Personalized biophysical modeling of the heart is a useful approach for noninvasively analyzing and predicting in vivo cardiac mechanics. Three main developments support this style of analysis: state-of-the-art cardiac imaging technologies, modern computational infrastructure, and advanced mathematical modeling techniques. In vivo measurements of cardiac structure and function can be integrated using sophisticated computational methods to investigate mechanisms of myocardial function and dysfunction, and can aid in clinical diagnosis and developing personalized treatment. In this article, we review the state-of-the-art in cardiac imaging modalities, model-based interpretation of 3D images of cardiac structure and function, and recent advances in modeling that allow personalized predictions of heart mechanics. We discuss how using such image-based modeling frameworks can increase the understanding of the fundamental biophysics behind cardiac mechanics, and assist with diagnosis, surgical guidance, and treatment planning. Addressing the challenges in this field will require a coordinated effort from both the clinical-imaging and modeling communities. We also discuss future directions that can be taken to bridge the gap between basic science and clinical translation.


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Literature Cited

  1. Braunwald E, Bristow MR. 1.  2000. Congestive heart failure: fifty years of progress. Circulation 102:Suppl. 414–23 [Google Scholar]
  2. Redfield MM. 2.  2004. Understanding “diastolic” heart failure. N. Engl. J. Med. 350:1930–31 [Google Scholar]
  3. Teeters JC, Alexis JD. 3.  2009. Systolic heart failure. Manual of Heart Failure Management JD Bisognano, ML Baker, MB Earley 49–57 London: Springer [Google Scholar]
  4. Zile MR, Brutsaert DL. 4.  2002. New concepts in diastolic dysfunction and diastolic heart failure: Part I. Diagnosis, prognosis, and measurements of diastolic function. Circulation 105:1387–93 [Google Scholar]
  5. De Keulenaer GW, Brutsaert DL. 5.  2011. Systolic and diastolic heart failure are overlapping phenotypes within the heart failure spectrum. Circulation 123:1996–2005 [Google Scholar]
  6. Borlaug BA, Redfield MM. 6.  2011. Diastolic and systolic heart failure are distinct phenotypes within the heart failure spectrum. Circulation 123:2006–14 [Google Scholar]
  7. Zile MR. 7.  2003. Heart failure with preserved ejection fraction: is this diastolic heart failure?. J. Am. Coll. Cardiol. 41:1519–22 [Google Scholar]
  8. Mann DL, Bogaev R, Buckberg GD. 8.  2010. Cardiac remodelling and myocardial recovery: lost in translation?. Eur. J. Heart Fail. 12:789–96 [Google Scholar]
  9. Mann DL, Bristow MR. 9.  2005. Mechanisms and models in heart failure. Circulation 111:2837–49 [Google Scholar]
  10. McMurray JJV. 10.  2010. Systolic heart failure. N. Engl. J. Med. 362:228–38 [Google Scholar]
  11. Katz AM. 11.  2008. The “modern” view of heart failure: how did we get here?. Circ. Heart Fail. 1:63–71 [Google Scholar]
  12. Nordsletten DA, Niederer SA, Nash MP, Hunter PJ, Smith NP. 12.  2011. Coupling multi-physics models to cardiac mechanics. Prog. Biophys. Mol. Biol. 104:77–88 [Google Scholar]
  13. Trayanova NA. 13.  2011. Whole-heart modeling. Circ. Res. 108:113–28 [Google Scholar]
  14. Kerckhoffs RCP, Healy SN, Usyk TP, McCulloch AD. 14.  2006. Computational methods for cardiac electromechanics. Proc. IEEE 94:769–83 [Google Scholar]
  15. O'Brien JP, Srichai MB, Hecht EM, Kim DC, Jacobs JE. 15.  2007. Anatomy of the heart at multidetector CT: what the radiologist needs to know. RadioGraphics 27:1569–82 [Google Scholar]
  16. Pourmorteza A, Schuleri KH, Herzka DA, Lardo AC, McVeigh ER. 16.  2012. A new method for cardiac computed tomography regional function assessment: stretch quantifier for endocardial engraved zones (SQUEEZ). Circ. Cardiovasc. Imaging 5:243–50 [Google Scholar]
  17. Noble JA, Navab N, Becher H. 17.  2011. Ultrasonic image analysis and image-guided interventions. Interface Focus 1:673–85 [Google Scholar]
  18. Young AA, Frangi AF. 18.  2009. Computational cardiac atlases: from patient to population and back. Exp. Physiol. 94:578–96 [Google Scholar]
  19. Mor-Avi V, Lang RM, Badano LP, Belohlavek M, Cardim NM. 19.  et al. 2011. Current and evolving echocardiographic techniques for the quantitative evaluation of cardiac mechanics: ASE/EAE consensus statement on methodology and indications endorsed by the Japanese Society of Echocardiography. Eur. J. Echocardiogr. 12:167–205 [Google Scholar]
  20. Edelman RR, Dunkle EE, Wei L, Kissinger KV, Thangaraj K. 20.  2006. Practical considerations and image optimization. Clinical Magnetic Resonance Imaging 1, ed. RR Edelman, JR Hesselink, MB Zlatkin, JV Crues III. 58–104 Philadelphia: Elsevier/Saunders, 3rd ed.. [Google Scholar]
  21. Young AA, Cowan BR, Thrupp SF, Hedley WJ, Dell'Italia LJ. 21.  2000. Left ventricular mass and volume: fast calculation with guide-point modeling on MR images. Radiology 216:597–602 [Google Scholar]
