271
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

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

, , , , , & show all
Pages 283-295 | Received 08 May 2008, Accepted 08 Sep 2008, Published online: 27 Apr 2009

References

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

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.