A Parallel Multigrid Algorithm for Solving Elliptic Equations in the Cardiac Bidomain Model

[摘要] Elliptic partial differential equations (PDEs) are ubiquitous in problems concerned with modeling steady state field distributions in different media. In biology and medicine, the rapid numerical solution of elliptic PDEs are necessary for the bidomain model of myocardium and in the study of phenomena associated with external shock applications to the heart (defibrillation therapy). Here, we summarize the development and study of a novel parallel multigrid algorithm, adapted from a parallel multigrid solver from the hypre numerical library, for subsequent use in studying wave propagation in the two-dimensional(2D) bidomain model of the myocardium (with and without the presence of external defibrillation shocks). Our simulation study, using this novel multigrid algorithm and implemented on a massively parallel supercomputer, shows: (1) the computation time for the bidomain model fell by a factor of 10 (in comparison to the sequential multigrid implementation), while using 64 processors, without introducing significant error in the solution; (2) as the number of processors increased beyond the linear range of scalability, the computation time of the bidomain model continued to decrease, but only asymptotically; and (3) virtually identical distributions of Vm during 2D spiral wave propagations were produced by our original sequential implementation of the multigrid algorithm and our novel algorithm. The significant time savings realized by our novel algorithm will make possible future computer simulation studies of three-dimensional myocardium using the bidomain model, with particular emphases on defibrillation-associated phenomena.

[发布机构] UCLA Henry Samueli School of Engineering and Applied Science

[学科分类] 计算机科学（综合）