP-sensitive inward-rectifying potassium current on action potential duration, post-repolarization refractoriness, and conduction velocity, as the most critical factors in determining reentry vulnerability during ischemia. Our results show that the Grandi and O'Hara models required modifications to reproduce expected ischemic changes, specifically modifying the intracellular potassium concentration in the Grandi model and the sodium current in the O'Hara model. With these modifications, the four human ventricular cell AP models analyzed in this study reproduce the electrophysiological alterations in repolarization, refractoriness, and conduction velocity caused by acute myocardial ischemia. However, quantitative differences are observed between the models and overall, the ten Tusscher and modified O'Hara models show closest agreement to experimental data.

The effect of electrical conductivity of myocardium on cardiac pumping efficacy: a computational study

Background and aims

The existence of non-excitable cells in the myocardium leads to the increasing conduction non-uniformity and decreasing myocardial electrical conductivity. Slowed myocardial conduction velocity (MCV) believed to enhance the probability of cardiac arryhthmia and alter the cardiac mechanical pumping efficacy, even in sinus rhythm. Though several studies on the correlation between MCV and cardiac electrical instabilities exist, there has been no study concerning correlation or causality between MCV and cardiac mechanical pumping efficacy, due to the limitation in clinical methods to document and evaluate cardiac mechanical responses directly. The goal of this study was to examine quantitatively the cardiac pumping efficacy under various MCV conditions using three-dimensional (3D) electromechanical model of canine’s failing ventricle.

Methods

The electromechanical model used in this study composed of the electrical model coupled with the mechanical contraction model along with a lumped model of the circulatory system. The electrical model consisted of 241,725 nodes and 1,298,751 elements of tetrahedral mesh, whereas the mechanical model consisted of 356 nodes and 172 elements of hexahedral mesh with Hermite basis. First, we performed the electrical simulation for five different MCV conditions, from 30 to 70 cm/s with 10 cm/s interval during sinus pacing. Then, we compared the cardiac electrical and mechanical responses of each MCV condition, such as the electrical activation time (EAT), pressure, volume, and energy consumption of the myocardium. The energy consumption of the myocardium was calculated by integrating ATP consumption rate of each node in myofilament model.

Results

The result showed that under higher MCV conditions, the EAT, energy consumption, end diastolic and systolic volume are gradually decreased. Meanwhile, the systolic pressure, stroke volume, stroke work, and stroke work to ATP are increased as the MCV values increased. The cardiac functions and performances are more efficient under higher MCV conditions by consuming smaller energy (ATP) while carrying more works.

Conclusion

In conclusion, this study reveals that MCV has strong correlation with the cardiac pumping efficacy. The obtained results provide useful information to estimate the effect of MCV on the electro-physiology and hemodynamic responses of the ventricle and can be used for further study about arrhythmogeneis and heart failure.

Limitations in electrophysiological model development and validation caused by differences between simulations and experimental protocols

Models of ion channel dynamics are usually built by fitting isolated cell experimental values of individual parameters while neglecting the interaction between them. Another shortcoming regards the estimation of ionic current conductances, which is often based on quantification of Action Potential (AP)-derived markers. Although this procedure reduces the uncertainty in the calculation of conductances, many studies evaluate electrophysiological AP-derived markers from single cell simulations, whereas experimental measurements are obtained from tissue preparations. In this work, we explore the limitations of these approaches to estimate ion channel dynamics and maximum current conductances and how they could be overcome by using multiscale simulations of experimental protocols. Four human ventricular cell models, namely ten Tusscher and Panfilov (2006), Grandi et al. (2010), O'Hara et al. (2011), and Carro et al. (2011), were used. Two problems involving scales from ion channels to tissue were investigated: 1) characterization of L-type calcium voltage-dependent inactivation I_Ca,L; 2) identification of major ionic conductance contributors to steady-state AP markers, including APD₉₀, APD₇₅, APD₅₀, APD₂₅, Triangulation and maximal and minimal values of V and dV/dt during the AP (V_max, V_min, dV/dt_max, dV/dt_min). Our results show that: 1) I_Ca,L inactivation characteristics differed significantly when calculated from model equations and from simulations reproducing the experimental protocols. 2) Large differences were found in the ionic currents contributors to APD₂₅, Triangulation, V_max, dV/dt_max and dV/dt_min between single cells and 1D-tissue. When proposing any new model formulation, or evaluating an existing model, consistency between simulated and experimental data should be verified considering all involved effects and scales.

