Journal of Elasticity

, Volume 129, Issue 1–2, pp 283–305 | Cite as

Modelling Cardiac Tissue Growth and Remodelling

  • Vicky Y. Wang
  • Jagir R. Hussan
  • Hashem Yousefi
  • Chris P. Bradley
  • Peter J. Hunter
  • Martyn P. Nash
Article

Abstract

Cardiac growth and remodelling are key phenomena influencing the physiological performance of the heart and progression of various cardiac diseases. Our basic knowledge of the characteristics of cardiac growth and remodelling have benefitted from the study of the corresponding changes in tissue structure. Computational modelling is capable of integrating multi-scale biological and physiological information of the heart to better delineate the mechanisms underpinning normal physiological and abnormal pathological cardiac processes. In this article, we summarise recent state-of-the-art modelling studies of cardiac growth and remodelling in health and disease, demonstrate the use of finite element modelling approach in simulating growth of an embryonic linear heart tube and towards understanding the roles of structural remodelling in heart failure.

Keywords

Myocardial constitutive properties Cardiac development Cardiac growth Structural remodelling 

Mathematics Subject Classification (2010)

78M10 

Notes

Acknowledgements

VYW and MPN gratefully acknowledge New Zealand Government funding from the Marsden Fund (grant number 12-UOA-222) administered by the Royal Society of New Zealand and from the Health Research Council of New Zealand (grant number 13-317). JRH, HY, and PJH would also like to acknowledge funding from the MedTech Centre of Research Excellence and a Marsden Grant ‘How does the heart grow?’ funded by the Royal Society of New Zealand.

Conflict of Interest

The authors declare that they have no conflicts of interest.

