Real-time interactive simulations of large-scale systems on personal computers and cell phones: Toward patient-specific heart modeling and other applications

Chained occurrences of early afterdepolarizations may create a directional triggered activity to initiate reentrant ventricular tachyarrhythmias

BACKGROUND AND OBJECTIVE

It has been believed that polymorphic ventricular tachycardia (VT) such as torsades de pointes (TdP) seen in patients with long QT syndromes is triggered by creating early afterdepolarization (EAD)-mediated triggered activity (TA). Although the mechanisms creating the TA have been studied intensively, characteristics of the arrhythmogenic (torsadogenic) substrates that link EAD developments to TA formation are still not well understood.

METHODS

Computer simulations of excitation propagation in a homogenous two-dimensional ventricular tissue with an anisotropic conduction property were performed to characterize torsadogenic substrates that potentially form TA. We examined how the configuration of islands (clusters) of myocytes with synchronously chained occurrence of EADs within the tissue, each EAD cluster size and stimulation from different directions impact the TA creation.

RESULTS

The presence of EAD clusters within the tissue created local regions of cardiomyocytes maintained at a depolarized membrane potential above 0 mV due to the chained occurrence of EADs. When the local area contained a concave surface border, the TA was created depending on its curvature. We found that the distance of EAD clusters was a critical factor for the development of EAD-mediated TA and polymorphic VT in long QT syndromes, that there existed a region of the distance favorable for the development of TA and VT, and that the TA was always created along the myocardial fiber orientation regardless of stimulating directions.

CONCLUSION

The chained occurrences of EADs may create a directional TA. Our findings provide deeper understandings of the cardiac arrhythmogenic substrates for preventing and treating arrhythmias.

Simulation-free prediction of atrial fibrillation inducibility with the fibrotic kernel signature

Computational models of atrial fibrillation (AF) can help improve success rates of interventions, such as ablation. However, evaluating the efficacy of different treatments requires performing multiple costly simulations by pacing at different points and checking whether AF has been induced or not, hindering the clinical application of these models. In this work, we propose a classification method that can predict AF inducibility in patient-specific cardiac models without running additional simulations. Our methodology does not require re-training when changing atrial anatomy or fibrotic patterns. To achieve this, we develop a set of features given by a variant of the heat kernel signature that incorporates fibrotic pattern information and fiber orientations: the fibrotic kernel signature (FKS). The FKS is faster to compute than a single AF simulation, and when paired with machine learning classifiers, it can predict AF inducibility in the entire domain. To learn the relationship between the FKS and AF inducibility, we performed 2371 AF simulations comprising 6 different anatomies and various fibrotic patterns, which we split into training and a testing set. We obtain a median F1 score of 85.2% in test set and we can predict the overall inducibility with a mean absolute error of 2.76 percent points, which is lower than alternative methods. We think our method can significantly speed-up the calculations of AF inducibility, which is crucial to optimize therapies for AF within clinical timelines. An example of the FKS for an open source model is provided in https://github.com/tbanduc/FKS_AtrialModel_Ferrer.git.

Lipomatous Metaplasia Facilitates Ventricular Tachycardia in Patients With Nonischemic Cardiomyopathy

BACKGROUND

Ventricular tachycardia (VT) substrate in patients with nonischemic cardiomyopathy (NICM) is complex in distribution and intramural location.

OBJECTIVES

This study sought to test the hypothesis that myocardial lipomatous metaplasia (LM) is a vital anatomic substrate for VT corridors in patients with NICM and VT, and that LM stabilizes current propagation in VT corridors.

METHODS

Among 49 patients with NICM in the 2-center INFINITY (Prospective Intra-Myocardial Fat Deposition and Ventricular Tachycardia in Cardiomyopathy) Study, potential VT viable corridors within the myocardial scar and/or LM were computed from late gadolinium enhancement cardiac magnetic resonance images and were registered with electroanatomical maps. Corridors passing through VT entrance, isthmus, and/or exit sites, estimated by entrainment or pace mapping, were defined as VT corridors. LM was separately distinguished from scar using computed tomography. The SD of current amplitude along each corridor was measured.

RESULTS

Compared with 151 non-VT corridors, 35 VT corridors traversed a substantially higher volume of LM, with a median 236.6 mg (IQR: 13.5-903.4 mg) vs 5.8 mg (IQR: 0.0-57.9 mg) (P < 0.001). Among corridors with computable current amplitude, 28 VT corridors exhibited substantially lower current variation along the corridors, with SD 8.0 μA (25th-75th percentile: 6.1-10.3 μA) vs 14.9 μA (25th-75th percentile: 8.5-23.7 μA) among 71 non-VT corridors (P < 0.001). Individual VT circuit sites (95 out 118) were highly colocalized with LM.

CONCLUSIONS

VT circuitry corridors in NICM are more likely to traverse LM and exhibit reduced current amplitude variation compared with bystander corridors.