Changes in Intracellular Na+ following Enhancement of Late Na+ Current in Virtual Human Ventricular Myocytes

The slowly inactivating or late Na+ current, INa-L, can contribute to the initiation of both atrial and ventricular rhythm disturbances in the human heart. However, the cellular and molecular mechanisms that underlie these pro-arrhythmic influences are not fully understood. At present, the major working hypothesis is that the Na+ influx corresponding to INa-L significantly increases intracellular Na+, [Na+]i; and the resulting reduction in the electrochemical driving force for Na+ reduces and (may reverse) Na+/Ca2+ exchange. These changes increase intracellular Ca2+, [Ca2+]i; which may further enhance INa-L due to calmodulin-dependent phosphorylation of the Na+ channels. This paper is based on mathematical simulations using the O'Hara et al (2011) model of baseline or healthy human ventricular action potential waveforms(s) and its [Ca2+]i homeostasis mechanisms. Somewhat surprisingly, our results reveal only very small changes (≤ 1.5 mM) in [Na+]i even when INa-L is increased 5-fold and steady-state stimulation rate is approximately 2 times the normal human heart rate (i.e. 2 Hz). Previous work done using well-established models of the rabbit and human ventricular action potential in heart failure settings also reported little or no change in [Na+]i when INa-L was increased. Based on our simulations, the major short-term effect of markedly augmenting INa-L is a significant prolongation of the action potential and an associated increase in the likelihood of reactivation of the L-type Ca2+ current, ICa-L. Furthermore, this action potential prolongation does not contribute to [Na+]i increase.

Optogenetic defibrillation terminates ventricular arrhythmia in mouse hearts and human simulations

Ventricular arrhythmias are among the most severe complications of heart disease and can result in sudden cardiac death. Patients at risk currently receive implantable defibrillators that deliver electrical shocks to terminate arrhythmias on demand. However, strong electrical shocks can damage the heart and cause severe pain. Therefore, we have tested optogenetic defibrillation using expression of the light-sensitive channel channelrhodopsin-2 (ChR2) in cardiac tissue. Epicardial illumination effectively terminated ventricular arrhythmias in hearts from transgenic mice and from WT mice after adeno-associated virus-based gene transfer of ChR2. We also explored optogenetic defibrillation for human hearts, taking advantage of a recently developed, clinically validated in silico approach for simulating infarct-related ventricular tachycardia (VT). Our analysis revealed that illumination with red light effectively terminates VT in diseased, ChR2-expressing human hearts. Mechanistically, we determined that the observed VT termination is due to ChR2-mediated transmural depolarization of the myocardium, which causes a block of voltage-dependent Na+ channels throughout the myocardial wall and interrupts wavefront propagation into illuminated tissue. Thus, our results demonstrate that optogenetic defibrillation is highly effective in the mouse heart and could potentially be translated into humans to achieve nondamaging and pain-free termination of ventricular arrhythmia.

Human-based approaches to pharmacology and cardiology: an interdisciplinary and intersectorial workshop

Both biomedical research and clinical practice rely on complex datasets for the physiological and genetic characterization of human hearts in health and disease. Given the complexity and variety of approaches and recordings, there is now growing recognition of the need to embed computational methods in cardiovascular medicine and science for analysis, integration and prediction. This paper describes a Workshop on Computational Cardiovascular Science that created an international, interdisciplinary and inter-sectorial forum to define the next steps for a human-based approach to disease supported by computational methodologies. The main ideas highlighted were (i) a shift towards human-based methodologies, spurred by advances in new in silico, in vivo, in vitro, and ex vivo techniques and the increasing acknowledgement of the limitations of animal models. (ii) Computational approaches complement, expand, bridge, and integrate in vitro, in vivo, and ex vivo experimental and clinical data and methods, and as such they are an integral part of human-based methodologies in pharmacology and medicine. (iii) The effective implementation of multi- and interdisciplinary approaches, teams, and training combining and integrating computational methods with experimental and clinical approaches across academia, industry, and healthcare settings is a priority. (iv) The human-based cross-disciplinary approach requires experts in specific methodologies and domains, who also have the capacity to communicate and collaborate across disciplines and cross-sector environments. (v) This new translational domain for human-based cardiology and pharmacology requires new partnerships supported financially and institutionally across sectors. Institutional, organizational, and social barriers must be identified, understood and overcome in each specific setting.

Comparison of Electric- and Magnetic-Cardiograms Produced by Myocardial Ischemia in Models of the Human Ventricle and Torso

