Multiphysics and multiscale modelling, data–model fusion and integration of organ physiology in the clinic: Ventricular cardiac mechanics

Interface Focus

Volumn 6, Issue 2, 2016, Pages

  Chabiniok, Radomir ^a,b   Wang, Vicky Y ^c   Hadjicharalambous, Myrianthi ^a   Asner, Liya ^a   Lee, Jack ^a   Sermesant, Maxime ^e   Kuhl, Ellen ^f   Young, Alistair A ^c   Moireau, Philippe ^b   Nash, Martyn P ^c,d   Chapelle, Dominique ^b   Nordsletten, David A ^a  

^a ST THOMAS HOSPITAL   (United Kingdom)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c UNIVERSITY OF AUCKLAND   (New Zealand)

^d UNIVERSITY OF AUCKLAND   (New Zealand)

^e INRIA   (France)

^f STANFORD UNIVERSITY   (United States)

Author keywords

Cardiac mechanics; Data model fusion; Heart mechanics; Patient specific modelling; Translational cardiac modeling

Indexed keywords

EID: 84958781114     PISSN: 20428898     EISSN: 20428901     Source Type: Journal    
DOI: 10.1098/rsfs.2015.0083     Document Type: Article

References (292)

1. Hou Y, Crossman DJ, Rajagopal V, Baddeley D, Jayasinghe I, Soeller C. 2014 Super-resolution fluorescence imaging to study cardiac biophysics: a-actinin distribution and z-disk topologies in optically thick cardiac tissue slices. Prog. Biophys. Mol. Biol. 115, 328–339. (doi:10.1016/j.pbiomolbio.2014.07.003)
2. + release patterns in cardiomyocytes. PLOS Comput. Biol. 11, e1004417. (doi:10.1371/journal.pcbi.1004417)
3. Woods RH. 1892 A few applications of a physical theorem to membranes in the human body in a state of tension. Trans. R. Acad. Med. Ireland 10, 417–427. (doi:10.1007/BF03171228)
4. Mirsky I. 1969 Left ventricular stresses in the intact human heart. Biophys. J. 9, 189–208. (doi:10.1016/S0006-3495(69)86379-4)
5. Ghista DN, Patil KM, Gould P, Woo K. 1973 Computerized left ventricular mechanics and control system analyses models relevant for cardiac diagnosis. Comput. Biol. Med. 3, 27–46. (doi:10.1016/0010-4825(73)90017-6)
6. McCulloch A, Smaill B, Hunter P. 1987 Left ventricular epicardial deformation in the isolated arrested dog heart. Am. J. Physiol. 252, 233–241.
7. Hunter P, Smaill B. 1988 The analysis of cardiac function: a continuum approach. Prog. Biophys. Mol. Biol. 52, 101–164. (doi:10.1016/0079-6107(88)90004-1)
8. Mirsky I. 1973 Ventricular and arterial wall stresses based on large deformations analyses. Biophys. J. 13, 1141–1159. (doi:10.1016/S0006-3495(73)86051-5)
9. Janz R, Kubert B, Moriarty T, Grimm A. 1974 Deformation of the diastolic left ventricle. II. Nonlinear geometric effects. J. Biomech. 7, 509–516. (doi:10.1016/0021-9290(74)90085-2)
10. Hunter P. 1975 Finite element analysis of cardiac muscle mechanics. Oxford, UK: University of Oxford.
11. Panda S, Natarajan R. 1977 Finite-element method of stress analysis in the human left ventricular layered wall structure. Med. Biol. Eng. Comput. 15, 67–71. (doi:10.1007/BF02441577)
12. Demer LL, Yin F. 1983 Passive biaxial mechanical properties of isolated canine myocardium. J. Physiol. 339, 615–630. (doi:10.1113/jphysiol.1983.sp014738)
13. Yin FC, Strumpf RK, Chew PH, Zeger SL. 1987 Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading. J. Biomech. 20, 577–589. (doi:10.1016/0021-9290(87)90279-X)
14. LeGrice IJ, Smaill B, Chai L, Edgar S, Gavin J, Hunter PJ. 1995 Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. Heart. Circ. Physiol. 269, H571–H582.
15. Nielsen P, Le Grice I, Smaill B, Hunter P. 1991 Mathematical model of geometry and fibrous structure of the heart. Am. J. Physiol. Heart. Circ. Physiol. 260, H1365–H1378.
16. Guccione JM, Costa KD, McCulloch AD. 1995 Finite element stress analysis of left ventricular mechanics in the beating dog heart. J. Biomech. 28, 1167–1177. (doi:10.1016/0021-9290(94)00174-3)
17. Nash M, Hunter P. 2000 Computational mechanics of the heart. J. Elast. 61, 113–141. (doi:10.1023/A:1011084330767)
18. Vahl C, Timek T, Bonz A, Fuchs H, Dillman R, Hagl S. 1998 Length dependence of calcium- and forcetransients in normal and failing human myocardium. J. Mol. Cell. Cardiol. 30, 957–966. (doi:10.1006/jmcc.1998.0670)
19. de Tombe PP, Ter Keurs H. 1990 Force and velocity of sarcomere shortening in trabeculae from rat heart. Effects of temperature. Circul. Res. 66, 1239–1254. (doi:10.1161/01.RES.66.5.1239)
20. Lewartowski B, Pytkowski B. 1987 Cellular mechanism of the relationship between myocardial force and frequency of contractions. Prog. Biophys. Mol. Biol. 50, 97–120. (doi:10.1016/0079-6107(87)90005-8)
21. Hunter P, McCulloch A, Ter Keurs H. 1998 Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69, 289–331. (doi:10.1016/S0079-6107(98)00013-3)
22. Nordsletten D, Niederer S, Nash M, Hunter P, Smith N. 2011 Coupling multi-physics models to cardiac mechanics. Prog. Biophys. Mol. Biol. 104, 77–88. (doi:10.1016/j.pbiomolbio.2009.11.001)
23. Panfilov AV, Holden AV. 1997 Computational biology of the heart. New York, NY: Wiley. 24. Trayanova NA. 2011 Whole-heart modeling applications to cardiac electrophysiology and electromechanics. Circul. Res. 108, 113–128. (doi:10.1161/CIRCRESAHA.110.223610)
24. McQueen DM, Peskin CS. 2000 A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. ACM SIGGRAPH Comput. Graph. 34, 56–60. (doi:10.1145/563788.604453)
25. Nordsletten D, McCormick M, Kilner P, Hunter P, Kay D, Smith N. 2011 Fluid–solid coupling for the investigation of diastolic and systolic human left ventricular function. Int. J. Numer. Methods Biomed. Eng. 27, 1017–1039. (doi:10.1002/cnm.1405)
26. Lee J, Smith NP. 2012 The multi-scale modelling of coronary blood flow. Ann. Thorac. Surg. Biomed. Eng. 40, 2399–2413. (doi:10.1007/s10439-012-0583-7)
27. Opie LH. 2004 Heart physiology: from cell to circulation. Philadelphia, PA: Lippincott Williams and Wilkins.
28. Suga H. 1990 Ventricular energetics. Physiol. Rev. 70, 247–277.
29. Clerico A, Recchia FA, Passino C, Emdin M. 2006 Cardiac endocrine function is an essential component of the homeostatic regulation network: physiological and clinical implications. Am. J. Physiol. Heart. Circ. Physiol. 290, H17–H29. (doi:10.1152/ajpheart.00684.2005)
30. Lamata P, Casero R, Carapella V, Niederer SA, Bishop MJ, Schneider JE, Kohl P, Grau V. 2014 Images as drivers of progress in cardiac computational modelling. Prog. Biophys. Mol. Biol. 115, 198–212. (doi:10.1016/j.pbiomolbio.2014.08.005)
31. Young A, Legrice I, Young M, Smaill B. 1998 Extended confocal microscopy of myocardial laminae and collagen network. J. Microsc. 192, 139–150. (doi:10.1046/j.1365-2818.1998.00414.x)
32. 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)
33. Vetter FJ, McCulloch AD. 1998 Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy. Prog. Biophys. Mol. Biol. 69, 157–183. (doi:10.1016/S0079-6107(98)00006-6)
34. Wang V, Lam H, Ennis D, Young A, Nash M. 2008 Passive ventricular mechanics modelling using MRI of structure and function. In Medical image computing and computer-assisted intervention– MICCAI 2008 (eds D Metaxas, L Axel, G Fichtinger, G Székely), pp. 814–821. Berlin, Germany: Springer.
35. Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Hsu EW, Saloner DA, Guccione JM. 2008 Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. J. Thorac. Cardiovasc. Surg. 135, 1094–1102. (doi:10.1016/j.jtcvs.2007.11.038)
36. Sermesant M, Forest C, Pennec X, Delingette H, Ayache N. 2003 Deformable biomechanical models: application to 4D cardiac image analysis. Med. Image Anal. 7, 475–488. (doi:10.1016/S1361-8415(03)00068-9)
37. Hoogendoorn C, Sukno FM, Ordás S, Frangi AF. 2009 Bilinear models for spatio-temporal point distribution analysis. Int. J. Comput. Vis. 85, 237–252. (doi:10.1007/s11263-009-0212-6)
38. Niederer SA, Plank G, Chinchapatnam P, Ginks M, Lamata P, Rhode KS, Rinaldi CA, Razavi R, Smith NP. 2011 Length-dependent tension in the failing heart and the efficacy of cardiac resynchronization therapy. Cardiovasc. Res. 89, 336–343. (doi:10.1093/cvr/cvq318)
39. Wenk JF et al. 2010 First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. Ann. Thorac. Surg. 89, 1546–1553. (doi:10.1016/j.athoracsur.2010.02.036)
40. Helm P, Beg MF, Miller MI, Winslow RL. 2005 Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor MR imaging. Ann. Thorac. Surg. NY Acad. Sci. 1047, 296–307. (doi:10.1196/annals.1341.026)
41. 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, 295–306. (doi:10.1007/s10237-010-0235-5)
42. Lamata P, Niederer S, Barber D, Norsletten D, Lee J, Hose R, Smith N. 2010 Personalization of cubic hermite meshes for efficient biomechanical simulations. In Medical image computing and computer-assisted intervention–MICCAI 2010 (eds T Jiang, N Navab, JPW Pluim, MA Viergever), pp. 380–387. Berlin, Germany: Springer.
43. Fonseca CG et al. 2011 The Cardiac Atlas Project— an imaging database for computational modeling and statistical atlases of the heart. Bioinformatics 27, 2288–2295. (doi:10.1093/bioinformatics/btr360)
44. Zhang Y et al. 2012 An atlas-based geometry pipeline for cardiac hermite model construction and diffusion tensor reorientation. Med. Image Anal. 16, 1130–1141. (doi:10.1016/j.media.2012.06.005)
45. Streeter DD, Spotnitz HM, Patel DP, Ross J, Sonnenblick EH. 1969 Fiber orientation in the canine left ventricle during diastole and systole. Circul. Res. 24, 339–347. (doi:10.1161/01.RES.24.3.339)
46. Bayer J, Blake R, Plank G, Trayanova N. 2012 A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann. Biomed. Eng. 40, 2243–2254. (doi:10.1007/s10439-012-0593-5)
47. Nagler A, Bertoglio C, Gee M, Wall W. 2013 Personalization of cardiac fiber orientations from image data using the unscented Kalman filter. In Functional imaging and modeling of the heart (eds S Ourselin, D Rueckert, N Smith), pp. 132–140. Berlin, Germany: Springer.
48. Costa KD, Holmes JW, McCulloch AD. 2001 Modelling cardiac mechanical properties in three dimensions. Phil. Trans. R. Soc. Lond. A 359, 1233–1250. (doi:10.1098/rsta.2001.0828)
49. LeGrice I, Takayama Y, Covell J. 1995 Transverse shear along myocardial cleavage planes provides a mechanism for normal systolic wall thickening. Circul. Res. 77, 182–193. (doi:10.1161/01.RES.77.1.182)
50. Basser PJ, Mattiello J, LeBihan D. 1994 MR diffusion tensor spectroscopy and imaging. Biophys. J. 66, 259. (doi:10.1016/S0006-3495(94)80775-1)
51. Plank G et al. 2009 Generation of histo-anatomically representative models of the individual heart: tools and application. Phil. Trans. R. Soc. A 367, 2257–2292. (doi:10.1098/rsta.2009.0056)
52. Gilbert SH, Benoist D, Benson AP, White E, Tanner SF, Holden AV, Dobrzynski H, Bernus O, Radjenovic A. 2012 Visualization and quantification of whole rat heart laminar structure using high-spatial resolution contrast-enhanced MRI. Am. J. Physiol. Heart. Circ. Physiol. 302, H287–H298. (doi:10.1152/ajpheart.00824.2011)
53. Humphrey J, Yin F. 1989 Biomechanical experiments on excised myocardium: theoretical considerations. J. Biomech. 22, 377–383. (doi:10.1016/0021-9290(89)90052-3)
54. Humphrey J, Yin F. 1987 A new constitutive formulation for characterizing the mechanical behavior of soft tissues. Biophys. J. 52, 563–570. (doi:10.1016/S0006-3495(87)83245-9)
55. Horowitz A, Lanir Y, Yin FC, Perl M, Sheinman I, Strumpf RK. 1988 Structural three-dimensional constitutive law for the passive myocardium. J. Biomech. Eng. 110, 200–207. (doi:10.1115/1.3108431)
56. Novak VP, Yin FCP, Humphrey JD. 1994 Regional mechanical properties of passive myocardium. J. Biomech. 27, 403–412. (doi:10.1016/0021-9290(94)90016-7)
57. Humphrey J, Strumpf R, Yin F. 1990 Determination of a constitutive relation for passive myocardium. II. Parameter estimation. J. Biomech. Eng. 112, 340–346. (doi:10.1115/1.2891194)
58. McCulloch AD, Smaill BH, Hunter PJ. 1989 Regional left ventricular epicardial deformation in the passive dog heart. Circul. Res. 64, 721–733. (doi:10.1161/01.RES.64.4.721)
59. Guccione JM, McCulloch AD, Waldman L. 1991 Passive material properties of intact ventricular myocardium determined from a cylindrical model. J. Biomech. Eng. 113, 42–55. (doi:10.1115/1.2894084)
60. Lin D, Yin F. 1998 A multiaxial constitutive law for mammalian left ventricular myocardium in steadystate barium contracture or tetanus. J. Biomech. Eng. 120, 504–517. (doi:10.1115/1.2798021)
61. Criscione JC, Douglas AS, Hunter WC. 2001 Physically based strain invariant set for materials exhibiting transversely isotropic behavior. J. Mech. Phys. Solids 49, 871–897. (doi:10.1016/S0022-5096(00)00047-8)
62. Smaill B, Hunter P. 1991 Structure and function of the diastolic heart: material properties of passive myocardium. In Theory of heart (eds L Glass, P Hunter, A McCulloch), pp. 1–29. New York, NY: Springer.
63. Nikolić S, Yellin EL, Tamura K, Vetter H, Tamura T, Meisner JS, Frater RW. 1988 Passive properties of canine left ventricle: diastolic stiffness and restoring forces. Circul. Res. 62, 1210–1222. (doi:10.1161/01.RES.62.6.1210)
64. Kerckhoffs R, Bovendeerd P, Kotte J, Prinzen F, Smits K, Arts T. 2003 Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: a model study. Ann. Biomed. Eng. 31, 536–547. (doi:10.1114/1.1566447)
65. Dokos S, Smaill BH, Young AA, LeGrice IJ. 2002 Shear properties of passive ventricular myocardium. Am. J. Physiol. Heart. Circ. Physiol. 283, H2650–H2659. (doi:10.1152/ajpheart.00111.2002)
66. Holzapfel GA, Ogden RW. 2009 Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Phil. Trans. R. Soc. A 367, 3445–3475. (doi:10.1098/rsta.2009.0091)
67. Loeffler L, Sagawa K. 1975 A one-dimensional viscoelastic model of cat heart muscle studied by small length perturbations during isometric contraction. Circul. Res. 36, 498–512. (doi:10.1161/01.RES.36.4.498)
68. Yang M, Taber LA. 1991 The possible role of poroelasticity in the apparent viscoelastic behavior of passive cardiac muscle. J. Biomech. 24, 587–597. (doi:10.1016/0021-9290(91)90291-T)
69. van Heuningen R, Rijnsburger WH, ter Keurs HE. 1982 Sarcomere length control in striated muscle. Am. J. Physiol. Heart. Circ. Physiol. 242, H411–H420.
70. Huyghe JM, van Campen DH, Arts T, Heethaar RM. 1991 The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation. J. Biomech. 24, 841–849. (doi:10.1016/0021-9290(91)90309-B)
71. Holzapfel GA, Gasser TC. 2001 A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications. Comput. Methods Appl. Mech. Eng. 190, 4379–4403. (doi:10.1016/S0045-7825(00)00323-6)
72. Cansz FBC, Dal H, Kaliske M. 2015 An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment. Comput. Methods Biomech. Biomed. Eng. 18, 1160–1172. (doi:10.1080/10255842.2014.881475)
73. Costa KD, Takayama Y, McCulloch AD, Covell JW. 1999 Laminar fiber architecture and threedimensional systolic mechanics in canine ventricular myocardium. Am. J. Physiol. Heart. Circ. Physiol. 276, H595–H607.