  22. Axel L, Dougherty L. 22.  1989. Heart wall motion: improved method of spatial modulation of magnetization for MR imaging. Radiology 172:349–50 [Google Scholar]
  23. Young AA, Prince JL. 23.  2013. Cardiovascular magnetic resonance: deeper insights through bioengineering. Annu. Rev. Biomed. Eng. 15:433–61 [Google Scholar]
  24. Zerhouni EA, Parish DM, Rogers WJ, Yang A, Shapiro EP. 24.  1988. Human heart: tagging with MR imaging—a method for noninvasive assessment of myocardial motion. Radiology 169:59–63 [Google Scholar]
  25. Hess AT, Zhong X, Spottiswoode BS, Epstein FH, Meintjes EM. 25.  2009. Myocardial 3D strain calculation by combining cine displacement encoding with stimulated echoes (DENSE) and cine strain encoding (SENC) imaging. Magn. Reson. Med. 62:77–84 [Google Scholar]
  26. Föll D, Jung B, Schilli E, Staehle F, Geibel A. 26.  et al. 2010. Magnetic resonance tissue phase mapping of myocardial motion: new insight in age and gender. Circ. Cardiovasc. Imaging 3:54–64 [Google Scholar]
  27. Wagner RF, Smith SW, Sandrik JM, Lopez H. 27.  1983. Statistics of Speckle in ultrasound B-scans. IEEE Trans. Sonics Ultrason. 30:156–63 [Google Scholar]
  28. Meunier J, Bertrand M. 28.  1995. Ultrasonic texture motion analysis: theory and simulation. IEEE Trans. Med. Imaging 14:293–300 [Google Scholar]
  29. Behar V, Adam D, Lysyansky P, Friedman Z. 29.  2004. The combined effect of nonlinear filtration and window size on the accuracy of tissue displacement estimation using detected echo signals. Ultrasonics 41:743–53 [Google Scholar]
  30. Uematsu M, Miyatake K, Tanaka N, Matsuda H, Sano A. 30.  et al. 1995. Myocardial velocity gradient as a new indicator of regional left ventricular contraction: detection by a two-dimensional tissue Doppler imaging technique. J. Am. Coll. Cardiol. 26:217–23 [Google Scholar]
  31. McVeigh E. 31.  1998. Regional myocardial function. Cardiol. Clin. 16:189–206 [Google Scholar]
  32. Apfaltrer P, Schoendube H, Schoepf UJ, Allmendinger T, Tricarico F. 32.  et al. 2013. Enhanced temporal resolution at cardiac CT with a novel CT image reconstruction algorithm: initial patient experience. Eur. J. Radiol. 82:270–74 [Google Scholar]
  33. Manzke R, Grass M, Nielsen T, Shechter G, Hawkes D. 33.  2003. Adaptive temporal resolution optimization in helical cardiac cone beam CT reconstruction. Med. Phys. 30:3072–80 [Google Scholar]
  34. Waldman LK, Nosan D, Villarreal F, Covell JW. 34.  1988. Relation between transmural deformation and local myofiber direction in canine left ventricle. Circ. Res. 63:550–62 [Google Scholar]
  35. Hooks DA, Tomlinson KA, Marsden SG, LeGrice IJ, Smaill BH. 35.  et al. 2002. Cardiac microstructure. Circ. Res. 91:331–38 [Google Scholar]
  36. Holmes JW. 36.  2004. Determinants of left ventricular shape change during filling. J. Biomech. Eng. 126:98–103 [Google Scholar]
  37. Ubbink SWJ, Bovendeerd PHM, Delhaas T, Arts T, van de Vosse FN. 37.  2006. Towards model-based analysis of cardiac MR tagging data: relation between left ventricular shear strain and myofiber orientation. Med. Image Anal. 10:632–41 [Google Scholar]
  38. Streeter DD, Spotnitz HM, Patel DP, Ross J, Sonnenblick EH. 38.  1969. Fiber orientation in the canine left ventricle during diastole and systole. Circ. Res. 24:339–47 [Google Scholar]
  39. LeGrice IJ, Smaill BH, Chai LZ, Edgar SG, Gavin JB, Hunter PJ. 39.  1995. Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. Heart Circ. Physiol. 269:H571–82 [Google Scholar]
  40. Young AA, Legrice IJ, Smaill BH. 40.  1998. Extended confocal microscopy of myocardial laminae and collagen network. J. Microsc. 192:139–50 [Google Scholar]
  41. Costa KD, Holmes JW, Mcculloch AD. 41.  2001. Modelling cardiac mechanical properties in three dimensions. Philos. Trans. A 359:1233–50 [Google Scholar]
  42. Usyk TP, Mazhari R, McCulloch AD. 42.  2000. Effect of laminar orthotropic myofiber architecture on regional stress and strain in the canine left ventricle. J. Elasticity 61:143–64 [Google Scholar]
  43. Costa KD, Takayama Y, McCulloch AD, Covell JW. 43.  1999. Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. Am. J. Physiol. 276:H595–607 [Google Scholar]
  44. Basser PJ, Mattiello J, LeBihan D. 44.  1994. MR diffusion tensor spectroscopy and imaging. Biophys. J. 66:259–67 [Google Scholar]
  45. Peyrat J-M, Sermesant M, Pennec X, Delingette H, Xu C. 45.  et al. 2006. Towards a statistical atlas of cardiac fiber structure. Med. Image Comput. Comput. Assist. Interv. 9:Pt. 1297–304 [Google Scholar]
  46. Lombaert H, Peyrat J-M, Fanton L, Cheriet F, Delingette H. 46.  et al. 2012. Statistical atlas of human cardiac fibers: comparison with abnormal hearts. Statistical Atlases and Computational Models of the Heart Imaging and Modelling Challenges O Camara, E Konukoglu, M Pop, K Rhode, M Sermesant, A Young 207–13 Berlin/Heidelberg: Springer [Google Scholar]
  47. Vadakkumpadan F, Gurev V, Constantino J, Arevalo H, Trayanova N. 47.  2010. Modeling of whole-heart electrophysiology and mechanics: toward patient-specific simulations. Patient-Specific Modeling of the Cardiovascular System RCP Kerckhoffs 145–65 New York: Springer [Google Scholar]
