Heart Mechanical Model Based on Holzapfel Experiments

Conference paper
Part of the Learning and Analytics in Intelligent Systems book series (LAIS, volume 11)


We have formulated orthotropic material model for human heart tissue based on experimental investigation of passive material properties of myocardium [1]. The Cauchy stress/stretch and shear stress/amount of shear relation curves are used, which are established experimentally under different loading conditions: biaxial extension and triaxial shear. The averaged curves obtained from all considered specimens in [1] are reconstructed and used in our FE computational model. A computational procedure for determination of stresses for current stretches and amounts of shear at integration points of the FE model is implemented in the code PAK. Compressibility condition is imposed to couple the normal stresses using a penalty formulation. Applicability and reliability of this material model is tested on simple 3D models and on a heart wall segment under passive conditions. This numerical model offers an accurate description of the ventricular mechanics and can be used in studying heart problems in order to improve medical treatment of heart diseases.


Heart mechanics Heart material model Biaxial loading Sommer and Holzapfel experiment 



The authors acknowledge support from the City of Kragujevac, Serbia.


This work is supported by the SILICOFCM project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 777204. This research was also funded by Ministry of Education and Science of Serbia, grants OI 174028 and III 41007.


  1. 1.
    Sommer, G., Schriefl, A.J., Andrä, M., Sacherer, M., Viertler, C., Wolinski, H., Holzapfel, G.A.: Biomechanical properties and microstructure of human ventricular myocardium. Acta Biomater. 24, 172–192 (2015)CrossRefGoogle Scholar
  2. 2.
    Roy, C.: The elastic properties of the arterial wall. J. Physiol. 3, 125–159 (1881)CrossRefGoogle Scholar
  3. 3.
    Holzapfel, G.A., Ogden, R.W.: Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos. Trans. R. Soc. A 367, 3445–3475 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Gültekin, O., Sommer, G., Holzapfel, G.A.: An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment. Comput. Methods Biomech. Biomed. Eng. 19(15), 1647–1664 (2016)CrossRefGoogle Scholar
  5. 5.
    McEvoy, E., Holzapfel, G.A., McGarry, P.: Compressibility and anisotropy of the ventricular myocardium: experimental analysis and microstructural modeling. J. Biomech. Eng. 140, 081004–1,10 (2018)Google Scholar
  6. 6.
    Kojic, M., Slavkovic, R., Zivkovic, M., Grujovic, N., Filipovic, N., Milosevic, M.: PAK - finite element program for linear and nonlinear analysis. Univ Kragujevac and R&D Center for Bioengineering, Kragujevac, Serbia (2010)Google Scholar
  7. 7.
    Kojic, M., Bathe, K.J.: Inelastic Analysis of Solids and Structures. Springer, Heidelberg (2005)Google Scholar
  8. 8.
    Kojic, M., Slavkovic, R., Zivkovic, M., Grujovic, N.: Metod konacnih elemenata I – linearna analiza, Masinski Fakultet. Univerzitet u Kragujevcu, Kragujevac (2010). ISBN 86-80581-27-5Google Scholar
  9. 9.
    Bathe, K.J.: Finite Element Procedures. Prentice Hall, Hew Jersey (2006). ISBN-13: 978-0979004957zbMATHGoogle Scholar
  10. 10.
    Kojic, M., Milosevic, M., Simic, V., Milicevic, B., Geroski, V., Nizzero, S., Ziemys, A., Filipovic, N., Ferrari, M.: Smeared multiscale finite element models for mass transport and electrophysiology coupled to muscle mechanics. Front. Bioeng. Biotechnol. 7 (2019)., ISSN: 2296-4185
  11. 11.
    Santiago, A.: Fluid-electro-mechanical model of the human heart for supercomputers. Universitat Politècnica de Catalunya, Bacelona (2018)Google Scholar
  12. 12.
    Hunter, P.J., McCulloch, A.D., Ter Keurs, H.E.D.J.: Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69, 289–331 (1998)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.The Department of NanomedicineHouston Methodist Research InstituteHoustonUSA
  2. 2.Bioengineering Research and Development Center BioIRC KragujevacKragujevacSerbia
  3. 3.Serbian Academy of Sciences and ArtsBelgradeSerbia
  4. 4.Belgrade Metropolitan UniversityBelgradeSerbia
  5. 5.Faculty for Engineering SciencesUniversity of KragujevacKragujevacSerbia

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