An active strain electromechanical model for cardiac tissue

F. Nobile, A. Quarteroni, R. Ruiz-Baier

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We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the active strain assumption, in which it is assumed that there is a multiplicative decomposition of the deformation tensor into a passive and active part holds, the latter carrying the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of either incompressible or compressible nonlinear elasticity, governing the mechanical response of the biological material. In addition, by changing from a Eulerian to a Lagrangian configuration, the bidomain or monodomain equations modeling the evolution of the electrical propagation exhibit a nonlinear diffusion term. Piecewise quadratic finite elements are employed to approximate the displacements field, whereas for pressure, electrical potentials and ionic variables are approximated by piecewise linear elements. Various numerical tests performed with a parallel finite element code illustrate that the proposed model can capture some important features of the electromechanical coupling and show that our numerical scheme is efficient and accurate.

Original languageEnglish
Pages (from-to)52-71
Number of pages20
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number1
Publication statusPublished - 1 Jan 2012
Externally publishedYes


  • Active strain
  • Bidomain equations
  • Cardiac electromechanical coupling
  • Finite elements
  • Nonlinear elasticity
  • Reaction-diffusion problem

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