A finite volume method for modeling discontinuous electrical activation in cardiac tissue

Annals of Biomedical Engineering

Volumn 33, Issue 5, 2005, Pages 590-602

  Trew, Mark ^a   Le Grice, Ian ^a   Smaill, Bruce ^a   Pullan, Andrew ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Activation times; Bidomain equations; Bipolar stimulus; Cleavage planes; Computational efficiency; Numerical simulation; Shock; Tissue microstructure

Indexed keywords

ACTIVATION ANALYSIS; BOUNDARY CONDITIONS; CELLS; COLLAGEN; COMPUTER SIMULATION; ELECTRIC CURRENTS; FINITE ELEMENT METHOD; LEAKAGE CURRENTS; MICROSTRUCTURE; TISSUE;

ACTIVATION TIMES; BIODOMAIN EQUATIONS; BIPOLAR STIMULUS; CLEAVAGE PLANES; COMPUTATIONAL EFFICIENCY; SHOCK; TISSUE MICROSTRUCTURE;

CARDIOLOGY;

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; COMPUTER SIMULATION; ELECTROCARDIOGRAPHY; EVALUATION; FINITE ELEMENT ANALYSIS; HEART CONTRACTION; HEART MUSCLE CELL; HEART MUSCLE CONDUCTION SYSTEM; HEART PACING; HEART VENTRICLE; HUMAN; METHODOLOGY; PHYSIOLOGY; VALIDATION STUDY;

ACTION POTENTIALS; ANIMALS; BODY SURFACE POTENTIAL MAPPING; CARDIAC PACING, ARTIFICIAL; COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; HEART CONDUCTION SYSTEM; HEART VENTRICLES; HUMANS; MODELS, CARDIOVASCULAR; MODELS, NEUROLOGICAL; MYOCARDIAL CONTRACTION; MYOCYTES, CARDIAC;

EID: 21244433958     PISSN: 00906964     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10439-005-1434-6     Document Type: Article

References (46)

