Virtual cell and tissue dynamics of ectopic activation of the ventricles

A simple approach for image-based modelling of the heart that enables robust simulation of highly heterogeneous electrical excitation

Remodelling of cardiac tissue structure, including intercellular electrical coupling, is a major determinant of the complex and heterogeneous excitation patterns associated with cardiac arrhythmias. Evaluation of the precise mechanisms by which local tissue structure determines global arrhythmic excitation patterns is a major challenge that may be critically important for the development of effective treatment strategies. Computational modelling is a key tool in the study of cardiac arrhythmias, yet the established approaches for organ-scale modelling are unsuitable to capture the impact of local conduction heterogeneities; a novel approach is required to provide this multi-scale mechanistic insight. We present a fundamentally simple yet powerful approach to simulate electrical excitation in highly heterogeneous whole-heart models that exploits the underlying discreteness of the myocardium. Preliminary simulations demonstrate that this approach can capture lower conduction velocities and reproduce wave breakdown and the development of re-entry in a range of conditions.

Arrhythmia mechanisms and spontaneous calcium release: Bi-directional coupling between re-entrant and focal excitation

Spontaneous sub-cellular calcium release events (SCRE) are conjectured to promote rapid arrhythmias associated with conditions such as heart failure and atrial fibrillation: they can underlie the emergence of spontaneous action potentials in single cells which can lead to arrhythmogenic triggers in tissue. The multi-scale mechanisms of the development of SCRE into arrhythmia triggers, and their dynamic interaction with the tissue substrate, remain elusive; rigorous and simultaneous study of dynamics from the nanometre to the centimetre scale is a major challenge. The aim of this study was to develop a computational approach to overcome this challenge and study potential bi-directional coupling between sub-cellular and tissue-scale arrhythmia phenomena. A framework comprising a hierarchy of computational models was developed, which includes detailed single-cell models describing spatio-temporal calcium dynamics in 3D, efficient non-spatial cell models, and both idealised and realistic tissue models. A phenomenological approach was implemented to reproduce SCRE morphology and variability in the efficient cell models, comprising the definition of analytical Spontaneous Release Functions (SRF) whose parameters may be randomly sampled from appropriate distributions in order to match either the 3D cell models or experimental data. Pro-arrhythmogenic pacing protocols were applied to initiate re-entry and promote calcium overload, leading to the emergence of SCRE. The SRF accurately reproduced the dynamics of SCRE and its dependence on environment variables under multiple different conditions. Sustained re-entrant excitation promoted calcium overload, and led to the emergence of focal excitations after termination. A purely functional mechanism of re-entry and focal activity localisation was demonstrated, related to the unexcited spiral wave core. In conclusion, a novel approach has been developed to dynamically model SCRE at the tissue scale, which facilitates novel, detailed multi-scale mechanistic analysis. It was revealed that complex re-entrant excitation patterns and SCRE may be bi-directionally coupled, promoting novel mechanisms of arrhythmia perpetuation.

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.

Trigger vs. Substrate: Multi-Dimensional Modulation of QT-Prolongation Associated Arrhythmic Dynamics by a hERG Channel Activator

Background: Prolongation of the QT interval of the electrocardiogram (ECG), underlain by prolongation of the action potential duration (APD) at the cellular level, is linked to increased vulnerability to cardiac arrhythmia. Pharmacological management of arrhythmia associated with QT prolongation is typically achieved through attempting to restore APD to control ranges, reversing the enhanced vulnerability to Ca²⁺-dependent afterdepolarisations (arrhythmia triggers) and increased transmural dispersion of repolarisation (arrhythmia substrate) associated with APD prolongation. However, such pharmacological modulation has been demonstrated to have limited effectiveness. Understanding the integrative functional impact of pharmacological modulation requires simultaneous investigation of both the trigger and substrate. Methods: We implemented a multi-scale (cell and tissue) in silico approach using a model of the human ventricular action potential, integrated with a model of stochastic 3D spatiotemporal Ca²⁺ dynamics, and parameter modification to mimic prolonged QT conditions. We used these models to examine the efficacy of the hERG activator MC-II-157c in restoring APD to control ranges, examined its effects on arrhythmia triggers and substrates, and the interaction of these arrhythmia triggers and substrates. Results: QT prolongation conditions promoted the development of spontaneous release events underlying afterdepolarisations during rapid pacing. MC-II-157c applied to prolonged QT conditions shortened the APD, inhibited the development of afterdepolarisations and reduced the probability of afterdepolarisations manifesting as triggered activity in single cells. In tissue, QT prolongation resulted in an increased transmural dispersion of repolarisation, which manifested as an increased vulnerable window for uni-directional conduction block. In some cases, MC-II-157c further increased the vulnerable window through its effects on I_Na. The combination of stochastic release event modulation and transmural dispersion of repolarisation modulation by MC-II-157c resulted in an integrative behavior wherein the arrhythmia trigger is reduced but the arrhythmia substrate is increased, leading to variable and non-linear overall vulnerability to arrhythmia. Conclusion: The relative balance of reduced trigger and increased substrate underlies a multi-dimensional role of MC-II-157c in modulation of cardiac arrhythmia vulnerability associated with prolonged QT interval.