Myocardial ventricular ischemia arises from a lack of blood supply to the heart, which may cause abnormal repolarization and excitation wave conduction patterns in the tissue, leading to cardiac arrhythmias and even sudden death. Current diagnosis of cardiac ischemia by the 12-lead electrocardiogram (ECG) has limitations as they are insensitive in many cases and may show unnoticeable differences to normal patterns. As the magnetic field provides extra information on cardiac excitation and is more sensitive to tangential currents to the surface of the chest, whereas the electric field is more sensitive to flux currents, it has been hypothesized that the magnetocardiogram (MCG) may provide a complementary method to the ECG in ischemic diagnosis. However, it is unclear yet about the differences in sensitivity regions of body surface ECG and MCG signals to ischemic conditions. The aim of this study was to investigate such differences by using 12-, 36- ECG and 36-MCG computed from multi-scale biophysically detailed computational models of the human ventricles and torso in both control and ischemic conditions. It was shown that ischemia produced changes in the ECG and MCG signals in the QRS complex, T-wave and ST-segment, with greater relative differences seen in the 36-lead ECG and MCG as compared to the 12-leads ECG (34% and 37% vs 26%, respectively). The 36-lead ECG showed more averaged sensitivity than the MCG in the change of T-wave due to ischemia (37% vs 32%, respectively), whereas the MCG showed greater sensitivity than the ECG in the change of the ST-segment (50% vs 40%, respectively). In addition, both MCG and ECG showed regional-dependent changes to ischemia, but with MCG showing a stronger correlation between ischemic region in the heart. In conclusion, MCG shows more sensitivity than ECG in response to ischemia, which may provide an alternative method for the diagnosis of ischemia.

Pro-arrhythmogenic effects of CACNA1C G1911R mutation in human ventricular tachycardia: insights from cardiac multi-scale models

Mutations in the CACNA1C gene are associated with ventricular tachycardia (VT). Although the CACNA1C mutations were well identified in patients with cardiac arrhythmias, mechanisms by which cardiac arrhythmias are generated in such genetic mutation conditions remain unclear. In this study, we identified a novel mechanism of VT resulted from enhanced repolarization dispersion which is a key factor for arrhythmias in the CACNA1C G1911R mutation using multi-scale computational models of the human ventricle. The increased calcium influx in the mutation prolonged action potential duration (APD), produced steepened action potential duration restitution (APDR) curves as well as augmented membrane potential differences among different cell types during repolarization, increasing transmural dispersion of repolarization (DOR) and the spatial and temporal heterogeneity of cardiac electrical activities. Consequentially, the vulnerability to unidirectional conduction block in response to a premature stimulus increased at tissue level in the G1911R mutation. The increased functional repolarization dispersion anchored reentrant excitation waves in tissue and organ models, facilitating the initiation and maintenance of VT due to less meandering rotor tip. Thus, the increased repolarization dispersion caused by the G1911R mutation is a primary factor that may primarily contribute to the genesis of cardiac arrhythmias in Timothy Syndrome.

Ventricular fiber optimization utilizing the branching structure

In this paper, we propose an algorithm that optimizes the ventricular fiber structure of the human heart. A number of histological studies and diffusion tensor magnetic resonance imaging analyses have revealed that the myocardial fiber forms a right-handed helix at the endocardium. However, the fiber formation changes its orientation as a function of transmural depth, becoming a left-handed helix at the epicardium. To determine how nature can construct such a structure, which obtains surprising pumping performance, we introduce macroscopic modeling of the branching structure of cardiac myocytes in our finite element ventricular model and utilize this in an optimization process. We put a set of multidirectional fibers around a central fiber orientation at each point of the ventricle walls and simulate heartbeats by generating contraction forces along each of these directions. We examine two optimization processes using the workloads or impulses measured in these directions to update the central fiber orientation. Both processes improve the pumping performance towards an optimal value within several tens of heartbeats, starting from an almost-flat fiber orientation. However, compared with the workload optimization, the impulse optimization produces better agreement with experimental studies on transmural changes of fiber helix angle, streamline patterns of characteristic helical structures, and temporal changes in strain. Furthermore, the impulse optimization is robust under geometrical changes of the heart and tends to homogenize various mechanical factors such as the stretch and stretch rate along the fiber orientation, the contraction force, and energy consumption. Copyright © 2015 John Wiley & Sons, Ltd.

Effects of Heterogeneous Diffuse Fibrosis on Arrhythmia Dynamics and Mechanism

Myocardial fibrosis is an important risk factor for cardiac arrhythmias. Previous experimental and numerical studies have shown that the texture and spatial distribution of fibrosis may play an important role in arrhythmia onset. Here, we investigate how spatial heterogeneity of fibrosis affects arrhythmia onset using numerical methods. We generate various tissue textures that differ by the mean amount of fibrosis, the degree of heterogeneity and the characteristic size of heterogeneity. We study the onset of arrhythmias using a burst pacing protocol. We confirm that spatial heterogeneity of fibrosis increases the probability of arrhythmia induction. This effect is more pronounced with the increase of both the spatial size and the degree of heterogeneity. The induced arrhythmias have a regular structure with the period being mostly determined by the maximal local fibrosis level. We perform ablations of the induced fibrillatory patterns to classify their type. We show that in fibrotic tissue fibrillation is usually of the mother rotor type but becomes of the multiple wavelet type with increase in tissue size. Overall, we conclude that the most important factor determining the formation and dynamics of arrhythmia in heterogeneous fibrotic tissue is the value of maximal local fibrosis.

