Coupling contraction, excitation, ventricular and coronary blood flow across scale and physics in the heart

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 367, Issue 1896, 2009, Pages 2311-2331

  Lee, Jack ^a   Niederer, Steven ^a   Nordsletten, David ^a   Le Grice, Ian ^b   Smail, Bruce ^b   Kay, David ^a   Smith, Nicolas ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Cardiac; Computational modelling; Coupling; Multi physics; Multi scale

Indexed keywords

BLOOD; HEMODYNAMICS; MEDICAL COMPUTING; SHRINKAGE;

BLOOD FLOW; CARDIAC; CARDIAC FUNCTIONS; COMPUTATIONAL IMPLEMENTATIONS; COMPUTATIONAL MODELLING; COUPLING MECHANISM; MECHANICAL COUPLING; MULTI-PHYSICS; MULTI-SCALE; MULTISCALE COUPLING; PARAMETRIZATION;

PHYSIOLOGICAL MODELS;

ARTICLE; CORONARY BLOOD VESSEL; HEART; HUMAN; PHYSIOLOGY;

CORONARY VESSELS; HEART; HUMANS;

EID: 67650863175     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2008.0311     Document Type: Article

References (84)

1. Bathe, K. & Zhang, H. 2004 Finite element developments for general fluid flows with structural interactions. Int. J. Numer. Methods Eng. 60, 213-232. (doi:10.1002/nme.959)
2. Beard, D. A. et al. 2009 CellML metadata standards, associated tools and repositories. Phil. Trans. R. Soc. A 367, 1845-1867. (doi:10.1098/rsta.2008.0310)
3. Cheng, Y., Oertel, H. & Schenkel, T. 2005 Fluid-structure coupled CFD simulation of the left ventricular flow during filling phase. Ann. Biomed. Eng. 8, 567-576. (doi:10.1007/s10439-005-4388-9)
4. Chilian, W. M. & DeFily, D. V. 1991 Methodological approaches used for the study of the coronary microcirculation in situ. Blood Vessels 28, 236-244.
5. Chinchapatnam, P. P. et al. 2007 Anisotropic wave propagation and apparent conductivity estimation in a fast electrophysiological model: application to XMR interventional imaging. Med. Image Comput. Comput. Assist. Interv. Int. Conf. 10(Pt 1), 575-583.
6. Crampin, E. J. & Smith, N. P. 2006 A dynamic model of excitation-contraction coupling during acidosis in cardiac ventricular myocytes. Biophys. J. 90, 3074-3090. (doi:10.1529/biophysj.105. 070557)
7. Dettmer, W. & Peri, D. 2006 A computational framework for fluid-structure interaction: finite element formulation and applications. Comput. Methods Appl. Mech. Eng. 195, 5754-5779. (doi:10.1016/j.cma.2005.10.019)
8. Domenichini, F., Pedrizzetti, G. & Baccani, B. 2005 Three-dimensional filling flow into a model left ventricle. J. Fluid Mech. 539, 179-198. (doi:10.1017/S0022112005005550)
9. i overloaded cardiac myocytes: a simulation study. Biophys. J. 78, 2392-2404. (doi:10.1016/S0006- 3495(00)76783-X)
10. Farhat, C., Lesoinne, M. & Maman, N. 1994 Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. Int. J. Numer. Methods Fluids 21, 807-835. (doi:10.1002/fld.1650211004)
11. Farhat, C., Lesoinne, M. & Letallec, P. 1998 Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput. Methods Appl. Mech. Eng. 157, 95-114. (doi:10.1016/S0045-7825(97)00216-8)
12. Fibich, G., Lanir, Y. & Liron, N. 1993 Mathematical model of blood flow in a coronary capillary. Am. J. Physiol. 265, H1829-H1840.
13. Formaggia, L., Nobile, F., Quarteroni, A. & Veneziani, A. 1999 Multiscale modelling of the circulatory system: a preliminary analysis. Comput. Vis. Sci. 2, 75-83. (doi:10.1007/ s007910050030)
14. Formaggia, L., Gerbeau, J., Nobile, F. & Quarteroni, A. 2001 On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191, 561-582. (doi:10.1016/S0045-7825(01)00302-4)