74. Sommer G, Haspinger DCh, Andra¨ M, Sacherer M, Viertler C, Regitnig P, Holzapfel GA. 2015 Quantification of shear deformations and corresponding stresses in the biaxially tested human myocardium. Ann. Thoroc. Surg. Biomed. Eng. 43, 2334–2348. (doi:10.1007/s10439-015-1281-z)
75. Sommer G, Schriefl AJ, Andrä M, Sacherer M, Viertler C, Wolinski H, Holzapfel GA. 2015 Biomechanical properties and microstructure of human ventricular myocardium. Acta biomaterialia 24, 172–192. (doi:10.1016/j.actbio.2015.06.031)
76. Holzapfel GA, Gasser TC, Ogden RW. 2000 A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. Phys. Sci. Solids 61, 1–48. (doi:10.1023/A1010835316564)
77. Gasser TC, Ogden RW, Holzapfel GA. 2006 Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3, 15–35. (doi:10.1098/rsif.2005.0073)
78. Mescher AL. 2010 Junqueira‘s basic histology: text and atlas, vol. 12. New York, NY: McGraw-Hill Medical.
79. Huxley A. 1957 Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255–318.
80. Wong AY. 1971 Mechanics of cardiac muscle, based on Huxley’s model: mathematical simulation of isometric contraction. J. Biomech. 4, 529–540. (doi:10.1016/0021-9290(71)90042-X)
81. Tözeren A. 1985 Continuum rheology of muscle contraction and its application to cardiac contractility. Biophys. J. 47, 303–309. (doi:10.1016/S0006-3495(85)83920-5)
82. Ter Keurs HE, Rijnsburger WH, Van Heuningen R, Nagelsmit MJ. 1980 Tension development and sarcomere length in rat cardiac trabeculae: evidence of length-dependent activation. In Cardiac dynamics (eds J Baan, AC Arntzenius), pp. 25–36. The Hague, The Netherlands: Martinus Nijhoff Publishers.
83. Guccione J, McCulloch A. 1993 Mechanics of active contraction in cardiac muscle: part I—constitutive relations for fiber stress that describe deactivation. J. Biomech. Eng. 115, 72–81. (doi:10.1115/1.2895474)
84. Niederer S, Hunter P, Smith N. 2006 A quantitative analysis of cardiac myocyte relaxation: a simulation study. Biophys. J. 90, 1697–1722. (doi:10.1529/biophysj.105.069534)
85. Rice JJ, Wang F, Bers DM, De Tombe PP. 2008 Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations. Biophys. J. 95, 2368–2390. (doi:10.1529/biophysj.107.119487)
86. Bestel J, Clément F, Sorine M. 2001 A biomechanical model of muscle contraction. In Medical image computing and computer-assisted intervention– MICCAI 2001 (eds WJ Niessen, MA Viergever), pp. 1159–1161. Berlin, Germany: Springer.
87. Chapelle D, Le Tallec P, Moireau P, Sorine M. 2012 Energy-preserving muscle tissue model: formulation and compatible discretizations. Int. J. Multiscale Comput. Eng. 10, 189–211. (doi:10.1615/IntJMultCompEng.2011002360)
88. Tangney JR et al. 2013 Novel role for vinculin in ventricular myocyte mechanics and dysfunction. Biophys. J. 104, 1623–1633. (doi:10.1016/j.bpj.2013.02.021)
89. 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, 143–164. (doi:10.1023/A1010883920374)
90. Rossi S, Ruiz-Baier R, Pavarino LF, Quarteroni A. 2012 Orthotropic active strain models for the numerical simulation of cardiac biomechanics. Int. J. Numer. Methods Biomed. Eng. 28, 761–788. (doi:10.1002/cnm.2473)
91. Yin F, Chan C, Judd RM. 1996 Compressibility of perfused passive myocardium. Am. J. Physiol. Heart. Circ. Physiol. 271, H1864–H1870.
92. Omens JH, MacKenna DA, McCulloch AD. 1993 Measurement of strain and analysis of stress in resting rat left ventricular myocardium. J. Biomech. 26, 665–676. (doi:10.1016/0021-9290(93)90030-I)
93. Bathe K-J. 2006 Finite element procedures. Englewood Cliffs, NJ: Klaus-Jurgen Bathe.
94. Vetter FJ, McCulloch AD. 2000 Three-dimensional stress and strain in passive rabbit left ventricle: a model study. Ann. Thor. Surg. Biomed. Eng. 28, 781–792. (doi:10.1114/1.1289469)
95. Thorvaldsen T, Osnes H, Sundnes J. 2005 A mixed finite element formulation for a non-linear, transversely isotropic material model for the cardiac tissue. Comput. Methods Biomech. Biomed. Eng. 8, 369–379. (doi:10.1080/10255840500448097)
96. Asner L, Hadjicharalambous M, Lee J, Nordsletten D. 2015 Stacom challenge: simulating left ventricular mechanics in the canine heart. In Statistical atlases and computational models of the heart-imaging and modelling challenges (eds O Camara, T Mansi, M Pop, K Rhode, M Sermesant, A Young), pp. 123–134. Basel, Switzerland: Springer.
97. Hadjicharalambous M, Lee J, Smith NP, Nordsletten DA. 2014 A displacement-based finite element formulation for incompressible and nearlyincompressible cardiac mechanics. Comput. Methods Appl. Mech. Eng. 274, 213–236. (doi:10.1016/j.cma.2014.02.009)
98. Sermesant M et al. 2012 Patient-specific electromechanical models of the heart for the prediction of pacing acute effects in CRT: a preliminary clinical validation. Med. Image Anal. 16, 201–215. (doi:10.1016/j.media.2011.07.003)
99. McCormick M, Nordsletten D, Kay D, Smith N. 2013 Simulating left ventricular fluid–solid mechanics through the cardiac cycle under LVAD support. J. Comput. Phys. 244, 80–96. (doi:10.1016/j.jcp.2012.08.008)
100. McCormick M, Nordsletten D, Lamata P, Smith NP. 2014 Computational analysis of the importance of flow synchrony for cardiac ventricular assist devices. Comput. Biol. Med. 49, 83–94. (doi:10.1016/j.compbiomed.2014.03.013)
101. Lee J, Cookson A, Chabiniok R, Rivolo S, Hyde E, Sinclair M, Michler C, Sochi T, Smith N. 2015 Multiscale modelling of cardiac perfusion. In Modeling the heart and the circulatory system (ed. A Quarteroni), pp. 51–96. Basel, Switzerland: Springer.
