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Accelerating cardiac excitation spread simulations using graphics processing units

The modeling of the electrical activity of the heart is of great medical and scientific interest, because it provides a way to get a better understanding of the related biophysical phenomena, allows the development of new techniques for diagnoses and serves as a platform for drug tests. The cardiac electrophysiology may be simulated by solving a partial differential equation coupled to a system of ordinary differential equations describing the electrical behavior of the cell membrane. The numerical solution is, however, computationally demanding because of the fine temporal and spatial sampling required. The demand for real‐time high definition 3D graphics made the new graphic processing units (GPUs) a highly parallel, multithreaded, many‐core processor with tremendous computational horsepower. It makes the use of GPUs a promising alternative to simulate the electrical activity in the heart. The aim of this work is to study the performance of GPUs for solving the equations underlying the electrical activity in a simple cardiac tissue. In tests on 2D cardiac tissues with different cell models it is shown that the GPU implementation runs 20 times faster than a parallel CPU implementation running with 4 threads on a quad–core machine, parts of the code are even accelerated by a factor of 180. Copyright

Experimental and theoretical ventricular electrograms and their relation to electrophysiological gradients in the adult rat heart

The electrical activity of adult mouse and rat hearts has been analyzed extensively, often as a prerequisite for genetic engineering studies or for the development of rodent models of human diseases. Some aspects of the initiation and conduction of the cardiac action potential in rodents closely resemble those in large mammals. However, rodents have a much higher heart rate and their ventricular action potential is triangular and very short. As a consequence, an interpretation of the electrocardiogram in the mouse and rat remains difficult and controversial. In this study, optical mapping techniques have been applied to an in vitro left ventricular adult rat preparation to obtain patterns of conduction and action potential duration measurements from the epicardial surface. This information has been combined with previously published mathematical models of the rat ventricular myocyte to develop a bidomain model for action potential propagation and electrogram formation in the rat left ventricle. Important insights into the basis for the repolarization waveform in the ventricular electrogram of the adult rat have been obtained. Notably, our model demonstrated that the biphasic shape of the rat ventricular repolarization wave can be explained in terms of the transmural and apex-to-base gradients in action potential duration that exist in the rat left ventricle.

Stochastic spontaneous calcium release events trigger premature ventricular complexes by overcoming electrotonic load

AIMS Premature ventricular complexes (PVCs) due to spontaneous calcium (Ca) release (SCR) events at the cell level can precipitate ventricular arrhythmias. However, the mechanistic link between SCRs and PVC formation remains incompletely understood. The aim of this study was to investigate the conditions under which delayed afterdepolarizations resulting from stochastic subcellular SCR events can overcome electrotonic source-sink mismatch, leading to PVC initiation. METHODS AND RESULTS A stochastic subcellular-scale mathematical model of SCR was incorporated in a realistic model of the rabbit ventricles and Purkinje system (PS). Elevated levels of diastolic sarcoplasmic reticulum Ca(2+) (CaSR) were imposed until triggered activity was observed, allowing us to compile statistics on probability, timing, and location of PVCs. At CaSR≥ 1500 µmol/L PVCs originated in the PS. When SCR was incapacitated in the PS, PVCs also emerged in the ventricles, but at a higher CaSR (≥1550 µmol/L) and with longer waiting times. For each model configuration tested, the probability of PVC occurrence increased from 0 to 100% within a well-defined critical CaSR range; this transition was much more abrupt in organ-scale models (∼50 µmol/L CaSR range) than in the tissue strand (∼100 µmol/L) or single-cell (∼450 µmol/L) models. Among PVCs originating in the PS, ∼68% were located near Purkinje-ventricular junctions (<1 mm). CONCLUSION SCR events overcome source-sink mismatch to trigger PVCs at a critical CaSR threshold. Above this threshold, PVCs emerge due to increased probability and reduced variability in timing of SCR events, leading to significant diastolic depolarization. Sites of lower electronic load, such as the PS, are preferential locations for triggering.

Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model

Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His–Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction–diffusion (R–D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.

Comparing CUDA, OpenCL and OpenGL implementations of the cardiac monodomain equations

Computer simulations of cardiac electrophysiology are a helpful tool in the study of bioelectric activity of the heart. The cardiac monodomain model comprises a nonlinear system of partial differential equations and its numerical solution represents a very intensive computational task due to the required fine spatial and temporal resolution. Recent studies have shown that the use of GPU as a general purpose processor can greatly improve the performance of simulations. The aim of this work is to study the performance of different GPU programming interfaces for the solution of the cardiac monodomain equations. Three different GPU implementations are compared, OpenGL, NVIDIA CUDA and OpenCL, to a CPU multicore implementation that uses OpenMP. The OpenGL approach showed to be the fastest with a speedup of 446 (compared to the multicore implementation) for the solution of the nonlinear system of ordinary differential equations (ODEs) associated to the solution of the cardiac model, whereas CUDA was the fastest for the numerical solution of the parabolic partial differential equation with a speedup of 8. Although OpenCL provides code portability between different accelerators, the OpenCL version was slower for the solution of the parabolic equation and as fast as CUDA for the solution of the system of ODEs, showing to be a portable way of programming scientific applications but not as efficient as CUDA when running on Nvidia GPUs.

