1. science
2. medicine
3. surgery

Tension Changes Within the Bundles of Anatomic
Double-Bundle Anterior Cruciate Ligament Reconstruction at
Different Knee Flexion Angles: A Study Using a 3-Dimensional
Finite Element Model
Heon Young Kim, Ph.D., Young-Jin Seo, M.D., Hak-Jin Kim, M.S., Trung Nguyenn, Ph.D.,
Nagraj S. Shetty, M.S., and Yon-Sik Yoo, M.D., Ph.D.
Purpose: The aim of this study was to determine the change in length and tension of the reconstructed
anterior cruciate ligament (ACL) double bundles at different knee flexion angles by use of a 3-dimensional
finite element model. Methods: The right knees of 12 living subjects were scanned with a high-resolution
computed tomography scanner at 0°, 45°, 90°, and 135° of knee flexion. Several modeling programs were
used to simulate double-bundle ACL reconstruction. A finite element model of each bundle with a tension
of 20 N was put into each tunnel followed by fixation of the bundles. The tension and length changes of
each bundle at different knee flexion angles were assessed. Results: For the anteromedial bundle, the
length decreased gradually between 45° and 90° of knee flexion and then reached a plateau, whereas the
length of the posterolateral bundle significantly decreased at 45° and 90° of flexion but then increased at
full flexion. The reaction force of the anteromedial graft slightly decreased at 45° and then remained
constant between 90° and 135° of knee flexion. The reaction force of the posterolateral bundle at full
extension slightly decreased at 45° and 90° of flexion, followed by a rebound increase at 135°.
Conclusions: We found that both bundles functioned throughout the arc of flexion with consistency in
tension, although their lengths decreased. The 2 ACL grafts did not function in a reciprocal manner, unlike
previous descriptions. Clinical Relevance: The data obtained for length and tension versus flexion angle
have the potential to suggest the appropriate knee position for graft fixation and tensioning to be near
extension in clinical situations.
T
From the Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, Republic of Korea;
and (H.Y.K., H-J.K., T.N.), Department of Orthopaedic Surgery,
Hallym University (Y-J.S., N.S.S., Y-S.Y.), Chuncheon, Republic of
Korea.
Presented at the 2010 Congress of the Arthroscopy Association of North America, May 2010, Hollywood, FL.
Supported by the National Research Foundation of Korea
(Grant #2010-0005967). The authors report no conflict of interest.
Received June 7, 2010; accepted May 13, 2011.
Address correspondence to Yon-Sik Yoo, M.D., Department of
Orthopaedic Surgery, College of Medicine, Hallym University, 153
Gyo-Dongl, Chuncheon, Gangwon-do, Republic of Korea. E-mail:
[email protected]
© 2011 by the Arthroscopy Association of North America
0749-8063/10345/$36.00
doi:10.1016/j.arthro.2011.05.012
he anterior cruciate ligament (ACL) is one of the
most frequently injured ligaments of the knee.
The ACL consists of 2 bundles: a slightly larger
anteromedial (AM) bundle and a posterolateral (PL)
bundle, named according to their relative tibial insertion sites. Recently, reconstruction techniques have
focused on the anatomic and double-bundle method
because each bundle (AM and PL) has been found to
have a different length, width, area, and function.1,2
Knowledge of tension changes within the ligaments
over the knee range of motion will contribute to a
better understanding of knee function and serve as a
useful basis for an improved anatomic ACL reconstruction. In general, the studies regarding ACL tension change have been performed using cadavers.3,4
However, recent in vivo data counter the notion about
the reciprocal relation between the bundles and advo-
Arthroscopy: The Journal of Arthroscopic and Related Surgery, Vol xx, No x (Month), 2011: pp xxx
1
2
H. Y. KIM ET AL.
cate that both bundles shorten with flexion.5,6 A few
studies have reported on the ligament tension that
might be generated as a result of the interaction and
contact between the 2 bundles.7-11 Therefore we conducted a finite element analysis of a 3-dimensional
(3D) knee model to measure the tension changes
within the 2 grafts created after the standard doublebundle ACL reconstruction procedure. The computational procedures were used to build a full-form computer-aided design (CAD) model from computed
tomography (CT) images, to simulate tensioning in
the initial extension state, and then to analyze the
behavior of the ligaments at different knee flexion
angles.
