Estimation of In-vivo Forces within Anterior Cruciate
Ligament in Response to Increased Weightbearing
By
Ali Hosseini
M.S. Mechanical Engineering, Isfahan University of Technology, 2003
B.S. Mechanical Engineering, Isfahan University of Technology, 2000
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING
AT THE
ARCHIVES
MASSACHUSETTS
INS~nlJTE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
OF TECHNOLOGY
JUNE 2010
SEP 0 1 2010
LIBRARIES
C2010 Ali Hosseini. All rights reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper
and electronic copies of this thesis document in whole or in part in any medium now
known or hereafter created.
Signature of Author:
Department of Mechanical Engineering
May 25, 2010
Certified by:
_
_
_
_
L_
_
Guoan Li
Professor of Orthopedic Surgery/Bioengineering, Harvard Medical School
Thesis Supervisor
~'
Certified by:
N-,
Derek Rowell
Professor of Mechanical Engineering
Thesis Committee Chairman
Accepted by:
David E. Hardt
Professor of Mechanical Engineering
Chairman, Department Committee on Graduate Students
Estimation of In-vivo Forces within Anterior Cruciate
Ligament in Response to Increased Weightbearing
By
Ali Hosseini
Submitted to the Department of Mechanical Engineering
on May 25, 2010 in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy in
Mechanical Engineering
ABSTRACT
The knowledge of Anterior Cruciate Ligament (ACL) forces in-vivo is instrumental for
understanding ACL injury mechanisms and for improvement of surgical ACL
reconstruction. The goal of this thesis was to develop and implement a non-invasive
method to determine the ACL forces under physiological loading using advanced
imaging techniques combined with a robotic testing system. First, the in-vivo elongation
of the ACL in response to increasing weightbearing was captured by a Dual Fluoroscopic
Imaging System (DFIS). Next, the force-elongation curves of the ACL were determined
in-situ by the robotic testing system. The in-vivo ACL elongation data were statistically
mapped to force-elongation curves and the in-vivo ACL forces were estimated. A gold
standard robotic testing protocol was implemented to validate the proposed force
estimation method in cadaveric specimens. Moreover, this methodology was extended to
the bundles of the ACL - i.e., anteromedial (AM) and posterolateral (PL) bundles - to
determine the force contribution of each bundle. The data showed that the ACL force is
greater at lower flexion angles. Generally, the AM bundle carried greater portion of the
tension within the ACL at all flexion angles. The data revealed that the load sharing
patterns of the two bundles were complementary.
The proposed force estimation method was then generalized to measure the contact
pressure distribution of the tibiofemoral cartilage. By knowing the tibiofemoral cartilage
deformation data in-vivo, and mapping them to in-vitro material property data, one can
determine the in-vivo contact pressure inside the tibiofemoral joint. As the first step of
application, the DFIS was employed to investigate the time-dependent responses of the
tibiofemoral cartilage under a constant bodyweight load (in-vivo creep). The cartilage
contact deformation in the lateral compartment was shown to be greater than that in the
medial compartment of the knee.
The findings of this work provide insight into the biomechanical role of the ACL during
in-vivo activities and can be used as quantitative guidelines for the development of
optimized surgical reconstruction techniques. The methodology could have a wide
application in determination of in-vivo loading of human musculoskeletal joints.
Thesis Supervisor: Guoan Li, Ph.D.
Professor of Orthopaedic Surgery/Bioengineering, Harvard Medical School
Committee Chair: Derek Rowell, Ph.D.
Professor of Mechanical Engineering, Massachusetts Institute of Technology
Committee Member: Alan J. Grodzinsky, Sc.D.
Professor of Electrical, Mechanical, and Biological Engineering
Massachusetts Institute of Technology
Acknowledgements
I would like to thank my advisor, Dr. Guoan Li, for giving me the opportunity to study
and work in a very exiting field. His enthusiasm, motivation, guidance and generosity are
admirable. It has been a privilege to work with him. I have learned a lot from his
knowledge and from his personality. I also would like to appreciate my thesis committee
members, Professors Derek Rowell and Alan Grodzinsky for guiding me through my
academic career at MIT and their insightful comments and support.
