Accelerating Cardiac Bidomain Simulations Using Graphics Processing Units

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, however, are computationally vastly demanding, which is a limiting factor for a wider adoption of in-silico modeling. While current trends in high-performance computing (HPC) hardware promise to alleviate this problem, exploiting the potential of such architectures remains challenging since strongly scalable algorithms are necessitated to reduce execution times. Alternatively, acceleration technologies such as graphics processing units (GPUs) are being considered. While the potential of GPUs has been demonstrated in various applications, benefits in the context of bidomain simulations where large sparse linear systems have to be solved in parallel with advanced numerical techniques are less clear. In this study, the feasibility of multi-GPU bidomain simulations is demonstrated by running strong scalability benchmarks using a state-of-the-art model of rabbit ventricles. The model is spatially discretized using the finite element methods (FEM) on fully unstructured grids. The GPU code is directly derived from a large pre-existing code, the Cardiac Arrhythmia Research Package (CARP), with very minor perturbation of the code base. Overall, bidomain simulations were sped up by a factor of 11.8 to 16.3 in benchmarks running on 6-20 GPUs compared to the same number of CPU cores. To match the fastest GPU simulation which engaged 20 GPUs, 476 CPU cores were required on a national supercomputing facility

Modeling and simulation of the electric activity of the heart using graphic processing units

Mathematical modelling and simulation of the electric activity of the heart (cardiac electrophysiology) offers and ideal framework to combine clinical and experimental data in order to help understanding the underlying mechanisms behind the observed respond under physiological and pathological conditions. In this regard, solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi- scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This thesis develops around the implementation of an electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA) for GPU computing. The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting and the finite element method for space discretization. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50× for three-dimensional problems when using an implicit scheme for the parabolic equation, whereas accelerations reach values up to 100× for the explicit implementation. The implemented solver has been applied to study pro-arrhythmic mechanisms during acute ischemia. In particular, we investigate on how hyperkalemia affects the vulnerability window to reentry and the reentry patterns in the heterogeneous substrate caused by acute regional ischemia using an anatomically and biophysically detailed human biventricular model. A three dimensional geometrically and anatomically accurate regionally ischemic human heart model was created. The ischemic region was located in the inferolateral and posterior side of the left ventricle mimicking the occlusion of the circumflex artery, and the presence of a washed-out zone not affected by ischemia at the endocardium has been incorporated. Realistic heterogeneity and fi er anisotropy has also been considered in the model. A highly electrophysiological detailed action potential model for human has been adapted to make it suitable for modeling ischemic conditions (hyperkalemia, hipoxia, and acidic conditions) by introducing a formulation of the ATP-sensitive K+ current. The model predicts the generation of sustained re-entrant activity in the form single and double circus around a blocked area within the ischemic zone for K+ concentrations bellow 9mM, with the reentrant activity associated with ventricular tachycardia in all cases. Results suggest the washed-out zone as a potential pro-arrhythmic substrate factor helping on establishing sustained ventricular tachycardia.Colli-Franzone P, Pavarino L. A parallel solver for reaction-diffusion systems in computational electrocardiology, Math. Models Methods Appl. Sci. 14 (06):883-911, 2004.Colli-Franzone P, Deu hard P, Erdmann B, Lang J, Pavarino L F. Adaptivity in space and time for reaction-diffusion systems in electrocardiology, SIAM J. Sci. Comput. 28 (3):942-962, 2006.Ferrero J M(Jr), Saiz J, Ferrero J M, Thakor N V. Simulation of action potentials from metabolically impaired cardiac myocytes: Role of atp-sensitive K+ current. Circ Res, 79(2):208-221, 1996.Ferrero J M (Jr), Trenor B. Rodriguez B, Saiz J. Electrical acticvity and reentry during acute regional myocardial ischemia: Insights from simulations.Int J Bif Chaos, 13:3703-3715, 2003.Heidenreich E, Ferrero J M, Doblare M, Rodriguez J F. Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology, Ann. Biomed. Eng. 38 (7):2331-2345, 2010.Janse M J, Kleber A G. Electrophysiological changes and ventricular arrhythmias in the early phase of regional myocardial ischemia. Circ. Res. 49:1069-1081, 1981.ten Tusscher K HWJ, Panlov A V. Alternans and spiral breakup in a human ventricular tissue model. Am. J.Physiol. Heart Circ. Physiol. 291(3):1088-1100, 2006.<br /

Cardiac ultrasound simulation for autonomous ultrasound navigation

Ultrasound is well-established as an imaging modality for diagnostic and interventional purposes. However, the image quality varies with operator skills as acquiring and interpreting ultrasound images requires extensive training due to the imaging artefacts, the range of acquisition parameters and the variability of patient anatomies. Automating the image acquisition task could improve acquisition reproducibility and quality but training such an algorithm requires large amounts of navigation data, not saved in routine examinations. Thus, we propose a method to generate large amounts of ultrasound images from other modalities and from arbitrary positions, such that this pipeline can later be used by learning algorithms for navigation. We present a novel simulation pipeline which uses segmentations from other modalities, an optimized volumetric data representation and GPU-accelerated Monte Carlo path tracing to generate view-dependent and patient-specific ultrasound images. We extensively validate the correctness of our pipeline with a phantom experiment, where structures' sizes, contrast and speckle noise properties are assessed. Furthermore, we demonstrate its usability to train neural networks for navigation in an echocardiography view classification experiment by generating synthetic images from more than 1000 patients. Networks pre-trained with our simulations achieve significantly superior performance in settings where large real datasets are not available, especially for under-represented classes. The proposed approach allows for fast and accurate patient-specific ultrasound image generation, and its usability for training networks for navigation-related tasks is demonstrated.Comment: 24 pages, 10 figures, 5 table