The purpose of this study was to determine the
change in length and tension of the reconstructed
ACL double bundles at different knee flexion angles
using a 3D finite element model. The hypothesis to
be tested is that the tension of the AM and PL grafts
may remain relatively consistent, despite substantial change in length, at different knee flexion angles after ACL reconstruction.
METHODS
Computational Procedures
A 3D CT image– based analysis study was conducted in 12 subjects (all men) with no history of knee
pathology or previous injury. We excluded subjects
who had any form of arthritis, infection, meniscal
injury, or previous surgery on the same knee. The
median age of the subjects at the time of the study was
29.4 ⫾ 5.3 years (range, 21 to 39 years). The study
was approved by our institutional review board, and
informed consent was obtained from all subjects. The
right knee of each subject was scanned with a highresolution CT scanner (SOMATOM Sensation; Siemens, Erlangen, Germany) with 1-mm slices taken at
0° and 3 different knee flexion angles (45°, 90°, and
135°) in the lateral decubitus position. The DICOM
(Digital Imaging and Communications in Medicine)
files obtained were imported into visualization software (Amira R 4.0; Mercury Computer Systems,
Chelmsford, MA) to construct virtual 3D models of 12
knees in total. These 3D images were then imported to
validated customized software (Rapidform 2006;
Rapidform, Seoul, South Korea) to analyze spatial
relations between anatomic structures followed by export of the 3D images to CAD software (Catia V5;
Dassault Systemes, Vélizy-Villacoublay, France). The
final CAD model was constructed by drilling tunnels
for the grafts. This converted CAD model was then
exported to the special-purpose finite element preprocessor HyperWorks (Altair Engineering, Troy, MI), in
which the final computational model was constructed
for virtual analysis. Finite element analysis was performed with Abaqus/Explicit code (Simulia, Providence, RI) in which the femur and tibia were modeled
as rigid bodies because the bony structure stiffness is
much higher than that of the soft tissues.
Insertion Site Identification
The anatomy of the ACL insertion site has been
extensively studied, and the lateral intercondylar and
bifurcate ridges have been highlighted as key structures to delineate the ACL footprint.12,13 The tibial
footprint has also been investigated, and the bony
geometry has been described.14 These geometric data
were usually achieved by use of CT because it includes irrefutable bony landmarks and reduces subjective evaluation.12,14 On the basis of these observations,
the centers of the AM and PL footprint were established on the 3D model of the tibia. On the femoral
side, these 2 points were also established. In some
subjects the identification of the tibial bony landmarks
was not possible; in such cases the subject’s knee
model was matched to available cadaveric knee models that were similar in size to the subject’s knee, and
the tibial points were obtained in the same manner as
described earlier. Femoral bony landmarks were identifiable in all knees.
Material Modeling of Reconstructed ACL
The femur and tibia were assumed to be rigid,
whereas the reconstructed ACL comprised hyperelastic rubberlike material. A hyperelastic model is generally used in engineering to represent large, incompressible deformation. The model is characterized by
a strain energy potential function, represented as equations.15
Simulation of Knee Flexion
To simulate a double-bundle ACL reconstruction,
in the 0° analytic model, four 7-mm-diameter tunnels
were drilled at the center of each AM and PL footprint
on the femur and tibia, leaving a bone bridge that is
1.5 mm thick on average between the 2 tunnels. The
simulation process was performed with Catia V5 (Fig
1). The AM and PL grafts under tension of 20 N were
put in each tunnel, and the grafts were fixed at the
middle of each tunnel. The grafts were bonded to
the tunnel by use of mesh tie kinematic constraints. The
TENSION CHANGES IN RECONSTRUCTED ACL
3
FIGURE 1. Construction of tunnels and ligaments. Seven-millimeter-diameter bone tunnels
were created at the center of each AM and PL
footprint (left, center), and the 2 grafts corresponding to the diameter of each tunnel were
inserted (right).