I must acknowledge all my teachers since my first grade. They educated me step by step
to this point of my life. Especially, I appreciate the knowledge I gained from Professors
Alan Grodzinsky, Neville Hogan and Gareth McKinley in their classes.
I am also very grateful to the staff of Mechanical Engineering Department, particularly
Leslie Regan, for all her help, guidance and support during my MIT experience.
I extend special thanks to the members of the Bioengineering Laboratory, past and
present, who have been available academically and socially: Jeff, Lou, Ram, George,
Jeremy, Angela, Kartik, Shaobai, Mike, Sam, Daniel, Hemanth, Dr. Nha and Dr. Seon.
Also, I would like to thank the Orthopaedic Department at the Massachusetts General
Hospital and the MGH Sports Medicine Services for all the support and the excellent
academic environment, in particular Dr. Thomas Gill who provided me with the clinical
insight of the work.
Since part of my research involved testing of human cadavers, I want to thank the donors
and their families for their generosity and support for improving the human health and
life. Also, the financial support of the National Institutes of Health (NIH) is greatly
appreciated.
I would like to thank all my friends for making my life happier and more joyful,
especially Pouyan and Mike. I am grateful to Natalie for all her love, understanding,
patience, and beautiful smile. I cherish the time we have spent together and look forward
to the time I hope to share.
Last but not least, I wish to thank my family for all their love and support. In particular, I
thank my mother, Fatemeh, for her unconditional love, devotion, inspiration and
guidance throughout my life. I appreciate her trust in my abilities and never-ending
support and patience so that I could always pursue my goals and dreams. I remember and
thank my father, Alireza, the first engineer in my life, who inspired me to be an engineer.
I also thank my sisters: Afsaneh, Azadeh and Alaleh for their help and encouragement. I
thank you so much for loving me. I give thanks to God for helping and holding me
through this period and whole my life. He has blessed me beyond measure.
This thesis is dedicated to my family.
~Ali
Table of Contents
ABSTRACT..............................................................................................
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
5
..........................................
............ 6
...............................
LIST OF FIGURES................................
LIST OF TABLES.........................
........
3
...
....................
CHAPTER 1 - INTRODUCTION.......................................
10
15
16
1.1 THE ANTERIOR CRUCIATE LIGAMENT ..............................................................................
16
1.2 BACKGROUND AND OBJECTIVES......................................................................................
17
1.3 ORGANIZATION OF THE THESIS ........................................................................................
20
1.4 R EFEREN CES........................................................................................................................
24
CHAPTER 2 - IN-VIVO ANTERIOR CRUCIATE LIGAMENT ELONGATION
IN RESPONSE TO AXIAL TIBIAL LOADS...........................
29
2.1 IN TRODU CTION ....................................................................................................................
29
2.2 M ATERIALS AND M ETHODS ............................................................................................
30
2.2.1 Magnetic Resonance Imaging and 3D Knee Models.............................................
30
2.2.2 FluoroscopicImaging of the Knee...........................................................................
35
2.2.3 Reproducing In-vivo Knee Kinematics ....................................................................
35
2.2.4 D ata A nalysis...............................................................................................................
38
2 .3 R ESU LTS ..............................................................................................................................
38
2.3.1 Single B undle ...............................................................................................................
38
2.3.2 Double B undles............................................................................................................
40
2.3.3 Multiple Surface FiberBundles ...............................................................................
42
2.4 D ISCU SSION .........................................................................................................................
45
48
2.5 ACKNOW LEDGEM ENTS.........................................................................
2.6 REFEREN CES........................................................................................................................
49
CHAPTER 3 - ESTIMATION OF IN-VIVO FORCES WITHIN ANTERIOR
CRUCIATE LIGAMENT IN RESPONSE TO WEIGHTBEARING.......... 53
3.1 IN TRO DU CTION ....................................................................................................................
53
3.2 MATERIALS AND METHODS .............................................................................................
54
3.2.1 Measurement of In-vivo Elongation of the ACL in Response to Increased
Weightbearing.......................................................................................................................
54
3.2.2 In-vitro Force-ElongationRelations of the A CL ......................................................
58
3.2.3 Estimation of In-vivo A CL Force Changes................................................................
61
3.2.4 Effect ofAssumed Tension in the ACL under Zero Weightbearingon In-vivo ACL
F orce Estim ation ..................................................................................................................
