Reduced-order preconditioning for bidomain simulations

IEEE Transactions on Biomedical Engineering

Volumn 54, Issue 5, 2007, Pages 938-942

  Deo, M ^a   Bauer, S ^b   Plank, G ^c   Vigmond, E ^a  

^a UNIVERSITY OF CALGARY   (Canada)

^b PHYSIKALISCH TECHNISCHE BUNDESANSTALT   (Germany)

^c MEDICAL UNIVERSITY OF GRAZ   (Austria)

Author keywords

Bidomain; Cardiac simulations; Preconditioning

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; INITIAL VALUE PROBLEMS; ITERATIVE METHODS; LINEAR SYSTEMS; OPTIMIZATION;

ARNOLDI METHOD; BIDOMAIN; CARDIAC SIMULATIONS; PRECONDITIONED CONJUGATE GRADIENT (PCG) METHOD; PRECONDITIONING; SUCCESSIVE OVERRELAXATION (SOR);

BIOMEDICAL ENGINEERING;

ACCURACY; ANALYTIC METHOD; ARTICLE; ELECTRIC ACTIVITY; FINITE ELEMENT ANALYSIS; HEART ELECTROPHYSIOLOGY; INTERMETHOD COMPARISON; LINEAR SYSTEM; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PERFORMANCE; SIMULATION;

ALGORITHMS; COMPUTER SIMULATION; ELECTRIC CAPACITANCE; ELECTRIC STIMULATION; ELECTROPHYSIOLOGY; FINITE ELEMENT ANALYSIS; HEART CONDUCTION SYSTEM; HEART VENTRICLES; HUMANS; MODELS, CARDIOVASCULAR; NONLINEAR DYNAMICS; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; REPRODUCIBILITY OF RESULTS; SOFTWARE;

EID: 34247351700     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2006.889203     Document Type: Article

References (13)

1. L. Tung, "A bi-domain model for describing ischemic myocardial d-c potentials," Ph.D. dissertation, MIT, Cambridge, MA, 1978.
2. N. G. Sepulveda, B. J. Roth, J. Wikswo, and J. P. , "Current injection into a two-dimensional anisotropic bidomain," Biophys. J., vol. 55, no. 5, pp. 987-999, 1989.
3. E. Vigmond, F. Aguel, and N. Trayanova, "Computational techniques for solving the bidomain equations in three dimensions," IEEE Trans. Biomed. Eng., vol. 49, no. 11, pp. 1260-1269, Nov. 2002.
4. B. Rodriguez and N. Trayanova, "Upper limit of vulnerability in a defibrillation model of the rabbit ventricles," J. Electrocardiol., vol. 36, no. Suppl, pp. 51-56, 2003.
5. H. Shao, K. Sampson, J. Pormann, D. Rose, and C. Henriquez, "A resistor interpretation of general anisotropic cardiac tissue," Math. Biosci., vol. 187, no. 2, pp. 155-174, 2004.
6. H. Saleheen and K. Ng, "A new three-dimensional finite-difference bidomain formulation for inhomogeneous anisotropic cardiac tissues," IEEE Trans. Biomed. Eng., vol. 45, no. 1, pp. 15-25, Jan. 1998.
7. R. W. dos Santos, G. Plank, S. Bauer, and E. Vigmond, "Parallel multigrid preconditioner for the cardiac bidomain model," IEEE Trans. Biomed. Eng., vol. 51, no. 11, pp. 1960-1968, Nov. 2004.
8. R. Achar and M. Nakhla, "Simulation of high-speed interconnects," Proc. IEEE, vol. 89, no. 5, pp. 693-728, May 2001.
9. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. Philadelphia, PA: SIAM, 2000.
10. N. Hooke, C. Henriquez, P. Lanzkron, and D. Rose, "Linear algebraic transformations of the bidomain equations: Implications for numerical methods," Math. Biosci., vol. 120, no. 2, pp. 127-145, 1994.
11. J. Drouhard and F. Roberge, "Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells," Comput. Biomed. Res., vol. 20, pp. 333-350, 1987.
12. P. Heres and W. Schilders, "Practical issues of model order reduction with Krylov-subspace methods," in Proc. PIERS, Pisa, Italy, 2004.
13. J. Shewchuk, An Introduction to Conjugate Gradient Method Without the Agonizing Pain, Ed. 1 Sch. Comput. Sci., Carnegie Mellon Univ., Pittsburgh, PA, 1994, Tech. Rep.