References

  1. 1.
    Rubin, M., Safadi, M., Jabareen, M.: A unified theoretical structure for modeling interstitial growth and muscle activation in soft tissues. Int. J. Eng. Sci. 90, 1–26 (2015) MathSciNetCrossRefGoogle Scholar
  2. 2.
    Sundgren, N.C., Giraud, G.D., Schultz, J.M., Lasarev, M.R., Stork, P.J., Thornburg, K.L.: Extracellular signal-regulated kinase and phosphoinositol-3 kinase mediate IGF-1 induced proliferation of fetal sheep cardiomyocytes. Am. J. Physiol., Regul. Integr. Comp. Physiol. 285(6), R1481–R1489 (2003) CrossRefGoogle Scholar
  3. 3.
    Sundgren, N., Giraud, G., Stork, P., Maylie, J., Thornburg, K.: Angiotensin II stimulates hyperplasia but not hypertrophy in immature ovine cardiomyocytes. J. Physiol. 548(3), 881–891 (2003) CrossRefGoogle Scholar
  4. 4.
    Paradis, A.N., Gay, M.S., Zhang, L.: Binucleation of cardiomyocytes: the transition from a proliferative to a terminally differentiated state. Drug Discov. Today 19(5), 602–609 (2014). doi:10.1016/j.drudis.2013.10.019 CrossRefGoogle Scholar
  5. 5.
    Taber, L.A.: Biomechanics of growth, remodeling, and morphogenesis. Evolution 490, 6 (1995) Google Scholar
  6. 6.
    Kuhl, E.: Growing matter: a review of growth in living systems. J. Mech. Behav. Biomed. Mater. 29, 529–543 (2014). doi:10.1016/j.jmbbm.2013.10.009 CrossRefGoogle Scholar
  7. 7.
    Ambrosi, D., Mollica, F.: The role of stress in the growth of a multicell spheroid. J. Math. Biol. 48(5), 477–499 (2004) MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Bayly, P., Taber, L., Kroenke, C.: Mechanical forces in cerebral cortical folding: a review of measurements and models. J. Mech. Behav. Biomed. Mater. 29, 568–581 (2014) CrossRefGoogle Scholar
  9. 9.
    De La Cruz, M., Markwald, R.R.: Living Morphogenesis of the Heart. Springer, Berlin (1998) CrossRefGoogle Scholar
  10. 10.
    Männer, J.: Cardiac looping in the chick embryo: a morphological review with special reference to terminological and biomechanical aspects of the looping process. Anat. Rec. 259(3), 248–262 (2000) CrossRefGoogle Scholar
  11. 11.
    Männer, J.: The anatomy of cardiac looping: a step towards the understanding of the morphogenesis of several forms of congenital cardiac malformations. Clin. Anat. 22(1), 21–35 (2009) CrossRefGoogle Scholar
  12. 12.
    Miquerol, L., Kelly, R.G.: Organogenesis of the vertebrate heart. Wiley Interdiscip. Rev.: Dev. Biol. 2(1), 17–29 (2013) CrossRefGoogle Scholar
  13. 13.
    Soufan, A.T., van den Berg, G., Ruijter, J.M., de Boer, P.A., van den Hoff, M.J., Moorman, A.F.: Regionalized sequence of myocardial cell growth and proliferation characterizes early chamber formation. Circ. Res. 99(5), 545–552 (2006) CrossRefGoogle Scholar
  14. 14.
    Srivastava, D., Olson, E.N.: A genetic blueprint for cardiac development. Nature 407(6801), 221–226 (2000) CrossRefGoogle Scholar
  15. 15.
    van den Berg, G., Abu-Issa, R., de Boer, B.A., Hutson, M.R., de Boer, P.A., Soufan, A.T., Ruijter, J.M., Kirby, M.L., van den Hoff, M.J., Moorman, A.F.: A caudal proliferating growth center contributes to both poles of the forming heart tube. Circ. Res. 104(2), 179–188 (2009) CrossRefGoogle Scholar
  16. 16.
    Ramasubramanian, A., Latacha, K.S., Benjamin, J.M., Voronov, D.A., Ravi, A., Taber, L.A.: Computational model for early cardiac looping. Ann. Biomed. Eng. 34(8), 1355–1369 (2006) CrossRefGoogle Scholar
  17. 17.
    Gruber, P.J., Wessels, A., Kubalak, S.W.: Development of the heart and great vessels. In: Pediatric Cardiac Surgery, pp. 1–26. Blackwell Sci. Oxford (2012) Google Scholar