63
3.2.5 Sensitivity Study ...........................................................................................................
64
3.2.6 StatisticalA nalysis ...................................................................................................
64
3.3 RE SU LTS ..............................................................................................................................
65
3.3.1 In-vivo A CL Elongation Due to Full Body Weight ..................................................
65
3.3.2 In-vitro Force-ElongationBehavior of the A CL.......................................................
66
3.3.3 In-vivo A CL Force IncreaseDue to Full Body Weight............................................
67
3.3.4 Estimation of In-vivo ACL Force.............................................................................
69
3.3.5 Sensitivity Study ...........................................................................................................
69
3.4 D ISCU SSION .........................................................................................................................
69
3.5 V ALIDATION STUDY ............................................................................................................
73
3.5.1 Validation of the In-vivo A CL Force Estimation Method.........................................
73
3.6 ACKNOW LEDGEM ENTS.....................................................................................................
78
3.7 REFEREN CES........................................................................................................................
79
CHAPTER 4 - ESTIMATION OF IN-VIVO FORCES WITHIN THE
ANTEROMEDIAL AND POSTEROLATERAL BUNDLES OF THE ANTERIOR
CRUCIATE LIGAMENT UNDER WEIGHTBEARING...................
83
4.1 IN TROD U CTION ....................................................................................................................
83
4.2 M ATERIALS AND M ETHODS ................................................................................................
84
4.2.1 In-vivo Elongation of the AM andPL Bundles in Response to Increased Weightbearing
..............................................................................................................................................
4.2.2 In-vitro Force-ElongationRelations of the AM and PL Bundles
84
........................ 85
4.2.3 Estimation of In-vivo AM and PL Forces....................................................................
87
4.2.4 StatisticalA nalysis...................................................................................................
87
88
4 .3 RESU LTS ..............................................................................................................................
88
4.3.1 In-vitro Force-ElongationBehavior of the AM and PL Bundles of the ACL .......
4.3.2 In-vivo ForceIncrease in the AM and PL Bundles of the ACL Due to Full Body Weight
..............................................................................................................................................
88
4.3.3 Estimation of In-vivo Forces within the AM and PL Bundles .................
89
4 .4 D ISCU SSIO N .........................................................................................................................
92
4.5 A CKNOW LEDGEM ENTS........................................................................................................
94
4.6 REFEREN CES........................................................................................................................
95
CHAPTER 5 - IN-SITU FORCES WITHIN THE ANTEROMEDIAL AND
POSTEROLATERAL BUNDLES OF THE ANTERIOR CRUCIATE LIGAMENT
98
UNDER SIMULATED FUNCTIONAL LOADING CONDITIONS ...........
5.1 IN TRODU CTION ....................................................................................................................
98
5.2 MATERIALS AND METHODS ............................................................................................
99
5.2.1 Specim en Preparation..............................................................................................
99
5.2.2 In-situ Forces within the AM and PL Bundles...........................................................
100
5.2.3 StatisticalA nalysis.....................................................................................................
101
5.3 RESU LTS ............................................................................................................................
5.3.1 In-situ Forces under 134 N Anterior Tibial Load..
.....................................
102
102
5.3.2 In-situ Forces under Combined Valgus and InternalTibial Torques........................
103
5.3.3 In-situ Forces under 400 N QuadricepsMuscle Load..............................................
103
5.4 D ISCU SSION .......................................................................................................................
105
5.5 A CKNOW LEDGEM ENTS......................................................................................................
107
5.6 REFEREN CES......................................................................................................................
108
CHAPTER 6 - IMPINGEMENT OF THE ANTERIOR CRUCIATE LIGAMENT
AGAINST THE FEMORAL INTERCONDYLAR NOTCH DURING IN-VIVO
WEIGHT BEARING....................................................................................................
112
6.1 IN TRODU CTION..................................................................................................................
112
6.2 MATERIALS AND METHODS ..............................................................................................
113
6.2.1 Subject Selection ........................................................................................................
