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Transcript
An Investigation of Anterior Cruciate Ligament Injuries and Analysis of the Bone-Patellar
Tendon-Bone Graft in Reconstruction Surgery
BME/ME 456 Final Project
For: Scott Hollister, Ph. D.
Professor, Biomedical Engineering
From: Maher Abubakr
Undergraduate Student, Mechanical Engineering
December 19, 2013
INTRODUCTION
The anterior cruciate ligament (ACL) is one of the most important ligaments in the knee and is important
for joint stability and knee functionality. ACL injuries are one of the most common knee injuries and it is
often a career ending injury for athletes. For the 2013 NFL season, 52 players have suffered from torn
ACLs and 27 in preseason [1]. This shows the need for analysis of the ACL and ways to improve the
surgical process and finding grafts that will suffice for the stresses endured on the knee during physical
activity. I’m studying ACLs because of the high percentage of athletes that tear their ACL. Also, I tore my
ACL in April and had surgery in May 2013, so I have a MRI scan of my knee that I will be using for
analysis. I chose the bone-patellar tendon bone (BPTB) graft, as it is the strongest graft to replace the
ACL. In this report, I will be using my own MRI scan to segment out the required knee components and
simulate ACL reconstruction surgery when the BPTB graft is attached to the femur and placed under
tension before securing it to the tibia. There have been countless studies about ACL injuries including
graft failure loads, graft selection, and tension applied before securing the graft and they will be
referenced in this study. In this analysis of the BPTB graft, two tests will be performed with certain
boundary conditions. During ACL reconstruction surgery, femoral and tibial tunnels are drilled through
the femur and tibia, then the BPTB graft is screwed into the femur, tension is applied, and lastly it is
attached to the tibia; therefore, in the first test the BPTB graft will be constrained where it attaches to
the femur and a force will be applied on the other end where it attaches to the tibia to simulate the
BPTB graft in tension. In the second test, the BPTB graft will be constrained on both ends, simulating the
attachment to the femur and tibia, and a force will be applied in the middle of the graft. To have a
foundational model that can be built upon for future analysis and for simplicity, 1-D linear elasticity will
be assumed and used as the constitutive model, where σ = Eε. σ is the Cauchy stress, E is the Young's
modulus, and ε is the small strain. In linear elasticity, it is assumed that the material undergoes small
deformation and after deformation it returns completely to its undeformed state.
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METHODS
In order to investigate the problem, I segmented the important components in my MRI scan using
MIMICS, created a volume mesh in 3-matic, and applied boundary conditions on the BPTB graft using
Hypermesh. The MRI scans of my knee with the torn ACL are shown in Figure 1.
Figure 1: 3 MRI scans of my knee were used to segment out necessary knee components for analysis.
With these images, the femur, tibia, posterior cruciate ligament (PCL), patellar tendon, patella,
meniscus, and fibula were segmented as shown in Figure 2 (p.3). Each knee component was segmented
by applying the correct threshold, then the edit mask tool was used to segment out on a "slice by slice"
basis. After segmenting the given knee component, the 3D model was calculated with the "Calculate 3D"
tool. Then, the polylines and cavity fill tool were used to fill each knee component segmented. Lastly,
each knee component was cleaned by using the smooth tool.
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Figure 2: Posterior, Lateral, and Anterior view of segmented components of knee.
The accuracy of the segmentation was not optimal because the MRI scans had thick slices. To
compensate this, more smoothing was necessary for each component. After segmenting the necessary
components of my knee, ACL surgery was simulated by using the "Cut with Cutting Plane" tool under the
Simulation tab of MIMICS to cut out a graft from the patellar tendon as shown in Figure 3.
Figure 3: Patellar tendon graft cut out from patellar tendon. 10 mm width.
The standard BPTB graft is 10 mm in width and spans from the patella bone to the tibia bone [2]. My
MRI scan was not big enough to include the segment of the patellar tendon where it attaches to the
tibia; therefore, I only cut out the patellar tendon without the bone segments from the patella and tibia.
This will also simplify the analysis later because only one material property will have to be assigned to
the patellar graft.
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After the patellar tendon was cut, the graft was placed appropriately between the femur and tibia as
shown in Figure 4. In ACL reconstruction, a bone tunnel is drilled in the femur and the tibia. These holes
are called the femoral and tibial tunnel. The BPTB graft is passed through the tunnel and secured in the
femur with a metal screw. Then, tension is applied and the other end of the BPTB graft is screwed into
the tibia [3]. This tension will be simulated in Hypermesh using finite element analysis to check the
displacement, strain, and stresses endured by the BPTB graft. If time permitted, I would secure the BPTB
graft in place and apply a force on the femur to check the stresses on the graft. Due to time constraints,
I will only be performing an analysis on the graft itself.
