Efficient simulation of cardiac electrical propagation using high order finite elements

Journal of Computational Physics

Volumn 231, Issue 10, 2012, Pages 3946-3962

  Arthurs, Christopher J ^a   Bishop, Martin J ^a,b   Kay, David ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Computational cardiology; Finite element method; Monodomain simulation; Numerical efficiency; p Version

Indexed keywords

HEART; NUMERICAL METHODS;

COMPUTATIONAL CARDIOLOGY; EFFICIENT SIMULATION; ELECTRICAL PROPAGATION; HIERARCHICAL FINITE ELEMENT; HIGH-ORDER; HIGH-ORDER FINITE ELEMENTS; HIGHER-ORDER; MONODOMAIN SIMULATION; NUMERICAL EFFICIENCY; P-VERSION;

FINITE ELEMENT METHOD;

EID: 84858752628     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.01.037     Document Type: Article

References (55)

1. Health Statistics Quarterly, chapter Death registrations in England and Wales, 2005: causes 2006, Palgrave Macmillan. P. Goldblatt, R. Chappell (Eds.).
2. Mirams G.R., Cui Y., Sher A., Fink M., Cooper J., Heath B.M., McMahon N.C., Gavaghan D.J., Noble D. Simulation of multiple ion channel block provides improved early prediction of compounds' clinical torsadogenic risk. Cardiovasc. Res. 2011, 91:53-61.
3. Redfern W.S., Carlsson L., Davis A.S., Lynch W.G., MacKenzie I., Palethorpe S., Siegl P.K.S., Strang I., Sullivan A.T., Wallis R., Camm A.J., Hammond T.G. Relationships between preclinical cardiac electrophysiology, clinical qt interval prolongation and torsade de pointes for a broad range of drugs: evidence for a provisional safety margin in drug development. Cardiovasc. Res. 2003, 58:32-45.
4. Efimov I.R., Nikolski V.P., Salama G. Optical imaging of the heart. Circ. Res. 2004, 95:21-33.
5. L. Tung, A bi-domain model for describing ischemic myocardial D-C potentials. PhD thesis, Massachusetts Institute of Technology, USA, 1978.
6. Keener J., Sneyd J. Mathematical Physiology 1998, Springer.
7. Bernabeu M.O., Pathmanathan P., Pitt-Francis J., Kay D. Stimulus protocol determines the most computationally efficient preconditioner for the bidomain equations. IEEE Trans. Biomed. Eng. 2010, 57:2806-2815.
8. Bernabeu M.O., Kay D. Scalable parallel preconditioners for an open source cardiac electrophysiology simulation package. Procedia Comput. Sci. 2011, 4:821-830.
9. Whiteley J.P. Physiology driven adaptivity for the numerical solution of the bidomain equations. IEEE Ann. Bio-Med. Eng. 2007, 35:1510-1520.
10. Cherry E.M., Greenside H.S., Henriquez C.S. Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh renement method. Chaos 2003, 13:853-865.
11. Colli Franzone P., Deuflhard P., Erdmann B., Lang J., Pavarino L.F. Adaptivity in space and time for reaction-diffusion systems in electrocardiology. SIAM J. Sci. Comput. 2006, 28:942-962.
12. Pennacchio M. The motar finite element method for the cardiac bidomain model of extracellular potential. J. Sci. Comput. 2004, 20:191-210.
13. Babuška I., Szabo B.A., Katz I.N. The p-version of the finite element method. SIAM J. Numer. Anal. 1981, 18:515-545.
14. Babuška I., Suri M. The p and h-p versions of the finite element method, an overview. Comput. Method Appl. M 1990, 80:5-26.
15. Babuška I., Suri M. The p and h-p versions of the finite element method, basic principles and properties. SIAM Rev. 1994, 36:578-632.
16. Colli Franzone P., Pavarino L.F., Taccardi B. Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models. Math. Biosci. 2005, 197(1):35-66.
