Biomedical Engineering Reference
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at 45 degrees of knee flexion was obtained from MR scanning. The virtual three-dimensional shape
of the meniscus was obtained by flexing the FE model of the knee joint to 45 degrees. After overlap-
ping the realistic meniscus and the FE meniscus, the mismatch volumes on the medial and lateral
sides were 22% and 26.5%, respectively. These mismatches were within the deviation of MR image
pixel resolution. The result of this validation could ensure the precision of the following applications.
6.3 aPPlICatIon oF the FInIte element model
The sequelae following ACL reconstruction, such as tunnel enlargement and osteoarthritis, have
been correlated to changes in the bone material and morphology. According to Wolff's law, the
postoperative mechanical environment plays an important role in these bone alterations, and
could influence the long-term surgical outcome. Therefore, characterization of the postoperative
mechanical environment and its potential influence on bone remodeling could help to understand
the pathomechanism of the sequelae, and may help advance the surgical procedure. In this light,
the following sections developed an FE model of the human knee joint with ACL reconstruction,
quantified the alteration of bone SED distribution in comparison with the intact knee, and analyzed
the effect of the interference screw material on the SED.
6.3.1 m
odel
of
acl r
econStruction
An anatomic single-bundle ACL reconstruction was performed on the validated model of the human
knee joint. A routine procedure was undertaken with the guidance of a surgeon. After the removal of
the natural ACL, a tibial bone tunnel was drilled from the medial side of the tibial tubercle through
the natural footprint of the ACL on the tibial plateau. The tunnel diameter was 9 mm, and the length
was approximately 40 mm. The femoral bone tunnel was drilled from the natural ACL footprint on
the femoral notch and through the lateral side of the femoral cortical bone. Specifically, an Endobutton
fixation requires the extra-articular part of the femoral tunnel to be 4.5 mm in diameter and 10 mm in
length. The intra-articular part of the tunnel was 9 mm in diameter and approximately 25 mm in length.
Bundles of nonlinear springs were used to simulate the graft in the FE model. The virtual graft
was placed within the bone tunnels and served as a connector between the femur and tibia. In real-
ity, the material properties of the tendon graft and Endobutton tape were different from the natural
ACL. However, this study focused on the SED redistribution induced by the tunnel and interference
screw. To eliminate the side effects of graft and Endobutton tape material on SED distribution, their
material properties were assumed to be equal to that of the ACL. On the intra-articular tunnel aper-
ture, the graft was free to move along the tunnel axis, whereas it was constrained in the direction
perpendicular to the tunnel axis. To simulate this motion pattern, a slip ring algorithm was utilized
in the interaction of “tunnel aperture-graft.”
An interference screw was utilized to fix the graft end within the tibial tunnel. As shown in Figure 6.1,
a screw 9 mm in diameter and 25 mm in length was placed in the distal tibial tunnel, whereby its head
engaged the extra-articular tunnel aperture. The screw was meshed with a four-node tetrahedral ele-
ment and assigned with a homogeneous linear elastic material. To quantify the influence of the screw
material on the SED distribution, an elastic modulus ranging from 0 to 113.5 GPa (modulus of titanium
alloy) was analyzed, with a Poisson ratio of 0.27. The FE model of the knee following ACL reconstruc-
tion is shown in Figure 6.1. Loading and boundary conditions were as follows: distal tibia was rigidly
fixed in all directions, and a compressive loading equal to the body weight was applied at the proximal
femur in the direction of the femoral shaft. Knee extension was maintained during the loading.
6.3.2 c
HanGe
of
Sed d
iStriBution
after
acl r
econStruction
After ACL reconstruction, the SED distributions changed in both femur and tibia, and these changes
occurred primarily around the tunnels (Figure 6.2). Adjacent to the femoral tunnel, a reduction
in SED occurred at both proximal and distal regions of the tunnel wall. The minimum SED was
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