  18. 18.
    Männer, J.: On the form problem of embryonic heart loops, its geometrical solutions, and a new biophysical concept of cardiac looping. Ann. Anat., Anat. Anz. 195(4), 312–323 (2013) CrossRefGoogle Scholar
  19. 19.
    Männer, J., Bayraktar, M.: Cardiac looping may be driven by compressive loads resulting from unequal growth of the heart and pericardial cavity. Observations on a physical simulation model. Front. Physiol. 5, 112 (2014) Google Scholar
  20. 20.
    Sissman, N.J.: Cell multiplication rates during development of the primitive cardiac tube in the chick embryo. Nature 210(5035), 504–507 (1966) ADSCrossRefGoogle Scholar
  21. 21.
    Manasek, F.J., Isobe, Y., Shimada, Y., Hopkins, W.: The embryonic myocardial cytoskeleton, interstitial pressure, and the control of morphogenesis. In: Nora, J., Takao, A. (eds.) Congenital Heart Diseases Causes Process, pp. 359–376. Futura Publishing, Mount Kisco (1984) Google Scholar
  22. 22.
    Baldwin, H.S., Solursh, M.: Degradation of hyaluronic acid does not prevent looping of the mammalian heart in situ. Dev. Biol. 136(2), 555–559 (1989) CrossRefGoogle Scholar
  23. 23.
    Linask, K.K., Han, M.D., Linask, K.L., Schlange, T., Brand, T.: Effects of antisense misexpression of CFC on downstream flectin protein expression during heart looping. Dev. Dyn. 228(2), 217–230 (2003) CrossRefGoogle Scholar
  24. 24.
    Latacha, K.S., Rémond, M.C., Ramasubramanian, A., Chen, A.Y., Elson, E.L., Taber, L.A.: Role of actin polymerization in bending of the early heart tube. Dev. Dyn. 233(4), 1272–1286 (2005) CrossRefGoogle Scholar
  25. 25.
    Manasek, F.J., Burnside, M.B., Waterman, R.E.: Myocardial cell shape change as a mechanism of embryonic heart looping. Dev. Biol. 29(4), 349–371 (1972) CrossRefGoogle Scholar
  26. 26.
    Nolan, G.P.: Cardiac development: transcription and the broken heart. Nature 392(6672), 129–130 (1998) ADSCrossRefGoogle Scholar
  27. 27.
    Bruneau, B.G.: The developmental genetics of congenital heart disease. Nature 451(7181), 943–948 (2008) ADSCrossRefGoogle Scholar
  28. 28.
    Zak, R.: Growth of the Heart in Health and Disease. Raven Press, New York (1984) Google Scholar
  29. 29.
    Li, G., Xiao, Y., Estrella, J.L., Ducsay, C.A., Gilbert, R.D., Zhang, L.: Effect of fetal hypoxia on heart susceptibility to ischemia and reperfusion injury in the adult rat. J. Soc. Gynecol. Investig. 10(5), 265–274 (2003) CrossRefGoogle Scholar
  30. 30.
    Braunwald, E.: Biomarkers in heart failure. N. Engl. J. Med. 358(20), 2148–2159 (2008). doi:10.1056/NEJMra0800239 CrossRefGoogle Scholar
  31. 31.
    Hill, J.A., Olson, E.N.: Cardiac plasticity. N. Engl. J. Med. 358(13), 1370–1380 (2008). doi:10.1056/NEJMra072139 CrossRefGoogle Scholar
  32. 32.
    Kitzman, D.W., Little, W.C., Brubaker, P.H., Anderson, R.T., Hundley, W.G., Marburger, C.T., Brosnihan, B., Morgan, T.M., Stewart, K.P.: Pathophysiological characterization of isolated diastolic heart failure in comparison to systolic heart failure. JAMA J. Am. Med. Assoc. 288(17), 2144–2150 (2002). doi:10.1001/jama.288.17.2144 CrossRefGoogle Scholar
  33. 33.
    van Heerebeek, L., Borbély, A., Niessen, H.W.M., Bronzwaer, J.G.F., van der Velden, J., Stienen, G.J.M., Linke, W.A., Laarman, G.J., Paulus, W.J.: Myocardial structure and function differ in systolic and diastolic heart failure. Circulation 113(16), 1966–1973 (2006). doi:10.1161/circulationaha.105.587519 CrossRefGoogle Scholar
  34. 34.