Reconstructing three-dimensional reentrant cardiac electrical wave dynamics using data assimilation

For many years, reentrant scroll waves have been predicted and studied as an underlying mechanism for cardiac arrhythmias using numerical techniques, and high-resolution mapping studies using fluorescence recordings from the surfaces of cardiac tissue preparations have confirmed the presence of visible spiral waves. However, assessing the three-dimensional dynamics of these reentrant waves using experimental techniques has been limited to verifying stable scroll-wave dynamics in relatively thin preparations. We propose a different approach to recovering the three-dimensional dynamics of reentrant waves in the heart. By applying techniques commonly used in weather forecasting, we combine dual-surface observations from a particular experiment with predictions from a numerical model to reconstruct the full three-dimensional time series of the experiment. Here, we use model-generated surrogate observations from a numerical experiment to evaluate the performance of the ensemble Kalman filter in reconstructing such time series for a discordant alternans state in one spatial dimension and for scroll waves in three dimensions. We show that our approach is able to recover time series of both observed and unobserved variables matching the truth. Where nearby observations are available, the error is reduced below the synthetic observation error, with a smaller reduction with increased distance from observations. Our findings demonstrate that state reconstruction for spatiotemporally complex cardiac electrical dynamics is possible and will lead naturally to applications using real experimental data.

Myokit: A simple interface to cardiac cellular electrophysiology

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

EFFECTS OF ACUTE GLOBAL ISCHEMIA ON RE-ENTRANT ARRHYTHMOGENESIS: A SIMULATION STUDY

Sudden cardiac death is mainly caused by arrhythmogenesis. For a functional abnormal heart, such as an ischemic heart, the probability of arrhythmia occurring is greatly increased. During myocardial ischemia, re-entry is prone to degenerate into ventricular fibrillation (VF). Therefore it has important meaning to investigate the intricate mechanisms underlying VF under an ischemic condition in order to better facilitate therapeutic interventions. In this paper, to analyze the functional influence of acute global ischemia on cardiac electrical activity and subsequently on re-entrant arrhythmogenesis, we take into account three main pathophysiological consequences of ischemia: hyperkalaemia, acidosis, and anoxia, and develop a 3D human ventricular ischemic model that combines a detailed biophysical description of the excitation kinetics of human ventricular cells with an integrated geometry of human ventricular tissue which incorporates fiber direction anisotropy and the stimulation activation sequence. The results show that under acute global ischemia, the tissue excitability and the slope of ventricular cellular action potential duration restitution (APDR) are greatly decreased. As a result, the complexity of VF activation patterns is reduced. For the three components of ischemia, hyperkalaemia is the dominant contributor to the stability of re-entry under acute global ischemia. Increasing [K+]o acts to prolong the cell refractory period, reduce the tissue excitability and slow the conduction velocity. Our results also show that VF can be eliminated by decreasing cellular excitability, primarily by elevating the concentration value of extracellular K+.

Abnormal calcium homeostasis in heart failure with preserved ejection fraction is related to both reduced contractile function and incomplete relaxation: an electromechanically detailed biophysical modeling study

Heart failure with preserved ejection fraction (HFpEF) accounts for about 50% of heart failure cases. It has features of incomplete relaxation and increased stiffness of the left ventricle. Studies from clinical electrophysiology and animal experiments have found that HFpEF is associated with impaired calcium homeostasis, ion channel remodeling and concentric left ventricle hypertrophy (LVH). However, it is still unclear how the abnormal calcium homeostasis, ion channel and structural remodeling affect the electro-mechanical dynamics of the ventricles. In this study we have developed multiscale models of the human left ventricle from single cells to the 3D organ, which take into consideration HFpEF-induced changes in calcium handling, ion channel remodeling and concentric LVH. Our simulation results suggest that at the cellular level, HFpEF reduces the systolic calcium level resulting in a reduced systolic contractile force, but elevates the diastolic calcium level resulting in an abnormal residual diastolic force. In our simulations, these abnormal electro-mechanical features of the ventricular cells became more pronounced with the increase of the heart rate. However, at the 3D organ level, the ejection fraction of the left ventricle was maintained due to the concentric LVH. The simulation results of this study mirror clinically observed features of HFpEF and provide new insights toward the understanding of the cellular bases of impaired cardiac electromechanical functions in heart failure.

A second-generation computational modeling of cardiac electrophysiology: response of action potential to ionic concentration changes and metabolic inhibition

Background

Cardiac arrhythmias are becoming one of the major health care problem in the world, causing numerous serious disease conditions including stroke and sudden cardiac death. Furthermore, cardiac arrhythmias are intimately related to the signaling ability of cardiac cells, and are caused by signaling defects. Consequently, modeling the electrical activity of the heart, and the complex signaling models that subtend dangerous arrhythmias such as tachycardia and fibrillation, necessitates a quantitative model of action potential (AP) propagation. Yet, many electrophysiological models, which accurately reproduce dynamical characteristic of the action potential in cells, have been introduced. However, these models are very complex and are very time consuming computationally. Consequently, a large amount of research is consecrated to design models with less computational complexity.