VisualPDE: Rapid Interactive Simulations of Partial Differential Equations

Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we provide a means to go one step further in using computers to understand complex models through instantaneous and interactive exploration. This ubiquitous infrastructure has enormous potential in education, outreach and research. Here, we present VisualPDE, an online, interactive solver for a broad class of 1D and 2D partial differential equation (PDE) systems. Abstract dynamical systems concepts such as symmetry-breaking instabilities, subcritical bifurcations and the role of initial data in multistable nonlinear models become much more intuitive when you can play with these models yourself, and immediately answer questions about how the system responds to changes in parameters, initial conditions, boundary conditions or even spatiotemporal forcing. Importantly, VisualPDE is freely available, open source and highly customisable. We give several examples in teaching, research and knowledge exchange, providing high-level discussions of how it may be employed in different settings. This includes designing web-based course materials structured around interactive simulations, or easily crafting specific simulations that can be shared with students or collaborators via a simple URL. We envisage VisualPDE becoming an invaluable resource for teaching and research in mathematical biology and beyond. We also hope that it inspires other efforts to make mathematics more interactive and accessible.

A smoothed boundary bidomain model for cardiac simulations in anatomically detailed geometries

This manuscript presents a novel finite difference method to solve cardiac bidomain equations in anatomical models of the heart. The proposed method employs a smoothed boundary approach that represents the boundaries between the heart and the surrounding medium as a spatially diffuse interface of finite thickness. The bidomain boundary conditions are implicitly implemented in the smoothed boundary bidomain equations presented in the manuscript without the need of a structured mesh that explicitly tracks the heart-torso boundaries. We reported some significant examples assessing the method's accuracy using nontrivial test geometries and demonstrating the applicability of the method to complex anatomically detailed human cardiac geometries. In particular, we showed that our approach could be employed to simulate cardiac defibrillation in a human left ventricle comprising fiber architecture. The main advantage of the proposed method is the possibility of implementing bidomain boundary conditions directly on voxel structures, which makes it attractive for three dimensional, patient specific simulations based on medical images. Moreover, given the ease of implementation, we believe that the proposed method could provide an interesting and feasible alternative to finite element methods, and could find application in future cardiac research guiding electrotherapy with computational models.

A Doppler-exclusive non-invasive computational diagnostic framework for personalized transcatheter aortic valve replacement

Given the associated risks with transcatheter aortic valve replacement (TAVR), it is crucial to determine how the implant will affect the valve dynamics and cardiac function, and if TAVR will improve or worsen the outcome of the patient. Effective treatment strategies, indeed, rely heavily on the complete understanding of the valve dynamics. We developed an innovative Doppler-exclusive non-invasive computational framework that can function as a diagnostic tool to assess valve dynamics in patients with aortic stenosis in both pre- and post-TAVR status. Clinical Doppler pressure was reduced by TAVR (52.2 ± 20.4 vs. 17.3 ± 13.8 [mmHg], p < 0.001), but it was not always accompanied by improvements in valve dynamics and left ventricle (LV) hemodynamics metrics. TAVR had no effect on LV workload in 4 patients, and LV workload post-TAVR significantly rose in 4 other patients. Despite the group level improvements in maximum LV pressure (166.4 ± 32.2 vs 131.4 ± 16.9 [mmHg], p < 0.05), only 5 of the 12 patients (41%) had a decrease in LV pressure. Moreover, TAVR did not always improve valve dynamics. TAVR did not necessarily result in a decrease (in 9 out of 12 patients investigated in this study) in major principal stress on the aortic valve leaflets which is one of the main contributors in valve degeneration and, consequently, failure of heart valves. Diastolic stresses increased significantly post-TAVR (34%, 109% and 81%, p < 0.001) for each left, right and non-coronary leaflets respectively. Moreover, we quantified the stiffness and material properties of aortic valve leaflets which correspond with the reduced calcified region average stiffness among leaflets (66%, 74% and 62%; p < 0.001; N = 12). Valve dynamics post-intervention should be quantified and monitored to ensure the improvement of patient conditions and prevent any further complications. Improper evaluation of biomechanical valve features pre-intervention as well as post-intervention may result in harmful effects post-TAVR in patients including paravalvular leaks, valve degeneration, failure of TAVR and heart failure.

Fiber Organization Has Little Effect on Electrical Activation Patterns During Focal Arrhythmias in the Left Atrium

Over the past two decades there has been a steady trend towards the development of realistic models of cardiac conduction with increasing levels of detail. However, making models more realistic complicates their personalization and use in clinical practice due to limited availability of tissue and cellular scale data. One such limitation is obtaining information about myocardial fiber organization in the clinical setting. In this study, we investigated a chimeric model of the left atrium utilizing clinically derived patient-specific atrial geometry and a realistic, yet foreign for a given patient fiber organization. We discovered that even significant variability of fiber organization had a relatively small effect on the spatio-temporal activation pattern during regular pacing. For a given pacing site, the activation maps were very similar across all fiber organizations tested.