113
6.2.2 Magnetic Resonance Imaging and Three-DimensionalModel of Knee .................... 114
6.2.3 FluoroscopicImaging of the Knee.............................................................................
114
6.2.4 In-vivo Knee Positionsand A CL Impingement..........................................................
115
6.2.5 StatisticalAnalysis.....................................................................................................
6.3 RESULTS ............................................................................................................................
119
120
6.3.1 M aximum Impingement (t).........................................................................................
120
6.3.2 Impingement Ratio (t/D)............................................................................................
121
6.3.3 Impingement angle ......
................................
...........................................
121
6.4 D ISCUSSION .......................................................................................................................
122
6.5 A CKNOW LEDGEMENTS......................................................................................................
126
6.6 REFERENCES......................................................................................................................
127
CHAPTER 7 - IN-VIVO TIME-DEPENDENT ARTICULAR CARTILAGE
CONTACT BEHAVIOR OF THE TIBIOFEMORAL JOINT.............. 132
7.1 INTRODUCTION ..................................................................................................................
132
7.2 MATERIALS AND M ETHODS ..............................................................................................
133
7.2.1 Subject selection ........................................................................................................
133
7.2.2 Magnetic Resonance Imaging and 3D Model ofKnee ..............................................
134
7.2.3 Dual FluoroscopicImaging and Reproduction ofKnee Kinematics.........................
135
7.2.4 In-vivo CartilageContact Behavior ..........................................................................
137
7.2.5 StatisticalAnalysis.....................................................................................................
138
7.3 RESULTS ............................................................................................................................
139
7.3.1 CartilageContact Deformation and Contact Area with Time...................................
142
7.3.2 Rate of Change ..........................................................................................................
143
7.4 D ISCUSSION .....................................................................................................................--
147
7.5 ACKNOW LEDGEM ENTS......................................................................................................
152
7.6 REFERENCES......................................................................................................................
153
CHAPTER 8 - CONCLUSIONS .................................................................................
157
8.1 SUM M ARY..........................................................................................................................
157
8.2 FUTURE D IRECTIONS .........................................................................................................
160
List of Figures
Figure 1.1: The Anterior Cruciate Ligament (ACL) originates from deep within the notch
of distal femur and attaches in front of tibia. The anterior and posterior
cruciate ligaments form a cross in the center of the knee (view at 900 of knee
flexion)......................................................................................................
. . 18
Figure 1.2: (A) The anteromedial (AM) and posterolateral (PL) bundles of the anterior
cruciate ligament; (B) Magnetic Resonance (MR) image of a healthy ACL
w ith its anatom ical bundles. .......................................................................
19
Figure 2.1: MR images of a knee in sagittal and coronal planes and construction of 3D
knee model using Magnetic Resonance Imaging. .....................................
31
Figure 2.2: Sagittal and coronal plane magnetic resonance images of the knee were
digitized and used to create the femoral and tibial attachment areas of the
A CL bundles...............................................................................................
33
Figure 2.3: The attachment areas were divided into two functional bundles. The
geometric centers of the attachment areas of each bundle were determined to
model the anteromedial (AM) and posterolateral (PL) bundles................ 33
Figure 2.4: (A) 3D Anterior Cruciate Ligament (ACL) model constructed from MR
Images; (B) ACL configuration of a cadaveric knee; and (C) Definition of
A CL surface fiber bundles.........................................................................
34
Figure 2.5: (A) Schematic of the Dual Fluoroscopic Imaging System (DFIS) for
measurement of kinematics of the knee joint and a subject during a lunge
activity; (B) The virtual dual fluoroscopic system constructed for reproducing
in-vivo knee position in space. ..................................................................
37
Figure 2.6: Length of the ACL central bundle when the knee is under no load and under
full body load at different flexion angles..................................................
39
Figure 2.7: The relative elongation of the ACL central bundle in response to the full body
w eight. .....................................................................................................
. . 40
Figure 2.8: Lengths of the (A) anteromedial (AM) bundle and (B) posterolateral (PL)
bundle when the knee is under no load and full body load at different flexion
an gles ........................................................................................................
. .41
Figure 2.9: The relative elongation of the anteromedial bundle (AMB) and posterolateral
bundle (PLB) in response to the full body weight....................................
