Adaptive Quasi-Linear Viscoelastic Modeling - Computational Modeling in Tissue Engineering - page 55

3 Calibration Protocols for QLV Models

In this section we review four common test protocols employed to calibrate quasi-
linear viscoelastic constitutive models and describe procedures for calibrating the
parameters of the Adaptive QLV, Generalized Fung QLV, and, when significantly
different, the Fung QLV models to data obtained following these protocols. All tests
are one dimensional and involve data acquired by monitoring the tissue stretch and
resistive force over time (Fig. 3 ), and all assume loading rates sufficiently small that
inertial effects could be neglected (e.g., [ 64 ]). The test specimen is assumed to be in a
fully relaxed state prior to application of load, so that the history of prior loading of
the specimen does not affect its subsequent mechanical response measurably. Axial
strain, e, is calculated in each case from axial stretch, Dl, through:

e ð t Þ¼ l ð t Þ l o ð Þ= l o ; ð 21 Þ

where l o is the initial (usually zero-force) length of the tissue. Uniaxial stress, r,is
calculated from axial force, f, through:

r ð t Þ¼ f ð t Þ= S o ; ð 22 Þ

where S o is the initial cross-sectional area of the tissue. Alternatively, one may
consider and calibrate the QLV models as representative of the constitutive law
between the force and the relative displacement of the ends of a specimen rather
than between the stress and the strain.

3.1 Relaxation Tests with Multiple Amplitudes

An ideal relaxation test involves an instantaneous (stepwise) stretch of a tissue,
followed by an isometric holding of the tissue at this level of stretch. The force
response of a viscoelastic material to such a stretch is a rapid increase in resistive
force followed by a gradual force relaxation over time (Fig. 3 a). Force relaxation
data should be measured until the force approaches a final steady state value. Each
relaxation test is defined by the initial tissue strain, e, (or displacement) and the
amplitude De of the stepwise strain (or displacement) increment. Before a relax-
ation test, the tissue force should have reached the steady value associated with the
initial strain. This is required for the subsequent relaxation data to represent only
the current relaxation test.
The goal here is to characterize the strain dependence of nonlinear viscoelastic
behavior. One suitable protocol is to perform a series of relaxation tests of different
amplitudes, all from the same initial length, with ample time for relaxation of the
specimen back to its initial configuration between tests. In this protocol the initial
length the tissue is ideally its stress free reference configuration, but this is not
always possible.