Fiber Organization has Little Effect on Electrical Activation Patterns during Focal Arrhythmias in the Left Atrium

Over the past two decades there has been a steady trend towards the development of realistic models of cardiac conduction with increasing levels of detail. However, making models more realistic complicates their personalization and use in clinical practice due to limited availability of tissue and cellular scale data. One such limitation is obtaining information about myocardial fiber organization in the clinical setting. In this study, we investigated a chimeric model of the left atrium utilizing clinically derived patient-specific atrial geometry and a realistic, yet foreign for a given patient fiber organization. We discovered that even significant variability of fiber organization had a relatively small effect on the spatio-temporal activation pattern during regular pacing. For a given pacing site, the activation maps were very similar across all fiber organizations tested.

An ultrasound-exclusive non-invasive computational diagnostic framework for personalized cardiology of aortic valve stenosis

Aortic stenosis (AS) is an acute and chronic cardiovascular disease and If left untreated, 50% of these patients will die within two years of developing symptoms. AS is characterized as the stiffening of the aortic valve leaflets which restricts their motion and prevents the proper opening under transvalvular pressure. Assessments of the valve dynamics, if available, would provide valuable information about the patient's state of cardiac deterioration as well as heart recovery and can have incredible impacts on patient care, planning interventions and making critical clinical decisions with life-threatening risks. Despite remarkable advancements in medical imaging, there are no clinical tools available to quantify valve dynamics invasively or noninvasively. In this study, we developed a highly innovative ultrasound-based non-invasive computational framework that can function as a diagnostic tool to assess valve dynamics (e.g. transient 3-D distribution of stress and displacement, 3-D deformed shape of leaflets, geometric orifice area and angular positions of leaflets) for patients with AS at no risk to the patients. Such a diagnostic tool considers the local valve dynamics and the global circulatory system to provide a platform for testing the intervention scenarios and evaluating their effects. We used clinical data of 12 patients with AS not only to validate the proposed framework but also to demonstrate its diagnostic abilities by providing novel analyses and interpretations of clinical data in both pre and post intervention states. We used transthoracic echocardiogram (TTE) data for the developments and transesophageal echocardiography (TEE) data for validation.

Mechanistic Insight into Wettability Enhancement of Lithium-Ion Batteries Using a Ceramic-Coated Layer

The crucial issue of wettability in high-energy-density lithium-ion batteries (LIBs) has not been comprehensively addressed to date. To overcome the challenge, state-of-the-art LIBs employing a ceramic-coated separator improves the safety- and wettability-related aspects of LIBs. Here, we present a mechanistic study of the effects of a ceramic-coated layer (CCL) on electrode wettability and report the optimal position of the CCL in LIBs. The electrolyte wetting was investigated using the multiphase lattice Boltzmann method and electrochemical impedance spectroscopy for capturing the electrolyte-transport dynamics in porous electrodes and impedance spectra in pouch-type LIBs, respectively. Results indicate that the CCL caused the velocity vector to transport the electrolyte further, resulting in an increase in the wetting rate. Moreover, the location of the CCL considerably affected the wettability of the LIBs. This study provides mechanical insight into the design and fabrication of high-performance LIBs by incorporating CCLs.

Lipomatous Metaplasia Enables Ventricular Tachycardia by Reducing Current Loss Within the Protected Corridor

BACKGROUND

Post-myocardial infarction ventricular tachycardia (VT) is due to re-entry through surviving conductive myocardial corridors across infarcted tissue. However, not all conductive corridors participate in re-entry.

OBJECTIVES

This study sought to test the hypothesis that critical VT corridors are more likely to traverse near lipomatous metaplasia (LM) and that current loss is reduced during impulse propagation through such corridors.

METHODS

Among 30 patients in the Prospective 2-center INFINITY (Intra-Myocardial Fat Deposition and Ventricular Tachycardia in Cardiomyopathy) study, potential VT-viable corridors within myocardial scar or LM were computed from late gadolinium enhancement cardiac magnetic resonance images. Because late gadolinium enhancement highlights both scar and LM, LM was distinguished from scar by using computed tomography. The SD of the current along each corridor was measured.

RESULTS

Scar exhibited lower impedance than LM (median Z-score -0.22 [IQR: -0.84 to 0.35] vs -0.07 [IQR: -0.67 to 0.54]; P < 0.001). Among all 381 corridors, 84 were proven to participate in VT re-entry circuits, 83 (99%) of which traversed or were adjacent to LM. In comparison, only 13 (4%) non-VT corridors were adjacent to LM. Critical corridors adjacent to LM displayed lower SD of current compared with noncritical corridors through scar but distant from LM (2.0 [IQR: 1.0 to 3.4] μA vs 8.4 [IQR: 5.5 to 12.8] μA; P < 0.001).

