A viscoactive constitutive modeling framework with variational updates for the myocardium
We present a constitutive modeling framework for contractile cardiac mechanics by formulating a single variational principle from which incremental stress–strain relations and kinetic rate equations for active contraction and relaxation can all be derived. The variational framework seamlessly incorp...
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Published in | Computer methods in applied mechanics and engineering Vol. 314; pp. 85 - 101 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Netherlands
Elsevier B.V
01.02.2017
Elsevier BV |
Subjects | |
Online Access | Get full text |
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Summary: | We present a constitutive modeling framework for contractile cardiac mechanics by formulating a single variational principle from which incremental stress–strain relations and kinetic rate equations for active contraction and relaxation can all be derived. The variational framework seamlessly incorporates the hyperelastic behavior of the relaxed and contracted tissue along with the rate–and length–dependent generation of contractile force. We describe a three-element, Hill-type model that unifies the active tension and active deformation approaches. As in the latter approach, we multiplicatively decompose the total deformation gradient into active and elastic parts, with the active deformation parametrizing the contractile Hill element. We adopt as internal variables the fiber, cross-fiber, and sheet normal stretch ratios. The kinetics of these internal variables are modeled via definition of a kinetic potential function derived from experimental force–velocity relations. Additionally, we account for dissipation during tissue deformation by adding a Newtonian viscous potential. To model the force activation, the kinetic equations are coupled with the calcium transient obtained from a cardiomyocyte electrophysiology model. We first analyze our model at the material point level using stress and strain versus time curves for different viscosity values. Subsequently, we couple our constitutive framework with the finite element method (FEM) and study the deformation of three-dimensional tissue slabs with varying cardiac myocyte orientation. Finally, we simulate the contraction and relaxation of an ellipsoidal left ventricular model and record common kinematic measures, such as ejection fraction, and myocardial tissue volume changes.
•Unifying constitutive modeling framework to simulate cardiac contraction.•Hill-like three element model together with a viscous dashpot.•Single variational principle for stress–strain relations and kinetic rate equations.•Hill’s force–velocity relationship as the basis for the kinetic equations.•Simulated contraction of a representative left ventricle geometry using FEM. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0045-7825 1879-2138 |
DOI: | 10.1016/j.cma.2016.09.022 |