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A viscoactive constitutive modeling framework with variational updates for the myocardium.

Abstract：

: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.

journal_name

Comput Methods Appl Mech Eng

journal_title

Computer methods in applied mechanics and engineering

authors

Ponnaluri AVS,Perotti LE,Ennis DB,Klug WS

doi

10.1016/j.cma.2016.09.022

keywords:

["Active contraction","Constitutive modeling","Myocardium","Variational update"]

subject

Has Abstract

pub_date

2017-02-01 00:00:00

pages

85-101

eissn

0045-7825

issn

1879-2138

journal_volume

314

pub_type

杂志文章

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