bone-ligament and ligament-ligament contacts were
modeled through the penalty formulation assuming
frictional coefficients of 0.1 and 0.001, respectively.16
Flexion in the reconstructed knee was simulated in 2
steps. (1) The tibia of the reconstructed knee is superimposed at 0° onto a discrete tibia at 45°, 90°, and
135° of knee flexion by use of the positional information of the coordinates. (2) The accuracy of the position and orientation of the femur is determined in
space at 45°, 90°, and 135° (Fig 2). As the software
creates a 3D coordinate system specific for each knee
with 6 dof (the x-, y-, and z-axes and pitch, roll, and
yaw), the precise position and orientation of the
femur at 45°, 90°, and 135° can be achieved by
translating and rotating the femur along the axes.
The position and orientation were both recorded to
the nearest 0.01 mm.
were determined alternatively through reaction force
calculations at both ends of the bundle insertion sites
by the finite element models. By balancing with the
reaction forces acting at the constrained locations, the
tensions in grafts were determined for 2 different
Measurement Method
The digital length of the 2 virtual bundles (AM and
PL) was measured from the center of the AM and PL
footprints of the femur to the center of the AM and PL
footprints of the tibia with validated customized software (Rapidform 2006); these measurements had an
accuracy of 0.1 mm. To minimize technical error of
measurement, the center of the footprints at 0° of knee
flexion was premarked before the superimposing process at 45°, 90°, and 135° of knee flexion. To decrease
the error, the tunnels in the tibia and femur were
placed by an expert knee arthroscopy surgeon. The
digital length was then measured based on pre-marking on the footprint with 0°, superimposed 45°, 90°,
and 135° of the knee model (Fig 3A). The tensions
within the ACL grafts at different knee flexion angles
FIGURE 2. Reconstructed knee models at different angles (0°, 45°,
90°, and 135°). The simulation of the knee flexion was conducted
by superimposing the tibia of the model with 0° of flexion onto a
tibia of the reconstructed model with 45°, 90°, and 135° of flexion,
then moving the femur from the model with 0° of flexion to a
discrete flexed position. This process enabled us to obtain more
accurate length data than those of our previous method, which had
been substantially affected by interobserver or intraobserver
variability.
AQ: 1
4
H. Y. KIM ET AL.
FIGURE 3. (A) Length change (in centimeters) of virtual straight AM and PL grafts at knee flexion angles of 0°, 45°, 90°, and 135°
(mean ⫾ standard error). The AM and PL length decreased with flexion (#P ⫽ .061, *P ⫽ .001). Also shown is an illustration of measuring the
digital length of the virtual straight grafts. (B) Patterns of reaction force changes (in newtons) of the AM and PL grafts at knee flexion angles
of 0°, 45°, 90°, and 135° (mean ⫾ standard error). The measuring point of the reaction forces at the tibial fixation site is also illustrated. The
patterns of the reaction forces of both the AM and PL grafts were relatively constant compared with length patterns between full extension
and discrete knee flexion angles (#P ⫽ .36, *P ⫽ .013, and *P ⫽ .012 for AM graft; †P ⫽ .08, *P ⫽ .044, and ‡P ⫽ .28 for PL graft).
Furthermore, both the AM and PL grafts have their greatest length and reaction force at full extension. P values represent level of significance
between 0° and each angle of flexion. *Statistically significant.
segments. Tension in the upper segment was in equilibrium with the reaction force at the insertion site on
the femur, whereas the reaction force on the tibia gave
information on tension in the lower segments of
grafts. The reaction force of grafts at different knee
flexion angles was measured at each tibial fixation
point (Fig 3B). The reaction forces can be used to
evaluate the amount of graft tension. The contacts
between the AM and PL bundles and between the
ligaments and surrounding bony structure were also
examined.
