Multi-level Parallelism in the Computational Modeling of the Heart

Computational modeling of the heart has demonstrated to be a useful tool for the investigation and comprehension of the complex biophysical processes that underlie cardiac function. Unfortunately, large scale simulations, such as those resulting from the discretization of an entire heart, remain a computational challenge. In order to reduce simulation execution times, parallel implementations have traditionally exploited data parallelism via numerical schemes based on domain-decomposition. However, it has been verified that the parallel efficiency of these implementations severely degrades as the number of processors increases. In this work, we propose and implement a new parallel algorithm for the solution of cardiac models. By relaxing the coherence of the execution, a new level of parallelism could be identified and exploited: pipelining. A synchronous parallel algorithm that uses both pipelining and data decomposition techniques was implemented and used the MPI library for communication. Numerical tests were performed in a 8-node Linux-cluster. Our preliminary results indicate that the proposed algorithm is able to increase the parallel efficiency up to 20% when compared to the traditional approach that uses pure data-level parallelism. In addition, the numerical precision was kept under control (relative errors under 4%) when the relaxed coherence execution was adopted.

[1]  Philippe Codognet,et al.  Compiling Constraints in clp(FD) , 1996, J. Log. Program..

[2]  Steven Swanson,et al.  Instruction scheduling for a tiled dataflow architecture , 2006, ASPLOS XII.

[3]  Rodrigo Weber dos Santos,et al.  Parallel multigrid preconditioner for the cardiac bidomain model , 2004, IEEE Transactions on Biomedical Engineering.

[4]  Jaehyuk Huh,et al.  Exploiting ILP, TLP, and DLP with the polymorphous TRIPS architecture , 2003, ISCA '03.

[5]  C. Henriquez,et al.  Validation of three-dimensional conduction models using experimental mapping: are we getting closer? , 1998, Progress in biophysics and molecular biology.

[6]  Kunle Olukotun,et al.  The case for a single-chip multiprocessor , 1996, ASPLOS VII.

[7]  Rina Dechter,et al.  Constraint Processing , 1995, Lecture Notes in Computer Science.

[8]  A. Tveito,et al.  An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso. , 2005, Mathematical biosciences.

[9]  Krishna M. Kavi,et al.  Execution and Cache Performance of the Scheduled Dataflow Architecture , 2000, J. Univers. Comput. Sci..

[10]  Eli Gafni,et al.  Concurrency in heavily loaded neighborhood-constrained systems , 1989, ICDCS.

[11]  Y. Rudy,et al.  Ionic Current Basis of Electrocardiographic Waveforms: A Model Study , 2002, Circulation research.

[12]  Gurindar S. Sohi,et al.  Speculative data-driven multithreading , 2001, Proceedings HPCA Seventh International Symposium on High-Performance Computer Architecture.

[13]  Trevor Mudge,et al.  MiBench: A free, commercially representative embedded benchmark suite , 2001 .

[14]  Rodrigo Weber dos Santos,et al.  Algebraic Multigrid Preconditioner for the Cardiac Bidomain Model , 2007, IEEE Transactions on Biomedical Engineering.

[15]  Lourdes Araujo,et al.  Parallel Execution Models for Constraint Programming over Finite Domains , 1999, PPDP.

[16]  Jean-Luc Gaudiot,et al.  Design and evaluation of a hierarchical decoupled architecture , 2006, The Journal of Supercomputing.

[17]  R. Plonsey Bioelectric sources arising in excitable fibers (Alza lecture) , 2006, Annals of Biomedical Engineering.

[18]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[19]  J.E. Smith,et al.  The Astronautics ZS-1 processor , 1988, Proceedings 1988 IEEE International Conference on Computer Design: VLSI.

[20]  I. Matosevic,et al.  The MLCA: A Solution Paradigm for Parallel Programmable SoCs , 2006, 2006 IEEE North-East Workshop on Circuits and Systems.

[21]  Anoop Gupta,et al.  The SPLASH-2 programs: characterization and methodological considerations , 1995, ISCA.

[22]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[23]  Natalia A. Trayanova,et al.  Computational techniques for solving the bidomain equations in three dimensions , 2002, IEEE Transactions on Biomedical Engineering.

[24]  D. Noble,et al.  A model for human ventricular tissue. , 2004, American journal of physiology. Heart and circulatory physiology.