Computational Modeling and Numerical Methods for Spaciotemporal Calcium Cycling in Ventricular Myocytes

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown

Real-time optical manipulation of cardiac conduction in intact hearts

Optogenetics has provided new insights in cardiovascular research, leading to new methods for cardiac pacing, resynchronization therapy and cardioversion. Although these interventions have clearly demonstrated the feasibility of cardiac manipulation, current optical stimulation strategies do not take into account cardiac wave dynamics in real time. Here, we developed an all‐optical platform complemented by integrated, newly developed software to monitor and control electrical activity in intact mouse hearts. The system combined a wide‐field mesoscope with a digital projector for optogenetic activation. Cardiac functionality could be manipulated either in free‐run mode with submillisecond temporal resolution or in a closed‐loop fashion: a tailored hardware and software platform allowed real‐time intervention capable of reacting within 2 ms. The methodology was applied to restore normal electrical activity after atrioventricular block, by triggering the ventricle in response to optically mapped atrial activity with appropriate timing. Real‐time intraventricular manipulation of the propagating electrical wavefront was also demonstrated, opening the prospect for real‐time resynchronization therapy and cardiac defibrillation. Furthermore, the closed‐loop approach was applied to simulate a re‐entrant circuit across the ventricle demonstrating the capability of our system to manipulate heart conduction with high versatility even in arrhythmogenic conditions. The development of this innovative optical methodology provides the first proof‐of‐concept that a real‐time optically based stimulation can control cardiac rhythm in normal and abnormal conditions, promising a new approach for the investigation of the (patho)physiology of the heart

An electromechanics-driven fluid dynamics model for the simulation of the whole human heart

We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four-chamber electromechanical model. We first present a study on the calibration of the biophysically detailed RDQ20 active contraction model (Regazzoni et al., 2020) that is able to reproduce the physiological range of hemodynamic biomarkers. Then, we demonstrate that the ability of the force generation model to reproduce certain microscale mechanisms, such as the dependence of force on fiber shortening velocity, is crucial to capture the overall physiological mechanical and fluid dynamics macroscale behavior. This motivates the need for using multiscale models with high biophysical fidelity, even when the outputs of interest are relative to the macroscale. We show that the use of a high-fidelity electromechanical model, combined with a detailed calibration process, allows us to achieve a remarkable biophysical fidelity in terms of both mechanical and hemodynamic quantities. Indeed, our electromechanical-driven CFD simulations – carried out on an anatomically accurate geometry of the whole heart – provide results that match the cardiac physiology both qualitatively (in terms of flow patterns) and quantitatively (when comparing in silico results with biomarkers acquired in vivo). Moreover, we consider the pathological case of left bundle branch block, and we investigate the consequences that an electrical abnormality has on cardiac hemodynamics thanks to our multiphysics integrated model. The computational model that we propose can faithfully predict a delay and an increasing wall shear stress in the left ventricle in the pathological condition. The interaction of different physical processes in an integrated framework allows us to faithfully describe and model this pathology, by capturing and reproducing the intrinsic multiphysics nature of the human heart

High-efficient Bloch simulation of magnetic resonance imaging sequences based on deep learning

Objective: Bloch simulation constitutes an essential part of magnetic resonance imaging (MRI) development. However, even with the graphics processing unit (GPU) acceleration, the heavy computational load remains a major challenge, especially in large-scale, high-accuracy simulation scenarios. This work aims to develop a deep learning-based simulator to accelerate Bloch simulation. Approach: The simulator model, called Simu-Net, is based on an end-to-end convolutional neural network and is trained with synthetic data generated by traditional Bloch simulation. It uses dynamic convolution to fuse spatial and physical information with different dimensions and introduces position encoding templates to achieve position-specific labeling and overcome the receptive field limitation of the convolutional network. Main Results: Compared with mainstream GPU-based MRI simulation software, Simu-Net successfully accelerates simulations by hundreds of times in both traditional and advanced MRI pulse sequences. The accuracy and robustness of the proposed framework were verified qualitatively and quantitatively. Besides, the trained Simu-Net was applied to generate sufficient customized training samples for deep learning-based T2 mapping and comparable results to conventional methods were obtained in the human brain. Significance: As a proof-of-concept work, Simu-Net shows the potential to apply deep learning for rapidly approximating the forward physical process of MRI and may increase the efficiency of Bloch simulation for optimization of MRI pulse sequences and deep learning-based methods.Comment: 18 pages, 8 figure