Multiscale Modeling of Ligaments and Tendons - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 108

vessel

MCL

nerve

cells

Macro
~ligament

Meso
~fascicle

Micro
~fiber

Fig. 3 Multiscale force transmission. Force transmission within a macroscale tissue structure
(e.g., an MCL, shown on the left) is mediated at the mesoscale by fascicles (center) and at the
microscale by fiber (right)

However, hydration also plays an important role in modulating equilibrium elastic
response [ 45 ]. The viscoelastic response is experimentally measured by per-
forming mechanical testing at varied strain rates, stress relaxation testing, creep
testing and harmonic testing [ 34 , 135 , 145 , 241 ]. The viscoelastic response is
attributed to both fluid flow-dependent and fluid flow-independent effects. Flow-
independent effects refer to an intrinsic viscoelasticity of the solid phase (e.g. a
viscous sliding of fibrils), while flow-dependent effects refer to the pressure driven
transport of free water through a permeable tissue (e.g. described using biphasic
theory, discussed in Sect. 4.3 )[ 46 , 233 , 235 , 236 , 253 ].

3.2 Macroscopic Material Characterization

For this chapter, the macroscale will be defined as tissue structures that are within
the range of millimeters to centimeters, most commonly consisting of whole lig-
ament and tendon preparations or subsamples that are dissected or punched out
[ 27 , 131 , 144 , 147 , 249 ]. The 3D elastic response of ligament and tendon tissue is
complex and difficult to fully characterize. The material response is highly
dependent on the predominant alignment of the collagen fiber families. Although
some capsular ligaments appear to have an isotropic fiber distribution (e.g. gle-
nohumeral capsule [ 63 , 64 ]), the material symmetry of most ligaments and tendons
is reasonably described by transverse isotropy, with the collagen fibers predomi-
nantly aligned in the direction of in vivo loading [ 233 , 235 ]. To fully characterize
the elastic material response of these tissues, a combination of tensile, compression
and shear testing must be performed in parallel and transverse directions to the
predominate fiber family [ 34 , 147 , 232 , 234 ].
Tensile testing in the fiber direction reveals a nonlinear stress-strain response
consisting of a so called ''toe region'' and a linear region [ 34 , 233 ] (Fig. 4 , left).