  48. Gamper U, Boesiger P, Kozerke S. 48.  2007. Diffusion imaging of the in vivo heart using spin echoes—considerations on bulk motion sensitivity. Magn. Reson. Med. 57:331–37 [Google Scholar]
  49. Toussaint N, Sermesant M, Stoeck C, Kozerke S, Batchelor PG. 49.  2010. In vivo human 3D cardiac fibre architecture: reconstruction using curvilinear interpolation of diffusion tensor images. Med. Image Comput. Comput. Assist. Interv. 13:Pt. 1418–25 [Google Scholar]
  50. Wei H, Viallon M, Delattre BMA, Wang L, Pai VM. 50.  et al. 2013. Assessment of cardiac motion effects on the fiber architecture of the human heart in vivo. IEEE Trans. Med. Imaging 32:1928–38 [Google Scholar]
  51. Plank G, Burton RAB, Hales P, Bishop M, Mansoori T. 51.  et al. 2009. Generation of histo-anatomically representative models of the individual heart: tools and application. Philos. Trans. A 367:2257–92 [Google Scholar]
  52. Gilbert S, Benoist D, Benson A, White E, Tanner S. 52.  et al. 2012. Visualization and quantification of whole rat heart laminar structure using high-spatial resolution contrast-enhanced MRI. Am. J. Physiol. Heart Circ. Physiol. 302:H287–98 [Google Scholar]
  53. Schultz T, Burgeth B, Weickert J. 53.  2006. Flexible segmentation and smoothing of DT-MRI fields through a customizable structure tensor. Advances in Visual Computing G Bebis, R Boyle, B Parvin, D Koracin, P Remagnino 455–64 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  54. Potse M, Dube B, Richer J, Vinet A, Gulrajani RM. 54.  2006. A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng. 53:2425–35 [Google Scholar]
  55. Bishop MJ, Hales P, Plank G, Gavaghan DJ, Scheider J, Grau V. 55.  2009. Comparison of rule-based and DTMRI-derived fibre architecture in a whole rat ventricular computational model. Functional Imaging and Modeling of the Heart N Ayache, H Delingette, M Sermesant 87–96 Lect. Notes Comput. Sci. Vol. 5528 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  56. Kroon W, Delhaas T, Bovendeerd P, Arts T. 56.  2009. Computational analysis of the myocardial structure: adaptation of cardiac myofiber orientations through deformation. Med. Image Anal. 13:346–53 [Google Scholar]
  57. Hsu EW, Henriquez CS. 57.  2001. Myocardial fiber orientation mapping using reduced encoding diffusion tensor imaging. J. Cardiovasc. Magn. Reson. 3:339–47 [Google Scholar]
  58. Scollan DF, Holmes A, Winslow RL, Forder J. 58.  1998. Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am. J. Physiol. 275:H2308–18 [Google Scholar]
  59. Tseng W-YI, Wedeen VJ, Reese TG, Smith RN, Halpern EF. 59.  2003. Diffusion tensor MRI of myocardial fibers and sheets: correspondence with visible cut-face texture. J. Magn. Reson. Imaging 17:31–42 [Google Scholar]
  60. Ennis DB. 60.  2004. Assessment of myocardial structure and function using magnetic resonance imaging PhD Thesis, John Hopkins Univ. [Google Scholar]
  61. Wang VY. 61.  2012. Modeling in vivo cardiac mechanics using MRI and FEM PhD Thesis, Univ. Auckl. [Google Scholar]
  62. Alexander AL, Hasan KM, Lazar M, Tsuruda JS, Parker DL. 62.  2001. Analysis of partial volume effects in diffusion-tensor MRI. Magn. Reson. Med. 45:770–80 [Google Scholar]
  63. Holmes AA, Scollan DF, Winslow RL. 63.  2000. Direct histological validation of diffusion tensor MRI in formaldehyde-fixed myocardium. Magn. Reson. Med. 44:157–61 [Google Scholar]
  64. Wong AYK, Rautaharju PM. 64.  1968. Stress distribution within the left ventricular wall approximated as a thick ellipsoidal shell. Am. Heart J. 75:649–62 [Google Scholar]
  65. Mirsky I, Parmley WW. 65.  1973. Assessment of passive elastic stiffness for isolated heart muscle and the intact heart. Circ. Res. 33:233–43 [Google Scholar]
  66. Hunter PJ, Smaill BH. 66.  1988. The analysis of cardiac function: a continuum approach. Prog. Biophys. Mol. Biol. 52:101–64 [Google Scholar]
  67. Nielsen PMF. 67.  1987. The anatomy of the heart: a finite element model PhD Thesis, Univ. Auckl. [Google Scholar]
  68. Petitjean C, Dacher J-N. 68.  2011. A review of segmentation methods in short axis cardiac MR images. Med. Image Anal. 15:169–84 [Google Scholar]
  69. Lam H-I, Cowan BR, Nash MP, Young AA. 69.  2010. Interactive biventricular modeling tools for clinical cardiac image analysis. J. Cardiovasc. Magn. Reson. 12:P248 [Google Scholar]
  70. Lu X, Wang Y, Georgescu B, Littman A, Comaniciu D. 70.  2011. Automatic delineation of left and right ventricles in cardiac MRI sequences using a joint ventricular model. Functional Imaging and Modeling of the Heart D Metaxas, L Axel 250–58 Lect. Notes Comput. Sci. Vol. 6666 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  71. Zheng YF, Barbu A, Georgescu B, Scheuering M, Comaniciu D. 71.  2008. Four-chamber heart modeling and automatic segmentation for 3-D cardiac CT volumes using marginal space learning and steerable features. IEEE Trans. Med. Imaging 27:1668–81 [Google Scholar]
