Biomedical Engineering Reference
In-Depth Information
Chapter 13
Micro-structurally Based Kinematic Approaches
to Electromechanics of the Heart
Serdar Göktepe, Andreas Menzel, and Ellen Kuhl
Abstract
This contribution is concerned with a new kinematic approach to the
computational cardiac electromechanics. To this end, the deformation gradient is
multiplicatively decomposed into the active part and the passive part. The for-
mer is considered to be dependent on the transmembrane potential through a
micro-mechanically motivated evolution equation. Moreover, the proposed kine-
matic framework incorporates the inherently anisotropic, active architecture of car-
diac tissue. This kinematic setting is then embedded in the recently proposed, fully
implicit, entirely finite-element-based coupled framework. The implicit numerical
integration of the transient terms along with the internal variable formulation, and
the monolithic solution of the resultant coupled set of algebraic equations result in
an unconditionally stable, modular, and geometrically flexible structure. The capa-
bilities of the proposed approach are demonstrated by the fully coupled electrome-
chanical analysis of a generic heart model.
13.1 Introduction
Biological electro-active materials such as skeletal muscle and cardiac muscle
commonly undergo remarkable deformations in response to electric stimulation.
S. Göktepe (
)
Department of Civil Engineering, Middle East Technical University, 06800 Ankara, Turkey
e-mail:
sgoktepe@metu.edu.tr
A. Menzel
Institute of Mechanics, TU Dortmund, Leonhard-Euler-Str. 5, 44227 Dortmund, Germany
e-mail:
andreas.menzel@udo.edu
A. Menzel
Division of Solid Mechanics, Lund University, P.O. Box 118, 22100 Lund, Sweden
E. Kuhl
Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford
University, Stanford, CA 94305, USA
e-mail:
ekuhl@stanford.edu