15. Gebker, R., Gomaa, O., Schnackenburg, B., Rebakowski, J., Fleck, E. & Nagel, E. 2007 Comparison of different MRI techniques for the assessment of thoracic aortic pathology: 3D contrast enhanced MR angiography, turbo spin echo and balanced steady state free precession. Int. J. Cardiovasc. Imaging 23, 747-756. (doi:10.1007/s10554-006-9204-6)
16. Greenshields, C. & Weller, H. 2005 A unified formulation for continuum mechanics applied to fluid-structure interaction in flexible tubes. Int. J. Numer. Methods Eng. 64, 1575-1593. (doi:10. 1002/nme.1409)
17. Heinzer, S., Krucker, T., Stampanoni, M., Abela, R., Meyer, E. P., Schuler, A., Schneider, P. &Müller, R. 2006 Hierarchical microimaging for multiscale analysis of large vascular networks. NeuroImage 32, 626-636. (doi:10.1016/j.neuroimage.2006.03.043)
18. Hinch, R., Greenstein, J. L., Tanskanen, A. J., Xu, L. & Winslow, R. L. 2004 A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes. Biophys. J. 87, 3723-3736. (doi:10.1529/biophysj.104.049973)
19. Hunter, P. J., McCulloch, A. D. & ter Keurs, H. E. D. J. 1998 Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69, 289-331. (doi:10.1016/S0079-6107(98)00013-3)
20. Huyghe, J. M., Arts, T. & van Campen, D. H. 1992 Porous medium finite element model of the beating left ventricle. Am. J. Physiol. 262(Pt 2), H1256-H1267.
21. Iyer, V., Mazhari, R. & Winslow, R. L. 2004 A computational model of the human left-ventricular epicardial myocyte. Biophys. J. 87, 1507-1525. (doi:10.1529/biophysj.104.043299)
22. 2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys. J. 74, 1149-1168. (doi:10.1016/ S0006-3495(98)77832-4)
23. Jorgensen, S. M., Demirkaya, O. & Ritman, E. L. 1998 Three-dimensional imaging of vasculature and parenchyma in intact rodent organs with X-ray micro-CT. Am. J. Physiol. 275, H1103-H1114. (Heart Circ. Physiol. 44)
24. Kaufmann, R., Bayer, R., Fürniss, T., Krause, H. & Tritthart, H. 1974 Calcium-movement controlling cardiac contractility II. Analog computation of cardiac excitation-contraction coupling on the basis of calcium kinetics in a multi-compartment model. J. Mol. Cell. Cardiol. 6, 543-559. (doi:10.1016/0022-2828(74)90035-2)
25. Kerckhoffs, R. C. P., Bovendeerd, P. H. M., Prinzen, F. W., Smits, K. & Arts, T. 2003a Intra-and interventricular asynchrony of electromechanics in the ventricularly paced heart. J. Eng. Math. 47, 201-216. (doi:10.1023/B:ENGI.0000007972.73874.da)
26. Kerckhoffs, R. C. P., Faris, O. P., Bovendeerd, P. H. M., Prinzen, F. W., Smits, K., McVeigh, E. R. & Arts, T. 2003b Timing of depolarization and contraction in the paced canine left ventricle: model and experiment. J. Cardiovasc. Electrophys. 14, S188-S195. (doi:10.1046/ j.1540.8167.90310.x)
27. Kilner, P. J., Yang, G. Z., Wilkes, A. J., Mohiaddin, R. H., Firmin, D. N. & Yacoub, M. H. 2000 Asymmetric redirection of flow through the heart. Nature 404, 759-761. (doi:10.1038/35008075)
28. Kovács, S. J., McQueen, M. D. & Peskin, C. S. 2001 Modelling cardiac fluid dynamics and diastolic function. Phil. Trans. R. Soc. A 359, 1299-1314. (doi:10.1098/rsta.2001.0832)
29. Krause, H., Antoni, H. & Fleckenstein, A. 1966 An electronic model for the formation of local and transmitted stimuli on the myocardium fibers based upon variable current-voltage characteristics for potassium and sodium ions. Pflugers Arch. Gesamte Physiol. Menschen Tiere 289, 12-36. (doi:10.1007/BF00417641)
30. Lee, D. C., Simonetti, O. P., Harris, K. R., Holly, T. A., Judd, R. M., Wu, E. & Klocke, F. J. 2004 Magnetic resonance versus radionuclide pharmacological stress perfusion imaging for flowlimiting stenoses of varying severity. Circulation 110, 58-65. (doi:10.1161/01.CIR.0000133389. 48487.B6)