  72. Frangi A, Rueckert D, Schnabel J, Niessen W. 72.  2002. Automatic construction of multiple-object three-dimensional statistical shape models: application to cardiac modeling. IEEE Trans. Med. Imaging 21:1151–66 [Google Scholar]
  73. Ordas S, Oubel E, Sebastian R, Frangi AF. 73.  2007. Computational anatomy atlas of the heart Presented at 5th Int. Symp. Image Signal Process. Anal., ISPA 2007, Istanbul [Google Scholar]
  74. Hoogendoorn C, Sukno FM, Ordás S, Frangi AF. 74.  2009. Bilinear models for spatio-temporal point distribution analysis. Int. J. Computer Vis. 85:237–52 [Google Scholar]
  75. Cootes TF, Taylor CJ, Cooper DH, Graham J. 75.  1995. Active shape models—their training and application. Comput. Vis. Image Underst. 61:38–59 [Google Scholar]
  76. Medrano-Gracia P, Cowan BR, Ambale-Venkatesh B, Bluemke D, Eng J. 76.  et al. 2014. Left ventricular shape variation in asymptomatic populations: the multi-ethnic study of atherosclerosis. J. Cardiovasc. Magn. Reson. 16:56 [Google Scholar]
  77. Stevens C, Remme E, LeGrice IJ, Hunter PJ. 77.  2003. Ventricular mechanics in diastole: material parameter sensitivity. J. Biomech. 36:737–48 [Google Scholar]
  78. Gurev V, Lee T, Constantino J, Arevalo H, Trayanova N. 78.  2011. Models of cardiac electromechanics based on individual hearts imaging data: image-based electromechanical models of the heart. Biomech. Model. Mechanobiol. 10:295–306 [Google Scholar]
  79. Helm P, Beg MF, Miller MI, Winslow RL. 79.  2005. Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor MR imaging. Ann. N. Y. Acad. Sci. 1047:296–307 [Google Scholar]
  80. Wenk JF, Zhang Z, Cheng G, Malhotra D, Acevedo-Bolton G. 80.  et al. 2010. First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. Ann. Thorac. Surg. 89:1546–53 [Google Scholar]
  81. Xi J, Lamata P, Lee J, Moireau P, Chapelle D, Smith N. 81.  2011. Myocardial transversely isotropic material parameter estimation from in-silico measurements based on a reduced-order unscented Kalman filter. J. Mech. Behav. Biomed. Mater. 4:1090–102 [Google Scholar]
  82. Lamata P, Sinclair M, Kerfoot E, Lee A, Crozier A. 82.  et al. 2014. An automatic service for the personalization of ventricular cardiac meshes. Interface 11:20131023 [Google Scholar]
  83. Bishop MJ, Plank G, Burton RA, Schneider JE, Gavaghan DJ. 83.  et al. 2010. Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function. Am. J. Physiol. Heart Circ. Physiol. 298:H699–718 [Google Scholar]
  84. Sermesant M, Forest C, Pennec X, Delingette H, Ayache N. 84.  2003. Deformable biomechanical models: application to 4D cardiac image analysis. Med. Image Anal. 7:475–88 [Google Scholar]
  85. Sermesant M, Delingette H, Ayache N. 85.  2006. An electromechanical model of the heart for image analysis and simulation. IEEE Trans. Med. Imaging 25:612–25 [Google Scholar]
  86. Marchesseau S, Delingette H, Sermesant M, Ayache N. 86.  2013. Fast parameter calibration of a cardiac electromechanical model from medical images based on the unscented transform. Biomech. Model. Mechanobiol. 12:815–31 [Google Scholar]
  87. Zhang Y, Liang X, Ma J, Jing Y, Gonzales MJ. 87.  et al. 2012. An atlas-based geometry pipeline for cardiac Hermite model construction and diffusion tensor reorientation. Med. Image Anal. 16:1130–41 [Google Scholar]
  88. Wang VY, Lam HI, Ennis DB, Cowan BR, Young AA, Nash MP. 88.  2009. Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function. Med. Image Anal. 13:773–84 [Google Scholar]
  89. Krishnamurthy A, Villongco CT, Chuang J, Frank LR, Nigam V. 89.  et al. 2013. Patient-specific models of cardiac biomechanics. J. Comput. Phys. 244:4–21 [Google Scholar]
  90. Xi J, Lamata P, Niederer S, Land S, Shi W. 90.  et al. 2012. The estimation of patient-specific cardiac diastolic functions from clinical measurements. Med. Image Anal. 17:133–46 [Google Scholar]
  91. Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Edward BF. 91.  et al. 2004. Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. Am. J. Physiol. Heart Circ. Physiol. 289:H692–700 [Google Scholar]
  92. Malvern LE. 92.  1969. Introduction to the Mechanics of a Continuous Medium. Upper Saddle River, NJ: Prentice-Hall [Google Scholar]
  93. Tallarida RJ, Rusy BF, Loughnane MH. 93.  1970. Left ventricular wall acceleration and the law of Laplace. Cardiovasc. Res. 4:217–23 [Google Scholar]
  94. Moskowitz SE. 94.  1981. Effects of inertia and viscoelasticity in late rapid filling of the left ventricle. J. Biomech. 14:443–45 [Google Scholar]
  95. Lewkowicz M, Chadwick RS. 95.  1989. The effect of inertia on the mechanics of the left ventricle during the isovolumic phases Presented at Images of the Twenty-First Century: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Seattle, WA [Google Scholar]
  96. Demer LL, Yin FC. 96.  1983. Passive biaxial mechanical properties of isolated canine myocardium. J. Physiol. 339:615–30 [Google Scholar]
  97. Dokos S, Smaill BH, Young AA, LeGrice IJ. 97.  2002. Shear properties of passive ventricular myocardium. Am. J. Physiol. Heart Circ. Physiol. 283:H2650–59 [Google Scholar]