102. FitzHugh R. 1961 Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445. (doi:10.1016/S0006-3495(61)86902-6)
103. Aliev RR, Panfilov AV. 1996 A simple two-variable model of cardiac excitation. Chaos Solitons Fractals 7, 293–301. (doi:10.1016/0960-0779(95)00089-5)
104. Beeler GW, Reuter H. 1977 Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268, 177–210. (doi:10.1113/jphysiol.1977.sp011853)
105. Winslow RL, Rice J, Jafri S, Marban E, O’Rourke B. 1999 Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II model studies. Circul. Res. 84, 571–586. (doi:10.1161/01.RES.84.5.571)
106. Hodgkin AL, Huxley AF. 1952 A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544. (doi:10.1113/jphysiol.1952.sp004764)
107. Ten Tusscher K, Noble D, Noble P, Panfilov A. 2004 A model for human ventricular tissue. Am. J. Physiol. Heart. Circ. Physiol. 286, H1573–H1589. (doi:10.1152/ajpheart.00794.2003)
108. Sermesant M, Delingette H, Ayache N. 2006 An electromechanical model of the heart for image analysis and simulation. IEEE Trans. Med. Imag. 25, 612–625. (doi:10.1109/TMI.2006.872746)
109. Rogers JM, McCulloch AD. 1994 Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation. J. Cardiovasc. Electrophysiol. 5, 496–509. (doi:10.1111/j.1540-8167.1994.tb01290.x)
110. Nash MP, Panfilov AV. 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)
111. Göktepe S, Kuhl E. 2010 Electromechanics of the heart: a unified approach to the strongly coupled excitation–contraction problem. Comput. Mech. 45, 227–243. (doi:10.1007/s00466-009-0434-z)
112. Keldermann RH, Nash MP, Gelderblom H, Wang VY, Panfilov AV. 2010 Electromechanical wavebreak in a model of the human left ventricle. Am. J. Physiol. Heart. Circ. Physiol. 299, H134–H143. (doi:10.1152/ajpheart.00862.2009)
113. Wall ST, Guccione JM, Ratcliffe MB, Sundnes JS. 2012 Electromechanical feedback with reduced cellular connectivity alters electrical activity in an infarct injured left ventricle: a finite element model study. Am. J. Physiol. Heart. Circ. Physiol. 302, H206–H214. (doi:10.1152/ajpheart.00272.2011)
114. Aguado-Sierra J. 2011 Patient-specific modeling of dyssynchronous heart failure: a case study. Prog. Biophys. Mol. Biol. 107, 147–155. (doi:10.1016/j.pbiomolbio.2011.06.014)
115. Kohl P, Sachs F. 2001 Mechanoelectric feedback in cardiac cells. Phil. Trans. R. Soc. A 359, 1173–1185. (doi:10.1098/rsta.2001.0824)
116. Kuijpers NH, ten Eikelder HM, Bovendeerd PH, Verheule S, Arts T, Hilbers PA. 2007 Mechanoelectric feedback leads to conduction slowing and block in acutely dilated atria: a modeling study of cardiac electromechanics. Am. J. Physiol. Heart. Circ. Physiol. 292, H2832–H2853. (doi:10.1152/ajpheart.00923.2006)
117. Xia H, Wong K, Zhao X. 2012 A fully coupled model for electromechanics of the heart. Comput. Math. Methods Med. 2012, 927279–1172. (doi:10.1155/2012/927279)
118. Vigueras G, Roy I, Cookson A, Lee J, Smith N, Nordsletten D. 2014 Toward GPGPU accelerated human electromechanical cardiac simulations. Int. J. Numer. Methods Biomed. Eng. 30, 117–134. (doi:10.1002/cnm.2593)
119. Khalafvand S, Ng E, Zhong L. 2011 CFD simulation of flow through heart: a perspective review. Comput. Methods Biomech. Biomed. Eng. 14, 113–132. (doi:10.1080/10255842.2010.493515)
120. Chan BT, Lim E, Chee KH, Osman NAA. 2013 Review on CFD simulation in heart with dilated cardiomyopathy and myocardial infarction. Comput. Biol. Med. 43, 377–385. (doi:10.1016/j.compbiomed.2013.01.013)
121. Georgiadis J, Wang G, Pasipoularides A. 1992 Computational fluid dynamics of left ventricular ejection. Ann. Biomed. Eng. 20, 81–97. (doi:10.1007/BF02368507)
122. Baccani B, Domenichini F, Pedrizzetti G, Tonti G. 2002 Fluid dynamics of the left ventricular filling in dilated cardiomyopathy. J. Biomech. 35, 665–671. (doi:10.1016/S0021-9290(02)00005-2)
123. Domenichini F, Pedrizzetti G, Baccani B. 2005 Threedimensional filling flow into a model left ventricle. J. Fluid Mech. 539, 179–198. (doi:10.1017/S0022112005005550)
124. Pedrizzetti G, Domenichini F. 2005 Nature optimizes the swirling flow in the human left ventricle. Phys. Rev. 95, 1–4. (doi:10.1103/physrevlett.95.108101)
125. Saber NR, Wood NB, Gosman A, Merrifield RD, Yang G-Z, Charrier CL, Gatehouse PD, Firmin DN. 2003 Progress towards patient-specific computational flow modeling of the left heart via combination of magnetic resonance imaging with computational fluid dynamics. Ann. Biomed. Eng. 31, 42–52. (doi:10.1114/1.1533073)
126. Merrifield R, Long Q, Xu X, Kilner PJ, Firmin DN, Yang G-Z. 2004 Combined CFD/MRI analysis of left ventricular flow. In Medical imaging and augmented reality (eds G-Z Yang, T Jiang), pp. 229–236. Berlin, Germany: Springer.
127. Doenst T, Spiegel K, Reik M, Markl M, Hennig J, Nitzsche S, Beyersdorf F, Oertel H. 2009 Fluiddynamic modelling of the human left ventricle: methodology and application to surgical ventricular reconstruction. Ann. Thorac. Surg. 87, 1187–1197. (doi:10.1016/j.athoracsur.2009.01.036)
128. Oertel H, Krittian S. 2011 Modelling the human cardiac fluid mechanics. Karlsruhe, Germany: KIT Scientific Publishing.
129. Khalafvand SS, Ng EY-K, Zhong L, Hung T. 2012 Fluid-dynamics modelling of the human left ventricle with dynamic mesh for normal and myocardial infarction: preliminary study. Comput. Biol. Med. 42, 863–870. (doi:10.1016/j.compbiomed.2012.06.010)
130. de Vecchi A, Gomez A, Pushparajah K, Schaeffter T, Nordsletten D, Simpson J, Penney G, Smith N. 2014 Towards a fast and efficient approach for modelling the patient-specific ventricular haemodynamics. Prog. Biophys. Mol. Biol. 116, 3–10. (doi:10.1016/j.pbiomolbio.2014.08.010)
131. Su B, Zhang J-M, Tang HC, Wan M, Lim CCW, Su Y, Zhao X, San Tan R, Zhong L. 2014 Patient-specific blood flows and vortex formations in patients with hypertrophic cardiomyopathy using computational fluid dynamics. In Biomedical Engineering and Sciences (IECBES), 2014 IEEE Conf., Kuala Lumpur, Malaysia, 8–10 December, pp. 276–280. New York, NY: IEEE.
132. Peskin C. 1972 Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10, 252–271. (doi:10.1016/0021-9991(72)90065-4)
133. Yoganathan A, He Z, Jones S. 2004 Fluid mechanics of heart valves. Annu. Rev. Biomed. Eng. 6, 331–362. (doi:10.1146/annurev.bioeng.6.040803.140111)
134. Le TB, Sotiropoulos F. 2013 Fluid–structure interaction of an aortic heart valve prosthesis driven by an animated anatomic left ventricle. J. Comput. Phys. 244, 41–62. (doi:10.1016/j.jcp.2012.08.036)
135. Cheng Y, Zhang H. 2010 Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow. Comput. Fluids 39, 871–881. (doi:10.1016/j.compfluid.2010.01.003)
136. Su B, Zhong L, Wang X-K, Zhang J-M, San Tan R, Allen JC, Tan SK, Kim S, Leo HL. 2014 Numerical simulation of patient-specific left ventricular model with both mitral and aortic valves by FSI approach. Comput. Methods Prog. Biomed. 113, 474–482. (doi:10.1016/j.cmpb.2013.11.009)
137. Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJ. 2014 Fluid–structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput. Mech. 54, 1055–1071. (doi:10.1007/s00466-014-1059-4)
138. Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJ. 2015 An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves. Comput. Methods Appl. Mech. Eng. 284, 1005–1053. (doi:10.1016/j.cma.2014.10.040)
139. McQueen D, Peskin C. 1989 A 3D computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid. J. Comput. Phys. 81, 372–405. (doi:10.1016/0021-9991(89)90213-1)
140. McQueen D, Peskin C. 1989 A 3D computational method for blood flow in the heart. II. Contractile fibers. J. Comput. Phys. 82, 289–297. (doi:10.1016/0021-9991(89)90050-8)
141. Yoganathan A, Lemmon J, Kim Y, Walker P, Levine R, Vesier C. 1994 A computational study of a thinwalled three-dimensional left ventricle during early systole. J. Biomech. Eng. 116, 307–314. (doi:10.1115/1.2895735)
142. Taylor T, Suga H, Goto Y, Okino H, Yamaguchi T. 1996 The effects of cardiac infarction on realistic three-dimensional left ventricular blood ejection. J. Biomech. Eng. 118, 106–110. (doi:10.1115/1.2795934)
143. Jones T, Metaxas D. 1998 Patient-specific analysis of left ventricular blood flow. Lect. Notes Comput. Sci. 1496, 156–166. (doi:10.1007/BFb0056198)
144. Lemmon J, Yoganathan A. 2000 Computational modeling of left heart diastolic function: examination of ventricular dysfunction. J. Elast. 122, 297–303. (doi:10.1115/1.1286559)
145. Kovacs SJ, McQueen DM, Peskin CS. 2001 Modelling cardiac fluid dynamics and diastolic function. Phil. Trans. R. Soc. Lond. A 359, 1299–1314. (doi:10.1098/rsta.2001.0832)
146. Vigmod E, Clements C, McQueen D, Peskin C. 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)
147. Chahboune B, Crolet J. 1998 Numerical simulation of the blood-wall interaction in the human left ventricle. Eur. Phys. J. Appl. Phys. 2, 291–297. (doi:10.1051/epjap1998195)
148. Ong C, Chan B, Lim E-G, Abu Osman N, Abed A, Dokos S, Lovell NH. 2012 Fluid structure interaction simulation of left ventricular flow dynamics under left ventricular assist device support. In Engineering in Medicine and Biology Society (EMBC), 2012 Annual Int. Conf. of the IEEE, San Diego, CA, 28 August–1 September, pp. 6293–6296. New York, NY: IEEE.