    Paulus, W.J., Tschöpe, C., Sanderson, J.E., Rusconi, C., Flachskampf, F.A., Rademakers, F.E., Marino, P., Smiseth, O.A., De Keulenaer, G., Leite-Moreira, A.F., Borbély, A., Édes, I., Handoko, M.L., Heymans, S., Pezzali, N., Pieske, B., Dickstein, K., Fraser, A.G., Brutsaert, D.L.: How to diagnose diastolic heart failure: a consensus statement on the diagnosis of heart failure with normal left ventricular ejection fraction by the Heart Failure and Echocardiography Associations of the European Society of Cardiology. Eur. Heart J. 28(20), 2539–2550 (2007). doi:10.1093/eurheartj/ehm037 CrossRefGoogle Scholar
  35. 35.
    LeGrice, I.J., Pope, A.J., Sands, G.B., Whalley, G., Doughty, R.N., Smaill, B.H.: Progression of myocardial remodeling and mechanical dysfunction in the spontaneously hypertensive rat. Am. J. Physiol., Heart Circ. Physiol. 303(11), 65 (2012). doi:10.1152/ajpheart.00748.2011 CrossRefGoogle Scholar
  36. 36.
    Tanaka, M., Fujiwara, H., Onodera, T., Wu, D.J.: Quantitative analysis of myocardial fibrosis in normals, hypertensive hearts, and hypertrophic cardiomyopathy. Br. Heart. J. 55(6), 575–581 (1986) CrossRefGoogle Scholar
  37. 37.
    Shirwany, A., Weber, K.T.: Extracellular matrix remodeling in hypertensive heart disease. J. Am. Coll. Cardiol. 48(1), 97–98 (2006). doi:10.1016/j.jacc.2006.04.004 CrossRefGoogle Scholar
  38. 38.
    Leonard, B.L., Smaill, B.H., LeGrice, I.J.: Structural remodeling and mechanical function in heart failure. Microsc. Microanal. 18(01), 50–67 (2012). doi:10.1017/S1431927611012438 ADSCrossRefGoogle Scholar
  39. 39.
    Zile, M.R., Baicu, C.F., Gaasch, W.H.: Diastolic heart failure—abnormalities in active relaxation and passive stiffness of the left ventricle. N. Engl. J. Med. 350(19), 1953–1959 (2004). doi:10.1056/NEJMoa032566 CrossRefGoogle Scholar
  40. 40.
    Opie, L.H., Commerford, P.J., Gersh, B.J., Pfeffer, M.A.: Controversies in ventricular remodelling. Lancet 367, 9507 (2016), 356–367. doi:10.1016/S0140-6736(06)68074-4 Google Scholar
  41. 41.
    Grossman, W., Jones, D., McLaurin, L.: Wall stress and patterns of hypertrophy in the human left ventricle. J. Clin. Invest. 56(1), 56 (1975) CrossRefGoogle Scholar
  42. 42.
    Marijianowski, M.M.H., Teeling, P., Mann, J., Becker, A.E.: Dilated cardiomyopathy is associated with an increase in the type I/type III collagen ratio: a quantitative assessment. J. Am. Coll. Cardiol. 25(6), 1263–1272 (1995). doi:10.1016/0735-1097(94)00557-7 CrossRefGoogle Scholar
  43. 43.
    Ryan, T.D., Rothstein, E.C., Aban, I., Tallaj, J.A., Husain, A., Lucchesi, P.A., Dell’Italia, L.J.: Left ventricular eccentric remodeling and matrix loss are mediated by bradykinin and precede cardiomyocyte elongation in rats with volume overload. J. Am. Coll. Cardiol. 49(7), 811–821 (2007). doi:10.1016/j.jacc.2006.06.083 CrossRefGoogle Scholar
  44. 44.
    Mann, D.L., Bogaev, R., Buckberg, G.D.: Cardiac remodelling and myocardial recovery: lost in translation? Eur. J. Heart Fail. 12(8), 789–796 (2010). doi:10.1093/eurjhf/hfq113 CrossRefGoogle Scholar
  45. 45.
    Teeters, J.C., Alexis, J.D.: Systolic heart failure. In: Manual of Heart Failure Management, pp. 1–9. Springer, London (2009) Google Scholar
  46. 46.
    Diamond, J.A., Phillips, R.A.: Hypertensive heart disease. Hypertens. Res. 28(3), 191–202 (2005) CrossRefGoogle Scholar
  47. 47.
    Hershberger, R.E., Hedges, D.J., Morales, A.: Dilated cardiomyopathy: the complexity of a diverse genetic architecture. Nat. Rev. Cardiol. 10(9), 531–547 (2013). doi:10.1038/nrcardio.2013.105 CrossRefGoogle Scholar
  48. 48.