Statistical Analysis
The differences in length and tension within each
bundle at the 4 different angles were analyzed statis-
tically by 1-way analysis of variance, with the Tukey
honestly significant difference test for pair-wise comparisons. The significance level was set at P ⬍ .05.
RESULTS
Both the AM and PL bundles were longest at full
extension (3.82 ⫾ 0.18 cm and 2.89 ⫾ 0.14 cm,
respectively). For the AM bundle, the length decreased gradually between 45° and 90° of knee flexion
(3.50 ⫾ 0.14 cm and 3.39 ⫾ 0.13 cm, respectively)
and then reached a plateau (3.40 ⫾ 0.13 cm); while,
the length of the PL bundle significantly decreased at
45° and 90° of flexion (2.32 ⫾ 0.12 cm and 2.18 ⫾
0.16 cm, respectively) but then increased at full flex-
TENSION CHANGES IN RECONSTRUCTED ACL
ion (2.48 ⫾ 0.12 cm). A statistical difference was
found in the AM bundle between full extension and
more than 90° of knee flexion (P ⬍ .001) and in the
PL bundle between full extension and more than 45°
of knee flexion (P ⬍ .001). The reaction force of the
AM graft with a tension of 20 N at full extension
slightly decreased at 45° and then remained constant
between 90° and 135° of knee flexion. A statistical
difference was detected in the AM bundle between
full extension and more than 90° of knee flexion (P ⫽
.013 and P ⫽ .012, respectively); the reaction force of
the PL bundle at full extension slightly decreased at
45° and 90° of flexion, followed by a rebound increase
at 135°. A statistical difference was observed in the
PL bundle between full extension and 90° of knee
flexion (P ⫽ .044) (Fig 3).
The pattern of contact stress in the different angles
of the knee is shown in Fig 4. The contact stresses
between 2 bundles were close to 0 MPa at extension
and 45° of knee flexion but then increased at 90° and
135° of knee flexion (Fig 4A). The maximum stresses
5
between bone and bundles at full extension were monitored in the lateral portion of the bundles near the
femoral tunnel, where the measured stress in the AM
bundle was 11.3 ⫾ 2.2 MPa and the measured stress in
the PL bundle was 7.0 ⫾ 3.1 MPa. With the flexion
progressed, the portion of highest contact stresses was
moved to the distal end of the bundles near the orifice
of the tibial tunnels by way of the midportion of the
bundle around the lateral intercondylar tubercle,
where the measured stresses in the AM and PL bundles were 3.5 ⫾ 3.6 MPa and 9.6 ⫾ 4.1 MPa, respectively (Fig 4B).
The fringes of distributed contact sites and contact
stresses at each knee flexion angle are given in Fig 5.
DISCUSSION
We plotted the length-versus-flexion and tensionversus-flexion curves between 0°, 45°, 90°, and 135°
of flexion using a 3D finite element knee model and
generating virtual grafts. The most important findings
FIGURE 4. (A) Contact stress pattern between bundle and bundle. Interbundle impingement just occurred at 90° and 135° with the change
in alignment of the AM and PL femoral tunnel, which allows AM and PL grafts to form a crossing pattern. (B) Contact stress pattern between
bundle and bone. The contact stresses of the femur/AM bundle and femur/PL bundle were highest at full extension and gradually decreased
with increasing flexion, reaching 0 MPa at 135° because of increments in the femoral tunnel– graft angle. At 135°, the contact stresses of both
bundles were mainly localized on the tibial side. At 90°, the contact stress of the tibia/PL bundle was significantly higher than that of the
femur/PL bundle, which indicated that regaining the tension within the PL bundle at this flexion range was largely due to interaction between
the PL bundle and the tibial bone. Meanwhile, the contact stresses of the tibia/AM bundle were relatively constant throughout the entire arc
of flexion because of minimal change in tibial tunnel– graft angle. The contact stresses of the tibia/PL bundle were slightly lower than those
of the femur/AM bundle at 90°, implying that both the femoral and tibial contact stresses could contribute to regaining the tension within
the AM bundle at this angle.