  98. Loeffler L, Sagawa K. 98.  1975. A one-dimensional viscoelastic model of cat heart muscle studied by small length perturbations during isometric contraction. Circ. Res. 36:498–512 [Google Scholar]
  99. Yang M, Taber LA. 99.  1991. The possible role of poroelasticity in the apparent viscoelastic behavior of passive cardiac muscle. J. Biomech. 24:587–97 [Google Scholar]
  100. Huyghe JM, van Campen DH, Arts T, Heethaar RM. 100.  1991. The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation. J. Biomech. 24:841–49 [Google Scholar]
  101. Holzapfel GA, Gasser TC. 101.  2001. A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications. Comput. Methods Appl. Mech. Eng. 190:4379–403 [Google Scholar]
  102. Sermesant M, Moireau P, Camara O, Sainte-Marie J, Andriantsimiavona R. 102.  et al. 2006. Cardiac function estimation from MRI using a heart model and data assimilation: advances and difficulties. Med. Image Anal. 10:642–56 [Google Scholar]
  103. Cansız BC, Dal H, Kaliske M. 103.  2015. An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment. Comput. Methods Biomech. Biomed. Eng. 18:1160–72 [Google Scholar]
  104. Holzapfel GA, Ogden RW. 104.  2009. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos. Trans. A 367:3445–75 [Google Scholar]
  105. Guccione JM, McCulloch AD, Waldman LK. 105.  1991. Passive material properties of intact ventricular myocardium determined from a cylindrical model. J. Biomech. Eng. 113:43–55 [Google Scholar]
  106. Schmid H, Nash MP, Young AA, Hunter PJ. 106.  2006. Myocardial material parameters estimation—a comparative study for simple shear. J. Biomech. Eng. 128:742–51 [Google Scholar]
  107. Göktepe S, Acharya S, Wong J, Kuhl E. 107.  2011. Computational modeling of passive myocardium. Int. J. Numer. Methods Biomed. Eng. 27:1–12 [Google Scholar]
  108. Rausch MK, Dam A, Göktepe S, Abilez OJ, Kuhl E. 108.  2011. Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech. Model. Mechanobiol. 10:799–811 [Google Scholar]
  109. Rossi S, Ruiz-Baier R, Pavarino LF, Quarteroni A. 109.  2012. Orthotropic active strain models for the numerical simulation of cardiac biomechanics. Int. J. Numer. Methods Biomed. Eng. 28:761–88 [Google Scholar]
  110. Eriksson TSE, Prassl AJ, Plank G, Holzapfel GA. 110.  2013. Modeling the dispersion in electromechanically coupled myocardium. Int. J. Numer. Methods Biomed. Eng. 29:1267–84 [Google Scholar]
  111. LeGrice IJ, Pope AJ, Sands GB, Whalley G, Doughty RN, Smaill BH. 111.  2012. Progression of myocardial remodeling and mechanical dysfunction in the spontaneously hypertensive rat. Am. J. Physiol. Heart Circ. Physiol. 303:H1353–65 [Google Scholar]
  112. Niestrawska JA. 112.  2013. A structure-based analysis of cardiac remodelling—a constitutive modelling approach Master's Thesis, RWTH Aachen Univ. of Technol. [Google Scholar]
  113. Messroghli DR, Plein S, Higgins DM, Walters K, Jones TR. 113.  et al. 2006. Human myocardium: single-breath-hold MR T1 mapping with high spatial resolution—reproducibility study. Radiology 238:1004–12 [Google Scholar]
  114. Hill AV. 114.  1938. The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. Ser. B Biol. Sci. 126:136–95 [Google Scholar]
  115. Huxley AF. 115.  1957. Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7:255–318 [Google Scholar]
  116. Smith DA. 116.  1998. A strain-dependent ratchet model for [phosphate]- and [ATP]-dependent muscle contraction. J. Muscle Res. Cell Motil. 19:189–211 [Google Scholar]
  117. Zahalak GI. 117.  1981. A distribution-moment approximation for kinetic theories of muscular contraction. Math. Biosci. 55:89–114 [Google Scholar]
  118. Tözeren A. 118.  1985. Continuum rheology of muscle contraction and its application to cardiac contractility. Biophys. J. 47:303–9 [Google Scholar]
  119. Pinto JG. 119.  1987. A constitutive description of contracting papillary muscle and its implications to the dynamics of the intact heart. J. Biomech. Eng. 109:181 [Google Scholar]
  120. Bergel DA, Hunter PJ. 120.  1979. The mechanics of the heart. Quantitative Cardiovascular Studies: Clinical and Research Applications of Engineering Principles NHC Hwang, DR Gross, DJ Patel 151–213 Baltimore: Univ. Park Press [Google Scholar]
  121. Guccione JM, McCulloch AD. 121.  1993. Mechanics of active contraction in cardiac muscle: Part I—constitutive relations for fiber stress that describe deactivation. J. Biomech. Eng. 115:72–81 [Google Scholar]
  122. Hunter PJ. 122.  1995. Myocardial constitutive laws for continuum mechanics models of the heart. Molecular and Subcellular Cardiology: Effects of Structure and Function S Sideman, R Beyar 303–18 New York: Springer [Google Scholar]
  123. Hunter PJ, McCulloch AD, ter Keurs HEDJ. 123.  1998. Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69:289–331 [Google Scholar]
  124. Nash MP. 124.  1998. Mechanics and material properties of the heart using an anatomically accurate mathematical model PhD Thesis, Univ. Auckl. [Google Scholar]
  125. Niederer SA, Hunter PJ, Smith NP. 125.  2006. A quantitative analysis of cardiac myocyte relaxation: a simulation study. Biophys. J. 90:1697–722 [Google Scholar]