    Savoye, C., Equine, O., Tricot, O., Nugue, O., Segrestin, B., Sautière, K., Elkohen, M., Pretorian, E.M., Taghipour, K., Philias, A., Aumégeat, V., Decoulx, E., Ennezat, P.V., Bauters, C.: Left ventricular remodeling after anterior wall acute myocardial infarction in modern clinical practice (from the REmodelage VEntriculaire [REVE] study group). Am. J. Cardiol. 98(9), 1144–1149 (2006). doi:10.1016/j.amjcard.2006.06.011 CrossRefGoogle Scholar
  49. 49.
    Russell, B., Curtis, M.W., Koshman, Y.E.: Mechanical stress-induced sarcomere assembly for cardiac muscle growth in length and width. J. Mol. Cell. Cardiol. 48(5), 817–823 (2010). doi:10.1016/j.yjmcc.2010.02.016 CrossRefGoogle Scholar
  50. 50.
    Ruwhof, C., van der Laarse, A.: Mechanical stress-induced cardiac hypertrophy: mechanisms and signal transduction pathways. Cardiovasc. Res. 47(1), 23–37 (2000). doi:10.1016/s0008-6363(00)00076-6 CrossRefGoogle Scholar
  51. 51.
    Nash, M.P., Hunter, P.J.: Computational mechanics of the heart—from tissue structure to ventricular function. J. Elast. 61(1), 113–141 (2000). doi:10.1023/a:1011084330767 MathSciNetCrossRefMATHGoogle Scholar
  52. 52.
    LeGrice, I.J., Smaill, B.H., Chai, L.Z., Edgar, S.G., Gavin, J.B., Hunter, P.J.: Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol., Heart Circ. Physiol. 269(2), H571–H582 (1995) Google Scholar
  53. 53.
    Menzel, A., Kuhl, E.: Frontiers in growth and remodeling. Mech. Res. Commun. 42, 1–14 (2012). doi:10.1016/j.mechrescom.2012.02.007 CrossRefGoogle Scholar
  54. 54.
    Wyczalkowski, M.A., Varner, V.D., Taber, L.A.: Computational and experimental study of the mechanics of embryonic wound healing. J. Mech. Behav. Biomed. Mater. 28, 125–146 (2013) CrossRefGoogle Scholar
  55. 55.
    Shi, Y., Yao, J., Young, J.M., Fee, J.A., Perucchio, R., Taber, L.A.: Bending and twisting the embryonic heart: a computational model for C-looping based on realistic geometry. Front. Physiol. 5, 297 (2014) CrossRefGoogle Scholar
  56. 56.
    Lin, I.E., Taber, L.A.: A model for stress-induced growth in the developing heart. J. Biomech. Eng. 117(3), 343–349 (1995). doi:10.1115/1.2794190 CrossRefGoogle Scholar
  57. 57.
    Bradley, C., Bowery, A., Britten, R., Budelmann, V., Camara, O., Christie, R., Cookson, A., Frangi, A.F., Gamage, T.B., Heidlauf, T., Krittian, S., Ladd, D., Little, C., Mithraratne, K., Nash, M., Nickerson, D., Nielsen, P., Nordbø, Ø., Omholt, S., Pashaei, A., Paterson, D., Rajagopal, V., Reeve, A., Röhrle, O., Safaei, S., Sebastián, R., Steghöfer, M., Wu, T., Yu, T., Zhang, H., Hunter, P.: OpenCMISS: a multi-physics & multi-scale computational infrastructure for the VPH/Physiome project. Prog. Biophys. Mol. Biol. 107(1), 32–47 (2011). doi:10.1016/j.pbiomolbio.2011.06.015 CrossRefGoogle Scholar
  58. 58.
    Conrad, C.H., Brooks, W.W., Hayes, J.A., Sen, S., Robinson, K.G., Bing, O.H.: Myocardial fibrosis and stiffness with hypertrophy and heart failure in the spontaneously hypertensive rat. Circulation 91(1), 161–170 (1995) CrossRefGoogle Scholar
  59. 59.
    Reinhardt, D., Sigusch, H.H., Henße, J., Tyagi, S.C., Körfer, R., Figulla, H.R.: Cardiac remodelling in end stage heart failure: upregulation of matrix metalloproteinase (MMP) irrespective of the underlying disease, and evidence for a direct inhibitory effect of ACE inhibitors on MMP. Heart 88(5), 525–530 (2002). doi:10.1136/heart.88.5.525 CrossRefGoogle Scholar
  60. 60.
    Cohn, J.N., Ferrari, R., Sharpe, N.: Cardiac remodeling—concepts and clinical implications: a consensus paper from an international forum on cardiac remodeling. J. Am. Coll. Cardiol. 35(3), 569–582 (2000). doi:10.1016/S0735-1097(99)00630-0 CrossRefGoogle Scholar