149. Chan B, Ong C, Lim E-G, Abu Osman N, Al Abed A, Lovell NH, Dokos S. 2012 Simulation of left ventricle flow dynamics with dilated cardiomyopathy during the filling phase. In Engineering in Medicine and Biology Society (EMBC), 2012 Annual Int. Conf. of the IEEE, San Diego, CA, 28 August–1 September, pp. 6289–6292. New York, NY: IEEE.
150. Chan BT, Abu NA, Lim E, Chee KH, Abdul YF, Abed AA, Lovell NH, Dokos S. 2013 Sensitivity analysis of left ventricle with dilated cardiomyopathy in fluid structure simulation. PLoS ONE 8, e67097. (doi:10.1371/journal.pone.0067097)
151. 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)
152. Watanabe H, Sugiura S, Hisada T. 2008 The looped heart does not save energy by maintaining the momentum of blood flowing in the ventricle. Am. J. Physiol. 294, 2191–2196. (doi:10.1152/ajpheart.00041.2008)
153. 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)
154. Yang C, Tang D, Haber I, Geva T, Pedro J. 2007 In vivo MRI-based 3D FSI RV/LV models for human right ventricle and patch design for potential computer-aided surgery optimization. Comput. Struct. 85, 988–997. (doi:10.1016/j.compstruc.2006.11.008)
155. Tang D, Yang C, Geva T, Pedro J. 2010 Image-based patient-specific ventricle models with fluid– structure interaction for cardiac function assessment and surgical design optimization. Prog. Pediatr. Cardiol. 30, 51–62. (doi:10.1016/j.ppedcard.2010.09.007)
156. Tang D, Yang C, Geva T, Gaudette G, Pedro J. 2011 Multi-physics MRI-based two-layer fluid–structure interaction anisotropic models of human right and left ventricles with different patch materials: cardiac function assessment and mechanical stress analysis. Comput. Struct. 89, 1059–1068. (doi:10.1016/j.compstruc.2010.12.012)
157. Nordsletten D, Kay D, Smith N. 2010 A nonconforming monolithic finite element method for problems of coupled mechanics. J. Comput. Phys. 229, 7571–7593. (doi:10.1016/j.jcp.2010.05.043)
158. De Vecchi A, Nordsletten D, Razavi R, Greil G, Smith N. 2013 Patient specific fluid–structure ventricular modelling for integrated cardiac care. Med. Biol. Eng. Comput. 51, 1261–1270. (doi:10.1007/s11517-012-1030-5)
159. de Vecchi A, Nordsletten DA, Remme EW, Bellsham- Revell H, Greil G, Simpson JM, Razavi R, Smith NP. 2012 Inflow typology and ventricular geometry determine efficiency of filling in the hypoplastic left heart. Ann. Thorac. Surg. 94, 1562–1569. (doi:10.1016/j.athoracsur.2012.05.122)
160. McCormick M, Nordsletten D, Kay D, Smith N. 2011 Modelling left ventricular function under assist device support. Int. J. Numer. Methods Biomed. Eng. 27, 1073–1095. (doi:10.1002/cnm.1428)
161. Krittian S, Schenkel T, Janoske U, Oertel H. 2010 Partitioned fluid–solid coupling for cardiovascular blood flow: validation study of pressure-driven fluid-domain deformation. Ann. Thor. Surg. Biomed. Eng. 38, 2676–2689. (doi:10.1007/s10439-010-0024-4)
162. Gao H, Carrick D, Berry C, Griffith BE, Luo X. 2014 Dynamic finite-strain modelling of the human left ventricle in health and disease using an immersed boundary-finite element method. IMA J. Appl. Math. 79, 978–1010. (doi:10.1093/imamat/hxu029)
163. Westerhof N, Boer C, Lamberts RR, Sipkema P. 2006 Cross-talk between cardiac muscle and coronary vasculature. Physiol. Rev. 86, 1263–1308. (doi:10.1152/physrev.00029.2005)
164. Quarteroni A, Formaggia L. 2004 Mathematical modelling and numerical simulation of the cardiovascular system. In Computational models for the human body, volume 12 of handbook of numerical analysis (eds PG Ciarlet, N Ayache), pp. 3–127. Amsterdam, The Netherlands: Elsevier.
165. Huyghe JM, van Campen DH, Arts T, Heethaar RM. 1991 A two-phase finite element model of the diastolic left ventricle. J. Biomech. 24, 527–538. (doi:10.1016/0021-9290(91)90286-V)
166. Vankan W, Huyghe J, Janssen J, Huson A. 1996 Poroelasticity of saturated solids with an application to blood perfusion. Int. J. Eng. Sci. 34, 1019–1031. (doi:10.1016/0020-7225(96)00009-2)
167. Hornung U. 2012 Homogenization and porous media, vol. 6. Munich, Germany: Springer Science & Business Media.
168. Rohan E, Cimrman R. 2010 Two-scale modeling of tissue perfusion problem using homogenization of dual porous media. Int. J. Multiscale Comput. Eng. 8, 81–102. (doi:10.1615/IntJMultCompEng.v8.i1.70)
169. Biot MA. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164. (doi:10.1063/1.1712886)
170. Bowen RM. 1980 Incompressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 18, 1129–1148. (doi:10.1016/0020-7225(80)90114-7)
171. Coussy O. 2004 Poromechanics. Chichester, UK: John Wiley and Sons.
172. Loret B, Simões FM. 2005 A framework for deformation, generalized diffusion, mass transfer and growth in multi-species multi-phase biological tissues. Eur. J. Mech. A Solids 24, 757–781. (doi:10.1016/j.euromechsol.2005.05.005)
173. Chapelle D, Moireau P. 2014 General coupling of porous flows and hyperelastic formulations: From thermodynamics principles to energy balance and compatible time schemes. Eur. J. Mech. B Fluids 46, 82–96. (doi:10.1016/j.euromechflu.2014.02.009)
174. Hughes T, Liu W, Zimmermann T. 1981 Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29, 329–349. (doi:10.1016/0045-7825(81)90049-9)
175. Vuong A-T, Yoshihara L, Wall W. 2015 A general approach for modeling interacting flow through porous media under finite deformations. Comput. Methods Appl. Mech. Eng. 283, 1240–1259. (doi:10.1016/j.cma.2014.08.018)
176. May-Newman K, Omens JH, Pavelec RS, McCulloch AD. 1994 Three-dimensional transmural mechanical interaction between the coronary vasculature and passive myocardium in the dog. Circul. Res. 74, 1166–1178. (doi:10.1161/01.RES.74.6.1166)
177. Reeve AM, Nash MP, Taberner AJ, Nielsen PM. 2014 Constitutive relations for pressure-driven stiffening in poroelastic tissues. J. Biomech. Eng. 136, 081011. (doi:10.1115/1.4027666)
178. Chapelle D, Gerbeau J-F, Sainte-Marie J, Vignon- Clementel I. 2010 A poroelastic model valid in large strains with applications to perfusion in cardiac modeling. Comput. Mech. 46, 91–101. (doi:10.1007/s00466-009-0452-x)
179. Spaan JA et al. 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)
180. Michler C et al. 2013 A computationally efficient framework for the simulation of cardiac perfusion using a multi-compartment Darcy porous-media flow model. Int. J. Numer. Methods Biomed. Eng. 29, 217–232. (doi:10.1002/cnm.2520)
181. Smith AF, Shipley RJ, Lee J, Sands GB, LeGrice IJ, Smith NP. 2014 Transmural variation and anisotropy of microvascular flow conductivity in the rat myocardium. Ann. Biomed. Eng. 42, 1966–1977. (doi:10.1007/s10439-014-1028-2)
182. Hyde ER et al. 2014 Multi-scale parameterisation of a myocardial perfusion model using whole-organ arterial networks. Ann. Biomed. Eng. 42, 797–811. (doi:10.1007/s10439-013-0951-y)
183. Cookson A, Lee J, Michler C, Chabiniok R, Hyde E, Nordsletten D, Smith N. 2014 A spatially-distributed computational model to quantify behaviour of contrast agents in MR perfusion imaging. Med. Image Anal. 18, 1200–1216. (doi:10.1016/j.media.2014.07.002)
184. Carusi A, Burrage K, Rodriguez B. 2012 Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology. Am. J. Physiol. Heart. Circ. Physiol. 303, H144–H155. (doi:10.1152/ajpheart.01151.2011)
185. Sadrieh A et al. 2014 Multiscale cardiac modelling reveals the origins of notched T waves in long QT syndrome type 2. Nat. Commun. 5, 5069. (doi:10.1038/ncomms6069)
186. Pathmanathan P, Shotwell MS, Gavaghan DJ, Cordeiro JM, Gray RA. 2015 Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology. Prog. Biophys. Mol. Biol. 117, 4–18. (doi:10.1016/j.pbiomolbio.2015.01.008)
187. Hill TL. 2012 Free energy transduction and biochemical cycle kinetics. New York, NY: Springer Science and Business Media.
