Tendons and Ligaments: Current State and Future Directions - Multiscale Modeling in Biomechanics and Mechanobiology - page 185

Because of the important role validation plays in interpreting the results of compu-
tational studies, it is desirable to develop multiscale simulation strategies and exper-
imental validation methods concurrently. Although macroscale validation methods
have been described, microscale validation methods are still in need of improvement
and development. In order to validate microscale models, data regarding stress and
strain at lower scale levels (e.g., within fascicles, fibers and fibrils) must be obtained.
One possible route involves isolating and mechanically testing individual tissue con-
stituents, such as those described in Sects. 1.6 - 1.9 . However, such methods have
yielded widely variable results, likely due to the difficulty in consistently isolating
substructures without causing tissue damage. Microscopic imaging studies, such as
the confocal studies described in Sect. 1.8 , provide considerable promise for use in
validation of microscale models. However, the highly inhomogeneous strain fields
and the complex microscale fiber structure make this a challenging starting point [ 124 ,
126 , 127 ]. In order to address these challenges, our lab has developed a surrogate
material for use as a physical model to aid in the development of multiscale modeling
and validation methods [ 254 ]. A physical model reduces the number of uncontrolled
variables related to the structural organization of ligaments and tendons. To create
the physical surrogates, dense (

25 % collage/wt), extruded collagen fibers were
embedded within a collagen gel matrix (

∼

0.5 % collagen/wt). Surrogates served as
physical models to emulate features of ligament and tendon tissuein a controlled and
reproducible manner. Two different colors of fluorescent beads were embedded in
the fibers and gel matrix (Fig. 8.14 , top left) for use as microscopic fiducial markers.
3D micromechanical FE models of the surrogates were then constructed (Fig. 8.14 ,
middle-left and bottom). A constitutive model based on a continuous elliptical fiber
distribution was used to describe the mechanical behavior of the collagen gel and
embedded fibers [ 255 ]. This constitutive model emulated the reorganization of fib-
rils with applied strain. The model was curve fit to tensile testing data for isolated
gel and extruded fiber samples and was found to accurately model both the uniax-
ial stress-strain behavior and the 2D strain behavior (i.e., the nonlinear Poisson's
function). Micromechanical FE models were subjected to uniaxial strain, and the
macroscale and microscale stress and 2D strain were determined. FEBio was used
for all analysis ( http://www.febio.org ) [ 210 ]. To validate the FE models, the physi-
cal surrogates were subjected to tensile loading in a custom testing apparatus on an
inverted confocal microscope. Confocal images were acquired at 6 strain increments
at both 4X and 10X, while force was measured simultaneously. Texture correlation
was used to measure strain at the macroscale and to measure strain within the fibers
and strain in the interfiber matrix at the microscale [ 256 ].
The microscopic 2D strains were inhomogeneous, and the macroscopic 2D strain
was not representative of the microscopic 2D strain (Fig. 8.14 , right). The magni-
tude of the transverse strain in the fibers greatly exceeded the macroscopic trans-
verse strain, while the magnitude of the transverse matrix strain was significantly
less than the macroscopic strain. The macroscopically measured Poisson's ratio was
1.72

∼

0.26, which is comparable to experimentally measured values for tendon and
ligament [ 129 , 139 ]. The micromechanical FE model was able to simultaneously pre-
dict the macroscopic stress-strain behavior and the 2D macroscale and microscale

±