CONCLUSIONS

Corridors critical to VT circuitry traverse infarcted tissue through or near LM. This association is likely mediated by increased regional resistance and reduced current loss as impulses traverse corridors adjacent to LM.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

Predicting and understanding arterial elasticity from key microstructural features by bidirectional deep learning

Microstructural features and mechanical properties are closely related in all soft biological tissues. Both yet exhibit considerable inter-individual differences and are affected by factors such as aging and disease and its progression. Histological analysis, modern in situ imaging, and biomechanical testing have deepened our understanding of these complex interrelations, yet two key questions remain: (1) Given the specific microstructure, can one predict the macroscopic mechanical properties without mechanical testing? (2) Can one quantify individual contributions of the different microstructural features to the macroscopic mechanical properties in an automated, systematic and largely unbiased way? Here we propose a bidirectional deep learning architecture to address these two questions. Our architecture uses data from standard histological analyses, two-photon microscopy and biaxial biomechanical testing. Its capabilities are demonstrated by predicting with high accuracy (R²=0.92) the evolving mechanical properties of the murine aorta during maturation and aging. Moreover, our architecture reveals that the extracellular matrix composition and organization are the most prominent factors governing the macroscopic mechanical properties of the tissues studied herein. STATEMENT OF SIGNIFICANCE:  .

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

Simulation of atrial fibrillation in a non-ohmic propagation model with dynamic gap junctions

Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel-Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100  μm resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.

Fast Characterization of Inducible Regions of Atrial Fibrillation Models With Multi-Fidelity Gaussian Process Classification

Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites. A critical step to assess the effect of an ablation pattern is to pace the model from different, potentially random, locations to determine whether arrhythmias can be induced in the atria. In this work, we propose to use multi-fidelity Gaussian process classification on Riemannian manifolds to efficiently determine the regions in the atria where arrhythmias are inducible. We build a probabilistic classifier that operates directly on the atrial surface. We take advantage of lower resolution models to explore the atrial surface and combine seamlessly with high-resolution models to identify regions of inducibility. We test our methodology in 9 different cases, with different levels of fibrosis and ablation treatments, totalling 1,800 high resolution and 900 low resolution simulations of atrial fibrillation. When trained with 40 samples, our multi-fidelity classifier that combines low and high resolution models, shows a balanced accuracy that is, on average, 5.7% higher than a nearest neighbor classifier. We hope that this new technique will allow faster and more precise clinical applications of computational models for atrial fibrillation. All data and code accompanying this manuscript will be made publicly available at: https://github.com/fsahli/AtrialMFclass.

Voltage-mediated mechanism for calcium wave synchronization and arrhythmogenesis in atrial tissue

A wide range of atrial arrythmias are caused by molecular defects in proteins that regulate calcium (Ca) cycling. In many cases, these defects promote the propagation of subcellular Ca waves in the cell, which can perturb the voltage time course and induce dangerous perturbations of the action potential (AP). However, subcellular Ca waves occur randomly in cells and, therefore, electrical coupling between cells substantially decreases their effect on the AP. In this study, we present evidence that Ca waves in atrial tissue can synchronize in-phase owing to an order-disorder phase transition. In particular, we show that, below a critical pacing rate, Ca waves are desynchronized and therefore do not induce substantial AP fluctuations in tissue. However, above this critical pacing rate, Ca waves gradually synchronize over millions of cells, which leads to a dramatic amplification of AP fluctuations. We exploit an underlying Ising symmetry of paced cardiac tissue to show that this transition exhibits universal properties common to a wide range of physical systems in nature. Finally, we show that in the heart, phase synchronization induces spatially out-of-phase AP duration alternans which drives wave break and reentry. These results suggest that cardiac tissue exhibits a phase transition that is required for subcellular Ca cycling defects to induce a life-threatening arrhythmia.

Current progress of computational modeling for guiding clinical atrial fibrillation ablation

Atrial fibrillation (AF) is one of the most common arrhythmias, associated with high morbidity, mortality, and healthcare costs, and it places a significant burden on both individuals and society. Anti-arrhythmic drugs are the most commonly used strategy for treating AF. However, drug therapy faces challenges because of its limited efficacy and potential side effects. Catheter ablation is widely used as an alternative treatment for AF. Nevertheless, because the mechanism of AF is not fully understood, the recurrence rate after ablation remains high. In addition, the outcomes of ablation can vary significantly between medical institutions and patients, especially for persistent AF. Therefore, the issue of which ablation strategy is optimal is still far from settled. Computational modeling has the advantages of repeatable operation, low cost, freedom from risk, and complete control, and is a useful tool for not only predicting the results of different ablation strategies on the same model but also finding optimal personalized ablation targets for clinical reference and even guidance. This review summarizes three-dimensional computational modeling simulations of catheter ablation for AF, from the early-stage attempts such as Maze III or circumferential pulmonary vein isolation to the latest advances based on personalized substrate-guided ablation. Finally, we summarize current developments and challenges and provide our perspectives and suggestions for future directions.

