Myocardial material parameter estimation: A comparison of invariant based orthotropic constitutive equations

Computer Methods in Biomechanics and Biomedical Engineering

Volumn 12, Issue 3, 2009, Pages 283-295

  Schmid, H ^a   Wang, Y K ^b   Ashton, J ^b   Ehret, A E ^a   Krittian, S B S ^c   Nash, M P ^b   Hunter, P J ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

^c UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Fibre dispersion; Myocardium; Orthotropic; Parameter estimation; Polyconvexity; Transversely isotropic

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; COMPRESSIVE STRENGTH; COMPUTER SIMULATION; ELASTICITY; HEART MUSCLE; HUMAN; PHYSIOLOGY; SHEAR STRENGTH;

ANIMALS; COMPRESSIVE STRENGTH; COMPUTER SIMULATION; ELASTICITY; HUMANS; MODELS, CARDIOVASCULAR; MYOCARDIUM; SHEAR STRENGTH;

EID: 67449098111     PISSN: 10255842     EISSN: 14768259     Source Type: Journal    
DOI: 10.1080/10255840802459420     Document Type: Article

References (36)

1. Akaike H. 1973. Information theory as an extension of the maximum likelihood principle. In: Petrov BN, Csaki F, editors. Second International Symposium on Information Theory. Budapest: Akademiai Kiadó. p. 267-281.
2. Arts T, Costa K, Covell J, McCulloch A. 2001. Relating myocardial laminar architecture to shear strain and muscle fiber orientation. Am J Physiol. 280:H2222-H2229.
3. Augenstein K, Cowan B, LeGrice I, Nielsen P, Young A. 2005. Method and apparatus for soft tissue material parameter estimation using tissue tagged magnetic resonance imaging. J Biomech Eng. 127(1):148-157.
4. Ball J. 1977. Convexity conditions and existence theorems in nonlinear elasticity. Arch Rat Mech Anal. 63:337-403.
5. Balzani D, Neff P, Schröder J, Holzapfel G. 2006. A polyconvex framework for soft biological tissues. Adjustment to experimental data. Int J Solids Struct. 43/20:6052-6070.
6. Burnham K, Anderson D. 2002. Model selection and multimodel inference: a practical information-theoretic approach. 2nd ed. New York: Springer.
7. Costa K, Holmes J, McCulloch A. 2001. Modelling cardiac mechanical properties in three dimensions. Philos Trans R Soc. 359(1783):1233-1250.
8. Criscione J. 2003. Rivlin's representation formula is illconceived for the determination of response functions via biaxial testing. J Elasticity. 70:129-147.
9. Dokos S, Smaill B, Young A, LeGrice I. 2002. Shear properties of passive ventricular myocardium. Am J Physiol Heart Circ Physiol. 283:H2650-H2659.
10. Ehret A, Itskov M. 2007. A polyconvex hyperelastic model for fibre reinforced materials in application to soft tissues. J Mat Sci. 42:8853-8863.
11. Freed A, Einstein D, Vesely I. 2005. Invariant formulation for dispersed transverse isotropy in aortic heart valves. Biomech Model Mechanobiol. 4(2-3):100-117.
12. Gasser T, Ogden R, Holzapfel G. 2006. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3:15-35.
13. Guccione J, McCulloch A, Waldmann L. 1991. Passive material properties of intact ventricular myocardium determined from a cylindrical model. J Biomech Eng. 113:42-55.
14. Hartmann S, Neff P. 2003. Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility. Int J Solids Struct. 40:2767-2791.
15. Hartmann S, Neff P, Balzani D. 2005. A variational approach for materially stable anisotropic hyperelasticity. Int J Solids Struct. 42:4352-4371.
16. Holzapfel G, Gasser T, Ogden R. 2000. A new constitutive framework for arterial wall mechanics and a comparative study for material models. J Elasticity 61:1-48.
17. Holzapfel G, Gasser T, Ogden R. 2004. Comparison of a multilayer structural model for arterial walls with a fung-type model, and issues of material stability. J Biomech Eng. 126: 264-275.
18. Itskov M, Aksel N. 2004. A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function. Int J Solids Struct. 41: 3833-3848.
19. Itskov M, Ehret A, Mavrilas D. 2006. A polyconvex strain-energy function for soft collagenous tissue. Biomech Model Mechanobiol. 5:17-26.
20. LeGrice, I. 1992. A finite element model of myocardial structure: implications for electrical activation in the heart [PhD thesis]. New Zealand: University of Auckland.
21. LeGrice I, Smaill B, Chai L, Edgar S, Gavin J, Hunter P. 1995a. Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol Heart Circ Physiol. 269:H571-H582.
22. LeGrice I, Takayama Y, Covell J. 1995b. Transverse shear along myocardial cleavage planes provides a mechanism for normal systolic wall thickening. Circ Res. 77:182-193.
23. Leite-Moreira AF. 2006. Current perspectives in diastolic dysfunction and diastolic heart failure. Heart 92:712-718.
24. Markert B, Ehlers W, Karajan N. 2005. A general polyconvex energy function for fiber reinforced materials. PAMM 5: 245-246.
25. Moulton M, Creswell L, Actis R, Myers K, Vannier M, Szabo B, Pasque M. 1995. An inverse approach to determining myocardial material properties. J Biomech. 28(8):935-948.
26. Pope A, Sands G, Smaill B, LeGrice I. 2007. Three-dimensional transmural organization of perimysial collagen in the heart. Am J Heart Physiol. 295:H1243-H1252.
27. Schmid H. 2006. Passive myocardial mechanics - constitutive laws and material parameter estimation. PhD thesis, University of Auckland, New Zealand.
28. Schmid H, Nash M, Walker C, Sands G, Pope A, LeGrice I, Young A, Nielsen P, Hunter P. 2005. A framework for multi-scale modeling of the heart. In:Hozman J,Kneppo P, editors. IFMBE Proceedings, Prague: IFMBE, ISSN 1727-1983. (Proceedings of the 3rd European Medical & Biological Engineering Conference - EMBEC 05. Prague, Czech Republic, 20-25 November 2005), Id. 2535, Vol. 11. p. 4201-4205.
29. Schmid H, Nash M, Young A, Hunter P. 2006. Myocardial material parameter estimation - a comparative study for simple shear. J Biomech Eng. 128(5):742-750.
30. Schmid H, Nash M, Young A, Röhrle O, Hunter P. 2007a. A computationally efficient optimization kernel for material parameter estimation procedures. J Biomech Eng. 129(2): 279-283.
31. Schmid H, O'Callaghan P, Nash M, Lin W, Legrice I, Smaill B, Young A, Hunter P. 2007b. Myocardial material parameter estimation from simple shear tests - a non-homogeneous finite element study. Biomech Model Mechanobiol. 7(3): 161-173, ISSN: 1617-7959.
32. Schröder J, Neff P. 2001. On the construction of polyconvex transversely isotropic free energy functions. In: Miehe C, editor. Proceedings of the IUTAM Symposium on Computational Mechanics of Solid Materials at Large Starins, Dordrecht (The Netherlands): Kluwer Academic Publishers. p. 171-180.
33. Schröder J, Neff P. 2003. Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions. Int J Solids Struct. 40:401-445.
34. Small C, Wang J. 2003. Numerical methods for nonlinear estimating equations. Oxford: Oxford University Press.
35. Spencer A. 1980. Continuum mechanics. New York: Longman Group Ltd.
36. Walter E. 1982. Identifiability of state space models, with applications to transformation systems. New York: Springer.