Biomechanics and Modeling in Mechanobiology

, Volume 13, Issue 3, pp 627–641 | Cite as

Simulation of the contraction of the ventricles in a human heart model including atria and pericardium

Finite element analysis of a frictionless contact problem
  • Thomas FritzEmail author
  • Christian Wieners
  • Gunnar Seemann
  • Henning Steen
  • Olaf Dössel
Original Paper


During the contraction of the ventricles, the ventricles interact with the atria as well as with the pericardium and the surrounding tissue in which the heart is embedded. The atria are stretched, and the atrioventricular plane moves toward the apex. The atrioventricular plane displacement (AVPD) is considered to be a major contributor to the ventricular function, and a reduced AVPD is strongly related to heart failure. At the same time, the epicardium slides almost frictionlessly on the pericardium with permanent contact. Although the interaction between the ventricles, the atria and the pericardium plays an important role for the deformation of the heart, this aspect is usually not considered in computational models. In this work, we present an electromechanical model of the heart, which takes into account the interaction between ventricles, pericardium and atria and allows to reproduce the AVPD. To solve the contact problem of epicardium and pericardium, a contact handling algorithm based on penalty formulation was developed, which ensures frictionless and permanent contact. Two simulations of the ventricular contraction were conducted, one with contact handling of pericardium and heart and one without. In the simulation with contact handling, the atria were stretched during the contraction of the ventricles, while, due to the permanent contact with the pericardium, their volume increased. In contrast to that, in the simulations without pericardium, the atria were also stretched, but the change in the atrial volume was much smaller. Furthermore, the pericardium reduced the radial contraction of the ventricles and at the same time increased the AVPD.


Cardiac electromechanical modeling  Pericardium Atria Contact problem Finite element simulation 



We acknowledge the support of the KIT competence field Mathematical Models in form of a start-up grant.

Supplementary material

Supplementary material 1 (mpg 4788 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Thomas Fritz
    • 1
    Email author
  • Christian Wieners
    • 2
  • Gunnar Seemann
    • 1
  • Henning Steen
    • 3
  • Olaf Dössel
    • 1
  1. 1.Department of Electrical Engineering and Information Technology, Institute of Biomedical EngineeringKarlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Department of Mathematics, Institute for Applied and Numerical Mathematics 3Karlsruhe Institute of Technology (KIT)KarlsruheGermany
  3. 3.Department of Internal Medicine IIIUniversity Hospital HeidelbergHeidelbergGermany

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