  61. 61.
    Iles, L., Pfluger, H., Phrommintikul, A., Cherayath, J., Aksit, P., Gupta, S.N., Kaye, D.M., Taylor, A.J.: Evaluation of diffuse myocardial fibrosis in heart failure with cardiac magnetic resonance contrast-enhanced T1 mapping. J. Am. Coll. Cardiol. 52(19), 1574–1580 (2008). doi:10.1016/j.jacc.2008.06.049 CrossRefGoogle Scholar
  62. 62.
    Liu, C.-Y., Liu, Y.-C., Wu, C., Armstrong, A., Volpe, G.J., van der Geest, R.J., Liu, Y., Hundley, W.G., Gomes, A.S., Liu, S., Nacif, M., Bluemke, D.A., Lima, J.A.C.: Evaluation of age-related interstitial myocardial fibrosis with cardiac magnetic resonance contrast-enhanced T1 mapping MESA (Multi-Ethnic Study of Atherosclerosis). J. Am. Coll. Cardiol. 62(14), 1280–1287 (2013). doi:10.1016/j.jacc.2013.05.078 CrossRefGoogle Scholar
  63. 63.
    Fomovsky, G.M., Thomopoulos, S., Holmes, J.W.: Contribution of extracellular matrix to the mechanical properties of the heart. J. Mol. Cell. Cardiol. 48(3), 490–496 (2010). doi:10.1016/j.yjmcc.2009.08.003 CrossRefGoogle Scholar
  64. 64.
    Donekal, S., Venkatesh, B.A., Liu, Y.C., Liu, C.-Y., Yoneyama, K., Wu, C.O., Nacif, M., Gomes, A.S., Hundley, W.G., Bluemke, D.A.: Interstitial fibrosis, left ventricular remodeling and myocardial mechanical behavior in a population-based multi-ethnic cohort: MESA Study. CI, Cardiovasc. Imaging CIRCIMAGING. 113.001073 (2014) Google Scholar
  65. 65.
    Guccione, J.M., McCulloch, A.D., Waldman, L.: Passive material properties of intact ventricular myocardium determined from a cylindrical model. J. Biomech. Eng. 113(1), 42–55 (1991) CrossRefGoogle Scholar
  66. 66.
    Costa, K.D., Takayama, Y., McCulloch, A.D., Covell, J.W.: Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. Am. J. Physiol., Heart Circ. Physiol. 276(2), H595–H607 (1999) Google Scholar
  67. 67.
    Dokos, S., Smaill, B.H., Young, A.A., LeGrice, I.J.: Shear properties of passive ventricular myocardium. Am. J. Physiol., Heart Circ. Physiol. 283(6), H2650–H2659 (2002) CrossRefGoogle Scholar
  68. 68.
    Sommer, G., Schriefl, A.J., Andrä, M., Sacherer, M., Viertler, C., Wolinski, H., Holzapfel, G.A.: Biomechanical properties and microstructure of human ventricular myocardium. Acta Biomater. 24, 172–192 (2015) CrossRefGoogle Scholar
  69. 69.
    Cansız, B.F., Dal, H., Kaliske, M.: An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment. Comput. Methods Biomech. Biomed. Eng. 18(11), 1160–1172 (2014). doi:10.1080/10255842.2014.881475 CrossRefGoogle Scholar
  70. 70.
    Gültekin, O., Sommer, G., Holzapfel, G.A.: An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment. Comput. Methods Biomech. Biomed. Eng. 19(15), 1647–1664 (2016). doi:10.1080/10255842.2016.1176155 CrossRefGoogle Scholar
  71. 71.
    Holzapfel, G.A., Gasser, T.C., Ogden, R.W.: A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. 61(1), 1–48 (2000). doi:10.1023/a:1010835316564 MathSciNetCrossRefMATHGoogle Scholar
  72. 72.
    Holzapfel, G.A., Niestrawska, J.A., Ogden, R.W., Reinisch, A.J., Schriefl, A.J.: Modelling non-symmetric collagen fibre dispersion in arterial walls. J. Roy. Soc. Interface 12 20150188 (2015). doi:10.1098/rsif.2015.0188 CrossRefGoogle Scholar
  73. 73.
    Holzapfel, G.A., Ogden, R.W.: Constitutive modelling of arteries. Proc. R. Soc. A, Math. Phys. Eng. Sci. 466(2118), 1551–1597 (2010). doi:10.1098/rspa.2010.0058 ADSMathSciNetCrossRefMATHGoogle Scholar
  74. 74.
    Ogden, R.W.: Anisotropy and nonlinear elasticity in arterial wall mechanics. In: Holzapfel, G.A., Ogden, R.W. (eds.) Biomechanical Modelling at the Molecular, Cellular and Tissue Levels, pp. 179–258. Springer, Vienna (2009) CrossRefGoogle Scholar