Figure 4: X-ray scan shows the location of BPTB graft in my knee. Subsequent graft location in MIMICS.
After segmentation and placing the BPTB graft in the proper location, 3-matic was used to create
volume meshes for the BPTB graft, PCL, femur, and tibia as shown in Figure 5 (p.5). 3-matic is reached by
going to the FEA/CFD toolbar and clicking on "Remesh". Even though the PCL, femur, and tibia will not
be used for analysis, they were only meshed for future analysis.
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Figure 5: Wrap, smooth, reduce & auto remesh were used to create a volume mesh of the BPTB graft,
PCL, femur, and tibia. Only the BPTB graft volume mesh will be used for analysis as shown on the right
Once the meshing was completed, the volume mesh of the BPTB was exported via an Abaqus file. Then
material properties were assigned to the BPTB mesh with MIMICS as shown in Figure 6. The Young's
Modulus, E, used for the patellar tendon was 507.38 MPa [4].
Figure 6: Assigning material properties to BPTB with MIMICS.
After assigning the material properties, the file was exported as an Abaqus file and opened in
Hypermesh for analysis. In Hypermesh, two analyses were performed to simulate the BPTB graft in the
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ACL position undergoing stress. In the first test (Figure 7), the BPTB graft was constrained where it
connects to the femur and pulled with a 22 N force on the opposite end where it attaches to the tibia.
This would simulate the recommended tension applied during ACL reconstruction surgery [5].
Figure 7: BPTB graft was constrained at the Femur location and pulled on the opposite end.
In the second analysis, the BPTB tendon was constrained on both ends where it attaches to the femur
and tibia, then a force was applied to the middle of the tendon as shown in Figure 8.
Figure 8: A second analysis was performed, securing the ends of the BPTB graft where it would attach
to the femur and tibia. Then a 22 N force was applied in the middle of the BPTB graft.
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RESULTS
In the first test, the BPTB graft was assumed to be an isotropic linear elastic material. It was constrained
at the femur attachment location and a 22N force was applied downward as recommended during ACL
reconstruction surgery before securing the graft to the tibia [5]. The subsequent displacement and
maximum principal stress for the 22 N force are 36 mm and 69 Pa, respectively. The contour plots of
displacement, strain, and maximum principal stress are shown in Figure 9.
Figure 9: Contour plots of displacement, strain, and stress after 22 N force applying tension.
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For the second test performed, bending was simulated by constraining the two ends of the BPTB graft,
where it attaches to the femur and tibia, and a 22 N force was applied at the middle of the BPTB graft.
The subsequent displacement and maximum principal stress were 5 mm and 49 Pa, respectively. Figure
10 shows the contour plots of displacement, strain, and maximum principal stress. The max stress was
located at the graft locations where it would attach to the femur and tibia. The stress where the force
was applied was about 25 Pa. This analysis shows that when a force is applied to the middle of the BPTB
graft it is more likely to fail at the attachment points because there was about 2 times more stress at the
attachment points than the middle of the BPTB graft where the force was applied.
Figure 10: Contour plots of displacement, strain, and maximum principal stress of bending test.
8
DISCUSSION
In this analysis of the BPTB graft, I found that when the recommended tension is applied to the BPTB
graft with a 22 N force, it displaces 36 mm and 69 Pa of stress is developed. This seems to be a
reasonable result as in a surgery you would not want to plastically deform the BPTB tendon, so a small
force is applied to keep tension in the graft yet not lose its properties. In the second test, the two ends
of the graft were secured in place with constraints to simulate the graft being attached to the femur and
tibia. Then, a force was applied to the middle of the graft to check it’s bending properties. It was found
that the graft displaces 5 mm and has a maximum principal stress of 49 Pa. This is also a reasonable
result as the graft has to be strong enough so that it can undergo stresses when it is inside the knee joint
and not plastically deform nor fail.
