Simulations of complex and microscopic models of cardiac electrophysiology powered by multi-GPU platforms

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.

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

Large-scale Interactive Numerical Experiments of Chaos, Solitons and Fractals in Real Time via GPU in a Web Browser

The study of complex systems has emerged as an important field with many discoveries still to be made. Computer simulation and visualization provide important tools for studying complex dynamics including chaos, solitons, and fractals, but available computing power has been a limiting factor. In this work, we describe a novel and highly efficient computing and visualization paradigm using a Web Graphics Library (WebGL 2.0) methodology along with our newly developed library (Abubu.js). Our approach harnesses the power of widely available and highly parallel graphics cards while maintaining ease of use by simplifying programming through hiding implementation details, running in a web browser without the need for compilation, and avoiding the use of plugins. At the same time, it allows for interactivity, such as changing parameter values on the fly, and its computing is so fast that zooming in on a region of a fractal like the Mandelbrot set can incur no delay despite having to recalculate values for the entire plane. We demonstrate our approach using a wide range of complex systems that display dynamics from fractals to standing and propagating waves in 1, 2 and 3 dimensions. We also include some models with instabilities that can lead to chaotic dynamics. For all the examples shown here we provide links to the codes for anyone to use, modify and further develop with other models. Overall, the enhanced visualization and computation capabilities provided by WebGL together with Abubu.js have great potential to facilitate new discoveries about complex systems.

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

Cardiac dynamics modeling has been useful for studying and treating arrhythmias. However, it is a multiscale problem requiring the solution of billions of differential equations describing the complex electrophysiology of interconnected cells. Therefore, large-scale cardiac modeling has been limited to groups with access to supercomputers and clusters. Many areas of computational science face similar problems where computational costs are too high for personal computers so that supercomputers or clusters currently are necessary. Here, we introduce a new approach that makes high-performance simulation of cardiac dynamics and other large-scale systems like fluid flow and crystal growth accessible to virtually anyone with a modest computer. For cardiac dynamics, this approach will allow not only scientists and students but also physicians to use physiologically accurate modeling and simulation tools that are interactive in real time, thereby making diagnostics, research, and education available to a broader audience and pushing the boundaries of cardiac science.

Discretization-dependent model for weakly connected excitable media

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

Simulation of Ectopic Pacemakers in the Heart: Multiple Ectopic Beats Generated by Reentry inside Fibrotic Regions

The inclusion of nonconducting media, mimicking cardiac fibrosis, in two models of cardiac tissue produces the formation of ectopic beats. The fraction of nonconducting media in comparison with the fraction of healthy myocytes and the topological distribution of cells determines the probability of ectopic beat generation. First, a detailed subcellular microscopic model that accounts for the microstructure of the cardiac tissue is constructed and employed for the numerical simulation of action potential propagation. Next, an equivalent discrete model is implemented, which permits a faster integration of the equations. This discrete model is a simplified version of the microscopic model that maintains the distribution of connections between cells. Both models produce similar results when describing action potential propagation in homogeneous tissue; however, they slightly differ in the generation of ectopic beats in heterogeneous tissue. Nevertheless, both models present the generation of reentry inside fibrotic tissues. This kind of reentry restricted to microfibrosis regions can result in the formation of ectopic pacemakers, that is, regions that will generate a series of ectopic stimulus at a fast pacing rate. In turn, such activity has been related to trigger fibrillation in the atria and in the ventricles in clinical and animal studies.

Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU

Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation) and the other is the diffusion term of the monodomain model (partial differential equation). Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations.

Multiscale cardiac modelling reveals the origins of notched T waves in long QT syndrome type 2

The heart rhythm disorder long QT syndrome (LQTS) can result in sudden death in the young or remain asymptomatic into adulthood. The features of the surface electrocardiogram (ECG), a measure of the electrical activity of the heart, can be equally variable in LQTS patients, posing well-described diagnostic dilemmas. Here we report a correlation between QT interval prolongation and T-wave notching in LQTS2 patients and use a novel computational framework to investigate how individual ionic currents, as well as cellular and tissue level factors, contribute to notched T waves. Furthermore, we show that variable expressivity of ECG features observed in LQTS2 patients can be explained by as little as 20% variation in the levels of ionic conductances that contribute to repolarization reserve. This has significant implications for interpretation of whole-genome sequencing data and underlies the importance of interpreting the entire molecular signature of disease in any given individual.