Detecting spiral wave tips using deep learning

The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. The organizing centers of these waves are called wave tips (2D) or filaments (3D) and they play a key role in understanding and controlling the complex and chaotic electrical dynamics. Therefore, in many experimental and numerical setups it is required to detect the tips of the observed spiral waves. Most of the currently used methods significantly suffer from the influence of noise and are often adjusted to a specific situation (e.g. a specific numerical cardiac cell model). In this study, we use a specific type of deep neural networks (UNet), for detecting spiral wave tips and show that this approach is robust against the influence of intermediate noise levels. Furthermore, we demonstrate that if the UNet is trained with a pool of numerical cell models, spiral wave tips in unknown cell models can also be detected reliably, suggesting that the UNet can in some sense learn the concept of spiral wave tips in a general way, and thus could also be used in experimental situations in the future (ex-vivo, cell-culture or optogenetic experiments).

Interactive 3D Human Heart Simulations on Segmented Human MRI Hearts

Understanding cardiac arrhythmic mechanisms and developing new strategies to control and terminate them using computer simulations requires realistic physiological cell models with anatomically accurate heart structures. Furthermore, numerical simulations must be fast enough to study and validate model and structure parameters. Here, we present an interactive parallel approach for solving detailed cell dynamics in high-resolution human heart structures with a local PC's GPU. In vitro human heart MRI scans were manually segmented to produce 3D structures with anatomically realistic electrophysiology. The Abubu.js library was used to create an interactive code to solve the OVVR human ventricular cell model and the FDA extension of the model in the human MRI heart structures, allowing the simulation of reentrant waves and investigation of their dynamics in real time. Interactive simulations of a physiological cell model in a detailed anatomical human heart reveals propagation of waves through the fine structures of the trabeculae and pectinate muscle that can perpetuate arrhythmias, thereby giving new insights into effects that may need to be considered when planning ablation and other defibrillation methods.

A Network-based Cardiac Electrophysiology Simulator with Realistic Signal Generation and Response to Pacing Maneuvers

Diagnosis and localization of cardiac arrhythmias, especially supraventricular tachycardia (SVT), by inspecting intracardiac signals and performing pacing maneuvers is the core of electrophysiology studies. Acquiring and maintaining complex skill sets can be facilitated by using simulators, allowing the operator to practice in a safe and controlled setting. An electrophysiology simulator should not only display arrhythmias but it has to respond to the user's arbitrary inputs. While, in principle, it is possible to model the heart using a detailed anatomical and cellular model, such a system would be unduly complex and computationally intensive. In this paper, we describe a freely available web-based electrophysiology simulator (http://svtsim.com), which is composed of a visualization/interface unit and a heart model based on a dynamical network. In the network, nodes represent the points of interest, such as the sinus and the atrioventricular nodes, and links model the conduction system and pathways. The dynamics are encoded explicitly in the state machines attached to the nodes and links. Simulated intracardiac signals and surface ECGs are generated from the internal state of the heart model. Reentrant tachycardias, especially various forms of SVT, can emerge in this system in response to the user's actions in the form of pacing maneuvers. Additionally, the resulting arrhythmias respond realistically to various inputs, such as overdrive pacing and delivery of extra stimuli, cardioversion, ablation, and infusion of medications. For nearly a decade, svtsim.com has been used successfully to train electrophysiology practitioners in many institutions. We will present our experience regarding best practices in designing and using electrophysiology simulators for training and testing. We will also discuss the current trends in clinical cardiac electrophysiology and the anticipated next generation electrophysiology simulators.

Real-Time Interactive Simulations of Complex Ionic Cardiac Cell Models in 2D and 3D Heart Structures with GPUs on Personal Computers

AIMS

Cardiac modeling in heart structures for the study of arrhythmia mechanisms requires the use of software that runs on supercomputers. Therefore, computational studies are limited to groups with access to computer clusters and personnel with high-performance computing experience. We present how to use and implement WebGL programs via a custom-written library to run and visualize simulations of the most complex ionic models in 2D and 3D, in real time, interactively using the multi-core GPU of a single computer.

METHODS

We use Abubu.js, a library we developed for solving partial differential equations such as those describing crystal growth and fluid flow, along with a newly implemented visualization algorithm, to simulate complex ionic cell models. By combining this library with JavaScript, we allow direct real-time interactions with simulations. We implemented: 1) modification of any model parameters and equations at any time, with direct access to the code while it runs, 2) electrode stimulation anywhere in the 2D/3D tissue with a mouse click, 3) saving the solution of the system at any time to re-initiate the dynamics from saved initial conditions, and 4) rotation/visualization of 3D structures at any angle.

RESULTS

As examples of this modeling platform, we implemented a phenomenological cell model and the human ventricular OVVR model (41 variables). In 2D we illustrate the dynamics in an annulus, disk, and square tissue; in 2D and 3D porcine ventricles, we show the initiation of functional/anatomical reentry, spiral wave dynamics in different regimes, initiation of early afterdepolarizations (EADs), and the effects of model parameter variations in real time.