There were some strengths and weaknesses of the analysis performed. First, it was a great first step in
analysis of the BPTB graft to perform these tests with simplicity. A foundation was developed and the
tests can be made more realistic in the future. The results seemed to be reasonable, so it provides a
stepping stone to increase the complexity of the tests. Some weaknesses were that the test was
oversimplified and should be more realistic. The tests can be made more realistic by changing the
material properties from isotropic linear elastic to isotropic non-linear elastic. Some isotropic non-linear
elastic models that could be tested are the Neo-Hookean, Mooney-Rivlin, and Ogden models. Each of
these models could be tested and the best results would be considered. In a one study of the behavior
of ligaments and menisci of a healthy human knee, the Neo-Hookean model was used for describing the
properties of the MCL, LCL, ACL, PCL, and the patellar tendon [7]. These models could be used to
describe the behavior of the BPTB graft in a future analysis for more accuracy of graft behavior.
9
A few methods would be changed if this analysis were performed again to make it more realistic and
accurate. The isotropic linear elastic model would be changed to an isotropic non-linear elastic model,
so that the BPTB tendon would take on more of its realistic qualities and material properties. Also, the
3D model itself would be made more realistic by using the volume meshes of the femur, tibia, and PCL
and giving them each the correct models and properties. Then, the femur, tibia, PCL, and BPTB graft
would all be attached and meshed together. The BPTB graft would be attached by creating femoral and
tibial tunnels in the appropriate location as shown in Figure 4 (p.4), then attached to the femur and
tibia. Also, another area that the analysis could be improved would be to segment out the bone as well
with the BPTB graft, as I only segmented out the patellar tendon in my analysis. A correct BPTB graft
with bone plugs is shown in Figure 11.
Figure 11: The Bone-Patellar Tendon-Bone graft with bone and tendon properties [6].
Another area that the analysis could be improved would be to include the lateral collateral ligament,
medial collateral ligament, and menisci. These knee components would add stability to the knee and the
knee could undergo more stress because the stress would be distributed to all four ligaments when
forces are applied to the knee.
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In conclusion, this analysis of the BPTB graft is a great stepping stone to make the model more realistic.
In the future, the following tests can be performed to make the analysis more realistic and accurate:
1. Change material properties of BPTB graft to isotropic non-linear elastic models and perform
same FEA tests outlined in methods.
2. Segment out the BPTB tendon with bone plugs and assign different material properties to bone,
and perform same FEA tests outlined in methods.
3. Attach BPTB graft to femur and tibia with femoral and tibial tunnels and perform FEA tests by
applying a force to the femur or tibia and check the stresses on the BPTB graft.
4. Segment out the Medial and Lateral Collateral Ligaments and meniscus and rerun the FEA tests
as performed in 3.
5. Perform tests with other graft choices and compare stresses to the BPTB graft.
All of these tests will make the analysis of the BPTB graft more realistic and will help aid in improving
ACL reconstruction surgeries by finding a suitable tension to be applied to the graft before attachment
to the tibia and finding the optimal location for the ACL graft with the least stresses.
11
REFERENCES
[1] Schudel, J. (14 December 2013). Jeff Schudel’s NFL notes: Cause of ACL injury increase is unclear.
http://www.news-herald.com/sports/20131215/jeff-schudels-nfl-notes-cause-of-acl-injuryincrease-is-unclear
[2] Mall, N.A., Van Thiel, G.S., Bedi, A., Cole, B.J. (July 2012). Graft Selection in Anterior Cruciate
Ligament Reconstruction. http://www.rockfordortho.com/wp-content/uploads/2012/07/GraftSelection-in-ACL-Surgery.pdf.
[3] Cluett, J. (03 April 2012). Steps of ACL Surgery – How ACL Surgery Is Performed.
http://orthopedics.about.com/od/aclinjury/p/reconstruction.htm.
[4] Hashemi, J., Chandrashekar, N., Slauterbeck, J. (23 November 2004). The mechanical properties
of the human patellar tendon are correlated to its mass density and are independent of sex.
http://www.ncbi.nlm.nih.gov/pubmed/15927738.
[5] Gertel, T.H., Lew, W.D, Lewis, J.L., Stewart, N.J., Hunter, R.E. (1993). Effect of anterior cruciate
ligament graft tensioning direction, magnitude, and flexion angle on knee biomechanics. The
American Journal of Sports Medicine. Vol. 21, No.4.
http://ajs.sagepub.com/content/21/4/572.short.
[6] A Patient’s Guide to Patellar Tendon Graft Reconstruction of the ACL. eOrthopod.
http://www.eorthopod.com/content/patellar-tendon-graft-reconstruction-acl
[7] Peña, E., Calvo, B., Martínez, M.A., Doblaré, M. (28 April 2005). A three-dimensional finite
element analysis of the combined behavior of ligaments and menisci in the healthy human knee
joint. http://www.sciencedirect.com/science/article/pii/S0021929005002113#.
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