Adaptive Quasi-Linear Viscoelastic Modeling - Computational Modeling in Tissue Engineering - page 44

Adaptive Quasi-Linear Viscoelastic
Modeling

Ali Nekouzadeh and Guy M. Genin

Abstract Engineered tissues are often designed to serve a mechanical role. The
design and evaluation of such tissues requires a mechanical model. An important
component of such models is often viscoelasticity, or the dependence of
mechanical response on loading rate and loading history. In a great number of
biological and bio-artificial tissues the passive tissue force (or stress) relates to
changes in tissue length (or strain) in a nonlinear viscoelastic manner. Choosing
and fitting nonlinear viscoelastic models to data for a specific tissue can be a
computational challenge. This chapter describes the range of such models, criteria
for selecting amongst them, and computational and experimental techniques
needed to fit these to uniaxial data. The chapter begins with Fung's quasi-linear
viscoelastic (QLV) model, which is nearly a standard first model to try for non-
linear viscoelastic tissues. The chapter then describes the two major limitations of
the Fung QLV model, and presents approaches for overcoming these. The first
limitation is accuracy: the Fung QLV model imposes a severe set of restrictions on
constitutive behavior, and a generalized form of the Fung QLV model is needed in
many cases. The second limitation is that the Fung QLV model is cumbersome
computationally, especially for calibration experiments. The Adaptive QLV model
is far simpler to calibrate and provides greater flexibility than the Fung QLV
model. The Adaptive QLV model extends linear viscoelastic models to incorporate
nonlinearity using a principle different from that of the Fung QLV model: it adapts
nonlinearity according to the instantaneous level of strain. The Adaptive QLV
model can be used in simple or generalized form. The chapter concludes with a

A. Nekouzadeh
Cardiac Bioelectricity and Arrhythmia Center, Department of Biomedical Engineering,
Washington University in Saint Louis, Saint Louis, MO, USA
G. M. Genin (

)
Department of Mechanical Engineering and Materials Science,
Washington University in Saint Louis, Saint Louis, MO, USA
e-mail: [e-mail]

&