An orthotropic active-strain model for the myocardium mechanics and its numerical approximation

European Journal of Mechanics, A/Solids

Volumn 48, Issue 1, 2014, Pages 83-96

  Pezzuto, S ^a,c   Ambrosi, D ^a   Quarteroni, A ^b  

^a POLITECNICO DI MILANO   (Italy)

^b EPFL   (Switzerland)

^c SIMULA RESEARCH LABORATORY   (Norway)

Author keywords

Active strain; Cardiac mechanics; Numerical simulation

Indexed keywords

BENCHMARKING; COMPUTER SIMULATION; HEART; MECHANICS; STRAIN ENERGY; TENSORS;

CARDIAC MECHANICS; DEFORMATION GRADIENTS; FINITE ELEMENT SPACE; HYPERELASTIC MATERIALS; MATHEMATICAL PROPERTIES; MULTIPLICATIVE DECOMPOSITION; NUMERICAL APPROXIMATIONS; STRUCTURAL MECHANICS;

LAGRANGE MULTIPLIERS;

EID: 85027920270     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2014.03.006     Document Type: Article

References (31)

1. Aguado-Sierra, J., Krishnamurthy, A., Villongco, C., Chuang, J., Howard, E., Gonzales, M.J., Omens, J., Krummen, D.E., Narayan, S., Kerckhoffs, R.C., et al., 2011. Patient-specific modeling of dyssynchronous heart failure: a case study. Prog. Biophys. Mol. Biol. 107 (1), 147-155.
2. Alford, P.W., Feinberg, A.W., Sheehy, S.P., Parker, K.K., 2010. Biohybrid thin films for measuring contractility in engineered cardiovascular muscle. Biomaterials 31 (13), 3613-3621.
3. Ambrosi, D., Pezzuto, S., 2012. Active stress vs. active strain in mechanobiology: constitutive issues. J. Elast. 107 (2), 199-212.
4. Antman, S.S., 2005. Nonlinear Problems of Elasticity, vol. 107. Springer.
5. Baker, M., Ericksen, J., 1954. Inequalities restricting the form of the stress-deformation relations for isotropic elastic solids and Reiner-Rivlin fluids. J. Wash. Acad. Sci. 44, 33-35.
6. Böl, M., Reese, S., Parker, K.K., Kuhl, E., 2009. Computational modeling of muscular thin films for cardiac repair. Comput. Mech. 43 (4), 535-544.
7. Boyett, M., Frampton, J., Kirby, M., 1991. The length, width and volume of isolated rat and ferret ventricular myocytes during twitch contractions and changes in osmotic strength. Exp. Physiol. 76 (2), 259-270.
8. Destrade, M., Murphy, J.G., Saccomandi, G., 2012. Simple shear is not so simple. Int. J. Non-Linear Mech. 47 (2), 210-214.
9. Feinberg, A.W., Feigel, A., Shevkoplyas, S.S., Sheehy, S., Whitesides, G.M., Parker, K.K., 2007. Muscular thin films for building actuators and powering devices. Science 317 (5843), 1366-1370.
10. Geuzaine, C., Remacle, J.-F., 2009. Gmsh: a 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int. J. Numer. Methods Eng. 79 (11), 1309-1331.
11. Göktepe, S., Acharya, S., Wong, J., Kuhl, E., 2011. Computational modeling of passive myocardium. Int. J. Numer. Methods Biomed. Eng. 27 (1), 1-12.
12. Holzapfel, G.A., Ogden, R.W., 2009. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 367 (1902), 3445-3475.
13. Hughes, T.J., Marsden, J.E., 1994. Mathematical Foundations of Elasticity. Dover Publications.
14. Iribe, G., Helmes, M., Kohl, P., 2007. Force-length relations in isolated intact cardiomyocytes subjected to dynamic changes in mechanical load. Am. J. Physiol. Heart Circ. Physiol. 292 (3), H1487-H1497.
15. LeGrice, I., Hunter, P., Young, A., Smaill, B., 2001. The architecture of the heart: a data-based model. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 359 (1783), 1217-1232.
16. Liu, I.-S., 1982. On representations of anisotropic invariants. Int. J. Eng. Sci. 20 (10), 1099-1109.
17. Logg, A., Mardal, K.-A.,Wells, G., 2012. Automated Solution of Differential Equations by the Finite Element Method: the Fenics Book, vol. 84. Springer.
18. Merodio, J., Ogden, R., 2006. The influence of the invariant I8 on the stresse deformation and ellipticity characteristics of doubly fiber-reinforced non-linearly elastic solids. Int. J. Non-Linear Mech. 41 (4), 556-563.
19. Nobile, F., Quarteroni, A., Ruiz-Baier, R., 2012. An active strain electromechanical model for cardiac tissue. Int. J. Numer. Methods Biomed. Eng. 28 (1), 52-71.
20. Quarteroni, A., 2014. Numerical Models for Differential Problems, second ed. Springer.
21. Rossi, S., Ruiz-Baier, R., Pavarino, L.F., Quarteroni, A., 2012. Orthotropic active strain models for the numerical simulation of cardiac biomechanics. Int. J. Numer. Methods Biomed. Eng. 28 (6-7), 761-788.
22. Schröder, J., Neff, P., 2003. Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions. Int. J. Solids Struct. 40 (2), 401-445.
23. Shariff, M., 2013. Nonlinear orthotropic elasticity: only six invariants are independent. J. Elast. 110 (2), 237-241.
24. Shim, J., Grosberg, A., Nawroth, J.C., Kit Parker, K., Bertoldi, K., 2012. Modeling of cardiac muscle thin films: pre-stretch, passive and active behavior. J. Biomech. 45 (5), 832-841.
25. Simo, J.C., Taylor, R.L., 1991. Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Comput. Methods Appl. Mech. Eng. 85 (3), 273-310.
26. Usyk, T., Mazhari, R., McCulloch, A., 2000. Effect of laminar orthotropic myofiber architecture on regional stress and strain in the canine left ventricle. J. Elast. Phys. Sci. Solids 61 (1-3), 143-164.
27. Wakatsuki, T., Kolodney, M.S., Zahalak, G.I., Elson, E.L., 2000. Cell mechanics studied by a reconstituted model tissue. Biophys. J. 79 (5), 2353-2368.
28. Wang, H., Luo, X., Gao, H., Ogden, R., Griffith, B., Berry, C., Wang, T., 2013a. A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole. Biomech. Model. Mechanobiol., 1-15.
29. Wang, H., Gao, H., Luo, X., Berry, C., Griffith, B., Ogden, R.,Wang, T., 2013b. Structure-based finite strain modelling of the human left ventricle in diastole. Int. J. Numer. Methods Biomed. Eng. 29 (1), 83-103.
30. Weiwad, W.K., Linke, W.A., Wussling, M.H., 2000. Sarcomere lengthetension relationship of rat cardiac myocytes at lengths greater than optimum. J. Mol. Cell. Cardiol. 32 (2), 247-259.
31. Yin, F., Chan, C., Judd, R.M., 1996. Compressibility of perfused passive myocardium. Am. J. Physiol. Heart Circ. Physiol. 271 (5), H1864-H1870.