Activation Models for the Numerical Simulation of Cardiac Electromechanical Interactions - Computer Models in Biomechanics - page 180

Chapter 14
Activation Models for the Numerical Simulation
of Cardiac Electromechanical Interactions

Ricardo Ruiz-Baier, Davide Ambrosi, Simone Pezzuto, Simone Rossi,
and Alfio Quarteroni

Abstract This contribution addresses the mathematical modeling and numerical
approximation of the excitation-contraction coupling mechanisms in the heart.
The main physiological issues are preliminarily sketched along with an extended
overview to the relevant literature. Then we focus on the existing models for the
electromechanical interaction, paying special attention to the active strain formula-
tion that provides the link between mechanical response and electrophysiology. We
further provide some critical insight on the expected mathematical properties of the
model, the ability to provide physiological results, the accuracy and computational
cost of the numerical simulations. This chapter ends with a numerical experiment
studying the electromechanical coupling on the anisotropic myocardial tissue.

14.1 Introduction

The interaction mechanism between contraction of the cardiac muscle and elec-
trical propagation is a complex multiscale phenomenon of vital importance in a
wide range of medical applications (Smith et al., 2004 ). From a purely mechani-
cal point of view, key features of muscle behavior include large deformations, fiber
anisotropy, heterogeneity of the tissue, and the ability to shorten when a substantial

R. Ruiz-Baier ( A. Quarteroni

CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
e-mail: [e-mail]
A. Quarteroni
e-mail: [e-mail]
S. Rossi
e-mail: [e-mail]

) · S. Rossi ·

D. Ambrosi A. Quarteroni

MOX—Politecnico de Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy
D. Ambrosi
e-mail: [e-mail]
S. Pezzuto
e-mail: [e-mail]

· S. Pezzuto ·