  126. Niederer SA, Plank G, Chinchapatnam P, Ginks M, Lamata P. 126.  et al. 2011. Length-dependent tension in the failing heart and the efficacy of cardiac resynchronization therapy. Cardiovasc. Res. 89:336–43 [Google Scholar]
  127. Bestel J, Clément F, Sorine M. 127.  2001. A biomechanical model of muscle contraction. Medical Image Computing and Computer-Assisted Intervention—MICCAI 2001 WJ Niessen, MA Viergever 1159–61 Lect. Notes Comput. Sci. Vol. 2208 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  128. Chapelle D, Le Tallec P, Moireau P, Sorine M. 128.  2012. Energy-preserving muscle tissue model: formulation and compatible discretizations. Int. J. Multiscale Comput. Eng. 10:189–211 [Google Scholar]
  129. Wong KCL, Wang L, Shi P. 129.  2009. Active model with orthotropic hyperelastic material for cardiac image analysis. Functional Imaging and Modeling of the Heart N Ayache, H Delingette, M Sermesant 229–38 Lect. Notes Comput. Sci. Vol. 5528 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  130. Roriz P, Frazão O, Lobo-Ribeiro AB, Santos JL, Simões JA. 130.  2013. Review of fiber-optic pressure sensors for biomedical and biomechanical applications. J. Biomed. Opt. 18:50903 [Google Scholar]
  131. Rotman OM, Zaretsky U, Shitzer A, Einav S. 131.  2014. Method for high accuracy differential pressure measurements using fluid-filled catheters. Ann. Biomed. Eng. 42:1705–16 [Google Scholar]
  132. Hatle L, Brubakk A, Tromsdal A, Angelsen B. 132.  1978. Noninvasive assessment of pressure drop in mitral stenosis by Doppler ultrasound. Br. Heart J. 40:131–40 [Google Scholar]
  133. Dave JK, Halldorsdottir VG, Eisenbrey JR, Raichlen JS, Liu J-B. 133.  et al. 2012. Noninvasive LV pressure estimation using subharmonic emissions from microbubbles. JACC Cardiovasc. Imaging 5:87–92 [Google Scholar]
  134. Ebbers T, Farnebäck G. 134.  2009. Improving computation of cardiovascular relative pressure fields from velocity MRI. J. Magn. Reson. Imaging 30:54–61 [Google Scholar]
  135. Cao JJ, Wang Y, McLaughlin J, Haag E, Rhee P. 135.  et al. 2011. Left ventricular filling pressure assessment using left atrial transit time by cardiac magnetic resonance imaging. Circ. Cardiovasc. Imaging 4:130–38 [Google Scholar]
  136. Westerhof N, Elzinga G, Sipkema P. 136.  1971. An artificial arterial system for pumping hearts. J. Appl. Physiol. 31:776–81 [Google Scholar]
  137. Stergiopulos N, Westerhof BE, Westerhof N. 137.  1999. Total arterial inertance as the fourth element of the windkessel model. Am. J. Physiol. 276:H81–88 [Google Scholar]
  138. Arts T, Delhaas T, Bovendeerd P, Verbeek X, Prinzen FW. 138.  2005. Adaptation to mechanical load determines shape and properties of heart and circulation: the CircAdapt model. Am. J. Physiol. Heart Circ. Physiol. 288:H1943–54 [Google Scholar]
  139. Kerckhoffs RCP, Neal M, Gu Q, Bassingthwaighte JB, Omens JH, McCulloch AD. 139.  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. 35:1–18 [Google Scholar]
  140. Aguado-Sierra J, Krishnamurthy A, Villongco C, Chuang J, Howard E. 140.  et al. 2011. Patient-specific modeling of dyssynchronous heart failure: a case study. Prog. Biophys. Mol. Biol. 107:147–55 [Google Scholar]
  141. Kuijpers NHL, Hermeling E, Bovendeerd PHM, Delhaas T, Prinzen FW. 141.  2012. Modeling cardiac electromechanics and mechanoelectrical coupling in dyssynchronous and failing hearts. J. Cardiovasc. Transl. Res. 5:159–69 [Google Scholar]
  142. Kerckhoffs RCP, Lumens J, Vernooy K, Omens JH, Mulligan LJ. 142.  et al. 2008. Cardiac resynchronization: insight from experimental and computational models. Prog. Biophys. Mol. Biol. 97:543–61 [Google Scholar]
  143. Moulton MJ, Creswell LL, Downing SW, Actis RL, Szabo BA, Pasque MK. 143.  1996. Myocardial material property determination in the in vivo heart using magnetic resonance imaging. Int. J. Card. Imaging 12:153–67 [Google Scholar]
  144. Omens JH, MacKenna DA, McCulloch AD. 144.  1993. Measurement of strain and analysis of stress in resting rat left ventricular myocardium. J. Biomech. 26:665–76 [Google Scholar]
  145. Okamoto RJ, Moulton MJ, Peterson SJ, Li D, Pasque MK, Guccione JM. 145.  2000. Epicardial suction: a new approach to mechanical testing of the passive ventricular wall. J. Biomech. Eng. 122:479–87 [Google Scholar]
  146. Schmid H, O'Callaghan P, Nash MP, Lin W, LeGrice IJ. 146.  et al. 2008. Myocardial material parameter estimation—a non-homogeneous finite element study from simple shear tests. Biomech. Model. Mechanobiol. 7:161–73 [Google Scholar]
  147. Augenstein KF, Cowan BR, LeGrice IJ, Nielsen PM, Young AA. 147.  2005. Method and apparatus for soft tissue material paramter estimation using tissue tagged magnetic resonance imaging. J. Biomech. Eng. 127:148–57 [Google Scholar]
  148. Wang VY, Lam HI, Ennis DB, Young AA, Nash MP. 148.  2008. Passive ventricular mechanics modelling using MRI of structure and function. Med. Image Comput. Comput. Assist. Interv. 11:Pt. 2814–21 [Google Scholar]