Results

This paper is presenting a new model for analyzing the propagation of ionic concentrations and electrical potential in space and time. In this model, the transport of ions is governed by Nernst-Planck flux equation (NP), and the electrical interaction of the species is described by a new cable equation. These set of equations form a system of coupled partial nonlinear differential equations that is solved numerically. In the first we describe the mathematical model. To realize the numerical simulation of our model, we proceed by a finite element discretization and then we choose an appropriate resolution algorithm.

Conclusions

We give numerical simulations obtained for different input scenarios in the case of suicide substrate reaction which were compared to those obtained in literature. These input scenarios have been chosen so as to provide an intuitive understanding of dynamics of the model. By accessing time and space domains, it is shown that interpreting the electrical potential of cell membrane at steady state is incorrect. This model is general and applies to ions of any charge in space and time domains. The results obtained show a complete agreement with literature findings and also with the physical interpretation of the phenomenon. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of the proposed method. In particular, we show that the scheme is second-order accurate in space.

Electrophysiological and structural remodeling in heart failure modulate arrhythmogenesis. 1D simulation study

Background

Heart failure is a final common pathway or descriptor for various cardiac pathologies. It is associated with sudden cardiac death, which is frequently caused by ventricular arrhythmias. Electrophysiological remodeling, intercellular uncoupling, fibrosis and autonomic imbalance have been identified as major arrhythmogenic factors in heart failure etiology and progression.

Objective

In this study we investigate in silico the role of electrophysiological and structural heart failure remodeling on the modulation of key elements of the arrhythmogenic substrate, i.e., electrophysiological gradients and abnormal impulse propagation.

Methods

Two different mathematical models of the human ventricular action potential were used to formulate models of the failing ventricular myocyte. This provided the basis for simulations of the electrical activity within a transmural ventricular strand. Our main goal was to elucidate the roles of electrophysiological and structural remodeling in setting the stage for malignant life-threatening arrhythmias.

Results

Simulation results illustrate how the presence of M cells and heterogeneous electrophysiological remodeling in the human failing ventricle modulate the dispersion of action potential duration and repolarization time. Specifically, selective heterogeneous remodeling of expression levels for the Na⁺/Ca²⁺ exchanger and SERCA pump decrease these heterogeneities. In contrast, fibroblast proliferation and cellular uncoupling both strongly increase repolarization heterogeneities. Conduction velocity and the safety factor for conduction are also reduced by the progressive structural remodeling during heart failure.

Conclusion

An extensive literature now establishes that in human ventricle, as heart failure progresses, gradients for repolarization are changed significantly by protein specific electrophysiological remodeling (either homogeneous or heterogeneous). Our simulations illustrate and provide new insights into this. Furthermore, enhanced fibrosis in failing hearts, as well as reduced intercellular coupling, combine to increase electrophysiological gradients and reduce electrical propagation. In combination these changes set the stage for arrhythmias.

Adverse remodeling of the electrophysiological response to ischemia-reperfusion in human heart failure is associated with remodeling of metabolic gene expression

BACKGROUND

Ventricular arrhythmias occur more frequently in heart failure during episodes of ischemia-reperfusion although the mechanisms underlying this in humans are unclear. We assessed, in explanted human hearts, the remodeled electrophysiological response to acute ischemia-reperfusion in heart failure and its potential causes, including the remodeling of metabolic gene expression.

METHODS AND RESULTS

We optically mapped coronary-perfused left ventricular wedge preparations from 6 human end-stage failing hearts (F) and 6 donor hearts rejected for transplantation (D). Preparations were subjected to 30 minutes of global ischemia, followed by 30 minutes of reperfusion. Failing hearts had exaggerated electrophysiological responses to ischemia-reperfusion, with greater action potential duration shortening (P<0.001 at 8-minute ischemia; P=0.001 at 12-minute ischemia) and greater conduction slowing during ischemia, delayed recovery of electric excitability after reperfusion (F, 4.8±1.8 versus D, 1.0±0 minutes; P<0.05), and incomplete restoration of action potential duration and conduction velocity early after reperfusion. Expression of 46 metabolic genes was probed using custom-designed TaqMan arrays, using extracted RNA from 15 failing and 9 donor hearts. Ten genes important in cardiac metabolism were downregulated in heart failure, with SLC27A4 and KCNJ11 significantly downregulated at a false discovery rate of 0%.

CONCLUSIONS

We demonstrate, for the first time in human hearts, that the electrophysiological response to ischemia-reperfusion in heart failure is accelerated during ischemia with slower recovery after reperfusion. This can enhance spatial conduction and repolarization gradients across the ischemic border and increase arrhythmia susceptibility. This adverse response was associated with downregulation of expression of cardiac metabolic genes.

