Fusion during entrainment of orthodromic reciprocating tachycardia is enhanced for basal pacing sites but diminished when pacing near Purkinje system end points

Countering reproducibility issues in mathematical models with software engineering techniques: A case study using a one-dimensional mathematical model of the atrioventricular node

One should assume that in silico experiments in systems biology are less susceptible to reproducibility issues than their wet-lab counterparts, because they are free from natural biological variations and their environment can be fully controlled. However, recent studies show that only half of the published mathematical models of biological systems can be reproduced without substantial effort. In this article we examine the potential causes for failed or cumbersome reproductions in a case study of a one-dimensional mathematical model of the atrioventricular node, which took us four months to reproduce. The model demonstrates that even otherwise rigorous studies can be hard to reproduce due to missing information, errors in equations and parameters, a lack in available data files, non-executable code, missing or incomplete experiment protocols, and missing rationales behind equations. Many of these issues seem similar to problems that have been solved in software engineering using techniques such as unit testing, regression tests, continuous integration, version control, archival services, and a thorough modular design with extensive documentation. Applying these techniques, we reimplement the examined model using the modeling language Modelica. The resulting workflow is independent of the model and can be translated to SBML, CellML, and other languages. It guarantees methods reproducibility by executing automated tests in a virtual machine on a server that is physically separated from the development environment. Additionally, it facilitates results reproducibility, because the model is more understandable and because the complete model code, experiment protocols, and simulation data are published and can be accessed in the exact version that was used in this article. We found the additional design and documentation effort well justified, even just considering the immediate benefits during development such as easier and faster debugging, increased understandability of equations, and a reduced requirement for looking up details from the literature.

A comprehensive, multiscale framework for evaluation of arrhythmias arising from cell therapy in the whole post-myocardial infarcted heart

Direct remuscularization approaches to cell-based heart repair seek to restore ventricular contractility following myocardial infarction (MI) by introducing new cardiomyocytes (CMs) to replace lost or injured ones. However, despite promising improvements in cardiac function, high incidences of ventricular arrhythmias have been observed in animal models of MI injected with pluripotent stem cell-derived cardiomyocytes (PSC-CMs). The mechanisms of arrhythmogenesis remain unclear. Here, we present a comprehensive framework for computational modeling of direct remuscularization approaches to cell therapy. Our multiscale 3D whole-heart modeling framework integrates realistic representations of cell delivery and transdifferentiation therapy modalities as well as representation of spatial distributions of engrafted cells, enabling simulation of clinical therapy and the prediction of emergent electrophysiological behavior and arrhythmogenensis. We employ this framework to explore how varying parameters of cell delivery and transdifferentiation could result in three mechanisms of arrhythmogenesis: focal ectopy, heart block, and reentry.

Simulation of ventricular rate control during atrial fibrillation using ionic channel blockers

BACKGROUND

The atrioventricular (AV) node is the only compartment that conducts an electrical impulse between the atria and the ventricles. The main role of the AV node is to facilitate efficient pumping by conducting excitation slowly between the two chambers as well as reduce the ventricular rate during atrial fibrillation (AF).

METHODS

Using computer simulations, we investigated excitation conduction from the right atrium to the bundle of His during high-rate atrial excitation with or without partial blocking of the calcium or potassium ionic current.

RESULTS

Our simulations revealed differences in rate reduction and repolarization effects between calcium and potassium current blocking and high degree of potassium current blocking required to reduce the ventricular rate during AF.

CONCLUSIONS

Our simulation results explain why potassium current blockers are not recommended for controlling ventricular rate during AF.

