Biomedical Engineering Reference
In-Depth Information
utilizing a computational micromechanical model, estimates of fluid shear stress
on fibroblasts as well as cell membrane strains were able to be correlated to these
experimental results. No tractable experimental methods currently have been
proposed for obtaining microscale values of this sort, highlighting the important
role that such modeling studies can play in extending our understanding of
mechanotransduction within tendon tissue.
5.3 1st Order FE
2
Methods
The aforementioned micromechanical models report both macroscale and micro-
scale measures, but are limited to a specific set of loading conditions. A more
general approach is offered by the 1st order FE
2
homogenization method described
in
Sect. 4.5
. To date, no FE
2
models have been proposed for the simulation of
ligament and tendon. However, an FE
2
approach has been developed and applied
to model collagen hydrogels, which have characteristics in common with con-
nective tissues [
43
,
195
,
196
]. In this work, FE
2
models were made of type I
collagen gels that were molded into a cruciform shape. The gels were seeded with
fibroblasts and were allowed to undergo cell mediated compaction of the fibril
network. The gels were subjected to biaxial testing and the macroscopic stress and
strain were measured. Additionally, polarametric fiber alignment imaging (PFAI)
was used to measure fibril orientations during testing. A quarter symmetric mac-
roscopic FE model was constructed (Fig.
13
, left) that mimicked the geometry and
loading conditions of the experimentally tested cruciform gels. The fibril orien-
tation (e.g. the angular distribution of fibrils) measured in the reference position
was used in order to generate 3D RVE models that consisted of beam elements,
which represented collagen fibrils within the gel (Fig.
13
, middle). A constitutive
model specific to collagen fibrils was developed for use in the RVEs. The mac-
roscopic FE model utilized an FE
2
methodology described in
Sect. 4.5
, whereby
the RVE homogenization was utilized as the constitutive model for the macro-
scopic simulation. The results of the FE simulations generated both macroscopic
stress and strain as well as microscopic stress and strain within the fibril network.
The FE predicted principle angles for fiber orientation were extracted from the
microscale RVE simulations and compared to the experimentally obtained prin-
ciple angles (via PFAI). There was good agreement between the predicted and
measured orientation of the fibrillar network, which provided validation of the
methodology. The microscale RVE simulations revealed realignment of the
fibrillar network with applied strain. A considerable percentage of the fibrils were
subjected to compressive buckling, revealing microscale inhomogeneity in
response to a homogenous macroscale deformation. Collagen hydrogels are sub-
stantially different from tendon and ligament; however, this same microscale
heterogeneity has been observed in tendon fascicles [
201
] (refer to
Sects. 3.3
and
3.4
). Although not directly applicable to tendon and ligament, this study provides a
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