Electrophysiological and structural remodeling in heart failure modulate arrhythmogenesis. 2D simulation study

BACKGROUND

Heart failure is operationally defined as the inability of the heart to maintain blood flow to meet the needs of the body and it is the final common pathway of various cardiac pathologies. Electrophysiological remodeling, intercellular uncoupling and a pro-fibrotic response have been identified as major arrhythmogenic factors in heart failure.

OBJECTIVE

In this study we investigate vulnerability to reentry under heart failure conditions by incorporating established electrophysiological and anatomical remodeling using computer simulations.

METHODS

The electrical activity of human transmural ventricular tissue (5 cm × 5 cm) was simulated using the human ventricular action potential model Grandi et al. under control and heart failure conditions. The MacCannell et al. model was used to model fibroblast electrical activity, and their electrotonic interactions with myocytes. Selected degrees of diffuse fibrosis and variations in intercellular coupling were considered and the vulnerable window (VW) for reentry was evaluated following cross-field stimulation.

RESULTS

No reentry was observed in normal conditions or in the presence of HF ionic remodeling. However, defined amount of fibrosis and/or cellular uncoupling were sufficient to elicit reentrant activity. Under conditions where reentry was generated, HF electrophysiological remodeling did not alter the width of the VW. However, intermediate fibrosis and cellular uncoupling significantly widened the VW. In addition, biphasic behavior was observed, as very high fibrotic content or very low tissue conductivity hampered the development of reentry. Detailed phase analysis of reentry dynamics revealed an increase of phase singularities with progressive fibrotic components.

CONCLUSION

Structural remodeling is a key factor in the genesis of vulnerability to reentry. A range of intermediate levels of fibrosis and intercellular uncoupling can combine to favor reentrant activity.

Developing a novel comprehensive framework for the investigation of cellular and whole heart electrophysiology in the in situ human heart: historical perspectives, current progress and future prospects

Understanding the mechanisms of fatal ventricular arrhythmias is of great importance. In view of the many electrophysiological differences that exist between animal species and humans, the acquisition of basic electrophysiological data in the intact human heart is essential to drive and complement experimental work in animal and in-silico models. Over the years techniques have been developed to obtain basic electrophysiological signals directly from the patients by incorporating these measurements into routine clinical procedures which access the heart such as cardiac catheterisation and cardiac surgery. Early recordings with monophasic action potentials provided valuable information including normal values for the in vivo human heart, cycle length dependent properties, the effect of ischaemia, autonomic nervous system activity, and mechano-electric interaction. Transmural recordings addressed the controversial issue of the mid myocardial "M" cell. More recently, the technique of multielectrode mapping (256 electrodes) developed in animal models has been extended to humans, enabling mapping of activation and repolarisation on the entire left and right ventricular epicardium in patients during cardiac surgery. Studies have examined the issue of whether ventricular fibrillation was driven by a "mother" rotor with inhomogeneous and fragmented conduction as in some animal models, or by multiple wavelets as in other animal studies; results showed that both mechanisms are operative in humans. The simpler spatial organisation of human VF has important implications for treatment and prevention. To link in-vivo human electrophysiological mapping with cellular biophysics, multielectrode mapping is now being combined with myocardial biopsies. This technique enables region-specific electrophysiology changes to be related to underlying cellular biology, for example: APD alternans, which is a precursor of VF and sudden death. The mechanism is incompletely understood but related to calcium cycling and APD restitution. Multielectrode sock mapping during incremental pacing enables epicardial sites to be identified which exhibit marked APD alternans and sites where APD alternans is absent. Whole heart electrophysiology is assessed by activation repolarisation mapping and analysis is performed immediately on-site in order to guide biopsies to specific myocardial sites. Samples are analysed for ion channel expression, Ca(2+)-handling proteins, gap junctions and extracellular matrix. This new comprehensive approach to bridge cellular and whole heart electrophysiology allowed to identify 20 significant changes in mRNA for ion channels Ca(2+)-handling proteins, a gap junction channel, a Na(+)-K(+) pump subunit and receptors (particularly Kir 2.1) between the positive and negative alternans sites.

