Constitutive modelling of passive myocardium: A structurally based framework for material characterization

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 367, Issue 1902, 2009, Pages 3445-3475

  Holzapfel, Gerhard A ^a,b   Ogden, Ray W ^c  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Constitutive modelling; Muscle fibres; Myocardium; Myocyte sheet structure; Orthotropy

Indexed keywords

BIAXIAL TESTS; CONSTITUTIVE MODELLING; EXPERIMENTAL DATA; INCOMPRESSIBLE MATERIAL; LEFT VENTRICULAR MYOCARDIUMS; MATERIAL CHARACTERIZATIONS; MATERIAL RESPONSE; MECHANICAL RESPONSE; MYOCARDIUM; MYOCYTE SHEET STRUCTURE; NON-HOMOGENEOUS; ORTHOGONAL DIRECTIONS; ORTHOTROPIC MATERIALS; ORTHOTROPY; SHEET STRUCTURE; SIMPLE SHEAR; THEORETICAL FRAMEWORK;

MUSCLE;

ANIMAL; BIOLOGICAL MODEL; BIOMECHANICS; CYTOLOGY; HEART; HEART CONTRACTION; HEART MUSCLE CELL; HEART VENTRICLE; HEART VENTRICLE FUNCTION; HISTOLOGY; HUMAN; PHYSIOLOGY; REVIEW;

ANIMALS; BIOMECHANICS; HEART; HEART VENTRICLES; HUMANS; MODELS, CARDIOVASCULAR; MYOCARDIAL CONTRACTION; MYOCYTES, CARDIAC; VENTRICULAR FUNCTION;

EID: 69649106670     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0091     Document Type: Article

References (49)

