Multiscale Modeling of Ligaments and Tendons - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 125

Tendon Endomysium Muscle Fibers

Myotendinous Junction

Applied
Stretch

Unit Cell

Periodic BCs on Edge

Fig. 9 Myotendinous junction micromechanical model [ 205 ]. (Top) The myotendinous junction
(MTJ) consists of muscle fibers (red) that insert into tendon tissue (gray) via the endomysium
(black). A micromechanical model was made of the MTJ by creating a unit cell (outlined in white
dashed box and shown on bottom) and subjecting it to periodic boundary conditions on the edge
and prescribed boundary conditions on the ends. Figure adapted from [ 205 ]

The most significant result of this study was that the FE micromechanical model
predicted stress concentration and microscale strains that were significantly larger
than the macroscale strains. This suggests that origins of damage mechanisms may
initiate within the myotendinous junction, demonstrating the utility of microme-
chanical models in the study of damage initiation. The FE models predicted the
experimentally measured deflection of the A-bands of muscle fibers. Although not a
direct validation of the 2D strains within the unit cell, this validation provides
evidence of the accuracy of the FE simulations. By creating micromechanical FE
simulations driven by macroscopic loading, this study was able to utilize modeling
as a means for investigating microscale strain concentrations, something that would
have been difficult using experimental methods alone.
The aforementioned studies utilized 2D simulations. In our own research, we
have used 3D micromechanical FE models to study structure function relationships
in tendon and ligament tissue [ 187 ]. The aim of this research was to examine how
fibril organization contributes to the elastic volumetric response. The volumetric
response is quantified using the Poisson's ratio in linear theory and the Poisson's
function in nonlinear theory. Experimentally observed Poisson's ratios range from
1.0 to 3.0 for tendon and ligament [ 105 , 147 ], yet the structural underpinnings for
these large values are not known. It was hypothesized that a planar, crimped
arrangement of fibrils would not account for these large Poisson's ratios, while a
helical organization of fibrils would.
To test this hypothesis, 3D unit cells were created that explicitly modeled
collagen fibrils embedded within a matrix material (Fig. 10 , top). The fibrils were
given crimped, helical and combined crimped with a superhelical organization
(Fig. 10 , top). The models were given periodic boundary conditions and subjected
to simulated tensile loading in the fiber direction, which yielded a homogenized