CONCLUSIONS

We present the first simulations of complex models in anatomical structures with enhanced visualization and extended interactivity that run on a single PC, without software downloads, and as fast as in real-time even for 3D full ventricles.

Interactive Simulation of the ECG: Effects of Cell Types, Distributions, Shapes and Duration

The shape of the ECG depends on the lead positions but also on the distribution and dispersion of different cell types and their action potential (AP) durations and shapes. We present an interactive JavaScript program that allows fast simulations of the ECG by solving and displaying the dynamics of cardiac cells in tissue using a web browser. We use physiologically accurate ODE models of cardiac cells of different types including SA node, right and left atria, AV node, Purkinje, and right and left ventricular cells with dispersion that accounts for apex-to-base and epi-to-endo variations. The software allows for real-time variations for each cell type and their spatial range so as to identify how the shape of the ECG varies as a function of cell type, distribution, excitation duration and AP shape. The propagation of the wave is visualized in real time through all the regions as parameters are kept fixed or varied to modify ECG morphology. The code solves thousands of simulated cells in real time and is independent of operating system, so it can run on PCs, laptops, tablets and cellphones. This program can be used to teach students, fellows and the general public how and why lead positions and the different cell physiology in the heart affect the various features of the ECG.

Unimapper: An Online Interactive Analyzer/Visualizer of Optical Mapping Experimental Data

Time series of spatially-extended two-dimensional recordings are the cornerstone of basic and clinical cardiac electrophysiology. The data source may be either multipolar catheters, multi-electrode arrays, optical mapping with the help of voltage and calcium-sensitive fluorescent dyes, or the output of simulation studies. The resulting data cubes (usually two spatial and one temporal dimension) are shared either as movie files or, after additional processing, various graphs and tables. However, such data products can only convey a limited view of the data. It will be beneficial if the data consumers can interactively process the data, explore different processing options and change its visualization. This paper presents the Unified Electrophysiology Mapping Framework (Unimapper) to facilitate the exchange of electrophysiology data. Its pedigree includes a Java-based optical mapping application. The core of Unimapper is a website and a collection of JavaScript utility functions for data import and visualization (including multi-channel visualization for simultaneous voltage/calcium mapping), basic image processing (e.g., smoothing), basic signal processing (e.g., signal detrending), and advanced processing (e.g., phase calculation using the Hilbert transform). Additionally, Unimapper can optionally use graphics processing units (GPUs) for computationally intensive operations. The Unimapper ecosystem also includes utility libraries for commonly used scientific programming languages (MATLAB, Python, and Julia) that allow the data producers to convert images and recorded signals into a standard format readable by Unimapper. Unimapper can act as a nexus to share electrophysiology data - whether recorded experimentally, clinically or generated by simulation - and enhance communication and collaboration among researchers.

Quantifying arrhythmic long QT effects of hydroxychloroquine and azithromycin with whole-heart optical mapping and simulations

Background

In March 2020, hydroxychloroquine (HCQ) alone or combined with azithromycin (AZM) was authorized as a treatment for COVID-19 in many countries. The therapy proved ineffective with long QT and deadly cardiac arrhythmia risks, illustrating challenges to determine the new safety profile of repurposed drugs.

Objective

To investigate proarrhythmic effects and mechanism of HCQ and AZM (combined and alone) with high doses of HCQ as in the COVID-19 clinical trials.

Methods

Proarrhythmic effects of HCQ and AZM are quantified using optical mapping with voltage-sensitive dyes in ex vivo Langendorff-perfused guinea pig (GP) hearts and with numerical simulations of a GP Luo-Rudy and a human O’Hara-Virag-Varro-Rudy models, for Epi, Endo, and M cells, in cell and tissue, incorporating the drug’s effect on cell membrane ionic currents.

Results

Experimentally, HCQ alone and combined with AZM leads to long QT intervals by prolonging the action potential duration and increased spatial dispersion of action potential (AP) repolarization across the heart, leading to proarrhythmic discordant alternans. AZM alone had a lesser arrhythmic effect with less triangulation of the AP shape. Mathematical cardiac models fail to reproduce most of the arrhythmic effects observed experimentally.

Conclusions

During public health crises, the risks and benefits of new and repurposed drugs could be better assessed with alternative experimental and computational approaches to identify proarrhythmic mechanisms. Optical mapping is an effective framework suitable to investigate the drug’s adverse effects on cardiac cell membrane ionic channels at the cellular level and arrhythmia mechanisms at the tissue and whole-organ level.