1. Bischoff, J. E., Arruda, E. M. & Grosh, K. 2002 A microstructurally based orthotropic hyperelastic constitutive law. J. Appl. Mech. 69, 570-579. (doi:10.1115/l.1485754)
2. Costa, K. D., Hunter, P. J., Wayne, J. S., Waldman, L. K., Guccione, J. M. & McCulloch, A. D. 1996 A three-dimensional finite element method for large elastic deformations of ventricular myocardium. II. Prolate spheroidal coordinates. J. Biomech. Eng. 118, 464-472. (doi:10.1115/1.2796032)
3. Costa, K. D., May-Newman, K., Farr, D., O'Dell, W. G., McCulloch, A. D. & Omens, J. H. 1997 Three-dimensional residual strain in midanterior canine left ventricle. Am. J. Physiol. Heart Circ. Physiol. 273, H1968-H1976. (Pubitemid 127751848) (Pubitemid 127819740)
4. Costa, K. D., Holmes, J. W. & McCulloch, A. D. 2001 Modeling cardiac mechanical properties in three dimensions. Phil. Trans. R. Soc. Lond. A 359, 1233-1250. (doi:10.1098/rsta.2001.0828)
5. Demer, L. L. & Yin, F. C. P. 1983 Passive biaxial mechanical properties of isolated canine myocardium. J. Physiol. Lond. 339, 615-630.
6. Demiray, H. 1972 A note on the elasticity of soft biological tissues. J. Biomech. 5, 309-311. (doi:10.1016/0021-9290(72)90047-4)
7. Demiray, H. 1976 Stresses in ventricular wall. J. Appl. Mech. 98, 194-197.
8. Dokos, S., Smaill, B. H., Young, A. A. & LeGrice, I. J. 2002 Shear properties of passive ventricular myocardium. Am. J. Physiol. Heart Circ. Physiol. 283, H2650-H2659. (doi:10.1152/ ajpheart.00111.2002) (Pubitemid 35345975)
9. Frank, J. S. & Langer, G. A. 1974 The myocardial interstitium: its structure and its role in ionic exchange. J. Cell Biol. 60, 586-601. (doi:10.1083/jcb.60.3.586)
10. Fung, Y. C. 1993 Biomechanics: mechanical properties of living tissues, 2nd edn. New York, NY: Springer.
11. Gilbert, S. H., Benson, A. P., Li, P. & Holden, A. V. 2007 Regional localisation of left ventricular sheet structure: integration with current models of cardiac fibre, sheet and band structure. Eur. J. Cardiothorac. Surg. 32, 231-249. (doi:10.1016/j.ejcts.2007.03.032) (Pubitemid 47033889)
12. Guccione, J. M., McCulloch, A. D. & Waldman, L. K. 1991 Passive material properties of intact ventricular myocardium determined from a cylindrical model. J. Biomech. Eng. 113, 42-55. (doi:10.1115/1.2894084)
13. Holzapfel, G. A. 2000 Nonlinear solid mechanics: a continuum approach for engineering. Chichester, UK: Wiley.
14. Holzapfel, G. A. & Ogden, R. W. 2003 Biomechanics of soft tissue in cardiovascular systems. CISM Courses and Lectures, no.441. Wien, NY: Springer.
15. Holzapfel, G. A. & Ogden, R. W. 2009 Biomechanical modelling at the molecular, cellular and tissue levels. CISM Courses and Lectures, no.508. Wien, Austria: Springer.
16. Holzapfel, G. A. & Ogden, R. W. In press. On planar biaxial tests for anisotropic nonlinearly elastic solids: a continuum mechanical framework. Math. Mech. Solids. (doi:10.1177/ 1081286507084411)
17. Holzapfel, G. A., Gasser, T. C. & Ogden, R. W. 2000 A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity 61, 1-48. (doi:10.1023/A:1010835316564)
18. Holzapfel, G. A., Gasser, T. C. & Ogden, R. W. 2004 Comparison of a multi-layer structural model for arterial walls with a Fung-type model, and issues of material stability. J. Biomech. Eng. 126, 264-275. (doi:10.1115/1.1695572)
19. Horowitz, A., Lanir, Y., Yin, F. C. P., Perl, M., Sheinman, I. & Strumpf, R. K. 1988 Structural three-dimensional constitutive law for the passive myocardium. J. Biomech. Eng. 110, 200-207. (Pubitemid 18202997)
20. Humphrey, J. D. & Yin, F. C. P. 1987 On constitutive relations and finite deformations of passive cardiac tissue. Part I. A pseudo-strain energy function. J. Biomech. Eng. 109, 298-304.
21. Humphrey, J. D., Strumpf, R. K. & Yin, F. C. P. 1990 Determination of constitutive relation for passive myocardium. I. A new functional form. J. Biomech. Eng. 112, 333-339. (doi:10.1115/1.2891193)
22. Hunter, P. J., Nash, M. P. & Sands, G. B. 1997 Computational electromechanics of the heart. In Computational biology of the heart (eds A. V. Panfilov & A. V. Holden), pp. 345-407. Chichester, UK: Wiley.
23. Huyghe, J. M., van Campen, D. H., Arts, T. & Heethaar, R. M. 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)
24. Huyghe, J. M., Arts, T., van Campen, D. H. & Reneman, R. S. 1992 Porous medium finite element model of the beating left ventricle. Am. J. Physiol. Heart Circ. Physiol. 262, H1256-H1267.
25. Katz, L. N. 1977 Physiology of the heart. New York, NY: Raven Press.
26. Kerckhoffs, R. C. P., Bovendeerd, P. H. M., Kotte, J. C. S., Prinzen, F. W., 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/l.566447)