Early somatic mosaicism is a rare cause of long-QT syndrome

Somatic mosaicism, the occurrence and propagation of genetic variation in cell lineages after fertilization, is increasingly recognized to play a causal role in a variety of human diseases. We investigated the case of life-threatening arrhythmia in a 10-day-old infant with long QT syndrome (LQTS). Rapid genome sequencing suggested a variant in the sodium channel Na_V1.5 encoded by SCN5A, NM_000335:c.5284G > T predicting p.(V1762L), but read depth was insufficient to be diagnostic. Exome sequencing of the trio confirmed read ratios inconsistent with Mendelian inheritance only in the proband. Genotyping of single circulating leukocytes demonstrated the mutation in the genomes of 8% of patient cells, and RNA sequencing of cardiac tissue from the infant confirmed the expression of the mutant allele at mosaic ratios. Heterologous expression of the mutant channel revealed significantly delayed sodium current with a dominant negative effect. To investigate the mechanism by which mosaicism might cause arrhythmia, we built a finite element simulation model incorporating Purkinje fiber activation. This model confirmed the pathogenic consequences of cardiac cellular mosaicism and, under the presenting conditions of this case, recapitulated 2:1 AV block and arrhythmia. To investigate the extent to which mosaicism might explain undiagnosed arrhythmia, we studied 7,500 affected probands undergoing commercial gene-panel testing. Four individuals with pathogenic variants arising from early somatic mutation events were found. Here we establish cardiac mosaicism as a causal mechanism for LQTS and present methods by which the general phenomenon, likely to be relevant for all genetic diseases, can be detected through single-cell analysis and next-generation sequencing.

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.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation.

Patient-derived models link re-entrant driver localization in atrial fibrillation to fibrosis spatial pattern

AIMS

The mechanisms underlying persistent atrial fibrillation (AF) in patients with atrial fibrosis are poorly understood. The goal of this study was to use patient-derived atrial models to test the hypothesis that AF re-entrant drivers (RDs) persist only in regions with specific fibrosis patterns.

METHODS AND RESULTS

Twenty patients with persistent AF (PsAF) underwent late gadolinium-enhanced MRI to detect the presence of atrial fibrosis. Segmented images were used to construct personalized 3D models of the fibrotic atria with biophysically realistic atrial electrophysiology. In each model, rapid pacing was applied to induce AF. AF dynamics were analysed and RDs were identified using phase mapping. Fibrosis patterns in RD regions were characterized by computing maps of fibrosis density (FD) and entropy (FE). AF was inducible in 13/20 models and perpetuated by few RDs (2.7 ± 1.5) that were spatially confined (trajectory of phase singularities: 7.6 ± 2.3 mm). Compared with the remaining atrial tissue, regions where RDs persisted had higher FE (IQR: 0.42-0.60 vs. 0.00-0.40, P < 0.05) and FD (IQR: 0.59-0.77 vs. 0.00-0.33, P < 0.05). Machine learning classified RD and non-RD regions based on FD and FE and identified a subset of fibrotic boundary zones present in 13.8 ± 4.9% of atrial tissue where 83.5 ± 2.4% of all RD phase singularities were located.

CONCLUSION

Patient-derived models demonstrate that AF in fibrotic substrates is perpetuated by RDs persisting in fibrosis boundary zones characterized by specific regional fibrosis metrics (high FE and FD). These results provide new insights into the mechanisms that sustain PsAF and could pave the way for personalized, MRI-based management of PsAF.

Modeling our understanding of the His-Purkinje system

The His-Purkinje System (HPS) is responsible for the rapid electric conduction in the ventricles. It relays electrical impulses from the atrioventricular node to the muscle cells and, thus, coordinates the contraction of ventricles in order to ensure proper cardiac pump function. The HPS has been implicated in the genesis of ventricular tachycardia and fibrillation as a source of ectopic beats, as well as forming distinct portions of reentry circuitry. Despite its importance, it remains much less well characterized, structurally and functionally, than the myocardium. Notably, important differences exist with regard to cell structure and electrophysiology, including ion channels, intracellular calcium handling, and gap junctions. Very few computational models address the HPS, and the majority of organ level modeling studies omit it. This review will provide an overview of our current knowledge of structure and function (including electrophysiology) of the HPS. We will review the most recent advances in modeling of the system from the single cell to the organ level, with considerations for relevant interspecies distinctions.

Computational modeling of cardiac optogenetics: Methodology overview & review of findings from simulations

Cardiac optogenetics is emerging as an exciting new potential avenue to enable spatiotemporally precise control of excitable cells and tissue in the heart with low-energy optical stimuli. This approach involves the expression of exogenous light-sensitive proteins (opsins) in target heart tissue via viral gene or cell delivery. Preliminary experiments in optogenetically-modified cells, tissue, and organisms have made great strides towards demonstrating the feasibility of basic applications, including the use of light stimuli to pace or disrupt reentrant activity. However, it remains unknown whether techniques based on this intriguing technology could be scaled up and used in humans for novel clinical applications, such as pain-free optical defibrillation or dynamic modulation of action potential shape. A key step towards answering such questions is to explore potential optogenetics-based therapies using sophisticated computer simulation tools capable of realistically representing opsin delivery and light stimulation in biophysically detailed, patient-specific models of the human heart. This review provides (1) a detailed overview of the methodological developments necessary to represent optogenetics-based solutions in existing virtual heart platforms and (2) a survey of findings that have been derived from such simulations and a critical assessment of their significance with respect to the progress of the field.