31. Lee, J. & Smith, N. P. 2008 Development and application of a one-dimensional blood flow model for microvascular networks. Proc. Inst. Mech. Eng. H J. Eng. Med. 222, 487-511. (doi:10.1243/ 09544119JEIM308)
32. Lee, J., Beighley, P., Ritman, E. & Smith, N. 2007 Automatic segmentation of 3D micro-CT coronary vascular images. Med. Image Anal. 11, 630-647. (doi:10.1016/j.media.2007.06.012)
33. Lemmon, J. & Yoganathan, A. 2000 Computational modeling of left heart diastolic function: examination of ventricular dysfunction. J. Biomech. Eng. 122, 297-303. (doi:10.1115/1.1286559)
34. Long, Q., Merrifield, R., Yang, G. Z., Kilner, P. J., Firmin, D. N. & Xu, X. Y. 2003 The influence of inflow boundary conditions on intra left ventricle flow predictions. Trans. ASME 125, 922-927. (doi:10.1115/1.1635404)
35. McCulloch, A. 2004 Functionally and structurally integrated computational modeling of ventricular physiology. Jpn J. Phys. 54, 531-539. (doi:10.2170/jjphysiol.54.531)
36. McQueen, D. & Peskin, C. 1989a A 3D computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid. J. Comp. Phys. 81, 372-405. (doi:10. 1016/0021-9991(89) 90213-1)
37. McQueen, D. & Peskin, C. 1989b A 3D computational method for blood flow in the heart. II. Contractile fibers. J. Comp. Phys. 82, 289-297. (doi:10.1016/0021-9991(89)90050-8)
38. McQueen, D. & Peskin, C. 2000 A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. Comput. Graph. 34, 56-60. (doi:10.1145/563788.604453)
39. Mynard, J. P. & Nithiarasu, P. 2008 A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method. Commun. Numer. Methods Eng. 24, 367-417. (doi:10.1002/cnm.1117)
40. Nagel, E. 2008 Magnetic resonance perfusion imaging for detection of ischemic heart disease. Metab. Imaging 38, 19-21.
41. Nash, M. P. 1998 Mechanics and material properties of the heart using an anatomically accurate mathematical model. PhD thesis, University of Auckland.
42. Nash, M. P. & Hunter, P. 2000 Computational mechanics of the heart. J. Elast. 61, 113-141. (doi:10.1023/A:1011084330767)
43. Nash, M. P. & Panfilov, A. V. 2004 Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias. Prog. Biophys. Mol. Biol. 85, 501-522. (doi:10.1016/j.pbiomolbio.2004.01.016)
44. Nickerson, D., Smith, N. & Hunter, P. 2005 New developments in a strongly coupled cardiac electromechanical model. Europace 7(Suppl. 2), S118-S127. (doi:10.1016/j.eupc.2005.04.009)
45. Nickerson, D. P. & Hunter, P. J. 2006 The noble cardiac ventricular electrophysiology models in CellML. Prog. Biophys. Mol. Biol. 90, 346-359. (doi:10.1016/j.pbiomolbio.2005.05.007)
46. Niederer, S. A. & Smith, N. P. 2007 A mathematical model of the slow force response to stretch in rat ventricular myocytes. Biophys. J. 92, 4030-4044. (doi:10.1529/biophysj.106.095463)
47. Niederer, S. A. & Smith, N. P. 2008 An improved numerical method for strong coupling of excitation and contraction models in the heart. Prog. Biophys. Mol. Biol. 96, 90-111. (doi:10. 1016/j.pbiomolbio.2007.08. 001)
48. Niederer, S. A., Hunter, P. J. & Smith, N. P. 2006 A quantitative analysis of cardiac myocyte relaxation: a simulation study. Biophys. J. 90, 1697-1722. (doi:10.1529/biophysj.105. 069534)
49. Niederer, S. A., Fink, M., Noble, D. & Smith, N. P. In press. A meta analysis of cardiac electrophysiology computational models. Exp. Phys. (doi:10.1113/expphysiol.2008.044610)