  149. Fleureau J, Garreau M, Donal E, Leclercq C, Hernández A. 149.  2009. A hybrid tissue-level model of the left ventricle: application to the analysis of the regional cardiac function in heart failure. Functional Imaging and Modeling of the Heart N Ayache, H Delingette, M Sermesant 258–67 Lect. Notes Comput. Sci. Vol 5528 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  150. Omens JH, Fung YC. 150.  1990. Residual strain in rat left ventricle. Circ. Res. 66:37–45 [Google Scholar]
  151. Costa KD, May-Newman K, Farr D, O'Dell WG, McCulloch AD, Omens JH. 151.  1997. Three-dimensional residual strain in midanterior canine left ventricle. Am. J. Physiol. Heart Circ. Physiol. 273:H1968–76 [Google Scholar]
  152. Rodriguez EK, Omens JH, Waldman LK, McCulloch AD. 152.  1993. Effect of residual stress on transmural sarcomere length distributions in rat left ventricle. Am. J. Physiol. Heart Circ. Physiol. 264:H1048–56 [Google Scholar]
  153. Xi JH, Lamata P, Shi WZ, Niederer SA, Land S. 153.  et al. 2011. An automatic data assimilation framework for patient-specific myocardial mechanical parameter estimation. Functional Imaging and Modeling of the Heart D Metaxas, L Axel 392–400 Lect. Notes Comput. Sci 6666 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  154. Wang HM, Luo XY, Gao H, Ogden RW, Griffith BE. 154.  et al. 2014. A modified Holzapfel–Ogden law for a residually stressed finite strain model of the human left ventricle in diastole. Biomech. Model. Mechanobiol. 13:99–113 [Google Scholar]
  155. Abraham T, Nishimura R. 155.  2001. Myocardial strain: can we finally measure contractility?. J. Am. Coll. Cardiol. 37:731–34 [Google Scholar]
  156. Claessens T, Rietzschel E, De Buyzere M, De Bacquer D, De Backer G. 156.  et al. 2007. Noninvasive assessment of left ventricular and myocardial contractility in middle-aged men and women: disparate evolution above the age of 50?. Am. J. Physiol. Heart Circ. Physiol. 292:H856–65 [Google Scholar]
  157. Niederer SA, Smith NP. 157.  2009. The role of the Frank–Starling law in the transduction of cellular work to whole organ pump function: a computational modeling analysis. PLOS Comput. Biol. 5:e1000371 [Google Scholar]
  158. Chabiniok R, Moireau P, Lesault P, Rahmouni A, Deux J, Chapelle D. 158.  2011. Trials on tissue contractility estimation from cardiac cine MRI using a biomechanical heart model. Functional Imaging and Modeling of the Heart D Metaxas, L Axel 304–12 Lect. Notes Comput. Sci. Vol. 6666 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  159. Imperiale A, Chabiniok R, Moireau P, Chapelle D. 159.  2011. Constitutive parameter estimation methodology using tagged-MRI data. Functional Imaging and Modeling of the Heart D Metaxas, L Axel 409–17 Lect. Notes Comput. Sci 6666 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  160. Wang VY, Ennis DB, Cowan BR, Young AA, Nash MP. 160.  2012. Myocardial contractility and regional work throughout the cardiac cycle using FEM and MRI. Proceedings of the Second International Conference on Statistical Atlases and Computational Models of the Heart: Imaging and Modelling Challenges O Camara, E Konukoglu, M Pop, K Rhode, M Sermesant, A Young 149–59 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  161. Wang VY, Nash MP, LeGrice IJ, Young AA, Smaill BH, Hunter PJ. 161.  2011. Mathematical Models of Cardiac Structure and Function: Mechanistic Insights from Models of Heart Failure Oxford, UK: Oxford Univ. Press [Google Scholar]
  162. Eriksson T, Plank G, Holzapfel GA. 162.  2011. A coupled model for the left ventricle including regional differences in structure. Proc. Appl. Math. Mech. 11:85–86 [Google Scholar]
  163. Nagler A, Hörman J, Bertoglio C, Wall WA. 163.  2014. Detailed myocardial fibre architecture modeling and its relevance to cardiac electromechanics Presented at 7th World Congress of Biomechanics, Boston [Google Scholar]
  164. Lombaert H, Peyrat J, Croisille P, Rapacchi S, Fanton L. 164.  et al. 2012. Human atlas of the cardiac fiber architecture: study on a healthy population. IEEE Trans. Med. Imaging 31:1436–47 [Google Scholar]
  165. Nielsen PMF, LeGrice IJ, Smaill BH, Hunter PJ. 165.  1991. Mathematical model of geometry and fibrous structure of the heart. Am. J. Physiol. Heart Circ. Physiol. 260:H1365–78 [Google Scholar]
  166. Schaper J, Kostin S, Hein S, Elsässer A, Arnon E, Zimmermann R. 166.  2002. Structural remodelling in heart failure. Exp. Clin. Cardiol. 7:64 [Google Scholar]
  167. Hein S, Arnon E, Kostin S, Schönburg M, Elsässer A. 167.  et al. 2003. Progression from compensated hypertrophy to failure in the pressure-overloaded human heart: structural deterioration and compensatory mechanisms. Circulation 107:984–91 [Google Scholar]
  168. Wang VY, Young AA, Cowan BR, Nash MP. 168.  2013. Changes in in vivo myocardial tissue properties due to heart failure. Functional Imaging and Modeling of the Heart S Ourselin, D Rueckert, N Smith 216–23 Lect. Notes Comput. Sci. Vol. 7945 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  169. Xi J, Shi W, Rueckert D, Razavi R, Smith NP, Lamata P. 169.  2014. Understanding the need of ventricular pressure for the estimation of diastolic biomarkers. Biomech. Model. Mechanobiol. 13:747–57 [Google Scholar]