6
H. Y. KIM ET AL.
FIGURE 5. Stress distribution within AM and PL bundles at different knee angles in a representative case. The contour shows the level of
stress on the grafts. At 0° and 45° of flexion (left 2 figures, posterior view), most of the contact force was generated at the sharp edge of the
anterior margin of the femoral tunnel. At 90° and 135° of flexion (right 2 figures, anterior view), contact force caused by both grafts being
deformed and rerouted by the lateral intercondylar tubercle was noted, which may be an important factor in maintaining tension within both
grafts despite a decrease in direct length at deep flexion.
of this study were that both grafts achieved their
greatest length and tension at full extension. Being
greatest at full extension, the length of the AM graft
was decreased gradually with knee flexion between
45° and 90° and increased thereafter. Being also greatest at full extension, the length of the PL graft dropped
suddenly with 45° of knee flexion and reached a
plateau between 45° and 90°; a rebound increase in
length was seen thereafter. These results corroborate
the findings of our previous in vivo study,17 showing
a significant reduction in the length of both the AM
and PL bundles with increasing knee flexion. In fact,
the measurement process in this study enabled us to
obtain more accurate length data than those from our
previous method, which had been substantially affected by interobserver or intraobserver variability. To
enhance the accuracy of the length data in this study,
we established the center of the footprint only on the
0° analytic model. By superimposing the tibia of the
model with 0° of flexion onto the tibia of the model
with a different degree of flexion, followed by moving
the femur from the model with 0° of flexion to a
discrete flexed position as per the coordinates, the
digital length can be obtained with high reliability
based on the marking on the center of the footprint
with 0° of knee flexion; one may then proceed with
measurements at each superimposed 45°, 90° and
135° of knee flexion model.
The tension of both bundles, which is represented as
the reaction force, was relatively consistent at all
flexion angles, although the patterns of the curves
were similar to those of the length curves. Being 20 N
at full extension, the reaction force of the AM graft
decreased slightly at 45° and then continued to be
maintained at 90° and 135° of knee flexion. Being
greatest at full extension, the reaction force of the PL
graft showed a pattern similar to that of the AM graft
and it decreased slightly between 45° and 90° and then
increased again at full flexion. These data would
therefore suggest that although the direct length between the femoral and tibial footprint decreases with
increasing flexion of the knee, both the AM and PL
grafts maintain relative constant tensile properties
throughout the range of movement.
The reaction forces of the bundles seen in our study
had patterns similar to those reported by Yasuda et
al.,18 and Vercillo et al.19 constructed the tensionversus-flexion curves of the 2 bundles and showed that
the tension of both bundles was greatest at full extension. However, the decrease in reaction force with
flexion of the PL graft18 was not as marked as that
observed in our study. Vercillo et al. reported that in
TENSION CHANGES IN RECONSTRUCTED ACL
situ forces of the AM and PL grafts were greatest at
45° and 15° of knee flexion, respectively.
Contrary to current knowledge, our observation is
that this disparity between the length-versus-flexion
and tension-versus-flexion curves might be attributable to another factor that generates tension without an
actual increase in length. The contact, friction, and
deformation caused by the graft impingement against
surrounding bone at different knee flexion angles
might play the role of transferring the force from the
graft to the bone and thus had a direct effect on the
tension in grafts. In other words, the actual deformation caused by the interaction between the 2 grafts and
the impingement between the grafts and surrounding
bony structures may play an important role in maintaining the tension within the grafts without an actual
increase in length. As flexion increases, there would
be more contact between the grafts and the bone
during knee flexion. The possible interaction between
the AM and PL bundles, as well as the frictional
contact caused by the grafts wrapping around the bone
for different knee flexion angles, is shown in Fig 4.