42
Figure 2.10: Lengths of the anterior surface bundle 4 and posterior surface bundle 7 when
the knee is under (A) no load and (B) under full body load at different flexion
angles; (C) The relative elongation of the eight ACL surface fiber bundles in
response to the full body weight...............................................................
Figure 3.1: Schematic of the dual fluoroscopic imaging system..................................
44
55
Figure 3.2: Virtual dual fluoroscopic imaging system created based on the geometry of
the actual experim ental system ..................................................................
57
Figure 3.3: Robotic testing system with installed knee specimen (before removing soft
tissu es). .....................................................................................................
Figure 3.4: MicroScribe* digitizer with six degrees-of-freedom. ................................
. . 60
60
Figure 3.5: Stretching the ACL along its long axis using the robot arm; all the soft tissues
of the knee joint were dissected away, except for the ACL. .....................
61
Figure 3.6: Schematic diagram showing the methodology used for determination of invivo ACL tension. (A) Weightbearing-elongation of the ACL from in-vivo
weightbearing, (B) Force-elongation of the ACL from in-vitro robotic test,
(C) Estimation of in-vivo ACL tension for each individual as a function of
weightbearing, (D) Average in-vivo ACL force-weightbearing data of all
living knees using weighted mean statistical method. (figures are only
conceptual and are not presenting experimental results, BW: Body Weight)62
Figure 3.7: In-vivo weightbearing-elongation behavior of the ACL at 150, 300 and 450 of
flexion ......................................................................................................
. . 65
Figure 3.8: In-vitro force-elongation curves of the ACL at 150, 300 and 450 of flexion
(Standard deviation bars for 300 are not shown for figure clarity purposes). 66
Figure 3.9: The increase in ACL force when the knee was under full body weightbearing
and different ACL tensions under zero weightbearing were assumed..... 68
Figure 3.10: (A) Set up of the Dual Fluoroscopic Imaging System around the robotic
testing system for validation study. (B) A knee specimen installed on the
robotic testing system with the fluoroscopes to image the knee joint during
applying load. ...........................................................................................
75
Figure 3.11: The in-vitro ACL force due to 130 N anterior tibial load and the
corresponding estimation of the ACL forces with different ACL tensions
under zero weightbearing at 150, 300 and 450 of knee flexion. At all three
different flexion angles, the actual ACL forces (labeled as in-vitro) were less
than the estimated ACL force with an ACL tension of 40 N under zero load
bearing ......................................................................................................
. . 77
Figure 4.1: The Anteromedial (AM) bundle and Posterolateral (PL) bundle of ACL were
identified and separated for tensile test. The bundles are hold separately using
sutures at 45* of knee flexion (anterior view). .........................................
86
Figure 4.2: In-vitro force-elongation curves of bundles of the ACL at 15', 300 and 450 of
flexion: (A) Anteromedial (AM) and (B) Posterolateral (PL). (Standard
deviation bars for 300 are not shown for figure clarity purposes)............. 90
Figure 4.3: The increase in bundle forces when the knee was under full body
weightbearing and different bundle tensions under zero weightbearing were
assumed: (A) Anteromedial (AM) and (B) Posterolateral (PL). ...............
91
Figure 5.1: The anteromedial (AM) bundle and posterolateral (PL) bundle of ACL
viewed from the anterior arthrotomy of the knee........................................
101
Figure 5.2: The in-situ forces in the anteromedial bundle (AMB) and posterolateral
bundle (PLB) in response to 134 N anterior tibial load. The PL bundle carried
significantly lower in-situ force than the AM bundle at all flexion angles
(p < 0 .0 5).......................................................................................................
102
Figure 5.3: The in-situ forces in the anteromedial bundle (AMB) and posterolateral
bundle (PLB) in response to combined 10 N.m valgus and 5 N.m internal
tibial torques. There was no significant difference between the two bundles at
00 of flexion, but the PL bundle shared significantly lower force than the AM
bundle at 30* of flexion (p<0.05). ...............................................................
104
Figure 5.4: The in-situ forces in the anteromedial bundle (AMB) and posterolateral
bundle (PLB) in response to 400 N quadriceps muscle load. There was also
no significant difference between two bundle forces at all flexion angles (p>
0 .0 5).............................................................................................................