  170. Axel L, Montillo A, Kim D. 170.  2005. Tagged magnetic resonance imaging of the heart: a survey. Med. Image Anal. 9:376–93 [Google Scholar]
  171. Lobo DN, Stanga Z, Aloysius MM, Wicks C, Nunes QM. 171.  et al. 2010. Effect of volume loading with 1 liter intravenous infusions of 0.9% saline, 4% succinylated gelatine (Gelofusine) and 6% hydroxyethyl starch (Voluven) on blood volume and endocrine responses: a randomized, three-way crossover study in healthy volunteers. Crit. Care Med. 38:464–70 [Google Scholar]
  172. Nordbø Ø, Lamata P, Land S, Niederer S, Aronsen JM. 172.  et al. 2014. A computational pipeline for quantification of mouse myocardial stiffness parameters. Comput. Biol. Med. 53:65–75 [Google Scholar]
  173. Holzapfel GA. 173.  2000. Nonlinear Solid Mechanics: A Continuum Approach for Engineering Hoboken, NJ: Wiley [Google Scholar]
  174. Holzapfel GA, Gasser TC, Ogden RW. 174.  2000. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity Phys. Sci. Solids 61:1–48 [Google Scholar]
  175. Niederer SA, Kerfoot E, Benson AP, Bernabeu MO, Bernus O. 175.  et al. 2011. Verification of cardiac tissue electrophysiology simulators using an N-version benchmark. Philos. Trans. A 369:4331–51 [Google Scholar]
  176. Mariappan YK, Glaser KJ, Ehman RL. 176.  2010. Magnetic resonance elastography: a review. Clin. Anat. 23:497–511 [Google Scholar]
  177. Kolipaka A, McGee KP, Araoz PA, Glaser KJ, Manduca A. 177.  et al. 2009. MR elastography as a method for the assessment of myocardial stiffness: comparison with an established pressure–volume model in a left ventricular model of the heart. Magn. Reson. Med. 62:135–40 [Google Scholar]
  178. Lee P, Bollensdorff C, Quinn TA, Wuskell JP, Loew LM, Kohl P. 178.  2011. Single-sensor system for spatially resolved, continuous, and multiparametric optical mapping of cardiac tissue. Heart Rhythm 8:1482–91 [Google Scholar]
  179. Wenk JF, Klepach D, Lee LC, Zhang Z, Ge L. 179.  et al. 2012. First evidence of depressed contractility in the border zone of a human myocardial infarction. Ann. Thorac. Surg. 93:1188–93 [Google Scholar]
  180. Lee LC, Wenk JF, Klepach D, Zhang Z, Saloner D. 180.  et al. 2011. A novel method for quantifying in-vivo regional left ventricular myocardial contractility in the border zone of a myocardial infarction. J. Biomech. Eng. 133:094506 [Google Scholar]
  181. Tondel K, Indahl U, Gjuvsland A, Omholt S, Martens H. 181.  2012. Multi-way metamodelling facilitates insight into the complex input–output maps of nonlinear dynamic models. BMC Syst. Biol. 6:88 [Google Scholar]
  182. Lee LC, Ge L, Zhang Z, Pease M, Nikolic SD. 182.  et al. 2014. Patient-specific finite element modeling of the Cardiokinetix Parachute® device: effects on left ventricular wall stress and function. Med. Biol. Eng. Comput. 52:557–66 [Google Scholar]
  183. Carrick R, Ge L, Lee LC, Zhang Z, Mishra R. 183.  et al. 2012. Patient-specific finite element-based analysis of ventricular myofiber stress after coapsys: importance of residual stress. Ann. Thorac. Surg. 93:1964–71 [Google Scholar]
  184. Tang D, Yang C, Geva T, del Nido PJ. 184.  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 [Google Scholar]
  185. Streeter DD, Hanna WT. 185.  1973. Engineering mechanics for successive states in canine left ventricular myocardium: I. Cavity and wall geometry. Circ. Res. 33:639–55 [Google Scholar]
  186. Vetter FJ, McCulloch AD. 186.  1998. Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy. Prog. Biophys. Mol. Biol. 69:157–83 [Google Scholar]
  187. Gilbert S, Bernus O, Holden A, Benson A. 187.  2009. A quantitative comparison of the myocardial fibre orientation in the rabbit as determined by histology and by diffusion tensor-MRI. Functional Imaging and Modeling of the Heart N Ayache, H Delingette, M Sermesant 49–57 Lect. Notes Comput. Sci. Vol. 5528 Berlin/Heidelberg: Springer-Verlag [Google Scholar]
  188. Walker JC, Guccione JM, Jiang Y, Zhang P, Wallace AW. 188.  et al. 2005. Helical myofiber orientation after myocardial infarction and left ventricular surgical restoration in sheep. J. Thorac. Cardiovasc. Surg. 129:382–90 [Google Scholar]
  189. Healy L, Jiang Y, Hsu E. 189.  2011. Quantitative comparison of myocardial fiber structure between mice, rabbit, and sheep using diffusion tensor cardiovascular magnetic resonance. J. Cardiovasc. Magn. Reson. 13:74 [Google Scholar]
  190. Hu Z, Metaxas D, Axel L. 190.  2003. In vivo strain and stress estimation of the heart left and right ventricles from MRI images. Med. Image Anal. 7:435–44 [Google Scholar]
  191. Wang VY, Lam HI, Ennis DB, Cowan BR, Young AA, Nash MP. 191.  2010. Cardiac active contraction parameters estimated from magnetic resonance imaging. Statistical Atlases and Computational Models of the Heart O Camara, M Pop, K Rhode, M Sermesant, N Smith, A Young 194–203 Berlin/Heidelberg: Springer-Verlag [Google Scholar]

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