Simulations of Complex and Microscopic Models of Cardiac Electrophysiology Powered by Multi-GPU Platforms

Hindawi Publishing Corporation Computational and Mathematical Methods in Medicine Volume 2012, Article ID 824569, 13 pages doi:10.1155/2012/824569 Research Article Simulations of Complex and Microscopic Models of Cardiac Electrophysiology Powered by Multi-GPU Platforms Bruno Gouvêa de Barros,1 Rafael Sachetto Oliveira,2, 3 Wagner Meira Jr.,3 Marcelo Lobosco,1 and Rodrigo Weber dos Santos1 1 Computational Modeling, Federal University of Juiz de Fora, 36036-900 Juiz de Fora, MG, Brazil 2 Computer Science, Federal University of São João del-Rei, 36307-352 São João del-Rei, MG, Brazil 3 Computer Science, Federal University of Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil Correspondence should be addressed to Rodrigo Weber dos Santos, Received 3 August 2012; Revised 28 September 2012; Accepted 1 October 2012 Academic Editor: Ling Xia Copyright © 2012 Bruno Gouvêa de Barros et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Key aspects of cardiac electrophysiology, such as slow conduction, conduction block, and saltatory effects have been the research topic of many studies since they are strongly related to cardiac arrhythmia, reentry, fibrillation, or defibrillation. However, to reproduce these phenomena the numerical models need to use subcellular discretization for the solution of the PDEs and nonuniform, heterogeneous tissue electric conductivity. Due to the high computational costs of simulations that reproduce the fine microstructure of cardiac tissue, previous studies have considered tissue experiments of small or moderate sizes and used simple cardiac cell models. In this paper, we develop a cardiac electrophysiology model that captures the microstructure of cardiac tissue by using a very fine spatial discretization (8 μm) and uses a very modern and complex cell model based on Markov chains for the characterization of ion channel’s structure and dynamics. To cope with the computational challenges, the model was parallelized using a hybrid approach: cluster computing and GPGPUs (general-purpose computing on graphics processing units). Our parallel implementation of this model using a multi-GPU platform was able to reduce the execution times of the simulations from more than 6 days (on a single processor) to 21 minutes (on a small 8-node cluster equipped with 16 GPUs, i.e., 2 GPUs per node). 1. Introduction Heart diseases are responsible for one third of all deaths worldwide [1]. Cardiac electrophysiology is the trigger to the mechanical deformation of the heart. Therefore, the knowledge of cardiac electrophysiology is essential to understand many aspects of cardiac physiological and physiopathological behavior [2]. Computer models of cardiac electrophysiology [3, 4] have become valuable tools for the study and comprehension of such complex phenomena, as they allow different information acquired from different physical scales and experiments to be combined to generate a better picture of the whole system functionality. Not surprisingly, the high complexity of the biophysical processes translates into complex mathematical and computational models. Modern cardiac models are described by nonlinear system of partial differential equations (PDEs) that may result in a problem with millions of unknowns. Mathematical models for cell electrophysiology are a key component of cardiac modeling. They serve both as standalone research tools, to investigate the behavior of single cardiac myocytes, and as an essential component of tissue and organ simulation based on the so-called bidomain or monodomain models [4]. The cell models can be written as a general non-linear system of ordinary differential equations (ODEs) and may vary in complexity from simple phenomenological models [5] (based on two variables) to complex models describing a large number of detailed physiological processes [6] (based on 40 to 80 differential variables). Simple models focus on the genesis of action potential (AP), that propagates from cell to cell and generates an electric wave that propagates on the heart. Complex models 2 account not only for the genesis of AP but also describe how this phenomenon is related to cardiac homeostasis and to different sub-cellular components, such as cell membrane’s ion channels. Advances in genetics, molecular biology, and electrophysiology experiments have provided new data and information related to the structure and function of ion channels. The Markov Chain (MC) model formalism has been increasingly used to describe both function and structure of ion channels. MC-based models have enabled simulations of structural abnormalities due to genetic diseases and drug-biding effects on ion channels [7–9]. Unfortunately, these modern cardiac myocyte models pose different challenges to both numerical methods, due to the stiffness of the ODEs introduced by MCs, and to high performance computing, due to the size of the problems, since the number of differential variables rises from a couple to near a hundred [10]. On the tissue level, the bidomain model [4] is considered to be the most complete description of the electrical activity. This nonlinear system of PDEs can be simplified to the so-called monodomain model, which may be less accurate but less computationally demanding than the bidomain model. Unfortunately, large scale simulations, such as those resulting from the discretization of an entire heart, remain a computational challenge. In addition, key aspects of cardiac electrophysiology, such as slow conduction, conduction block, and saltatory or sawtooth effects, demand sub-cellular discretization for the solution of the PDEs and nonuniform, heterogeneous tissue electric conductivity. These aspects of cardiac electrophysiology are strongly related to cardiac arrhythmia, reentry, fibrillation or defibrillation, and have been the research topic of many studies [11–20]. However, the demand of sub-cellular discretization for the solution of the PDEs and nonuniform, heterogeneous tissue electric conductivity have prevented the study of the aforementioned phenomena on large-scale tissue simulations. In addition, due to the high computational costs associated with the simulations of these microscopic models of cardiac tissue, previous works have adopted simple myocyte models, instead of modern MC-based models [6, 10]. In this work, we present a solution for this problem based on multi-GPU platforms (clusters equipped with graphics processing units) that allows fast simulations of microscopic tissue models combined with modern and complex myocyte models. The solution is based on merging two different highperformance techniques. We have previously investigated for cardiac modeling: cluster computing based on message passing communications (MPI) [21–24] and GPGPU (Generalpurpose computing on graphics processing (...truncated)