50. Nielson, P., Grice, I. L., Smaill, B. H. & Hunter, P. J. 1991 Mathematical model of geometry and fibrous structure of the heart. Am. J. Physiol. 260, H1365-H1378.
51. Nordsletten, D. A., Blackett, S., Bentley, M. D., Ritman, E. L. & Smith, N. P. 2006 Structural morphology of renal vasculature. Am. J. Physiol. Heart Circ. Physiol. 291, H296-H309. (doi:10. 1152/ajpheart.00814. 2005)
52. Nordsletten, D. A., Kay, D. & Smith, N. P. Submitted a. A non-conforming monolithic finite element method for problems of coupled mechanics.
53. Nordsletten, D. A., Smith, N. P. & Kay, D. A. Submitted b. Analysis of a non-conforming finite element method for fluid-solid mechanics.
54. Oertel, H. 2004 KAHMO-Karlsruhe Heart Model. Technical Report. Institute for Fluid Mechanics. University of Karlsruhe. 1.
55. Oertel, H. 2005 Modelling the human cardiac fluid mechanics. Institute for Fluid Mechanics. University of Karlsruhe. 1.
56. Pandit, S. V., Clark, R. B., Giles, W. R. & Demir, S. S. 2001 A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys. J. 81, 3029-3051. (doi:10.1016/S0006-3495(01)75943-7)
57. Pedrizzetti, G. & Domenichini, F. 2005 Nature optimizes the swirling flow in the human left ventricle. Phys. Rev. Lett. 95, 108101. (doi:10.1103/PhysRevLett.95.108101)
58. Plein, S., Kozerke, S., Suerder, D., Luescher, T. F., Greenwood, J. P., Boesiger, P. & Schwitter, J. 2008 High spatial resolution myocardial perfusion cardiac magnetic resonance for the detection of coronary artery disease. Eur. Heart J. 29, 2148-2155. (doi:10.1093/eurheartj/ ehn297)
59. Plouraboue, F., Cloetens, P., Fonta, C., Steyer, A., Lauwers, F. & Marc-Vergnes, J.-P. 2004 X-ray high-resolution vascular network imaging. J. Microsc. 215, 139-148. (doi:10.1111/j.0022-2720. 2004.01362.x)
60. Priebe, L. & Beuckelmann, D. J. 1998 Simulation study of cellular electric properties in heart failure. Circ. Res. 82, 1206-1223.
61. Pries, A. R. & Secomb, T. W. 2005 Microvascular blood viscosity in vivo and the endothelial surface layer. Am. J. Physiol. 289, H2657-H2664. (doi:10.1152/ajpheart.00297.2005)
62. Ribba, B., Tracqui, P., Boix, J. L., Boissel, J. P. & Thomas, S. R. 2006 QxDB: a generic database to support mathematical modelling in biology. Phil. Trans. R. Soc. A 364, 1517-1532. (doi:10. 1098/rsta.2006.1784)
63. Rice, J. J., Winslow, R. L. & Hunter, W. C. 1999 Comparison of putative cooperative mechanisms in cardiac muscle: length dependence and dynamic responses. Am. J. Physiol. 276, H1734-H1754.
64. Rice, J. J., Jafri, M. S. & Winslow, R. L. 2000 Modeling short-term interval-force relations in cardiac muscle. Am. J. Physiol. 278, H913-H931.
65. Saber, N. R., Gosman, A. D., Wood, N. B., Kilner, P. J., Charrier, C. L. & Firmin, D. N. 2001 Computational flow modeling of the left ventricle based on in vivo MRI data: initial experience. Ann. Biomed. Eng. 29, 275-283. (doi:10.1114/1.1359452)
66. Saber, N. R., Wood, N. B., Gosman, A. D., Merrifield, R. D., Yang, G. Z., Charrier, C. L., Gatehouse, P. D. & Firmin, D. 2003 Progress towards patient-specific computational flow modeling of the left heart via combination of MRI with computational fluid dynamics. Ann. Biomed. Eng. 31, 42-52. (doi:10.1114/1.1533073)
67. Sands, G. B., Gerneke, D. A., Hooks, D. A., Green, C. R., Smaill, B. H. & Legrice, I. J. 2005 Automated imaging of extended tissue volumes using confocal microscopy. Microsc. Res. Tech. 67, 227-239. (doi:10.1002/jemt.20200)
68. Sherwin, S. J., Franke, V., Peiró, J. & Parker, K. 2003 One-dimensional modelling of a vascular network in space-time variables. J. Eng. Math. 47, 217-250. (doi:10.1023/B:ENGI.0000007979. 32871.e2)
