Multiscale Modeling of Ligaments and Tendons - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 110

understood to be the result of fluid exudation during tensile loading, which has
been reported in the literature [ 94 , 101 ]. The elastic response is not spatially
homogenous. Strain measurements techniques such as speckle tracking and digital
image correlation have shown that strains are highly inhomogeneous during tensile
loading [ 53 , 55 , 133 , 158 ]. Although the origins of this behavior are unclear, it
may be due in part to variation in the tissue mechanical properties [ 163 ], clamping
artifacts or an uneven fascicle stiffness and preload [ 126 , 233 ]. It appears that
spatial inhomogeneity within strain distribution may be an intrinsic property of
ligament and tendon tissue.
The viscoelastic response of ligament and tendon is believed to play an
important role in the normal function of these tissues [ 34 ]. It is experimentally
manifested as stress relaxation under a step displacement, creep under a step
loading, hysteresis, and a phase shift during harmonic loading [ 134 ]. Stress
relaxation testing of ligament and tendon reveals a dependence of both the
relaxation rate and magnitude of relaxation on the strain level [ 2 , 131 , 145 , 179 ].
Similarly, the creep rate and creep magnitude are also strain dependent [ 218 ]. The
tensile modulus is strain rate dependent, while the damping is relatively inde-
pendent of strain rate [ 228 , 233 , 235 , 240 ]. During high rate loading, the volu-
metric behavior of ligament and tendon appears to be incompressible [ 233 ].
Although viscoelastic testing is most commonly reported for uniaxial tensile
testing in the fiber direction, both viscoelastic tensile testing in the transverse
direction and in shear has been reported [ 34 ]. The magnitude of stress relaxation is
relatively large for testing in the axial, transverse and shear directions, with times
to equilibrium on the order of ten minutes or more [ 2 , 131 , 145 , 147 ]. Because of
the considerable importance of the fluid phase to tissue viscoelasticity, it comes as
little surprise that the viscoelastic response is significantly altered by varied levels
of tissue hydration [ 144 ]. There is also an observed effect of temperature on the
elastic and viscoelastic response [ 45 ].
3.3 Mesoscale Material Characterization
Fascicles are the primary load bearing mesoscale structure found within ligament
and tendon, and range in diameter from 100 to 500 lm[ 50 , 121 , 230 ]. Experi-
mental studies at the mesoscale have interrogated the fascicle response by testing
both isolated individual fascicles as well as fascicles in situ. Rat tail tendons have
often been used in such studies because they are readily available, the tendons
have large aspect ratios, and it is relatively easy to isolate the fascicles from the
tendon. A number of studies have reported both elastic and viscoelastic properties
of rat tail tendon fascicles [ 95 , 184 , 191 ]. The qualitative elastic and viscoelastic
response is similar to that observed for macroscopic tissue, with a nonlinear toe
region and a large stress relaxation.
Several studies have performed tensile testing on progressively divided tendons
(e.g. into half and quarter sections) as well as individually isolated fascicles.