188. Huxley AF, Simmons RM. 1971 Proposed mechanism of force generation in striated muscle. Nature 233, 533–538. (doi:10.1038/233533a0)
189. Lymn R, Taylor EW. 1971 Mechanism of adenosine triphosphate hydrolysis by actomyosin. Biochemistry 10, 4617–4624. (doi:10.1021/bi00801a004)
190. Eisenberg E, Hill TL. 1979 A cross-bridge model of muscle contraction. Prog. Biophys. Mol. Biol. 33, 55–82. (doi:10.1016/0079-6107(79)90025-7)
191. Marcucci L, Truskinovsky L. 2010 Mechanics of the power stroke in myosin II. Phys. Rev. E 81, 051915. (doi:10.1103/PhysRevE.81.051915)
192. Zahalak GI. 1981 A distribution-moment approximation for kinetic theories of muscular contraction. Math. Biosci. 55, 89–114. (doi:10.1016/0025-5564(81)90014-6)
193. Guerin T, Prost J, Joanny J-F. 2011 Dynamical behavior of molecular motor assemblies in the rigid and crossbridge models. Eur. Phys. J. E 34, 1–21. (doi:10.1140/epje/i2011-11060-5)
194. Hill A. 1938 The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. B 126, 136–195. (doi:10.1098/rspb.1938.0050)
195. Suga H, Sagawa K, Shoukas AA. 1973 Load independence of the instantaneous pressure-volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. Circul. Res. 32, 314–322. (doi:10.1161/01.RES.32.3.314)
196. Caruel M, Chabiniok R, Moireau P, Lecarpentier Y, Chapelle D. 2014 Dimensional reductions of a cardiac model for effective validation and calibration. Biomech. Model. Mechanobiol. 13, 897–914. (doi:10.1007/s10237-013-0544-6)
197. Piazzesi G, Lombardi V. 1995 A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophys. J. 68, 1966. (doi:10.1016/S0006-3495(95)80374-7)
198. Tangney JR, Campbell SG, McCulloch AD, Omens JH. 2014 Timing and magnitude of systolic stretch affect myofilament activation and mechanical work. Am. J. Physiol. Heart. Circ. Physiol. 307, H353–H360. (doi:10.1152/ajpheart.00233.2014)
199. Mann DL, Zipes DP, Libby P, Bonow RO, Braunwald E. 2015 Braunwald’s heart disease. Philadelphia, PA: Sauders, Elsevier.
200. Ambrosi D et al. 2011 Perspectives on biological growth and remodeling. J. Mech. Phys. Solids 59, 863–883. (doi:10.1016/j.jmps.2010.12.011)
201. Taber LA. 1995 Biomechanics of growth, remodeling, and morphogenesis. Appl. Mech. Rev. 48, 487–545. (doi:10.1115/1.3005109)
202. Rodriguez EK, Hoger A, McCulloch AD. 1994 Stress– dependent finite growth in soft elastic tissues. J. Biomech. 27, 455–467. (doi:10.1016/0021-9290(94)90021-3)
203. Menzel A, Kuhl E. 2012 Frontiers in growth and remodeling. Mech. Res. Commun. 42, 1–14. (doi:10.1016/j.mechrescom.2012.02.007)
204. Göktepe S, Abilez OJ, Kuhl E. 2010 A generic approach towards finite growth with examples of athlete’s heart, cardiac dilation, and cardiac wall thickening. J. Mech. Phys. Solids 58, 1661–1680. (doi:10.1016/j.jmps.2010.07.003)
205. Humphrey JD, Rajagopal KR. 2002 A constrained mixture model for growth and remodeling of soft tissues. Math. Models Methods Appl. Sci. 12, 407–430. (doi:10.1142/S0218202502001714)
206. Truesdell C, Noll W. 2004 The non-linear field theories of mechanics. Berlin, Germany: Springer.
207. Göktepe S, Abilez OJ, Parker KK, Kuhl E. 2012 A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis. J. Theor. Biol. 265, 433–442. (doi:10.1016/j.jtbi.2010.04.023)
208. Genet M, Lee LC, Baillargeon B, Guccione JM, Kuhl E. 2015 Modeling pathologies of systolic and diastolic heart failure. Ann. Biomed. Eng. 44, 112–127. (doi:10.1007/s10439-015-1351-2)
209. Kerckhoffs RCP, Omens JH, McCulloch AD. 2012 A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload. Mech. Res. Commun. 42, 40–50. (doi:10.1016/j.mechrescom.2011.11.004)
210. Rausch MK, Dam A, Göktepe S, Abilez OJ, Kuhl E. 2011 Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech. Model. Mechanobiol. 10, 799–811. (doi:10.1007/s10237-010-0275-x)
211. Boovendeerd PHM. 2012 Modeling of cardiac growth and remodeling of myofiber orientation. J. Biomech. 45, 872–882. (doi:10.1016/j.jbiomech.2011.11.029)
212. Kroon W, Delhaas T, Arts T, Bovendeerd PHM. 2009 Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle. Biomech. Model. Mechanobiol. 8, 301–309. (doi:10.1007/s10237-008-0136-z)
213. Omens JH, McCulloch AD, Criscione JC. 2003 Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models. Biomech. Model. Mechanobiol. 1, 267–277. (doi:10.1007/s10237-002-0021-0)
214. Genet M, Rausch M, Lee L, Choy S, Zhao X, Kassab G, Kozerke S, Guccione J, Kuhl E. 2015 Heterogeneous growth-induced prestrain in the heart. J. Biomech. 48, 2080–2089. (doi:10.1016/j.jbiomech.2015.03.012)
215. Gerdes AM, Kellerman SE, Moore JA, Muffly KE, Clark LC, Reaves PY, Malec K, McKeown PP, Schocken DD. 1992 Structural remodeling of cardiac myocytes in patients with ischemic cardiomyopathy. Circulation 86, 426–430. (doi:10.1161/01.CIR.86.2.426)
216. Savinova OV, Gerdes AM. 2012 Myocyte changes in heart failure. Heart Fail. Clin. 8, 1–6. (doi:10.1016/j.hfc.2011.08.004)
217. Atkinson DJ, Edelman R. 1991 Cineangiography of the heart in a single breath hold with a segmented turboflash sequence. Radiology 178, 357–360. (doi:10.1148/radiology.178.2.1987592)
218. Usman M, Atkinson D, Heathfield E, Greil G, Schaeffter T, Prieto C. 2015 Whole left ventricular functional assessment from two minutes free breathing multi-slice cine acquisition. Phys. Med. Biol. 60, N93. (doi:10.1088/0031-9155/60/7/N93)
219. Wesbey G, Higgins C, McNamara M, Engelstad B, Lipton M, Sievers R, Ehman R, Lovin J, Brasch R. 1984 Effect of gadolinium-DTPA on the magnetic relaxation times of normal and infarcted myocardium. Radiology 153, 165–169. (doi:10.1148/radiology.153.1.6473778)
220. Delfaut EM, Beltran J, Johnson G, Rousseau J, Marchandise X, Cotten A. 1999 Fat suppression in MR imaging: techniques and pitfalls. Radiographics 19, 373–382. (doi:10.1148/radiographics.19.2.g99mr03373)
221. Mewton N, Liu CY, Croisille P, Bluemke D, Lima JA. 2011 Assessment of myocardial fibrosis with cardiovascular magnetic resonance. J. Am. Coll. Cardiol. 57, 891–903. (doi:10.1016/j.jacc.2010.11.013)
222. Ugander M et al. 2012 Extracellular volume imaging by magnetic resonance imaging provides insights into overt and sub-clinical myocardial pathology. Eur. Heart J. 33, 1268–1278. (doi:10.1093/eurheartj/ehr481)
223. Carpenter J-P et al. 2014 On T2* magnetic resonance and cardiac iron. Circulation 123, 1519– 1528. (doi:10.1161/CIRCULATIONAHA.110.007641)
224. Rutz AK, Ryf S, Plein S, Boesiger P, Kozerke S. 2008 Accelerated whole-heart 3D CSPAMM for myocardial motion quantification. Magn. Reson. Med. 59, 755–763. (doi:10.1002/mrm.21363)
225. Young AA. 1999 Model tags: direct three-dimensional tracking of heart wall motion from tagged magnetic resonance images. Med. Image Anal. 3, 361–372. (doi:10.1016/S1361-8415(99)80029-2)
226. Lambert SA et al. 2015 Bridging three orders of magnitude: multiple scattered waves sense fractal microscopic structures via dispersion. Phys. Rev. Lett. 115, 094301. (doi:10.1103/PhysRevLett.115.094301)