104
Figure 6.1: 3D model of the Anterior Cruciate Ligament (ACL) built based on the series
of MR im ages. .............................................................................................
117
Figure 6.2: (A) Impingement of the ACL against the intercondylar notch of the femur
(medial view, full extension), (B) intersection plane at the location of
maximum impingement; D: diameter on the ACL at the location of maximum
impingement; t: maximum impingement of the ACL. ................................
118
Figure 6.3: Definition of impingement angle (<p) in the clock coordinate system at notch
view ..............................................................................................................
119
Figure 6.4: Maximum impingement during weight bearing from minimum bodyweight
(OBW) to full bodyweight (1BW) at low flexion, (p<0.05). ....................... 120
Figure 6.5: Percentage of impingement ratio (t/D) during weight bearing from minimum
bodyweight (OBW) to full bodyweight (1BW) at low flexion, (p<0.05)..... 121
Figure 6.6: The location of maximum impingement during weight bearing from minimum
bodyweight (OBW) to full bodyweight (1BW) in low flexion, (p<0.05).... 122
Figure 7.1: A 3-Tesla Magnetic Resonance scanner was used to construct the threedimensional (3D) knee models in a relaxed, extended position.................. 134
Figure 7.2: A 3D knee model constructed using the series of MR images of a subject's
kn ee ..............................................................................................................
13 5
Figure 7.3: Subject performing single leg weight-bearing on a force plate while being
imaged by two orthogonally placed fluoroscopes. The pairs of fluoroscopic
images were imported into modeling software to reproduce the kinematics of
the tested knee joint in a virtual dual fluoroscopic imaging system............ 136
Figure 7.4: (A) Sagittal section of a typical knee showing the definition of contact area
and cartilage penetration. (B) Method of measuring cartilage thickness and
penetration depth from meshed surfaces. ....................................................
138
Figure 7.5: The peak contact deformation was determined as the maximum contact
deformation in the cartilage contact area.....................................................
139
Figure 7.6: (A) The variation of the peak cartilage contact deformation over time (mean ±
standard deviation) and the corresponding ground reaction force (normalized
for body weight). (B) Mean values of the rate of change of the peak cartilage
deform ation in tibial compartm ents.............................................................
140
Figure 7.7: (A) The variation of cartilage contact area over time (mean ± standard
deviation) and the corresponding ground reaction force (normalized for body
weight). (B) Mean values of the rate of change of the cartilage contact area in
tibial compartm ents. ....................................................................................
14 1
Figure 7.8: Contours of contact deformation distribution of a typical subject in the course
of time in the sagittal cross-sections (dashed lines) in medial and lateral
compartm ents...............................................................................................144
Figure 7.9: Patterns of contact deformation in the tibiofemoral cartilage. (A) Medial
compartment: contact is occurring on the concave (conforming) surface of
medial tibial cartilage, (B) Lateral compartment: contact is occurring on the
convex surface of lateral tibial cartilage......................................................
148
List of Tables
Table 2.1: The lengths of the eight surface fiber bundles of the anterior cruciate ligament
(M ean ±SD , N = 9)...................................................................................
43
Table 3.1: Clinical data on the subjects tested...............................................................
56
Table 3.2: History of the cadaver donors......................................................................
59
Table 3.3: Percentage of change in the ACL force increase under full body weight, due to
10 N increase in the ACL tension under zero body weight........................
67
Table 7.1: Cartilage contact deformation (%) as a function of time under full body
w eigh t. .........................................................................................................
14 5
Table 7.2: Contact area (mm 2 ) as a function of time under full body weight................. 146
Table 7.3: The thickness of tibial cartilage (mm) at the location of peak cartilage contact
deform ation..................................................................................................
149
Chapter 1 - Introduction
1.1 The Anterior Cruciate Ligament
The Anterior Cruciate Ligament (ACL) is one of the most important ligaments
inside the knee joint which has an important role in the stability of the knee. It originates
from the posterolateral part of the femur, courses interiorly and medially across the joint
and inserts in the anteromedial part of tibia (Figure 1.1). In general, ligaments are tough
bands of fibrous tissue that connect two bones across a joint and control the motion of the
joints passively. The main role of the ACL is to control anterior (forward) tibial
translation with respect to femur. As a secondary constrain, it restrains excessive internal
rotation of the tibia relative to femur.