Precision medicine in human heart modeling : Perspectives, challenges, and opportunities

Precision medicine is a new frontier in healthcare that uses scientific methods to customize medical treatment to the individual genes, anatomy, physiology, and lifestyle of each person. In cardiovascular health, precision medicine has emerged as a promising paradigm to enable cost-effective solutions that improve quality of life and reduce mortality rates. However, the exact role in precision medicine for human heart modeling has not yet been fully explored. Here, we discuss the challenges and opportunities for personalized human heart simulations, from diagnosis to device design, treatment planning, and prognosis. With a view toward personalization, we map out the history of anatomic, physical, and constitutive human heart models throughout the past three decades. We illustrate recent human heart modeling in electrophysiology, cardiac mechanics, and fluid dynamics and highlight clinically relevant applications of these models for drug development, pacing lead failure, heart failure, ventricular assist devices, edge-to-edge repair, and annuloplasty. With a view toward translational medicine, we provide a clinical perspective on virtual imaging trials and a regulatory perspective on medical device innovation. We show that precision medicine in human heart modeling does not necessarily require a fully personalized, high-resolution whole heart model with an entire personalized medical history. Instead, we advocate for creating personalized models out of population-based libraries with geometric, biological, physical, and clinical information by morphing between clinical data and medical histories from cohorts of patients using machine learning. We anticipate that this perspective will shape the path toward introducing human heart simulations into precision medicine with the ultimate goals to facilitate clinical decision making, guide treatment planning, and accelerate device design.

Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-Accelerated Monte Carlo Simulation

The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach.

On the Role of Ionic Modeling on the Signature of Cardiac Arrhythmias for Healthy and Diseased Hearts

Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies.

Data-Driven Uncertainty Quantification for Cardiac Electrophysiological Models: Impact of Physiological Variability on Action Potential and Spiral Wave Dynamics

Computational modeling of cardiac electrophysiology (EP) has recently transitioned from a scientific research tool to clinical applications. To ensure reliability of clinical or regulatory decisions made using cardiac EP models, it is vital to evaluate the uncertainty in model predictions. Model predictions are uncertain because there is typically substantial uncertainty in model input parameters, due to measurement error or natural variability. While there has been much recent uncertainty quantification (UQ) research for cardiac EP models, all previous work has been limited by either: (i) considering uncertainty in only a subset of the full set of parameters; and/or (ii) assigning arbitrary variation to parameters (e.g., ±10 or 50% around mean value) rather than basing the parameter uncertainty on experimental data. In our recent work we overcame the first limitation by performing UQ and sensitivity analysis using a novel canine action potential model, allowing all parameters to be uncertain, but with arbitrary variation. Here, we address the second limitation by extending our previous work to use data-driven estimates of parameter uncertainty. Overall, we estimated uncertainty due to population variability in all parameters in five currents active during repolarization: inward potassium rectifier, transient outward potassium, L-type calcium, rapidly and slowly activating delayed potassium rectifier; 25 parameters in total (all model parameters except fast sodium current parameters). A variety of methods was used to estimate the variability in these parameters. We then propagated the uncertainties through the model to determine their impact on predictions of action potential shape, action potential duration (APD) prolongation due to drug block, and spiral wave dynamics. Parameter uncertainty had a significant effect on model predictions, especially L-type calcium current parameters. Correlation between physiological parameters was determined to play a role in physiological realism of action potentials. Surprisingly, even model outputs that were relative differences, specifically drug-induced APD prolongation, were heavily impacted by the underlying uncertainty. This is the first data-driven end-to-end UQ analysis in cardiac EP accounting for uncertainty in the vast majority of parameters, including first in tissue, and demonstrates how future UQ could be used to ensure model-based decisions are robust to all underlying parameter uncertainties.

Creation and application of virtual patient cohorts of heart models

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Accelerating simulations of cardiac electrical dynamics through a multi-GPU platform and an optimized data structure

Simulations of cardiac electrophysiological models in tissue, particularly in 3D require the solutions of billions of differential equations even for just a couple of milliseconds, thus highly demanding in computational resources. In fact, even studies in small domains with very complex models may take several hours to reproduce seconds of electrical cardiac behavior. Today's Graphics Processor Units (GPUs) are becoming a way to accelerate such simulations, and give the added possibilities to run them locally without the need for supercomputers. Nevertheless, when using GPUs, bottlenecks related to global memory access caused by the spatial discretization of the large tissue domains being simulated, become a big challenge. For simulations in a single GPU, we propose a strategy to accelerate the computation of the diffusion term through a data-structure and memory access pattern designed to maximize coalescent memory transactions and minimize branch divergence, achieving results approximately 1.4 times faster than a standard GPU method. We also combine this data structure with a designed communication strategy to take advantage in the case of simulations in multi-GPU platforms. We demonstrate that, in the multi-GPU approach performs, simulations in 3D tissue can be just 4× slower than real time.