227. Henningsson M, Koken P, Stehning C, Razavi R, Prieto C, Botnar RM. 2012 Whole-heart coronary MR angiography with 2D self-navigated image reconstruction. Magn. Reson. Med. 67, 437–445. (doi:10.1002/mrm.23027)
228. Giorgi B, Dymarkowski S, Maes F, Kouwenhoven M. 2002 Improved visualization of coronary arteries using a new three-dimensional submillimeter MR coronary angiography sequence with balanced gradients. Am. J. Roentgenol. 179, 901–910. (doi:10.2214/ajr.179.4.1790901)
229. Axel L, Dougherty L. 1989 Improved method of spatial modulation of magnetization (SPAMM) for MRI of heart wall motion. Radiology 172, 349–350. (doi:10.1148/radiology.172.2.2748813)
230. Plein S, Ryf S, Schwitter J, Radjenovic A, Boesiger P, Kozerke S. 2007 Dynamic contrast-enhanced myocardial perfusion MRI accelerated with k-t SENSE. Magn. Reson. Med. 58, 777–785. (doi:10.1002/mrm.21381)
231. Jogiya R, Kozerke S, Morton G, De Silva K, Redwood S, Perera D, Nagel E, Plein S. 2012 Validation of dynamic 3-Dimensional whole heart magnetic resonance myocardial perfusion imaging against fractional flow reserve for the detection of significant coronary artery disease. J. Am. Coll. Cardiol. 60, 756–765. (doi:10.1016/j.jacc.2012.02.075)
232. Pedersen H, Kozerke S, Ringgaard S, Nehrke K, Kim W. 2009 k-t PCA: Temporally constrained k-t BLAST reconstruction using principal component analysis. Magn. Reson. Med. 62, 706–716. (doi:10.1002/mrm.22052)
233. Stoeck CT, von Deuster C, Genet M, Atkinson D, Kozerke S. 2015 Second-order motion-compensated spin echo diffusion tensor imaging of the human heart. Magn. Reson. Med. 17(Suppl 1), P81. (doi:10.1186/1532-429X-17-S1-P81)
234. Robert B, Sinkus R, Gennisson J-L, Fink M. 2009 Application of DENSE-MR-elastography to the human heart. Magn. Reson. Med. 62, 1155–1163. (doi:10.1002/mrm.22124)
235. Mariappan YK, Glaser KJ, Ehman RL. 2010 Magnetic resonance elastography: a review. Clin. Anat. 23, 497–511. (doi:10.1002/ca.21006)
236. Pernot M, Couade M, Mateo P, Crozatier B, Fischmeister R, Tanter M. 2011 Real-time assessment of myocardial contractility using shear wave imaging. J. Am. Coll. Cardiol. 58, 65–72. (doi:10.1016/j.jacc.2011.02.042)
237. Toussaint N, Stoeck CT, Schaeffter T, Kozerke S, Sermesant M, Batchelor PG. 2013 In vivo human cardiac fibre architecture estimation using shapebased diffusion tensor processing. Med. Image Anal. 17, 1243–1255. (doi:10.1016/j.media.2013.02.008)
238. Brett SE, Guilcher A, Clapp B, Chowienczyk P. 2012 Estimating central systolic blood pressure during oscillometric determination of blood pressure: proof of concept and validation by comparison with intraaortic pressure recording and arterial tonometry. Blood Press. Monit. 17, 132–136. (doi:10.1097/MBP.0b013e328352ae5b)
239. Shi W et al. 2012 A comprehensive cardiac motion estimation framework using both untagged and 3D tagged MR images based on non-rigid registration. IEEE Trans. Med. Imag. 31, 1263–1275. (doi:10.1109/TMI.2012.2188104)
240. Imperiale A, Chabiniok R, Moireau P, Chapelle D. 2011 Constitutive parameter estimation methodology using tagged-MRI data. In Functional imaging and modeling of the heart (eds D Metaxas, L Axel), pp. 409–417. Berlin, Germany: Springer.
241. Ecabert O, Peters J, Walker M, Ivan T, Lorenz C, von Berg J, Lessick J, Vembar M. 2011 Assessment of myocardial fibrosis with cardiovascular magnetic resonance. Med. Image Anal. 15, 863–876. (doi:10.1016/j.media.2011.06.004)
242. Shi W, Jantsch M, Aljabar P, Pizarro L, Bai W, Wang H, O’Regan D, Zhuang X, Rueckert D. 2013 Temporal sparse free-form deformations. Med. Image Anal. 17, 779–789. (doi:10.1016/j.media.2013.04.010)
243. Hadjicharalambous M et al. 2015 Analysis of passive cardiac constitutive laws for parameter estimation using 3D tagged MRI. Biomech. Model. Mechanobiol. 14, 807–828. (doi:10.1007/s10237-014-0638-9)
244. Augenstein KF, Cowan BR, LeGrice IJ, Nielsen PM, Young AA. 2005 Method and apparatus for soft tissue material parameter estimation using tissue tagged magnetic resonance imaging. J. Biomech. Eng. 127, 148–157. (doi:10.1115/1.1835360)
245. Wang VY, Lam H, Ennis DB, Cowan BR, Young AA, Nash MP. 2009 Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function. Med. Image Anal. 13, 773–784. (doi:10.1016/j.media.2009.07.006)
246. Xi J, Lamata P, Lee J, Moireau P, Chapelle D, Smith N. 2011 Myocardial transversely isotropic material parameter estimation from in-silico measurements based on a reduced-order unscented Kalman filter. J. Mech. Behav. Biomed. Mater. 4, 1090–1102. (doi:10.1016/j.jmbbm.2011.03.018)
247. Wang L, Dawoud F, Wong KC, Zhang H, Liu H, Lardo AC, Shi P. 2011 Transmural electrophysiologic and scar imaging on porcine heart with chronic infarction. In STACOM (eds O Camara, E Konukoglu, M Pop, K Rhode, M Sermesant, A Young), pp. 23–32. Berlin, Germany: Springer.
248. Chabiniok R, Moireau P, Lesault P-F, Rahmouni A, Deux J-F, Chapelle D. 2012 Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model. Biomech. Model. Mechanobiol. 11, 609–630. (doi:10.1007/s10237-011-0337-8)
249. Marchesseau S et al. 2013 Personalization of a cardiac electromechanical model using reduced order unscented Kalman filtering from regional volumes. Med. Image Anal. 17, 816–829. (doi:10.1016/j.media.2013.04.012)
250. Chabiniok R, Bhatia KK, King AP, Rueckert D, Smith N. 2015 Manifold learning for cardiac modeling and estimation framework. In statistical atlases and computational models of the heart-imaging and modelling challenges (eds O Camara, T Mansi, M Pop, K Rhode, M Sermesant, A Young), pp. 284–294. Basel, Switzerland: Springer.
251. Asner L et al. In press. Estimation of passive and active properties in the human heart using 3D tagged MRI. Biomech. Model. Mechanobiol. (doi:10.1007/s10237-015-0748-z)
252. Wong KC, Sermesant M, Rhode K, Ginks M, Rinaldi CA, Razavi R, Delingette H, Ayache N. 2014 Velocitybased cardiac contractility personalization from images using derivative-free optimization. J. Mech. Behav. Biomed. Mater. 43, 35–52. (doi:10.1016/j.jmbbm.2014.12.002)
253. Chabiniok R, Sammut E, Hadjicharalambous M, Asner L, Nordsletten D, Razavi R, Smith N. 2015 Steps towards quantification of the cardiological stress exam. In Functional imaging and modeling of the heart (eds H van Assen, P Bovendeerd, T Delhaas), pp. 12–20. Basel, Switzerland: Springer.
254. Krishnamurthy A et al. 2013 Patient-specific models of cardiac biomechanics. J. Comput. Phys. 244, 4–21. (doi:10.1016/j.jcp.2012.09.015)
255. Rohmer D, Sitek A, Gullberg GT. 2007 Reconstruction and visualization of fiber and laminar structure in the normal human heart from ex vivo. Invest. Radiol. 42, 777–789. (doi:10.1097/RLI.0b013e3181238330)
256. Eggen MD, Swingen CM, Iaizzo PA. 2009 Analysis of fiber orientation in normal and failing human hearts using diffusion tensor MRI. In IEEE Int. Symp. on Biomedical Imaging: From Nano to Macro, Boston, MA, 28 June–1 July, pp. 642–645. New York, NY: IEEE.