69. Smith, N. P., Pullan, A. J. & Hunter, P. J. 2002 An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62, 990-1018. (doi:10.1137/ S003613990037234X)
70. Smith, N. P., Buist, M. L. & Pullan, A. L. 2003 Altered T wave dynamics in a contracting cardiac model. J. Cardiovasc. Electrophys. 14, S203-S209. (doi:10.1046/j.1540.8167.90312.x)
71. Smith, N. P., Crampin, E. J., Niederer, S. A., Bassingthwaighte, J. B. & Beard, D. A. 2007 Computational biology of cardiac myocytes: proposed standards for the physiome. J. Exp. Biol. 210, 1576-1583. (doi:10.1242/jeb.000133)
72. Spaan, J. A., ter Wee, R., Van Teeffelen, J. W. G. E., Streekstra, G., Siebes, M., Kolyva, C., Vink, H., Fokkema, D. S. & Vanbavel, E. 2005 Visualisation of intramural coronary vasculature by an imaging cryomicrotome suggests compartmentalisation of myocardial perfusion areas. Med. Biol. Eng. Comput. 43, 431-435. (doi:10.1007/BF02344722)
73. Stevens, C. 2002 An anatomically-based computational study of cardiac mechanics and myocardial infarction. PhD thesis, University of Auckland.
74. Stevens, C., Remme, E., LeGrice, I. & Hunter, P. 2003 Ventricular mechanics in diastole: material parameter sensitivity. J. Biomech. 36, 737-748. (doi:10.1016/S0021-9290(02)00452-9)
75. ten Tusscher, K. H. W. J., Noble, D., Noble, P. J. & Panfilov, A. V. 2004 A model for human ventricular tissue. Am. J. Physiol. 286, H1573-H1589. (doi:10.1152/ajpheart.00794.2003)
76. Terkildsen, J. R., Niederer, S. A., Crampin, E. J., Hunter, P. J. & Smith, N. P. 2008 Using physiome standards to couple cellular functions for cardiac excitation contraction. Exp. Physiol. 93, 919-929. (doi:10.1113/expphysiol.2007.041871)
77. Tomlinson, K., Hunter, P. J. & Pullan, A. J. 2002 A finite element method for an eikonal equation model of myocardial excitation wavefront propagation. SIAM J. Appl. Math. 63, 324-350. (doi:10.1137/ S0036139901389513)
78. Uribe, S., Muthurangu, V., Boubertakh, R., Schaeffter, T., Razavi, R., Hill, D. L. G. & Hansen, M. S. 2007 Whole-heart cine MRI using real-time respiratory self-gating. Magn. Reson. Med. 57, 606-613. (doi:10.1002/mrm.21156)
79. Usyk, T. P. & McCulloch, A. D. 2003 Relationship between regional shortening and asynchronous electrical activation in a three-dimensional model of ventricular electromechanics. J. Cardiovasc. Electrophysiol. 14(Suppl. 10), S196-S202. (doi:10.1046/j.1540.8167.90311.x)
80. Vigmond, E. J., Clements, C., McQueen, D. M. & Peskin, C. S. 2008 Effect of bundle branch block on cardiac output: a whole heart simulation study. Prog. Biophys. Mol. Biol. 97, 520-542. (doi:10.1016/j.pbiomolbio. 2008.02.022)
81. Watanabe, H., Hisada, T., Sugiura, S., Okada, J.-I. & Fukunari, H. 2002 Computer simulation of blood flow, left ventricular wall motion and their interrelationship by fluid-structure interaction finite element method. JSM Int. J. 45, 1003-1012. (doi:10.1299/jsmec.45.1003)
82. Watanabe, H., Sugiura, S., Kafuku, H. & Hisada, T. 2004 Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. Biophys. J. 87, 2074-2085. (doi:10.1529/biophysj.103.035840)
83. Westerhof, N., Boer, C., Lamberts, R. R. & Sipkema, P. 2006 Cross-talk between cardiac muscle and coronary vasculature. Physiol. Rev. 86, 1263-1308. (doi:10.1152/physrev.00029.2005)
84. Young, A. A., LeGrice, I. J., Young, M. A. & Smaill, B. H. 1998 Extended confocal microscopy of myocardial laminae and collagen network. J. Microsc. 192, 139-150. (doi:10.1046/j.1365-2818. 1998.00414.x)