Delay differential equation-based models of cardiac tissue: Efficient implementation and effects on spiral-wave dynamics

Delay differential equations (DDEs) recently have been used in models of cardiac electrophysiology, particularly in studies focusing on electrical alternans, instabilities, and chaos. A number of processes within cardiac cells involve delays, and DDEs can potentially represent mechanisms that result in complex dynamics both at the cellular level and at the tissue level, including cardiac arrhythmias. However, DDE-based formulations introduce new computational challenges due to the need for storing and retrieving past values of variables at each spatial location. Cardiac tissue simulations that use DDEs may require over 28 GB of memory if the history of variables is not managed carefully. This paper addresses both computational and dynamical issues. First, we present new methods for the numerical solution of DDEs in tissue to mitigate the memory requirements associated with the history of variables. The new methods exploit the different time scales of an action potential to dynamically optimize history size. We find that the proposed methods decrease memory usage by up to 95% in cardiac tissue simulations compared to straightforward history-management algorithms. Second, we use the optimized methods to analyze for the first time the dynamics of wave propagation in two-dimensional cardiac tissue for models that include DDEs. In particular, we study the effects of DDEs on spiral-wave dynamics, including wave breakup and chaos, using a canine myocyte model. We find that by introducing delays to the gating variables governing the calcium current, DDEs can induce spiral-wave breakup in 2D cardiac tissue domains.

Simulating waves, chaos and synchronization with a microcontroller

The spatiotemporal dynamics of complex systems have been studied traditionally and visualized numerically using high-end computers. However, due to advances in microcontrollers, it is now possible to run what once were considered large-scale simulations using a very small and inexpensive single integrated circuit that can furthermore send and receive information to and from the outside world in real time. In this paper, we show how microcontrollers can be used to perform simulations of nonlinear ordinary differential equations with spatial coupling and to visualize their dynamics using arrays of light-emitting diodes and/or touchscreens. We demonstrate these abilities using three different models: two reaction-diffusion models (one neural and one cardiac) and a generic model of network oscillators. These models are commonly used to simulate various phenomena in biophysical systems, including bifurcations, waves, chaos, and synchronization. We also demonstrate how simple it is to integrate real-time user interaction with the simulations by showing examples with a light sensor, touchscreen, and web browser.

Synchronization-based reconstruction of electromechanical wave dynamics in elastic excitable media

The heart is an elastic excitable medium, in which mechanical contraction is triggered by nonlinear waves of electrical excitation, which diffuse rapidly through the heart tissue and subsequently activate the cardiac muscle cells to contract. These highly dynamic excitation wave phenomena have yet to be fully observed within the depths of the heart muscle, as imaging technology is unable to penetrate the tissue and provide panoramic, three-dimensional visualizations necessary for adequate study. As a result, the electrophysiological mechanisms that are associated with the onset and progression of severe heart rhythm disorders such as atrial or ventricular fibrillation remain insufficiently understood. Here, we present a novel synchronization-based data assimilation approach with which it is possible to reconstruct excitation wave dynamics within the volume of elastic excitable media by observing spatiotemporal deformation patterns, which occur in response to excitation. The mechanical data are assimilated in a numerical replication of the measured elastic excitable system, and within this replication, the data drive the intrinsic excitable dynamics, which then coevolve and correspond to a reconstruction of the original dynamics. We provide a numerical proof-of-principle and demonstrate the performance of the approach by recovering even complicated three-dimensional scroll wave patterns, including vortex filaments of electrical excitation from within a deformable bulk tissue with fiber anisotropy. In the future, the reconstruction approach could be combined with high-speed imaging of the heart's mechanical contractions to estimate its electrophysiological activity for diagnostic purposes.

Factors Promoting Conduction Slowing as Substrates for Block and Reentry in Infarcted Hearts

The development of effective and safe therapies for scar-related ventricular tachycardias requires a detailed understanding of the mechanisms underlying the conduction block that initiates electrical re-entries associated with these arrhythmias. Conduction block has been often associated with electrophysiological changes that prolong action potential duration (APD) within the border zone (BZ) of chronically infarcted hearts. However, experimental evidence suggests that remodeling processes promoting conduction slowing as opposed to APD prolongation mark the chronic phase. In this context, the substrate for the initial block at the mouth of an isthmus/diastolic channel leading to ventricular tachycardia is unclear. The goal of this study was to determine whether electrophysiological parameters associated with conduction slowing can cause block and re-entry in the BZ. In silico experiments were conducted on two-dimensional idealized infarct tissue as well as on a cohort of postinfarction porcine left ventricular models constructed from ex vivo magnetic resonance imaging scans. Functional conduction slowing in the BZ was modeled by reducing sodium current density, whereas structural conduction slowing was represented by decreasing tissue conductivity and including fibrosis. The arrhythmogenic potential of APD prolongation was also tested as a basis for comparison. Within all models, the combination of reduced sodium current with structural remodeling more often degenerated into re-entry and, if so, was more likely to be sustained for more cycles. Although re-entries were also detected in experiments with prolonged APD, they were often not sustained because of the subsequent block caused by long-lasting repolarization. Functional and structural conditions associated with slow conduction rather than APD prolongation form a potent substrate for arrhythmogenesis at the isthmus/BZ of chronically infarcted hearts. Reduced excitability led to block while slow conduction shortened the wavelength of propagation, facilitating the sustenance of re-entries. These findings provide important insights for models of patient-specific risk stratification and therapy planning.