Depending on the knee flexion, several potential contact sites are triggered and thus the size of contact
areas was determined numerically by the finite element tools. Potential contact sites include AM-to-PL,
AM-to-femur, AM-to-tibia (at tunnel edges and at
anterior intertubercular ridge), PL-to-femur, and PLto-tibia (at tunnel edges and at intercondylar tubercle)
contact areas. Among different knee flexion angles,
the local contact stress became highest when the graft
wrapped over the sharp edges of the tunnels and was
bent to make an acute angle. However, it is uncertain
whether the intensity of contact stress measured in our
experimental finite element graft could represent the
absolute value occurring by real graft interaction because we adopted graft having hyperelastic, incompressible, and isotropic properties. In fact, the behavior of tissues can effectively be represented by a
hyperelastic material with an assumption of a negligible time- and rate-dependent effect in the preconditioned state.20-22 Hyperelasticity has been suitably
used as an ideal framework for numeric simulation of
ligaments because of its capability of describing large
deformation.22 Meanwhile, the anisotropy should be
taken into account because the ACL is a dense connective tissue consisting of mainly parallel collagen
fibers embedded in a ground substance matrix of proteoglycans, glycolipids, water, and so on. However,
the anisotropic mechanical properties of the ACL
grafts were not available because of difficulties in
measurement. Hence, to accommodate and make use
7
of the available experimental data of tensile tests,6,20
we adopted an isotropic hyperelastic material model.
Besides the merits of simplicity, selection of such a
model was decided by consideration of the predominant tension loading condition of the grafts in our
study.
According to our simulation of knee flexion, the
AM and PL bundles were compressed and rerouted by
the surrounding bony structures as flexion progressed.
At 0° of flexion, the AM and PL bundles were initially
deformed with a tension of 20 N by being compressed
against the inner portion of the lateral femoral condyle. When flexion increased to 45°, both bundles
were still compressed by the lateral femoral condyle.
At 90°, the PL bundle started to wrap around the
lateral intercondylar tubercle of the tibia and bent over
it, losing contact with the inner portion of the lateral
femoral condyle. This phenomenon was seen more
intensely with the progression of knee flexion. These
findings would suggest that ligament tension is maintained despite a decrease in direct length with flexion
by increasing the contact area, as well as contact force.
These data further validate our observation that the
role of both the PL and AM bundles is not diminished
with increasing flexion.
As evident from Fig 5, the regaining of tension in
the PL bundle at high flexion may be attributable to
contact, friction, and deformation caused by impingement mainly against the lateral intercondylar tubercle
of the tibia, which enables it to restore practical bundle length.
Song et al.23 noted the importance of contact and
friction forces occurring as a result of the interaction
between the grafts themselves and the bony structures.
According to their study, the stress distribution of the
ACL might be influenced by the intensity of contact
and friction forces. They stated that the AM bundle
had more contact with bone under an anterior tibial
load at full extension. A similar contact pattern was
observed in our extension knee models.
At 0° and 135°, the contact stresses generated by
interaction between grafts and bone were higher than
those at 45° and 90°. Interbundle impingement just
occurred at 90° and 135°, although the intensity of
stresses was negligible.
One interesting finding of our study is that the
lateral intercondylar tubercle of the tibia plays a major
role in preserving the tension of the PL bundle in mid
to high flexion, as evident from the surface stress
parameters and gross findings. In addition, the inner
portion of the lateral femoral condyle has a similar
role in maintaining the tension of both bundles at low
8
H. Y. KIM ET AL.
flexion. In our opinion, our findings are highly reliable, because we simulated knee flexion models and
grafts similar to an actual reconstructed joint by tensioning the ligaments in full extension and then moving the joint to a discrete location as per the coordinates. So the same tensioned ligament was studied at
all positions of the joint, rather than by creating the
ligament individually at each joint position.