Computational generation of the Purkinje network driven by clinical measurements: the case of pathological propagations

To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff-Parkinson-White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models.

A comprehensive multiscale framework for simulating optogenetics in the heart

Optogenetics has emerged as an alternative method for electrical control of the heart, where illumination is used to elicit a bioelectric response in tissue modified to express photosensitive proteins (opsins). This technology promises to enable evocation of spatiotemporally precise responses in targeted cells or tissues, thus creating new possibilities for safe and effective therapeutic approaches to ameliorate cardiac function. Here, we present a comprehensive framework for multi-scale modelling of cardiac optogenetics, allowing both mechanistic examination of optical control and exploration of potential therapeutic applications. The framework incorporates accurate representations of opsin channel kinetics and delivery modes, spatial distribution of photosensitive cells, and tissue illumination constraints, making possible the prediction of emergent behaviour resulting from interactions at sub-organ scales. We apply this framework to explore how optogenetic delivery characteristics determine energy requirements for optical stimulation and to identify cardiac structures that are potential pacemaking targets with low optical excitation threshold.

The role of Purkinje-myocardial coupling during ventricular arrhythmia: a modeling study

The Purkinje system is the fast conduction network of the heart which couples to the myocardium at discrete sites called Purkinje-Myocyte Junctions (PMJs). However, the distribution and number of PMJs remains elusive, as does whether a particular PMJ is functional. We hypothesized that the Purkinje system plays a role during reentry and that the number of functional PMJs affect reentry dynamics. We used a computer finite element model of rabbit ventricles in which we varied the number of PMJs. Sustained, complex reentry was induced by applying an electric shock and the role of the Purkinje system in maintaining the arrhythmia was assessed by analyzing phase singularities, frequency of activation, and bidirectional propagation at PMJs. For larger junctional resistances, increasing PMJ density increased the mean firing rate in the Purkinje system, the percentage of successful retrograde conduction at PMJs, and the incidence of wave break on the epicardium. However, the mean firing of the ventricles was not affected. Furthermore, increasing PMJ density above 13/ did not alter reentry dynamics. For lower junctional resistances, the trend was not as clear. We conclude that Purkinje system topology affects reentry dynamics and conditions which alter PMJ density can alter reentry dynamics.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Transmural IK(ATP) heterogeneity as a determinant of activation rate gradient during early ventricular fibrillation: mechanistic insights from rabbit ventricular models

BACKGROUND

Activation rate (AR) gradients develop during ventricular fibrillation (VF), with the highest AR on the surface near Purkinje system (PS) terminals (endocardium in humans and rabbits and epicardium in pigs). The application of glibenclamide to block adenosine triphosphate (ATP)-sensitive potassium current (IK(ATP)) before VF induction eliminates transmural AR gradients and prevents the induction of sustained arrhythmia. It remains unclear whether the PS, which is resistant to ischemia, is also a factor in AR heterogeneity.

OBJECTIVE

To dissect IK(ATP) and PS contributions to AR gradients during VF by using detailed computer simulations.

METHODS

We constructed rabbit ventricular models with either subendocardial or subepicardial PS terminals. Physiologically relevant IK(ATP) gradients were implemented, and early VF was induced and observed.

RESULTS

Prominent AR gradients were observed only in models with large IK(ATP) gradients. The critical underlying factor of AR gradient maintenance was refractoriness in low-IK(ATP) regions, which blocked the propagation of action potentials from high-IK(ATP) regions. The PS played no role in transmural AR gradient maintenance, but did cause local spatial heterogeneity of AR on the surface adjacent to terminals. Simulated glibenclamide application during VF led to spontaneous arrhythmia termination within a few seconds in most cases, which builds on previous experimental findings of anti-VF properties of glibenclamide pretreatment.

CONCLUSION

Differential IK(ATP) across the ventricular wall is an important factor underlying AR gradients during VF; thus, higher epicardial AR in pigs is most likely due to an abundance of epicardial IK(ATP). For terminating early VF, our results suggest that IK(ATP) modulation is a stronger target than Purkinje ablation.