  75. 75.
    Eriksson, T.S., Prassl, A.J., Plank, G., Holzapfel, G.A.: Modeling the dispersion in electromechanically coupled myocardium. Int. J. Numer. Methods Biomed. Eng. 29(11), 1267–1284 (2013) MathSciNetCrossRefGoogle Scholar
  76. 76.
    Wang, V.Y., Nielsen, P.M.F., Nash, M.P.: Image-based predictive modeling of heart mechanics. Annu. Rev. Biomed. Eng. 17(1), 351–383 (2015). doi:10.1146/annurev-bioeng-071114-040609 CrossRefGoogle Scholar
  77. 77.
    Lanir, Y.: Constitutive equations for fibrous connective tissues. J. Biomech. 16(1), 1–12 (1983). doi:10.1016/0021-9290(83)90041-6 CrossRefGoogle Scholar
  78. 78.
    Nevo, E., Lanir, Y.: Structural finite deformation model of the left ventricle during diastole and systole. J. Biomech. Eng. 111(4), 342–349 (1989). doi:10.1115/1.3168389 CrossRefGoogle Scholar
  79. 79.
    Sacks, M.S.: Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J. Biomech. Eng. 125(2), 280–287 (2003). doi:10.1115/1.1544508 CrossRefGoogle Scholar
  80. 80.
    Holzapfel, G.A., Ogden, R.W.: Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos. Trans. R. Soc. Lond. A, Math. Phys. Eng. Sci. 367(1902), 3445–3475 (2009) ADSMathSciNetCrossRefMATHGoogle Scholar
  81. 81.
    Avazmohammadi, R., Hill, M.R., Simon, M.A., Zhang, W., Sacks, M.S.: A novel constitutive model for passive right ventricular myocardium: evidence for myofiber–collagen fiber mechanical coupling. Biomech. Model. Mechanobiol. 16(2), 561–581 (2016). doi:10.1007/s10237-016-0837-7 CrossRefGoogle Scholar
  82. 82.
    Karlon, W.J., McCulloch, A.D., Covell, J.W.: Regional dysfunction correlates with myofiber disarray in transgenic mice with ventricular expression ofras. regional dysfunction correlates with myofiber disarray in transgenic mice with ventricular expression of ras. Am. J. Physiol., Heart Circ. Physiol. 278(3), H898–H906 (2000) Google Scholar
  83. 83.
    Wang, V.Y., Wilson, A.J., Sands, G.B., Young, A.A., LeGrice, I.J., Nash, M.P.: Microstructural remodelling and mechanics of hypertensive heart disease. In: van Assen, H., Bovendeerd, P., Delhaas, T. (eds.) Proceedings of the 8th International Conference on Functional Imaging and Modeling of the Heart, FIMH 2015, Maastricht, The Netherlands. June 25–27, 2015 pp. 382–389. Springer, Cham (2015) CrossRefGoogle Scholar
  84. 84.
    Wang, V.Y., Niestrawska, J.A., Wilson, A.J., Sands, G.B., Young, A.A., LeGrice, I.J., Nash, M.P.: Image-driven constitutive modelling of myocardial fibrosis. Int. J. Comput. Methods Eng. Sci. Mech. (2016). doi:10.1080/15502287.2015.1082675 Google Scholar
  85. 85.
    Rodriguez, E.K., Hoger, A., McCulloch, A.D.: Stress-dependent finite growth in soft elastic tissues. J. Biomech. 27(4), 455–467 (1994) CrossRefGoogle Scholar
  86. 86.
    Skalak, R.: Growth as a finite displacement field. In: Proceedings of the IUTAM Symposium on Finite Elasticity, pp. 347–355. Springer, Berlin (1981) CrossRefGoogle Scholar
  87. 87.
    Göktepe, S., Abilez, O., Parker, K., Kuhl, E.: A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis. J. Theor. Biol. 265(3), 433–442 (2010). doi:10.1016/j.jtbi.2010.04.023 CrossRefGoogle Scholar
  88. 88.
    Lee, L., Genet, M., Acevedo-Bolton, G., Ordovas, K., Guccione, J.M., Kuhl, E.: A computational model that predicts reverse growth in response to mechanical unloading. Biomech. Model. Mechanobiol. 14(2), 217–229 (2015) CrossRefGoogle Scholar
  89. 89.
    Lee, L.C., Sundnes, J., Genet, M., Wenk, J.F.: An integrated electromechanical-growth heart model for simulating cardiac therapies. Biomech. Model. Mechanobiol. 15(4), 791–803 (2016) CrossRefGoogle Scholar