17. Plank G., Leon L.J., Kimber S., Vigmond E.J. Defibrillation depends on conductivity fluctuations and the degree of disorganization in reentry patterns. J. Cardiovasc. Electrophysiol. 2005, 16(2):205-216.
18. Trayanova N. Defibrillation of the heart: insights into mechanisms from modelling studies. Exp. Phys. 2006, 91(2):323-337.
19. Pitt-Francis J., Pathmanathan P., Bernabeu M.O., Bordas R., Cooper J., Fletcher A.G., Mirams G.R., Murray P., Osborne J.M., Walter A., Chapman S.J., Garny A., van Leeuwen I.M.M., Maini P.K., Rodrguez B., Waters S.L., Whiteley J.P., Byrne H.M., Gavaghan D.J. Chaste: A test-driven approach to software development for biological modelling. Comput. Phys. Comm. 2009, 180(12):2452-2471. 40 YEARS OF CPC: A celebratory issue focused on quality software for high performance, grid and novel computing architectures.
20. Bordas R., Carpentieri B., Fotia G., Maggio F., Nobes R., Pitt-Francis J., Southern J. Simulation of cardiac electrophysiology on next-generation high-performance computers. Phil. Trans. R. Soc. A 2009, 367:1951-1969.
21. F. Maggio, B. Carpentieri, G. Fotia. A 3d solver for the bidomain equations based on unstructured all-hexahedra spectral elements. Technical Report 09/50, CRS4, Center for Advanced Studies, Research and Development in Sardinia, Cagliari, Italy, aug Unpublished results 1.
22. F. Maggio, B. Carpentieri, G. Fotia, Spectral elements applied to cardiac simulation: A comparison with finite elements. Technical Report 09/51, CRS4, Center for Advanced Studies, Research and Development in Sardinia, Cagliari, Italy, Unpublished results 1.
23. Casadei F., Gabellini E., Fotia G., Maggio F., Quarteroni A. A mortar spectral/finite element method for complex 2d and 3d elastodynamic problems. Comput. Method Appl. M 2002, 191:5119-5148.
24. Luo C., Rudy Y. A model of the ventricular cardiac action potential. depolarization, repolarization, and their interaction. Circ. Res. 1991, 68:1501-1526.
25. Courtemanche M., Ramirez R.J., Nattel S. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am. J. Physiol. Heart Circ. Physiol. 1998, 275:301-321.
26. Winslow R.L., Rice J., Jafri S., Marbán E., O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: model studies. Circ. Res. 1999, 84:571-586.
27. Shannon T.R., Wand F., Puglisi J., Weber C., M Bers D. A mathematical treatment of integrated ca dynamics within the ventricular myocyte. Biophys. J. 2004, 87:3351-3371.
28. Scholarpedia (Flavio H Fenton and Elizabeth M. Cherry). Scholarpedia, 3(8):1868, 2008. [Online; accessed 5-January-2012].
29. Vigmond E.J., Weber dos Santos R., Prassl A.J., Deo M., Planck G. Solvers for the cardiac bidomain equations. Prog. Biophys. Mol. Bio. 2007, 96:3-18.
30. Potse M., Dubé B., Richer J., Vinet A., Gulrajani R.M. A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng. 2006, 53:2425-2435.
31. Bishop M., Plank G. Representing cardiac bidomain bath-loading effects by an augmented monodomain approach: application to complex ventricular models. IEEE Trans. Biomed. Eng. 2011.
32. Wikswo J.P., Lin S.-F., Abbas R.A. Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation. Biophys. J. 1995, 69:2195-2210.
33. Bishop M.J., PLank G., Burton R.A.B., Schneider J.E., Gavaghan D.J., Grau V., Kohl P. Development of an anatomically detailed mri-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function. Am. J. Physiol. Heart Circ. Physiol. 2009, 298:699-718.
34. Noble D. A modification of the Hodgkin-Huxley equations applicable to purkinje fiber action and pacemaker potential. J. Physiol. 1962, 160:317-352.