Effects of macroscopic heterogeneity on propagation in a computationally inexpensive 2D model of the heart

We have developed a computationally inexpensive, two-dimensional, bidomain model of the heart to demonstrate the effect of tissue heterogeneity on propagation of cardiac impulses generated by the sino-atrial node (SAN). The geometry consists of a thin sheet of cardiac tissue with designated areas that represent the SAN and atria. The SAN auto-generates continuous impulses that result in waves of normal propagation throughout the tissue. On the introduction of heterogeneous patches with low tissue conductivities, the rhythm of the waveform becomes irregular. The study suggests that simplified and computationally inexpensive models can be insightful tools to better understand the mechanisms that cause atrial fibrillation (AF) and hence more effective treatment methods.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Quantitative prediction of the arrhythmogenic effects of de novo hERG mutations in computational models of human ventricular tissues

Mutations to hERG which result in changes to the rapid delayed rectifier current I(Kr) can cause long and short QT syndromes and are associated with an increased risk of cardiac arrhythmias. Experimental recordings of I(Kr) reveal the effects of mutations at the channel level, but how these changes translate to the cell and tissue levels remains unclear. We used computational models of human ventricular myocytes and tissues to predict and quantify the effects that de novo hERG mutations would have on cell and tissue electrophysiology. Mutations that decreased I(Kr) maximum conductance resulted in an increased cell and tissue action potential duration (APD) and a long QT interval on the electrocardiogram (ECG), whereas those that caused a positive shift in the inactivation curve resulted in a decreased APD and a short QT. Tissue vulnerability to re-entrant arrhythmias was correlated with transmural dispersion of repolarisation, and any change to this vulnerability could be inferred from the ECG QT interval or T wave peak-to-end time. Faster I(Kr) activation kinetics caused cell APD alternans to appear over a wider range of pacing rates and with a larger magnitude, and spatial heterogeneity in these cellular alternans resulted in discordant alternans at the tissue level. Thus, from channel kinetic data, we can predict the tissue-level electrophysiological effects of any hERG mutations and identify how the mutation would manifest clinically, as either a long or short QT syndrome with or without an increased risk of alternans and re-entrant arrhythmias.

Construction and validation of anisotropic and orthotropic ventricular geometries for quantitative predictive cardiac electrophysiology

Reaction-diffusion computational models of cardiac electrophysiology require both dynamic excitation models that reconstruct the action potentials of myocytes as well as datasets of cardiac geometry and architecture that provide the electrical diffusion tensor D, which determines how excitation spreads through the tissue. We illustrate an experimental pipeline we have developed in our laboratories for constructing and validating such datasets. The tensor D changes with location in the myocardium, and is determined by tissue architecture. Diffusion tensor magnetic resonance imaging (DT-MRI) provides three eigenvectors e(i) and eigenvalues λ(i) at each voxel throughout the tissue that can be used to reconstruct this architecture. The primary eigenvector e(1) is a histologically validated measure of myocyte orientation (responsible for anisotropic propagation). The secondary and tertiary eigenvectors (e(2) and e(3)) specify the directions of any orthotropic structure if λ(2) is significantly greater than λ(3)-this orthotropy has been identified with sheets or cleavage planes. For simulations, the components of D are scaled in the fibre and cross-fibre directions for anisotropic simulations (or fibre, sheet and sheet normal directions for orthotropic tissues) so that simulated conduction velocities match values from optical imaging or plunge electrode experiments. The simulated pattern of propagation of action potentials in the models is partially validated by optical recordings of spatio-temporal activity on the surfaces of hearts. We also describe several techniques that enhance components of the pipeline, or that allow the pipeline to be applied to different areas of research: Q ball imaging provides evidence for multi-modal orientation distributions within a fraction of voxels, infarcts can be identified by changes in the anisotropic structure-irregularity in myocyte orientation and a decrease in fractional anisotropy, clinical imaging provides human ventricular geometry and can identify ischaemic and infarcted regions, and simulations in human geometries examine the roles of anisotropic and orthotropic architecture in the initiation of arrhythmias.

