A high-resolution computational model of the deforming human heart

Biomechanics and Modeling in Mechanobiology

Volumn 14, Issue 4, 2015, Pages 829-849

  Gurev, Viatcheslav ^a   Pathmanathan, Pras ^b   Fattebert, Jean Luc ^c   Wen, Hui Fang ^a   Magerlein, John ^a   Gray, Richard A ^b   Richards, David F ^c   Rice, J Jeremy ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b CENTER FOR DEVICES AND RADIOLOGICAL HEALTH   (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Cardiac mechanics; Parallel computations; Soft tissue mechanics; Ventricular model

Indexed keywords

BENCHMARKING; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; HEART; INVERSE PROBLEMS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; MATRIX ALGEBRA; MESH GENERATION; TISSUE;

ACTIVE STRESS; CARDIAC MECHANICS; CARDIAC TISSUES; HIGH RESOLUTION; INCOMPRESSIBLE MATERIAL; NUMBER OF DEGREES OF FREEDOM; PARALLEL COMPUTATION; SOFT TISSUES MECHANICS; SOLUTION OF LINEAR SYSTEMS; VENTRICULAR MODEL;

NUMERICAL METHODS;

ANISOTROPY; ARTICLE; FINITE ELEMENT ANALYSIS; HEART; HEART CYCLE; HEART ELECTROPHYSIOLOGY; HEART FUNCTION; HEART LEFT VENTRICLE; HEART MUSCLE; HEART RIGHT VENTRICLE; HEART VENTRICLE CONTRACTION; HEART VENTRICLE PRESSURE; HEART VENTRICLE VOLUME; HUMAN; LINEAR SYSTEM; MATHEMATICAL MODEL; MUSCLE CONTRACTION; MYOFILAMENT; NONLINEAR SYSTEM; PRIORITY JOURNAL; BIOLOGICAL MODEL; COMPUTER SIMULATION; HEART CONTRACTION; HEART VENTRICLE; MECHANICAL STRESS; PATHOPHYSIOLOGY; PHYSIOLOGY; REPRODUCIBILITY;

COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; HEART; HEART VENTRICLES; HUMANS; MODELS, CARDIOVASCULAR; MYOCARDIAL CONTRACTION; REPRODUCIBILITY OF RESULTS; STRESS, MECHANICAL;

EID: 84939418056     PISSN: 16177959     EISSN: 16177940     Source Type: Journal    
DOI: 10.1007/s10237-014-0639-8     Document Type: Article

References (60)