Automatic code generation for solvers of cardiac cellular membrane dynamics in GPUs

The modeling of the electrical activity of the heart is of great medical and scientific interest, as it provides a way to get a better understanding of the related biophysical phenomena, allows the development of new techniques for diagnoses and serves as a platform for drug tests. However, due to the multi-scale nature of the underlying processes, the simulations of the cardiac bioelectric activity are still a computational challenge. In addition to that, the implementation of these computer models is a time consuming and error prone process. In this work we present a tool for prototyping ordinary differential equations (ODEs) in the area of cardiac modeling that aim to provide the automatic generation of high performance solvers tailored to the new hardware architecture of the graphic processing units (GPUs). The performance of these automatic solvers was evaluated using four different cardiac myocyte models. The GPU version of the solvers were between 75 and 290 times faster than the CPU versions.

A 2D-computer model of atrial tissue based on histographs describes the electro-anatomical impact of microstructure on endocardiac potentials and electric near-fields

In experiments with cardiac tissue, local conduction is described by waveform analysis of the derivative of the extracellular potential Φ̇e and by the loop morphology of the near-field strength E (the components of the electric field parallel and very close to the tissue surface). The question arises whether the features of these signals can be used to quantify the degree of fibrosis in the heart. A computer model allows us to study the behavior of electric signals at the endocardium with respect to known configurations of microstructure which can not be detected during the electrophysiological experiments. This work presents a 2D-computer model with sub-cellular resolution of atrial micro-conduction in the rabbit heart. It is based on the monodomain equations and digitized histographs from tissue slices obtained post-experimentum. It could be shown that excitation spread in densely coupled regions produces uniform and anisotropic conduction. In contrast, zones with parallel fibers separated by uncoupling interstitial space or connective tissue may show uniform or complex signals depending on pacing site. These results suggest that the analysis of Φ̇e and E combined with multi-site pacing could be used to characterize the type and the size of fibrosis.

Simulations of the electrical activity in the heart with graphic processing units

The modeling of the electrical activity of the heart is of great medical and scientific interest, because it provides a way to get a better understanding of the related biophysical phenomena, allows the development of new techniques for diagnoses and serves as a platform for drug tests. The cardiac electrophysiology may be simulated by solving a partial differential equation (PDE) coupled to a system of ordinary differential equations (ODEs) describing the electrical behavior of the cell membrane. The numerical solution is, however, computationally demanding because of the fine temporal and spatial sampling required. The demand for real time high definition 3D graphics made the new graphic processing units (GPUs) a highly parallel, multithreaded, many-core processor with tremendous computational horsepower. It makes the use of GPUs a promising alternative to simulate the electrical activity in the heart. The aim of this work is to study the performance of the use of GPUs to solve the equations underlying the electrical activity in a simple cardiac tissue.

A finite element approach for modeling micro-structural discontinuities in the heart

The presence of connective tissue as well as interstitial clefts forms a natural barrier to the electrical propagation in the heart. At a microscopic scale, such uncoupling structures change the pattern of the electrical conduction from uniform towards complex and may play a role in the genesis of cardiac arrhythmias. The anatomical diversity of conduction structures and their topology at a microscopic size scale is overwhelming for experimental techniques. Mathematical models have been often employed to study the behavior of the electrical propagation at a sub-cellular level. However, very fine and computationally expensive meshes are required to capture all microscopic details found in the cardiac tissue. In this work, we present a numerical technique based on the finite element method which allows to reproduce the effects of microscopic conduction barriers caused by the presence of uncoupling structures without actually resolving these structures in a high resolution mesh, thereby reducing the computational costs significantly.

Patient-specific modeling of left ventricular electromechanics as a driver for haemodynamic analysis

Aims Models of blood flow in the left ventricle (LV) and aorta are an important tool for analysing the interplay between LV deformation and flow patterns. Typically, image-based kinematic models describing endocardial motion are used as an input to blood flow simulations. While such models are suitable for analysing the hemodynamic status quo, they are limited in predicting the response to interventions that alter afterload conditions. Mechano-fluidic models using biophysically detailed electromechanical (EM) models have the potential to overcome this limitation, but are more costly to build and compute. We report our recent advancements in developing an automated workflow for the creation of such CFD ready kinematic models to serve as drivers of blood flow simulations. Methods and results EM models of the LV and aortic root were created for four pediatric patients treated for either aortic coarctation or aortic valve disease. Using MRI, ECG and invasive pressure recordings, anatomy as well as electrophysiological, mechanical and circulatory model components were personalized. Results The implemented modeling pipeline was highly automated and allowed model construction and execution of simulations of a patient’s heartbeat within 1 day. All models reproduced clinical data with acceptable accuracy. Conclusion Using the developed modeling workflow, the use of EM LV models as driver of fluid flow simulations is becoming feasible. While EM models are costly to construct, they constitute an important and nontrivial step towards fully coupled electro-mechano-fluidic (EMF) models and show promise as a tool for predicting the response to interventions which affect afterload conditions.