Role of subendocardial Purkinje network in triggering torsade de pointes arrhythmia in experimental long QT syndrome

AIMS

The present study addresses the controversy regarding the 'primary' role of the subendocardial Purkinje network in triggering torsade de pointes (TdP) ventricular tachyarrhythmia (VAs) in the long QT syndrome (LQTS).

METHODS AND RESULTS

We investigated the well-established canine anthopleurin-A (AP-A) surrogate model of LQT3 to study the role of the subendocardial Purkinje network in triggering VAs. Three-dimensional activation and repolarization patterns were analysed from unipolar extracellular electrograms utilizing 64 plunge needle electrodes. In 6 dogs, the animals were placed on cardiopulmonary bypass and chemical ablation of the endocardial Purkinje network was obtained using Lugol's solution. Spontaneous VAs consistently developed in response to AP-A infusion and were triggered by a subendocardial focal activity acting on a substrate of spatial three-dimensional dispersion of repolarization. Endocardial ablation was considered successful by the development of complete atrioventricular block in the absence of ventricular escape rhythm. Following endocardial ablation spontaneous VAs were no longer observed. However, an appropriately coupled premature stimulus consistently induced re-entrant VAs.

CONCLUSION

The present study strongly suggests that in the LQTS, focal activity generated in subendocardial Purkinje tissue is the primary, if not the only, trigger for TdP VAs by acting on a substrate of three-dimensional dispersion of myocardial repolarization to induce re-entrant excitation.

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

We have constructed computational models of canine ventricular cells and tissues, ultimately combining detailed tissue architecture and heterogeneous transmural electrophysiology. The heterogeneity is introduced by modifying the Hund-Rudy canine cell model in order to reproduce experimentally reported electrophysiological properties of endocardial, midmyocardial (M) and epicardial cells. These models are validated against experimental data for individual ionic current and action potential characteristics, and their rate dependencies. 1D and 3D heterogeneous virtual tissues are constructed, with detailed tissue architecture (anisotropy and orthotropy, due to fibre orientation and sheet structure) of the left ventricular wall wedge extracted from a diffusion tensor imaging data set. The models are used to study the effects of tissue heterogeneity and class III drugs on transmural propagation and tissue vulnerability to re-entry. We have determined relationships between the transmural dispersion of action potential duration (APD) and the vulnerable window in the 1D virtual ventricular wall, and demonstrated how changes in the transmural heterogeneity, and hence tissue vulnerability, can lead to generation of re-entry in the 3D ventricular wedge. Two class III drugs with opposite qualitative effects on transmural APD heterogeneity are considered: d-sotalol that increases transmural APD dispersion, and amiodarone that decreases it. Simulations with the 1D virtual ventricular wall show that under d-sotalol conditions the vulnerable window is substantially wider compared to amiodarone conditions, primarily in the epicardial region where unidirectional conduction block persists until the adjacent M cells are fully repolarised. Further simulations with the 3D ventricular wedge have shown that ectopic stimulation of the epicardial region results in generation of sustained re-entry under d-sotalol conditions, but not under amiodarone conditions or in control. Again, APD increase in M cells was identified as the major contributor to tissue vulnerability--re-entry was initiated primarily due to ectopic excitation propagating around the unidirectional conduction block in the M cell region. This suggests an electrophysiological mechanism for the anti- and proarrhythmic effects of the class III drugs: the relative safety of amiodarone in comparison to d-sotalol can be explained by relatively low transmural APD dispersion, and hence, a narrow vulnerable window and low probability of re-entry in the tissue.

Introduction: Cardiovascular physics

The number of patients suffering from cardiovascular diseases increases unproportionally high with the increase of the human population and aging, leading to very high expenses in the public health system. Therefore, the challenge of cardiovascular physics is to develop high-sophisticated methods which are able to, on the one hand, supplement and replace expensive medical devices and, on the other hand, improve the medical diagnostics with decreasing the patient's risk. Cardiovascular physics-which interconnects medicine, physics, biology, engineering, and mathematics-is based on interdisciplinary collaboration of specialists from the above scientific fields and attempts to gain deeper insights into pathophysiology and treatment options. This paper summarizes advances in cardiovascular physics with emphasis on a workshop held in Bad Honnef, Germany, in May 2005. The meeting attracted an interdisciplinary audience and led to a number of papers covering the main research fields of cardiovascular physics, including data analysis, modeling, and medical application. The variety of problems addressed by this issue underlines the complexity of the cardiovascular system. It could be demonstrated in this Focus Issue, that data analyses and modeling methods from cardiovascular physics have the ability to lead to significant improvements in different medical fields. Consequently, this Focus Issue of Chaos is a status report that may invite all interested readers to join the community and find competent discussion and cooperation partners.