1. Ackerman MJ (1998) The visible human project. Proc IEEE 86(3):504–511
2. Augustin CM, Holzapfel GA, Steinbach O (2014) Classical and all-floating FETI methods for the simulation of arterial tissues. Int J Numer Methods Eng 99(4):290–312
3. Auricchio F, da Veiga LB, Lovadina C, Reali A, Taylor RL, Wriggers P (2013) Approximation of incompressible large deformation elastic problems: some unresolved issues. Comput Mech 52(5):1153–1167
4. Baker A, Kolev TV, Yang U (2010) Improving algebraic multigrid interpolation operators for linear elasticity problems. Numer Linear Algebra Appl 17(2–3):495–517
5. Bröker O, Grote MJ, Mayer C, Reusken A (2001) Robust parallel smoothing for multigrid via sparse approximate inverses. SIAM J Sci Comput 23(4):1396–1417
6. Campbell SG, Howard E, Aguado-Sierra J, Coppola BA, Omens JH, Mulligan LJ, McCulloch AD, Kerckhoffs RC (2009) Effect of transmurally heterogeneous myocyte excitation–contraction coupling on canine left ventricular electromechanics. Exp Physiol 94(5):541–552
7. Chamberland É, Fortin A, Fortin M (2010) Comparison of the performance of some finite element discretizations for large deformation elasticity problems. Comput Struct 88(11):664–673
8. Cgal, Computational Geometry Algorithms Library. http://www.cgal.org
9. Chapelle D, Bathe K (1993) The inf-sup test. Comput Struct 47(4):537–545
10. Costa KD, Holmes JW, McCulloch AD (2001) Modelling cardiac mechanical properties in three dimensions. Philos Trans R Soc Lond Ser A 359(1783):1233–1250
11. Council NR (2012) Assessing the reliability of complex models: mathematical and statistical foundations of verification, validation, and uncertainty quantification. The National Academies Press. http://www.nap.edu/openbook.php?record_id=13395
12. El maliki A, Fortin M, Tardieu N, Fortin A (2010) Iterative solvers for 3D linear and nonlinear elasticity problems: displacement and mixed formulations. Int J Numer Methods Eng 83(13):1780–1802
13. El maliki A, Guenette R, Fortin M (2011) An efficient hierarchical preconditioner for quadratic discretizations of finite element problems. Numer Linear Algebra Appl 18(5):789–803
14. Elman H, Howle V, Shadid J, Shuttleworth R, Tuminaro R (2006) Block preconditioners based on approximate commutators. SIAM J Sci Comput 27(5):1651–1668
15. Farhat C, Roux FX (1991) A method of finite element tearing and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32(6):1205–1227
16. Fortin M, Glowinski R (2000) Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems. Elsevier, Amsterdam
17. Fritz T, Wieners C, Seemann G, Steen H, Dössel O (2013) Simulation of the contraction of the ventricles in a human heart model including atria and pericardium. Biomech Model Mechanobiol 13(3):627–641
18. Göktepe S, Acharya S, Wong J, Kuhl E (2011) Computational modeling of passive myocardium. Int J Numer Methods Biomed Eng 27(1):1–12
19. Golub GH, Greif C (2003) On solving block-structured indefinite linear systems. SIAM J Sci Comput 24(6):2076–2092
20. Guccione J, McCulloch A, Waldman L et al (1991) Passive material properties of intact ventricular myocardium determined from a cylindrical model. J Biomech Eng 113(1):42
21. Gurev V, Lee T, Constantino J, Arevalo H, Trayanova NA (2011) Models of cardiac electromechanics based on individual hearts imaging data. Biomech Model Mechanobiol 10(3):295–306
22. Heil M, Hazel AL (2006) Fluid-structure interaction. Lecture notes in computational science and engineering, vol 53, pp. 19–49
23. Holzapfel GA, Ogden RW (2009) Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos Trans R Soc A 367(1902):3445–3475
24. Huxley AF (1957) Muscle structure and theories of contraction. Prog Biophys Biophys Chem 7:255–318
25. Hypre. High performance preconditioners. http://www.llnl.gov/CASC/linear_solvers
26. Jie X, Gurev V, Trayanova N (2010) Mechanisms of mechanically induced spontaneous arrhythmias in acute regional ischemia. Circ Res 106(1):185–192
27. Keldermann RH, Nash MP, Gelderblom H, Wang VY, Panfilov AV (2010) Electromechanical wavebreak in a model of the human left ventricle. Am J Physiol Cell Physiol 299(1):H134
28. Kerckhoffs R, Lumens J, Vernooy K, Omens J, Mulligan L, Delhaas T, Arts T, McCulloch A, Prinzen F (2008) Cardiac resynchronization: insight from experimental and computational models. Prog Biophys Mol Biol 97(2):543–561
29. Kerckhoffs RC, Neal ML, Gu Q, Bassingthwaighte JB, Omens JH, McCulloch AD (2007) Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Ann Biomed Eng 35(1):1–18
30. Klepach D, Lee LC, Wenk JF, Ratcliffe MB, Zohdi TI, Navia JL, Kassab GS, Kuhl E, Guccione JM (2012) Growth and remodeling of the left ventricle: a case study of myocardial infarction and surgical ventricular restoration. Mech Res Commun 42:134–141
31. Land S, Niederer SA, Aronsen JM, Espe EK, Zhang L, Louch WE, Sjaastad I, Sejersted OM, Smith NP (2012) An analysis of deformation-dependent electromechanical coupling in the mouse heart. J Physiol 590(18):4553–4569