35. Adams R.A. Sobolev Spaces 1975, Academic Press.
36. Brenner S.C., Scott L.R. The Mathematical Theory of Finite Element Methods 1994, Springer.
37. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, SIAM, classics in applied mathematics edition, 2002.
38. Babuška I., Suri M. The h-p version of the finite element method with quasiuniform meshes. RAIRO-Math. Model. Numer. 1987, 21:199-238.
39. Ainsworth M., Kay D. Approximation theory for thr hp-version finite element method and application to the non-linear laplacian. Appl. Numer. Math. 2000, 34:329-344.
40. Ainsworth M., Kay D. The approximation theory for the p-version finite element method and application to non-linear elliptic pdes. Numer. Math. 1999, 83:351-388.
41. Thomée V. Galerkin Finite Element Methods for Parabolic Problems 2006, Springer-Verlag. Second ed.
42. Hesthaven J.S. From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex. SIAM J. Numer. Anal. 1998, 35:655-676.
43. M. Hanslien, N. Holden, J. Sundnes, A note on discontinuous rate functions for the gate variables in mathematical models of cardiac cells, in International Conference on Computational Science ICCS 2010, (2010), pp. 939-944.
44. Bradley J. Roth. Artifacts, assumptions and ambiguity: pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart. Chaos, (12) (2002), pp. 973-981.
45. Bishop M., Boyle P.M., Plank G., Welsh D.G., Vigmond E.J. Modelling the role of the coronary vasculature during external field stimulation. IEEE Trans. Biomed. Eng. 2010.
46. Gibb M., Bishop M., Burton R., Kohl P., Grau V., plank G., Rodriguez B. The role of blood vessels in rabbit proagation dynamics and cardiac arrhythmias. Lect. Notes Comput. Sci. 2009, 5528:268-276.
47. Ackleh A.S., Allen E.J., Kearfott R.B., Seshaiyer P. Classical and Modern Numerical Analysis. Theory, Methods and Practice 2010, Chapman & Hall/CRC, CRC.
48. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1962, 1:445-466.
49. Ashihara T., Trayanova N.A. Asymmetry in membrane responses to electric shocks: Insights from bidomain simulations. Biophys. J. 2004, 87:2271-2282.
50. DeBruin K.A., Krassowska W. Modeling electroporation in a single cell. I. effects of field strength and rest potential. Biophys. J. 1999, 77:1213-1224.
51. Krassowvska W. Effects of electroporation on transmembrane potential induced by defibrillation shocks. PACE 1995, 18:1644-1660.
52. Pathmanathan P., Bernabeu M.O., Bordas R., Cooper J., Garny A., Pitt-Francis J.M., Whiteley J.P., Gavaghan D.J. A numerical guide to the solution of the bidomain equations of cardiac electrophysiology. Prog. Biophys. Mol. Biol. 2010, 102.
53. E.J. Vigmond, P.M. Boyle, L.J. Leon, G. Planck, Near-real-time simulations of biolelectric activity in small mammalian hearts using graphical processing units, in 31st Annual International Conference of the IEEE EMBS, 2009.
54. E. Bartocci, E.M. Cherry, J. Glimm, R. Grosu, S.A. Smolka, F.H. Fenton, Toward real-time simulation of cardiac dynamics, in CMSB 2011 9th International Conference on Computational Methods in Systems Biology, 2011.
55. Niederer S.A., Kerfoot E., Benson A.P., Bernabeu M.O., Bernus O., Bradley C., Cherry E.M., Clayton R., Fenton F.H., Garny A., Heidenreich E., Land S., Maleckar M., Pathmanathan P., Plank G., Rodríguez J.F., Roy I., Sachse F.B., Seemann G., Skavhaug O., Smith N.P. Verification of cardiac tissue electrophysiology simulators using a n-version benchmark. Phil. Trans. R. Soc. A 2011, 369:4331-4351.