On the basis of the data obtained from our study, we
postulate that both the bundles act in coordination
rather than reciprocally and the knee position near full
extension would be appropriate for graft fixation. On
the other hand, if the graft is secured at a high flexion
angle, the graft would be straight by tensioning during
final fixation and remain straight throughout the entire
flexion arc. For this reason, the fixation angle can be
recommended at the extension position to accomplish
the graft-bone relation during flexion progression. We
believe graft impingement might be 1 of the important
factors that can induce normal knee kinematics if the
graft is strong enough.
This study has some limitations. First, we considered both ligaments as incompressible hyperelastic
and isotropic materials, which is not feasible in a
normal knee. In particular, the incompressibility assumption may become imprecise when the water in
tissues is expelled; however, there is actually no clear
experimental evidence showing that the amount of
expelled water during the traction test is important
enough to jeopardize the incompressibility hypothesis.22,24-26 Second, the stress pattern was only considered at discrete flexion angles, rather than as a
continuum. Third, we used just 1 tendon diameter
regardless of the size of the knee, which can induce
excess friction between bundles or between the
bundle and the surrounding bony structure in case
of a small knee. Proper matching of the size of
the graft with knee size may be included in a future
study. In our study no data were collected under
anterior tibial loads or combined rotatory loads. A
better understanding of the strain patterns and behavior of each graft might be obtained in the future if
studied under the influence of an external force. Finally, the 3D modeling of the bone geometry from the
CT scan taken at axial planes and 1.0-mm intervals
does not express the cartilaginous components, which
may induce measurement errors. Therefore the use of
CT rather than magnetic resonance imaging in this
study can be a limitation. However, CT is advantageous over magnetic resonance imaging in constructing the concise portion of the knee such as the surrounding ridges on the ACL footprint in both the
femur and the tibia. Furthermore, in fact, the cartilage
thickness would be negligible on the lateral wall of the
femur or lateral intercondylar tubercle of the tibia.
Thus we believe that the measurement errors originating from the use of CT are not crucial in our study.
CONCLUSIONS
We found that both bundles functioned with consistent tension throughout the arc of flexion, although their lengths decreased. The 2 ACL grafts
did not function in a reciprocal manner, unlike
previous studies.
REFERENCES
1. Girgis F, Marshall JL, Monajem A. The cruciate ligaments of
the knee joint. Anatomical, functional and experimental analysis. Clin Orthop Relat Res 1975:216-231.
2. Basdekis G, Christel P, Anne F. Validation of the position of
the femoral tunnels in anatomic double-bundle ACL reconstruction with 3-D CT scan. Knee Surg Sports Traumatol
Arthrosc 2009;17:1089-1094.
3. Hame SL, Oakes DA, Markolf KL. Injury to the anterior
cruciate ligament during alpine skiing: A biomechanical analysis of tibial torque and knee flexion angle. Am J Sports Med
2002;30:537-540.
4. Yagi M, Wong EK, Kanamori A, Debski RE, Fu FH, Woo SL.
Biomechanical analysis of an anatomic anterior cruciate ligament reconstruction. Am J Sports Med 2002;30:660-666.
5. Li G, Defrate LE, Rubash HE, Gill TJ. In vivo kinematics of
the ACL during weight-bearing knee flexion. J Orthop Res
2005;23:340-344.
6. Miura K, Woo SL, Brinkley R, Fu YC, Noorani S. Effects of
knee flexion angles for graft fixation on force distribution in
double-bundle anterior cruciate ligament grafts. Am J Sports
Med 2006;34:577-585.
7. Peña E, Martínez MA, Calvo B, Palanca D, Doblaré M. A
finite element simulation of the effect of graft stiffness and
graft tensioning in ACL reconstruction. Clin Biomech 2005;
20:636-644.
8. Hirokawa S, Tsuruno R. Three-dimensional deformation and
stress distribution in an analytical/computational model of the
anterior cruciate ligament. J Biomech 2000;33:1069-1077.