32. Le Tallec P (1994) Numerical methods for nonlinear three-dimensional elasticity. In: Ciarlet P, lions J (eds) Handbook of numerical analysis, vol III. Elsevier Science, Amsterdam, p 465
33. Lumens J, Delhaas T, Kirn B, Arts T (2009) Three-wall segment (triseg) model describing mechanics and hemodynamics of ventricular interaction. Ann Biomed Eng 37(11):2234–2255
34. Mirams G, Arthurs C, Bernabeu M, Bordas R, Cooper J, Corrias A, Davit Y, Dunn SJ, Fletcher A, Harvey D, Marsh M, Osborne J, Pathmanathan P, Pitt-Francis J, Southern J, Zemzemi N, Gavaghan D (2013). Chaste: an open source C++ library for computational physiology and biology. PloS Comput Biol 9(3):e1002970
35. Murphy MF, Golub GH, Wathen AJ (2000) A note on preconditioning for indefinite linear systems. SIAM J Sci Comput 21(6):1969–1972
36. Niederer S, Kerfoot E, Benson A, Bernabeu M, Bernus O, Bradley C, Cherry E, Clayton R, Fenton F, Garny A et al (2011) Verification of cardiac tissue electrophysiology simulators using an n-version benchmark. Philos Trans R Soc A 369(1954):4331–4351
37. Niederer SA, Smith NP (2008) An improved numerical method for strong coupling of excitation and contraction models in the heart. Prog Biophys Mol Biol 96(1–3):90–111
38. Nobile F, Quarteroni A, Ruiz-Baier R (2012) An active strain electromechanical model for cardiac tissue. Int J Numer Methods Biomed Eng 28(1):52–71
39. Notay Y (2013) A new analysis of block preconditioners for saddle point problems. SIAM J Matrix Anal Appl 35(1):143–173
40. Oberkampf W, Trucano T, Hirsch C (2004) Verification, validation, and predictive capability in computational engineering and physics. Appl Mech Rev 57(5):345–384
41. Pantuso D, Bathe KJ (1997) On the stability of mixed finite elements in large strain analysis of incompressible solids. Finite Elem Anal Des 28(2):83–104
42. Pathmanathan P, Chapman S, Gavaghan D, Whiteley J (2010) Cardiac electromechanics: the effect of contraction model on the mathematical problem and accuracy of the numerical scheme. Q J Mech Appl Math 63(3):375–399
43. Pathmanathan P, Gray RA (2013) Ensuring reliability of safety-critical clinical applications of computational cardiac models. Front Physiol 4:358
44. Pathmanathan P, Gray R (2014). Verification of computational models of cardiac electrophysiology. Int J Numer Methods Biomed Eng 30(5):525–544
45. Pitt-Francis J, Pathmanathan P, Bernabeu M, Bordas R, Cooper J, Fletcher A, Mirams G, Murray P, Osbourne J, Walter A, Chapman S, Garny A, van Leeuwen I, Maini P, Rodriguez B, Waters S, Whiteley J, Byrne H, Gavaghan D (2009) Chaste: a test-driven approach to software development for biological modelling. Comput Phys Commun 180:2452–2471
46. Prassl AJ, Kickinger F, Ahammer H, Grau V, Schneider JE, Hofer E, Vigmond EJ, Trayanova NA, Plank G (2009) Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems. IEEE Trans Biomed Eng 56(5):1318–1330
47. Razumova MV, Bukatina AE, Campbell KB (1999) Stiffness-distortion sarcomere model for muscle simulation. J Appl Physiol 87(5):1861–1876
48. Richards DF, Glosli JN, Draeger EW, Mirin AA, Chan B, Fattebert JL, Krauss WD, Oppelstrup T, Butler CJ, Gunnels JA et al (2013) Towards real-time simulation of cardiac electrophysiology in a human heart at high resolution. Comput Methods Biomech Biomed Eng 16(7):802–805
49. Roache P (1998) Verification and validation in computational science and engineering. Hermosa, Albuquerque
50. Rossi S, Lassila T, Ruiz-Baier R, Sequeira A, Quarteroni A (2013). Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics. Eur J Mech A Solids 48:129–142
51. Saad Y (1993) A flexible inner–outer preconditioned GMRES algorithm. SIAM J Sci Comput 14(2):461–469
52. Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Comput 7:856–869
53. Schroder JB (2012) Smoothed aggregation solvers for anisotropic diffusion. Numer Linear Algebra Appl 19:296–312
54. Usyk T, Mazhari R, McCulloch A (2000) Effect of laminar orthotropic myofiber architecture on regional stress and strain in the canine left ventricle. J Elast Phys Sci Solids 61(1–3):143–164
55. Usyk TP, LeGrice IJ, McCulloch AD (2002) Computational model of three-dimensional cardiac electromechanics. Comput Vis Sci 4(4):249–257
56. Wang H, Gao H, Luo X, Berry C, Griffith B, Ogden R, Wang T (2013) Structure-based finite strain modelling of the human left ventricle in diastole. Int J Numer Methods Biomed Eng 29(1):83–103
57. Wang H, Luo X, Gao H, Ogden R, Griffith B, Berry C, Wang T (2014) A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole. Biomech Model Mechanobiol 13(1):99–113
58. Washio T, Hisada T (2011) Convergence analysis of inexact LU-type preconditioners for indefinite problems arising in incompressible continuum analysis. Jpn J Ind Appl Math 28(1):89–117
59. Washio T, Okada Ji, Takahashi A, Yoneda K, Kadooka Y, Sugiura S, Hisada T (2013) Multiscale heart simulation with cooperative stochastic cross-bridge dynamics and cellular structures. Multiscale Model Simul 11(4):965–999
60. Weiss J, Maker B, Govindjee S (1996) Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Applied Mech Eng 135(1):107–128