27. LeGrice, I. J., Smaill, B. H., Chai, L. Z., Edgar, S. G., Gavin, J. B. & Hunter, P. J. 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.
28. LeGrice, I. J., Hunter, P. J. & Smaill, B. H. 1997 Laminar structure of the heart: a mathematical model. Am. J. Physiol. Heart Circ. Physiol. 272, H2466-H2476. (Pubitemid 27235552) (Pubitemid 127750888) (Pubitemid 127828754)
29. MacKenna, D. A., Omens, J. H. & Covell, J. W. 1996 Left ventricular perimysial collagen fibers uncoil rather than stretch during diastolic filling. Basic Res. Cardiol. 91, 111-122. (doi:10.1007/BF00799683)
30. Merodio, J. & Ogden, R. W. 2002 Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation. Arch. Mech. 54, 525-552. (Pubitemid 36270120)
31. Merodio, J. & Ogden, R. W. 2003 Instabilities and loss of ellipticity in fiber-reinforced compressible nonlinearly elastic solids under plane deformation. Int. J. Solids Structures 40, 4707-4727. (doi:10.1016/S0020- 7683(03)00309-3) (Pubitemid 36901464)
32. Merodio, J. & Ogden, R. W. 2006 The influence of the invariant Jg on the stress-deformation and ellipticity characteristics of doubly fiber-reinforced non-linearly elastic solids. Int. J. Non-Linear Mech. 41, 556-563. (doi:10.1016/j.ijnonlinmec.2006.02.001)
33. Nash, M. P. 1998 Mechanics and material properties of the heart using an anatomically accurate mathematical model. PhD thesis, University of Auckland, Auckland, New Zealand.
34. Novak, V. P., Yin, F. C. P. & Humphrey, J. D. 1994 Regional mechanical properties of passive myocardium. J. Biomech. Eng. 27, 403-412. (doi:10.1016/0021-9290(94)90016-7)
35. Ogden, R. W. 1997 Non-linear elastic deformations. New York, NY: Dover Publications.
36. Ogden, R. W. 2003 Nonlinear elasticity, anisotropy and residual stresses in soft tissue. In Biomechanics of soft tissue in cardiovascular systems (eds G. A. Holzapfel & R. W. Ogden). CISM Courses and Lectures, no.441, pp. 65-108. Wien, Austria: Springer.
37. Ogden, R. W. 2009 Anisotropy and nonlinear elasticity in arterial wall mechanics. In Biomechanical modelling at the molecular, cellular and tissue levels (eds G. A. Holzapfel & R. W. Ogden). CISM Courses and Lectures, no.508, pp. 179-258. Wien, Austria: Springer.
38. Omens, J. H. & Fung, Y. C. 1990 Residual strain in rat left ventricle. Circ. Res. 66, 37-45.
39. Rachev, A. 1997 Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertensive conditions. J. Biomech. 30, 819-827. (doi:10.1016/S0021-9290(97)00032-8) (Pubitemid 27309606)
40. Rodriguez, E. K., Hoger, A. & McCulloch, A. D. 1994 Stress-dependent finite growth in soft elastic tissues. J. Biomech. 27, 455-467. (doi:10.1016/0021-9290(94)90021-3)
41. Sands, G. B., Gerneke, D. A., Hooks, D. A., Green, C. R., Smaill, B. H. & LeGrice, I. J. 2005 Automated imaging of extended tissue volumes using confocal microscopy. Microsc. Res. Tech. 67, 227-239. (doi:10.1002/jemt.20200)
42. Schmid, H., Nash, M. P., Young, A. A. & Hunter, P. J. 2006 Myocardial material parameter estimation-a comparative study for simple shear. J. Biomech. Eng. 128, 742-750. (doi:10.1115/1.2244576) (Pubitemid 44622803)
43. Schmid, H., O'Callaghan, P., Nash, M. P., Lin, W., LeGrice, I. J., Smaill, B. H., Young, A. A. & Hunter, P. J. 2008 Myocardial material parameter estimation: a non-homogeneous finite element study from simple shear tests. Biomech. Model. Mechanobiol. 7, 161-173. (doi:10.1007/s10237-007-0083-0) (Pubitemid 351768569)
44. Smaill, B. H. & Hunter, P. J. 1991 Structure and function of the diastolic heart: material properties of passive myocardium. In Theory of heart: biomechanics, biophysics, and nonlinear dynamics of cardiac function (eds L. Glass, P. J. Hunter & A. D. McCulloch), pp. 1-29. New York, NY: Springer.
45. Spencer, A. J. M. 1984 Constitutive theory for strongly anisotropic solids. In Continuum theory of the mechanics of fibre-reinforced composites (ed. A. J. M. Spencer). CISM Courses and Lectures, no.282, pp. 1-32. Wien, Austria: Springer.
46. Vossoughi, J., Vaishnav, R. N. & Patel, D. J. 1980 Compressibility of the myocardial tissue. In Advances in bioengineering (ed. Van C. Mow), pp. 45-48. New York, NY: Bioengineering Division, American Society of Mechanical Engineers.
47. Yin, F. C. P. 1981 Ventricular wall stress. Circ. Res. 49, 829-842.
48. Yin, F. C. P., Strumpf, R. K., Chew, P. H. & Zeger, S. L. 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)
49. Young, A. A., LeGrice, I. J., Young, M. A. & Smaill, B. H. 1998 Extended confocal microscopy of myocardial laminae and collagen network. J Microsc. 192, 139-150. (doi:10.1046/j.l365-2818.1998.00414.x)