9. Gao B, Zheng NN. Alterations in three-dimensional joint kinematics of anterior cruciate ligament-deficient and -reconstructed knees during walking. Clin Biomech 2010;25:222229.
10. Lam MH, Fong DT, Yung PS, Ho EP, Chan WY, Chan KM.
Knee stability assessment on anterior cruciate ligament injury:
Clinical and biomechanical approaches. Sports Med Arthrosc
Rehabil Ther Technol 2009;1:20.
11. Woo SL, Fisher MB. Evaluation of knee stability with use of a
robotic system. J Bone Joint Surg Am 2009;91:78-84 (Suppl 1).
12. Ferretti M, Ekdahl M, Shen W, Fu FH. Osseous landmarks of
the femoral attachment of the anterior cruciate ligament: An
anatomic study. Arthroscopy 2007;23:1218-1225.
13. Hutchinson MR, Ash SA. Resident’s ridge: Assessing the
cortical thickness of the lateral wall and roof of the intercondylar notch. Arthroscopy 2003;19:931-935.
14. Purnell ML, Larson AI, Clancy W. Anterior cruciate ligament
insertions on the tibia and femur and their relationships to
critical bony landmarks using high-resolution volume-render-
TENSION CHANGES IN RECONSTRUCTED ACL
15.
16.
17.
18.
19.
ing computed tomography. Am J Sports Med 2008;36:
2083-2090.
Takeda Y, Xerogeanes JW, Livesay GA, Fu FH, Woo SL.
Biomechanical function of the human anterior cruciate ligament. Arthroscopy 1994;10:140-147.
Chizari M, Wang B. 3D numerical analysis of an ACL
reconstructed knee. 2009 SIMULIA Customer Conference
2009:1-13.
Yoo YS, Jeong WS, Shetty NS, Ingham SJ, Smolinski P, Fu F.
Changes in ACL length at different knee flexion angles: An in
vivo biomechanical study. Knee Surg Sports Traumatol Arthrosc 2010;18:292-297.
Yasuda K, Ichiyama H, Kondo E, Miyatake S, Inoue M,
Tanabe Y. An in vivo biomechanical study on the tensionversus-knee flexion angle curves of 2 grafts in anatomic double-bundle anterior cruciate ligament reconstruction: Effects of
initial tension and internal tibial rotation. Arthroscopy 2008;
24:276-284.
Vercillo F, Woo SL, Noorani SY, Dede O. Determination of a
safe range of knee flexion angles for fixation of the grafts in
double-bundle anterior cruciate ligament reconstruction: A
human cadaveric study. Am J Sports Med 2007;35:1513-1520.
9
20. Woo SL, Hollis JM, Adams DJ, Lyon RM, Takai S. Tensile
properties of the human femur-anterior cruciate ligament-tibia
complex. The effects of specimen age and orientation. Am J
Sports Med 1991;19:217-225.
21. Fung YC. Biomechanics: Mechanical properties of living tissues. New York: Springer-Verlag, 1981.
22. Weiss JA, Maker BN, Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity.
Comput Methods Appl Mech Eng 1996;135:107-128.
23. Song Y, Debski RE, Musahl V, Thomas M, Woo SL. A
three-dimensional finite element model of the human anterior
cruciate ligament: A computational analysis with experimental
validation. J Biomech 2004;37:383-390.
24. Pioletti DP, Rakotomanana LR. Non-linear viscoelastic laws for
soft biological tissues. Eur J Mech A Solids 2000;19:749-759.
25. Pioletti DP, Rakotomanana LR, Benvenuti JF, Leyvraz PF.
Viscoelastic constitutive law in large deformations: Application to human knee ligaments and tendons. J Biomech 1998;
31:753-757.
26. Weiss JA, Gardiner JC, Ellis BJ, Lujan TJ, Phatak NS. Threedimensional finite element modeling of ligaments: Technical
aspects. Med Eng Phys 2005;27:845-861.