257. Gamper U, Boesiger P, Kozerke S. 2007 Diffusion imaging of the in vivo heart using spin echoes– considerations on bulk motion sensitivity. Magn. Reson. Med. 57, 331–337. (doi:10.1002/mrm.21127)
258. Schmid H, Nash M, Young A, Hunter P. 2006 Myocardial material parameter estimation—a comparative study for simple shear. J. Biomech. Eng. 128, 742–750. (doi:10.1115/1.2244576)
259. Schmid H, O’Callaghan P, Nash M, Lin W, LeGrice I, Smaill B, Young A, Hunter P. 2008 Myocardial material parameter estimation. Biomech. Model. Mechanobiol. 7, 161–173. (doi:10.1007/s10237-007-0083-0)
260. Blum J, Le Dimet F-X, Navon IM. 2009 Data assimilation for geophysical fluids. Handb. Numer. Anal. 14, 385–441. (doi:10.1016/S1570-8659(08)00209-3)
261. Chapelle D, Fragu M, Mallet V, Moireau P. 2013 Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euheart. Med. Biol. Eng. Comput. 51, 1221–1233. (doi:10.1007/s11517-012-0969-6)
262. Perotti LE, Ponnaluri AV, Krishnamoorthi S, Balzani D, Klug WS, Ennis DB. 2015 Identification of unique material properties for passive myocardium. Auckland, New Zealand: Cardiac Physiome Workshop.
263. Le Dimet F-X, Talagrand O. 1986 Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 38, 97–110. (doi:10.1111/j.1600-0870.1986.tb00459.x)
264. Delingette H, Billet F, Wong KC, Sermesant M, Rhode K, Ginks M, Rinaldi CA, Razavi R, Ayache N. 2012 Personalization of cardiac motion and contractility from images using variational data assimilation. IEEE Trans. Biomed. Eng. 59, 20–24. (doi:10.1109/TBME.2011.2160347)
265. Moireau P, Chapelle D, Le Tallec P. 2008 Joint state and parameter estimation for distributed mechanical systems. Comput. Methods Appl. Mech. Eng. 197, 659–677. (doi:10.1016/j.cma.2007.08.021)
266. Moireau P, Chapelle D. 2011 Reduced-order unscented Kalman filtering with application to parameter identification in large-dimensional systems. ESAIM Control Optimisation Calc. Var. 17, 380–405. (doi:10.1051/cocv/2010006)
267. Lakshmivarahan S, Lewis JM. 2013 Nudging methods: a critical overview. In Data assimilation for atmospheric, oceanic and hydrologic applications, vol. 2 (eds S Ki Park, L Xu), pp. 27–57. Berlin, Germany: Springer.
268. Moireau P, Chapelle D, Le Tallec P. 2009 Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging. Inverse Probl. 25, 035010. (doi:10.1088/0266-5611/25/3/035010)
269. Corrado C, Gerbeau J-F, Moireau P. 2015 Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography. J. Comput. Phys. 283, 271–298. (doi:10.1016/j.jcp.2014.11.041)
270. Imperiale A, Routier A, Durrleman S, Moireau P. 2013 Improving efficiency of data assimilation procedure for a biomechanical heart model by representing surfaces as currents. In Functional imaging and modeling of the heart (eds S Ourselin, D Rueckert, N Smith), pp. 342–351. Berlin, Germany: Springer.
271. Mancini D, Burkhoff D. 2005 Mechanical device– based methods of managing and treating heart failure. Circulation 112, 438–448. (doi:10.1161/CIRCULATIONAHA.104.481259)
272. Food and D. Administration. 2014 Reporting of computational modeling studies in medical device submissions. In Draft guidance for industry and food and drug administration staff. See http://www.fda.gov/MedicalDevices/DeviceRegulationandGuidance/GuidanceDocuments/ucm371016.htm.
273. Rausch M, Bothe W, Kvitting J-P, Swanson J, Miller D, Kuhl E. 2012 Mitral valve annuloplasty. Ann. Biomed. Eng. 40, 750–761. (doi:10.1007/s10439-011-0442-y)
274. Gee MW, Hirschvogel M, Basilious M, Wildhirt S. 2015 A closed loop 0D-3D model of patient specific cardiac mechanics for cardiac assist device engineering. In 4th Int. Conf. on Computational and Mathematical Biomedical Engineering, Paris, France, 9 June–1 July. Swansea, UK: CMBE Zeta Computational Resources Ltd.
275. Wang Q, Sirois E, Sun W. 2012 Patient-specific modeling of biomechanical interaction in transcatheter aortic valve deployment. J. Biomech. 45, 1965–1971. (doi:10.1016/j.jbiomech.2012.05.008)
276. Lafortune P, Ars R, Vázquez M, Houzeaux G. 2012 Coupled electromechanical model of the heart: parallel finite element formulation. Int. J. Numer. Methods Biomed. Eng. 28, 72–86. (doi:10.1002/cnm.1494)
277. Gurev V, Pathmanathan P, Fattebert J-L, Wen H-F, Magerlein J, Gray RA, Richards DF, Rice JJ. 2015 A high-resolution computational model of the deforming human heart. Biomech. Model. Mechanobiol. 14, 829–849. (doi:10.1007/s10237-014-0639-8)
278. Augustin CM, Neic A, Liebmann M, Prassl AJ, Niederer SA, Haase G, Plank G. 2016 Anatomically accurate high resolution modeling of human whole heart electromechanics: a strongly scalable algebraic multigrid solver method for nonlinear deformation. J. Comput. Phys. 305, 622–646. (doi:10.1016/j.jcp.2015.10.045)
279. Kayvanpour E et al. 2015 Towards personalized cardiology: multi-scale modeling of the failing heart. PLoS ONE 10, e0134869. (doi:10.1371/journal.pone.0134869)
280. Chapelle D, Felder A, Chabiniok R, Guellich A, Deux J-F, Damy T. 2015 Patient-specific biomechanical modeling of cardiac amyloidosis–a case study. In Functional imaging and modeling of the heart (eds H van Assen, P Bovendeerd, T Delhaas), pp. 295–303. Basel, Switzerland: Springer.
281. Qu Z, Garfinkel A, Chen P-S, Weiss JN. 2000 Mechanisms of discordant alternans and induction of reentry in simulated cardiac tissue. Circulation 102, 1664–1670. (doi:10.1161/01.CIR.102.14.1664)
282. Sato D et al. 2009 Synchronization of chaotic early afterdepolarizations in the genesis of cardiac arrhythmias. Proc. Natl Acad. Sci. USA 106, 2983–2988. (doi:10.1073/pnas.0809148106)
283. Moreno JD et al. 2011 A computational model to predict the effects of class I anti-arrhythmic drugs on ventricular rhythms. Sci. Transl. Med. 3, 98ra83. (doi:10.1126/scitranslmed.3002588)
284. Mansi T et al. 2011 A statistical model for quantification and prediction of cardiac remodelling: application to tetralogy of Fallot. IEEE Trans. Med. Imag. 30, 1605–1616. (doi:10.1109/TMI.2011.2135375)
285. Hlatky MA et al. 2009 Criteria for evaluation of novel markers of cardiovascular risk a scientific statement from the American heart association. Circulation 119, 2408–2416. (doi:10.1161/CIRCULATIONAHA.109.192278)
286. Tsamis A, Cheng A, Nguyen TC, Langer F, Miller D, Kuhl E. 2012 Kinematics of cardiac growth: In vivo characterization of growth tensors and strains. J. Mech. Behav. Biomed. Mater. 8, 165–177. (doi:10.1016/j.jmbbm.2011.12.006)
287. Zhang X et al. 2014 Atlas-based quantification of cardiac remodeling due to myocardial infarction. PLoS ONE 9, e110243. (doi:10.1371/journal.pone.0110243)
288. Tobon-Gomez C et al. 2013 Benchmarking framework for myocardial tracking and deformation algorithms: an open access database. Med. Image Anal. 17, 632–648. (doi:10.1016/j.media.2013.03.008)
289. Camara O, Mansi T, Pop M, Rhode K, Sermesant M, Young A. 2015 Statistical atlases and computational models of the heart-imaging and modelling challenges: 5th International Workshop, STACOM 2014. In Held in Conjunction with MICCAI 2014, Boston, MA, USA, 18 September 2014, revised Selected Papers, vol. 8896. Cham, Switzerland: Springer.
290. Konukoglu E et al. 2011 Efficient probabilistic model personalization integrating uncertainty on data and parameters: application to eikonal-diffusion models in cardiac electrophysiology. Prog. Biophys.Mol. Biol. 107, 134–146. (doi:10.1016/j.pbiomolbio.2011.07.002)
291. Zettinig O et al. 2014 Data-driven estimation of cardiac electrical diffusivity from 12-lead ECG signals. Med. Image Anal. 18, 1361–1376. (doi:10.1016/j.media.2014.04.011)
292. Neumann D et al. 2014 Robust image-based estimation of cardiac tissue parameters and their uncertainty from noisy data. In Medical image computing and computer-assisted intervention– MICCAI 2014 (eds P Golland, N Hata, C Barillot, J Hornegger, R Howe), pp. 9–16. Basel, Switzerland: Springer