A quantitative comparison of the behavior of human ventricular cardiac electrophysiology models in tissue

Numerical integration of mathematical models of heart cell electrophysiology provides an important computational tool for studying cardiac arrhythmias, but the abundance of available models complicates selecting an appropriate model. We study the behavior of two recently published models of human ventricular action potentials, the Grandi-Pasqualini-Bers (GPB) and the O'Hara-Virág-Varró-Rudy (OVVR) models, and compare the results with four previously published models and with available experimental and clinical data. We find the shapes and durations of action potentials and calcium transients differ between the GPB and OVVR models, as do the magnitudes and rate-dependent properties of transmembrane currents and the calcium transient. Differences also occur in the steady-state and S1–S2 action potential duration and conduction velocity restitution curves, including a maximum conduction velocity for the OVVR model roughly half that of the GPB model and well below clinical values. Between single cells and tissue, both models exhibit differences in properties, including maximum upstroke velocity, action potential amplitude, and minimum diastolic interval. Compared to experimental data, action potential durations for the GPB and OVVR models agree fairly well (although OVVR epicardial action potentials are shorter), but maximum slopes of steady-state restitution curves are smaller. Although studies show alternans in normal hearts, it occurs only in the OVVR model, and only for a narrow range of cycle lengths. We find initiated spiral waves do not progress to sustained breakup for either model. The dominant spiral wave period of the GPB model falls within clinically relevant values for ventricular tachycardia (VT), but for the OVVR model, the dominant period is longer than periods associated with VT. Our results should facilitate choosing a model to match properties of interest in human cardiac tissue and to replicate arrhythmia behavior more closely. Furthermore, by indicating areas where existing models disagree, our findings suggest avenues for further experimental work.

Characterization of Trans-septal Activation During Septal Pacing

Background—

Identification of intramural basal-septal ventricular tachycardia (VT) substrate is challenging in nonischemic cardiomyopathy. We sought to (1) characterize normal/abnormal trans-septal right ventricular (RV) to left ventricular activation; (2) assess the effect of opposite RV pacing on left ventricular septal bipolar electrograms (EGMs); and (3) establish criteria for the identification of intramural septal VT substrate.

Methods and Results—

Endocardial activation mapping and local EGM assessment of the left interventricular septum was performed during RV basal septal pacing in 40 patients undergoing VT ablation with no evidence of septal scar (group 1, n=14) and with septal scar (group 2, n=26) defined by low septal unipolar voltage (<8.3 mV) and delayed enhancement on cardiac MRI with/without abnormal bipolar voltage (<1.5 mV) in sinus rhythm. Left ventricular trans-septal activation time was prolonged in Group 2 compared with Group 1 (55.3±33.0 versus 25.7±8.8 ms; P =0.003). In 6 group 2 patients, left ventricular septal breakthrough was displaced to the scar border. During RV pacing, group 2 had fractionated (8.8%), late (2.8%), and split (5.7%) EGMs not seen in group 1. Trans-septal activation >40 ms (sensitivity 60%, specificity 100%; P <0.001) and EGM duration >95 ms during pacing (sensitivity 22%, specificity 91%; P <0.001) identified septal scar (13/26 pts).

Conclusions—

In patients with nonischemic cardiomyopathy, VT and septal scar, delayed transmural conduction time (>40 ms) and fractionated, late, split, and wide (>95 ms) bipolar EGMs during RV basal pacing identify intramural VT substrate. In select cases, the basal septum appears compartmentalized as the stimulated wavefront is rerouted to the scar border.

Hyperkalemic cardioplegia for adult and pediatric surgery: end of an era?

Despite surgical proficiency and innovation driving low mortality rates in cardiac surgery, the disease severity, comorbidity rate, and operative procedural difficulty have increased. Today's cardiac surgery patient is older, has a "sicker" heart and often presents with multiple comorbidities; a scenario that was relatively rare 20 years ago. The global challenge has been to find new ways to make surgery safer for the patient and more predictable for the surgeon. A confounding factor that may influence clinical outcome is high K(+) cardioplegia. For over 40 years, potassium depolarization has been linked to transmembrane ionic imbalances, arrhythmias and conduction disturbances, vasoconstriction, coronary spasm, contractile stunning, and low output syndrome. Other than inducing rapid electrochemical arrest, high K(+) cardioplegia offers little or no inherent protection to adult or pediatric patients. This review provides a brief history of high K(+) cardioplegia, five areas of increasing concern with prolonged membrane K(+) depolarization, and the basic science and clinical data underpinning a new normokalemic, "polarizing" cardioplegia comprising adenosine and lidocaine (AL) with magnesium (Mg(2+)) (ALM™). We argue that improved cardioprotection, better outcomes, faster recoveries and lower healthcare costs are achievable and, despite the early predictions from the stent industry and cardiology, the "cath lab" may not be the place where the new wave of high-risk morbid patients are best served.

In silico investigation of the short QT syndrome, using human ventricle models incorporating electromechanical coupling

INTRODUCTION

Genetic forms of the Short QT Syndrome (SQTS) arise due to cardiac ion channel mutations leading to accelerated ventricular repolarization, arrhythmias and sudden cardiac death. Results from experimental and simulation studies suggest that changes to refractoriness and tissue vulnerability produce a substrate favorable to re-entry. Potential electromechanical consequences of the SQTS are less well-understood. The aim of this study was to utilize electromechanically coupled human ventricle models to explore electromechanical consequences of the SQTS.

