Multiscale Modeling of Ligaments and Tendons - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 133

demonstrating the utility of this approach for the study of fibrous biological
composites. The use of physical surrogate materials provides a means for devel-
oping and validating more complex and physiologically relevant micromechanical
and multiscale mechanical models. This study illustrates the feasibility of simul-
taneous validation at macro and micro scales that could be extended to the vali-
dation of micromechanical or FE 2 models of native ligament or tendon [ 188 , 189 ].
5.5 Future Directions
There are a number of important areas of research that remain as future directions
and opportunities for multiscale modeling of tendon and ligament. As of yet, no
fully nested 1st or 2nd order FE 2 models have been proposed for tendon and
ligament. This will require the development and meshing of RVEs that sufficiently
characterize the microstructure (e.g. crimped fibers, sliding fascicles, etc.), con-
stitutive models capable of describing the nanoscale and microscale response
within the RVE (e.g., Eq. 9 ), software capable of performing the recursive FE 2
simulations using 1st and 2nd order procedures, as well as microscopic techniques
for validating model simulations. Given the multiple scales of organization in
these tissues (i.e. nanoscale fibrils, microscale fibers and mesoscale fascicles), it is
unclear whether two levels of scale linking is adequate, or whether additional scale
levels must be included. Furthermore, the criteria for RVE size in tendinous tissue
and the importance of using of 2nd order methods has yet to be investigated. The
use of physical surrogates may provide a controlled means for answering such
questions, as well as provide a simplified approach for developing multiscale
modeling and validation methods.
The development of validated multiscale models of tendons and ligaments will
provide insight into structure function relationships and will be invaluable in the
study of damage mechanisms, which appear to have microscale origins [ 58 , 72 ,
73 ]. In the future, such methods may provide a means for creating scaffolds with a
microstructure that can simultaneously address macroscale mechanical require-
ments of whole organs (e.g. an ACL graft) and the microscale mechanical
requirements necessary for cellular proliferation. Although this chapter has
focused primarily on the quasistatic elastic response, models that capture the
viscoelastic and biphasic response of these tissues will be of substantial impor-
tance. Homogenization methods have been developed to account for viscoelas-
ticity [ 38 , 44 , 90 , 130 ], but these methods have yet to be applied to biological
tissues. The next paradigm in multiscale modeling will likely address growth and
remodeling of tissue (e.g. remodeling in bone [ 86 , 93 , 138 ]). Nested FE 2 multi-
scale methods for such simulations remain to be developed for aligned collagenous
tissues.