Multiscale Modeling of Ligaments and Tendons - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 113

3.5 Nanoscale Mechanical Characterization
The collagen fibril is the primary load bearing structure at the nanoscale. A number
of methods have been employed to study the behavior of ligament and tendon
fibrils, including direct testing of isolated fibrils, atomic force microscopy of
strained fibrils and the use of X-ray diffraction techniques. Numerous studies have
isolated individual collagen fibrils and subjected them to uniaxial tensile testing
(e.g. [ 222 , 239 , 251 , 252 ]). The stiffness of fibrils varied between studies and was
dependent on hydration, mounting method, crosslinking and strain rate. Single
fibrils tested in this manner display viscoelastic behavior such as strain rate
dependence, hysteresis on unloading and stress relaxation [ 212 ]. In another study,
AFM was performed on strained fibrils within murine Achilles tendon tissue,
revealing that the local fibril strain was considerably less than the applied mac-
roscale strain (*2 % fibril strain for an applied 10 % macroscale strain). A large
lateral contraction (corresponding to a Poisson's ratio of *0.8) was also observed
[ 190 ]. Mechanical testing of single tropocollagen molecules has also been reported
[ 35 , 210 ]. In these studies, force-extension relationships were measured and
analyzed by fitting the data to a worm-like chain elasticity model. The contour
lengths reported ranged from approximately 200-300 nm.
It is believed that other nanoscale components may also contribute to the
macroscopic mechanical behavior of ligament and tendon, including proteogly-
cans such as decorin, biglycan and others [ 114 , 125 , 144 ]. Although not a direct
test of multiscale interactions, a number of knockout studies in mice have been
performed that suggest macroscale effects from the altered expression of various
nanoscale constituents [ 191 , 259 ]. For instance, decorin deficient mice have been
found to have mechanically inferior tendon fascicles [ 191 ]. In vitro studies have
also been used to investigate the role of nanoscale constituents such as decorin. In
a number of studies, samples of human MCL were subjected to tensile testing
before and after decorin digestion (via incubation in chondroitinase ABC, ChABC)
and no significant changes in mechanical behavior were found [ 131 , 144 , 145 ].
However, in similar studies that utilized single rat tail tendon fascicles, a change in
mechanical behavior was found in response to digestion incubation in ChABC.
This suggests that perhaps the mechanical function of certain proteoglycans may
vary between tissue types and scale levels [ 198 , 200 ]. Still, the changes in
mechanical behavior were minimal. Although there were some trends towards
incubation decreasing the stiffness and ultimate strength of the fascicles, the
increased strain at the onset of visible fiber sliding was the only significant dif-
ference found in the tensile test data from both studies [ 198 , 200 ].
In summary, it is clear that force is transmitted across scales in a complex manner.
Although there are conflicting reports, it appears that tissue constituents are stiffer at
lower scale levels than at higher scale levels (Fig. 5 ). In response to tensile loading
in the fiber direction, microscale strains are less than the applied macroscale strain,
often times by a large amount. Finally, strains are inhomogenously distributed at the
macroscale, mesoscale and microscale. These findings are summarized in Table 1 .