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

Gerhard A Holzapfel, Ray W Ogden

Research output: Contribution to journalArticlepeer-review

595 Citations (Scopus)


In this paper, we first of all review the morphology and structure of the myocardium and discuss the main features of the mechanical response of passive myocardium tissue, which is an orthotropic material. Locally within the architecture of the myocardium three mutually orthogonal directions can be identified, forming planes with distinct material responses. We treat the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develop a general theoretical framework based on invariants associated with the three directions. Within this framework we review existing constitutive models and then develop a structurally based model that accounts for the muscle fibre direction and the myocyte sheet structure. The model is applied to simple shear and biaxial deformations and a specific form fitted to the existing (and somewhat limited) experimental data, emphasizing the orthotropy and the limitations of biaxial tests. The need for additional data is highlighted. A brief discussion of issues of convexity of the model and related matters concludes the paper.
Original languageEnglish
Pages (from-to)3445-3475
Number of pages31
JournalPhilosophical Transactions of the Royal Society of London. Series A
Issue number1902
Early online date3 Aug 2009
Publication statusPublished - 13 Sept 2009


  • myocardium
  • constitutive modelling
  • orthotropy
  • muscle fibres
  • myocyte sheet structure


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