Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method

被引:44
作者
Pagani, Stefano [1 ]
Manzoni, Andrea [1 ]
Quarteroni, Alfio [1 ]
机构
[1] Politecn Milan, Dipartimento Matemat, MOX, Pza Leonardo da Vinci 32, I-20133 Milan, Italy
关键词
Cardiac electrophysiology; Parametrized monodomain model; Local reduced order model; Reduced basis method; Proper orthogonal decomposition; Empirical interpolation method; REACTION-DIFFUSION SYSTEMS; NONLINEAR MODEL-REDUCTION; BIDOMAIN MODEL; ELECTRIC-FIELD; DISCRETIZATION; SENSITIVITY; DYNAMICS;
D O I
10.1016/j.cma.2018.06.003
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The efficient solution of coupled PDEs/ODEs problems arising in cardiac electrophysiology is of key importance whenever interested to study the electrical behavior of the tissue for several instances of relevant physical and/or geometrical parameters. This poses significant challenges to reduced order modeling (ROM) techniques -such as the reduced basis method-traditionally employed when dealing with the repeated solution of parameter dependent differential equations. Indeed, the nonlinear nature of the problem, the presence of moving fronts in the solution, and the high sensitivity of this latter to parameter variations, make the application of standard ROM techniques very problematic. In this paper we propose a local ROM built through a k-means clustering in the state space of the snapshots for both the solution and the nonlinear term. Several comparisons among alternative local ROMs on a benchmark test case show the effectivity of the proposed approach. Finally, the application to a parametrized problem set on an idealized left-ventricle geometry shows the capability of the proposed ROM to face complex problems. (C) 2018 Elsevier B.Y. All rights reserved.
引用
收藏
页码:530 / 558
页数:29
相关论文
共 62 条
[1]   A simple two-variable model of cardiac excitation [J].
Aliev, RR ;
Panfilov, AV .
CHAOS SOLITONS & FRACTALS, 1996, 7 (03) :293-301
[2]  
Amsallem D., 2016, ADV MODELING SIMUL E, V3, P1
[3]   Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction [J].
Amsallem, David ;
Zahr, Matthew J. ;
Washabaugh, Kyle .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2015, 41 (05) :1187-1230
[4]   Nonlinear model order reduction based on local reduced-order bases [J].
Amsallem, David ;
Zahr, Matthew J. ;
Farhat, Charbel .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2012, 92 (10) :891-916
[5]  
[Anonymous], 42 AIAA FLUID DYN C
[6]   An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations [J].
Barrault, M ;
Maday, Y ;
Nguyen, NC ;
Patera, AT .
COMPTES RENDUS MATHEMATIQUE, 2004, 339 (09) :667-672
[7]   Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue [J].
Bendahmane, Mostafa ;
Karlsen, Kenneth H. .
NETWORKS AND HETEROGENEOUS MEDIA, 2006, 1 (01) :185-218
[8]   A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics [J].
Bonomi, Diana ;
Manzoni, Andrea ;
Quarteroni, Alfio .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 324 :300-326
[9]   A goal-oriented reduced-order modeling approach for nonlinear systems [J].
Borggaard, Jeff ;
Wang, Zhu ;
Zietsman, Lizette .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 71 (11) :2155-2169
[10]   Reduced-order modeling for cardiac electrophysiology. Application to parameter identification [J].
Boulakia, M. ;
Schenone, E. ;
Gerbeau, J-F. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, 2012, 28 (6-7) :727-744