METHODS AND RESULTS

The Rice et al. mechanical model was coupled to the ten Tusscher et al. ventricular cell model. Previously validated K(+) channel formulations for SQT variants 1 and 3 were incorporated. Functional effects of the SQTS mutations on [Ca(2+)] i transients, sarcomere length shortening and contractile force at the single cell level were evaluated with and without the consideration of stretch-activated channel current (I sac). Without I sac, at a stimulation frequency of 1Hz, the SQTS mutations produced dramatic reductions in the amplitude of [Ca(2+)] i transients, sarcomere length shortening and contractile force. When I sac was incorporated, there was a considerable attenuation of the effects of SQTS-associated action potential shortening on Ca(2+) transients, sarcomere shortening and contractile force. Single cell models were then incorporated into 3D human ventricular tissue models. The timing of maximum deformation was delayed in the SQTS setting compared to control.

CONCLUSION

The incorporation of I sac appears to be an important consideration in modeling functional effects of SQT 1 and 3 mutations on cardiac electro-mechanical coupling. Whilst there is little evidence of profoundly impaired cardiac contractile function in SQTS patients, our 3D simulations correlate qualitatively with reported evidence for dissociation between ventricular repolarization and the end of mechanical systole.

Genetic engineering of somatic cells to study and improve cardiac function

AIMS

To demonstrate the utility of genetically engineered excitable cells for studies of basic electrophysiology and cardiac cell therapy.

METHODS AND RESULTS

'Zig-zag' networks of neonatal rat ventricular myocytes (NRVMs) were micropatterned onto thin elastomeric films to mimic the slow action potential (AP) conduction found in fibrotic myocardium. Addition of genetically engineered excitable human embryonic kidney cells (HEK-293 cells) ('Ex-293' cells stably expressing Kir2.1, Na(v)1.5, and Cx43 channels) increased both cardiac conduction velocity by 370% and twitch force amplitude by 64%. Furthermore, we stably expressed mutant Na(v)1.5 [A1924T (fast sodium channel mutant (substitution of alanine by threonine at amino acid 1924)] channels with hyperpolarized steady-state activation and showed that, despite a 71.6% reduction in peak I(Na), these cells propagated APs at the same velocity as the wild-type Na(v)1.5-expressing Ex-293 cells. Stable expression of Ca(v)3.3 (T-type voltage-gated calcium) channels in Ex-293 cells (to generate an 'ExCa-293' line) significantly increased their AP duration and reduced repolarization gradients in cocultures of these cells and NRVMs. Additional expression of an optogenetic construct [ChIEF (light-gated Channelrhodopsin mutant)]enabled light-based control of AP firing in ExCa-293 cells.

CONCLUSION

We show that, despite being non-contractile, genetically engineered excitable cells can significantly improve both electrical and mechanical function of engineered cardiac tissues in vitro. We further demonstrate the utility of engineered cells for tissue-level studies of basic electrophysiology and cardiac channelopathies. In the future, this novel platform could be utilized in the high-throughput design of new genetically encoded indicators of cell electrical function, validation, and improvement of computer models of AP conduction, and development of novel engineered somatic cell therapies for the treatment of cardiac infarction and arrhythmias.

In vivo human left-to-right ventricular differences in rate adaptation transiently increase pro-arrhythmic risk following rate acceleration

Left-to-right ventricular (LV/RV) differences in repolarization have been implicated in lethal arrhythmias in animal models. Our goal is to quantify LV/RV differences in action potential duration (APD) and APD rate adaptation and their contribution to arrhythmogenic substrates in the in vivo human heart using combined in vivo and in silico studies. Electrograms were acquired from 10 LV and 10 RV endocardial sites in 15 patients with normal ventricles. APD and APD adaptation were measured during an increase in heart rate. Analysis of in vivo electrograms revealed longer APD in LV than RV (207.8 ± 21.5 vs 196.7 ± 20.1 ms; P<0.05), and slower APD adaptation in LV than RV (time constant τ(s) =47.0 ± 14.3 vs 35.6 ± 6.5 s; P<0.05). Following rate acceleration, LV/RV APD dispersion experienced an increase of up to 91% in 12 patients, showing a strong correlation (r(2) =0.90) with both initial dispersion and LV/RV difference in slow adaptation. Pro-arrhythmic implications of measured LV/RV functional differences were studied using in silico simulations. Results show that LV/RV APD and APD adaptation heterogeneities promote unidirectional block following rate acceleration, albeit being insufficient for establishment of reentry in normal hearts. However, in the presence of an ischemic region at the LV/RV junction, LV/RV heterogeneity in APD and APD rate adaptation promotes reentrant activity and its degeneration into fibrillatory activity. Our results suggest that LV/RV heterogeneities in APD adaptation cause a transient increase in APD dispersion in the human ventricles following rate acceleration, which promotes unidirectional block and wave-break at the LV/RV junction, and may potentiate the arrhythmogenic substrate, particularly in patients with ischemic heart disease.