1. Beeler, G., and H. Reuter. Reconstruction of the action potential of ventricular myocardial fibers. J. Physiol. 268:177-210, 1977.
2. Buist, M., G. Sands, P. Hunter, and A. Pullan. A deformable finite element derived finite difference method for cardiac activation problems. Ann. Biomed. Eng. 31:577-588, 2003.
3. Caulfield, J., and T. Borg. The collagen network of the heart. Lab. Invest. 40:364-372, 1979.
4. Christon, M., M. Martinez, and T. Voth. Generalized Fourier analysis of the advection-diffusion equation. Part I. One-dimensional domains. Int. J. Numer. Methods Fluids 45:839-887, 2004.
5. Colli-Frazone, P., L. Guerri, and B. Taccardi. Modeling ventricular excitation: Axial and orthotropic anisotropy effects on wavefronts and potentials. Math. Biosci. 188:191-205, 2004.
6. Costa, K., Y. Takayama, A. McCulloch, and J. Covell. Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. Am. J. Physiol. 276:H595-H607, 1999.
7. Drouhard, J., and F. Roberge. A simulation study of the ventricular myocardial action potential. IEEE Trans. Biomed. Eng. 29:494-502, 1982.
8. Fast, V., S. Rohr, A. Gillis, and A. Kleber. Activation of cardiac tissue by extracellular electrical shocks. Formation of 'secondary sources' at intercellular clefts in monolayers of cultured myocytes. Circ.Res. 82:375-385, 1998.
9. Feneis, H. Das gefüge des herzmuskels bei systole und diastole. Morphologi. J. 89:371-406, 1943.
10. Harrild, D., and C. Henriquez. A finite volume model of cardiac propagation. Ann. Biomed. Eng. 25:315-334, 1997.
11. Harrild, D., R. Penland, and C. Henriquez. A flexible method for simulating cardiac conduction in three-dimensional complex geometries. J. Electrocardiol. 33(3):241-251, 2000.
12. Henriquez, C. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit. Rev. Biomed. Eng. 21:1-77, 1993.
13. Hooks, D., K. Tomlinson, S. Marsden, I. LeGrice, B. Smaill, A. Pullan, and P. Hunter. Cardiac microstructure: Implications for electrical propagation and defibrillation in the heart. Circ. Res. 91(4):331-338, 2002.
14. Hort, W. Makroskopische und mikrometrische Untersuchungen am myokard verschieden stark gefüllter linker kammern. Virchows Archiv-Int. J.Pathol. 333:523-564, 1960.
15. Hunter, P., P. McNaughton, and D. Noble. Analytical models of propagation in excitable cells. Prog. Biophys. Mol. Biol. 30(2/3):99-144, 1975.
16. Jayantha, P., and I. Turner. On the use of surface interpolation techniques in generalised finite volume strategies for simulating transport in highly anisotropic porous media. J. Comput. Appl. Math. 152:199-216, 2003.
17. Krassowska, W., D. Frazier, T. Pilkington, and R. Ideker. Potential distribution in three-dimensional periodic myocardium. Part II. Application to extracellular stimulation. IEEE Trans. Biomed. Eng. 37:267-284, 1990.
18. Kucera, J., A. Kleber, and S. Rohr. Slow conduction in cardiac tissue. Part II. Effects of branching tissue geometry. Circ. Res. 83:795-805, 1998.
19. Latimer, D., and B. Roth. Electrical stimulation of cardiac tissue by a bipolar electrode in a conductive bath. IEEE Trans. Biomed. Eng. 45(12), 1998.
20. LeGrice, I., B. Smaill, L. Chai, S. Edgar, J. Gavin, and P. Hunter. Laminar structure of the heart: Ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. 269:H571-H582, 1995.
21. Liu, G. Mesh Free Methods: Moving beyond the finite element method. Boca Raton, FL: CRC Press, 2002. ISBN 0-8439-1238-8.
22. Newton, J., S. Knisley, X. Zhou, A. Pollard, and R. Ideker. Review of mechanisms by which electrical stimulation alters the transmembrane potential. J. Cardiovasc. Electrophysiol. 10:234-243, 1999.
23. Penland, R., D. Harrild, and C. Henriquez. Modeling impulse propagation and extracellular potential distributions in anisotropic cardiac tissue using a finite volume element discretization. Comput. Visual. Sci. 4:215-226, 2002.
24. Qu, Z., and A. Garfinkel. An advanced alogrithm for solving partial differential equation in cardiac conduction. IEEE Trans. Biomed. Eng. 46(9): 1166-1168, 1999.
25. Robinson, T., L. Cohen-Gould, and S. Factor. Skeletal framework of mammalian heart muscle. Lab. Invest. 49:482-498, 1983.
26. Rogers, J., and A. McCulloch. A collocation-Galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 41(8):743-757, 1994.
27. Rohr, S., J. Kucera, V. Fast, and A. Kleber. Paradoxical improvements of impulse conduction in cardiac tissue by partial cellular uncoupling. Science 275:841-844, 1997.
28. Roth, B. Electrical conductivity values used with the bidomain model of cardiac tissue. IEEE Trans. Biomed. Eng. 44(4):326-328, 1997.
29. Rudy, Y. Conductive bridges in cardiac tissue. A beneficial role or an arrhythmogenic substrate? Circ. Res. 2004.
30. Saleheen, H., and K. Ng. A new three-dimensional finite-difference bidomain formulation for inhomogeneous snisotropic cardiac tissues. IEEE Trans. Biomed. Eng. 45(1): 15-25, 1998.
31. Sharifov, O., and V. Fast. Optical mapping of transmural activation induced by electrical shocks in isolated left ventricular wall wedge preparations. JCE 14(11): 1215-1222, 2003.
32. Skouibine, K., N. Trayanova, and P. Moore. A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium. Math. Bio. 166:85-100, 2000.
33. Spach, M., and P. Dolber. Relating extracellular potentials and their derivatives to anisotropic propagation at the microscopic level in human cardiac muscle. Circ. Res. 58(3):356-371, 1996.
34. Sperelakis, N. An electric field mechanism for transmission of excitation between myocardial cells. Circ. Res. 91:985-987, 2002.
35. Sperelakis, N., and K. McConnell. Electric field interactions between closely abutting excitable cells. IEEE Eng. Med. Biol. 21(1):77-89, 2002.
36. Sundnes, J., G. Lines, K. Mardal, and A. Tveito. Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart. Comput. Methods Biomech. Biomed. Eng. 5(6):397-409, 2002.
37. Sundnes, J., G. Lines, and A. Tveito. Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells. Math. Biosci. 172:55-72, 2001.
38. Sundnes, J., G. Lines, and A. Tveito. ODE solvers for a stiff system arising in the modeling of the electrical activity of the heart. Int. J. Nonlinear Sci. Numer. Simul. 3(3), 2002.
39. Tang, D., C. Yang, S. Kobayashi, and D. Ku. Generalised finite difference method for 3-D viscous flow in stenotic tubes with large wall deformation and collapse. Appl. Numer. Math. 38:49-68, 2001.
40. Trayanova, N. Discrete versus syncytial tissue behavior in a model of cardiac stimulation. Part II. Results of simulation. IEEE Trans. Biomed. Eng. 43:1141-1150, 1996.
41. Trayanova, N. Far-field stimulation of cardiac tissue. Herzschr. Elektrophys. 10:137-148, 1999.
42. Vigmond, E., F. Aguel, and N. Trayanova. Computational techniques for solving the bidomain equations in three dimensions. IEEE Trans. Biomed. Eng. 49(1): 1260-1269, 2002.
43. Voth, T., M. Martinez, and M. Christon. Generalized Fourier analysis of the advection-diffusion equation. Part II. two-dimensional domains. Int. J. Numer. Methods Fluids 45:889-920, 2004.
44. Wikswo, J., Jr., S. Lin, and R. Abbas. Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation. Biophys. J. 69:2195-2210, 1995.
45. Young, A., I. LeGrice, M. Young, and B. Smaill. Extended confocal microscopy of myocardial laminae and collagen network. J. Microsc. 192(2): 139-150, 1998.
46. Yung, C. Application of a Stiff, Operator-Splitting Scheme to the Computational Modeling of Electrical Propagation in Cardiac Ventricles. Master's Thesis, Johns Hopkins University, Baltimore, Maryland, December 2000. Master of Science in Engineering.