  90. 90.
    Klepach, D., Lee, L.C., Wenk, J.F., Ratcliffe, M.B., Zohdi, T.I., Navia, J.L., Kassab, G.S., Kuhl, E., Guccione, J.M.: Growth and remodeling of the left ventricle: a case study of myocardial infarction and surgical ventricular restoration. Mech. Res. Commun. 42, 134–141 (2012). doi:10.1016/j.mechrescom.2012.03.005 CrossRefGoogle Scholar
  91. 91.
    Kerckhoffs, R.C.P., Omens, J.H., McCulloch, A.D.: A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload. Mech. Res. (2012). doi:10.1016/j.mechrescom.2011.11.004 Google Scholar
  92. 92.
    Kroon, W., Delhaas, T., Arts, T., Bovendeerd, P.: Constitutive Modeling of Cardiac Tissue Growth. Constitutive Modeling of Cardiac Tissue Growth. Springer, Berlin (2007) Google Scholar
  93. 93.
    Lanir, Y.: Mechanistic micro-structural theory of soft tissues growth and remodeling: tissues with unidirectional fibers. Biomech. Model. Mechanobiol. (2015). doi:10.1007/s10237-014-0600-x Google Scholar
  94. 94.
    Tsamis, A., Cheng, A., Nguyen, T.C., Langer, F., Miller, C.D., Kuhl, E.: Kinematics of cardiac growth: in vivo characterization of growth tensors and strains. J. Mech. Behav. Biomed. Mater. 8, 165–177 (2012). doi:10.1016/j.jmbbm.2011.12.006 CrossRefGoogle Scholar
  95. 95.
    Walker, J.C., Ratcliffe, M.B., Zhang, P., Wallace, A.W., Fata, B., Hsu, E.W., Saloner, D., Guccione, J.M.: MRI-based finite-element analysis of left ventricular aneurysm. Am. J. Physiol., Heart Circ. Physiol. 289(2), H692–H700 (2005). doi:10.1152/ajpheart.01226.2004 CrossRefGoogle Scholar
  96. 96.
    Walker, J.C., Ratcliffe, M.B., Zhang, P., Wallace, A.W., Hsu, E.W., Saloner, D.A., Guccione, J.M.: Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. J. Thorac. Cardiovasc. Surg. 135(5), 1102.e1-2 (2008). doi:10.1016/j.jtcvs.2007.11.038 CrossRefGoogle Scholar
  97. 97.
    Wenk, J.F., Eslami, P., Zhang, Z., Xu, C., Kuhl, E.: A novel method for quantifying the in-vivo mechanical effect of material injected into a myocardial infarction. Ann. Thorac. Surg. (2011). doi:10.1016/j.athoracsur.2011.04.089 Google Scholar
  98. 98.
    Wall, S.T., Walker, J.C., Healy, K.E., Ratcliffe, M.B.: Theoretical impact of the injection of material into the myocardium a finite element model simulation. Circulation (2006). doi:10.1161/CIRCULATIONAHA.106.657270 Google Scholar
  99. 99.
    Wenk, J.F., Wall, S.T., Peterson, R.C., Helgerson, S.L., Sabbah, H.N., Burger, M., Stander, N., Ratcliffe, M.B., Guccione, J.M.: A method for automatically optimizing medical devices for treating heart failure: designing polymeric injection patterns. J. Biomech. Eng. 131(12), 121011 (2009). doi:10.1115/1.4000165 CrossRefGoogle Scholar
  100. 100.
    Boukellal, H., Campás, O., Joanny, J.-F., Prost, J., Sykes, C.: Soft listeria: actin-based propulsion of liquid drops. Phys. Rev. E 69(6), 061906 (2004) ADSCrossRefGoogle Scholar
  101. 101.
    Lucio, A.A., Ingber, D.E., Campàs, O.: Generation of biocompatible droplets for in vivo and in vitro measurement of cell-generated mechanical stresses. Methods Cell Biol. 125, 373–390 (2015) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Vicky Y. Wang
    • 1
  • Jagir R. Hussan
    • 1
  • Hashem Yousefi
    • 1
  • Chris P. Bradley
    • 1
  • Peter J. Hunter
    • 1
  • Martyn P. Nash
    • 1
    • 2
  1. 1.Auckland Bioengineering InstituteUniversity of AucklandAucklandNew Zealand
  2. 2.Department of Engineering ScienceUniversity of AucklandAucklandNew Zealand

Personalised recommendations