Adaptive Quasi-Linear Viscoelastic Modeling

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 nonlinear 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 series of test protocols for calibrating QLV models along with the associated calibration procedures, using the nonlinear viscoelastic behavior of reconstituted collagen tissue as an example. The Adaptive QLV model is not only simpler to calibrate but also more accurate in predicting the mechanical response of the reconstituted collagen tissue.