The ACL consists of two anatomical bundles: the anteromedial (AM) bundle and
the posterolateral (PL) bundle, which are named according to their relative locations on
the tibial insertion sites (Figure 1.2). The AM bundle is slightly larger compared to the
PL bundle. Based on earlier cadaveric studies, the two bundles of the ACL have been
found to have a reciprocal function along the knee flexion path, with the PL bundle taut
at low flexion angles and the AM bundle taut at high flexion angles [1, 2]. Recent studies
on the other hand, demonstrated that the ACL bundles might function in a different way
in-vivo than previously described reciprocal behavior in-vitro. Both AM and PL bundles
were observed to be taut at near extension and then shorten with flexion, indicating that
the ACL bundles may function differently under physiological loading conditions when
compared to passive conditions [3].
1.2 Background and Objectives
ACL is frequently injured in sports and strenuous activities, especially in young
populations [2, 4, 5]. About 80,000 to 250,000 ACL injuries occur each year in the US
[6-8]. Movements of the knee that apply a great strain on the ACL can cause damage to
this ligament. The spectrum of ACL injury can range from a mild strain, partial tear or a
completely torn ACL. The injury almost always is due to at least one of the following
patterns of injury: I) a sudden stop, twist or change in the direction at the knee joint; II)
jumping and landing or III) Hyperextension of the knee joint. These are very routine in
skiing, basketball, football, soccer, and gymnastics. Injuries to the knee ligament
represent a significant impairment of normal knee joint function, causing pain, instability
in the knee, future damage to the structure of the knee joint - such as meniscal injuries
and osteochondral damages - and long-term development of osteoarthritis [9-12]. It has
been documented that ACL deficiency leads to abnormal tibiofemoral joint kinematics
with an increased anterior translation and internal rotation of the tibia [13] as well as a
medial translation of the tibia [13]. The medial shift of the tibia after ACL deficiency
would alter the contact stress distributions and increase the cartilage contact deformation
in the tibiofemoral cartilage near the medial tibial spine [14, 15], a region where
degeneration is observed in patients with chronic ACL injuries [16]. These findings have
led both clinicians and researchers to advocate surgical ACL reconstruction using a bonepatellar tendon-bone (BPTB) graft or a quadruple hamstring graft and a variety of
surgical techniques [17-21].
ACL reconstruction is one of the most common sports medicine procedures
performed in the US each year. It has been estimated that approximately 100,000 ACL
reconstructions are performed yearly only in the US [22], with an annual expenditures of
$2 billions [8]. Biomechanical studies have shown that ACL reconstruction restores
anterior-posterior (AP) stability under anterior tibial loads [23, 24]. However, recent
studies show that ACL reconstruction can not restore the knee stability in all six degreesof-freedom (DOF) under in-vivo or simulated physiological loading conditions [25-27].
In the literature, there are reports that 10 to 40% of ACL reconstruction patients have
abnormal knee laxity [28, 29] and 5 to 50% of patients have had a second operation
within 5 years of the first operation [28]. It is thought that the graft used in the
reconstruction should carry in-vivo loads similar to those of the ligament being replaced.
Therefore, a thorough understanding of the biomechanical role of the ACL in-vivo is
essential for improving the treatment of ligament injuries. Optimizing surgical
reconstruction of injured ligaments requires an accurate knowledge of the in-vivo
ligament forces and kinematics in the normal knee.
Femur
Posterior
cruciate
ligament
(thighbone)
Anterior
cruciate
ligament
Fibula
Tibia
(shinbone)
Figure 1.1: The Anterior Cruciate Ligament (ACL) originates from deep within the
notch of distal femur and attaches in front of tibia. The anterior and posterior
cruciate ligaments form a cross in the center of the knee (view at 900 of knee
flexion).
The importance of ACL injury to public health has led to numerous investigations
in ACL material properties and structural functions. Many studies have reported on the
force-elongation relationship [30-32] and stress-strain behavior [33] of the ACL in order
to understand the biomechanical properties of the ligament. Extensive efforts have been
devoted to determining the forces and strain in the ACL in-vitro, using buckle-type
transducers [34, 35], implantable pressure transducers [36], and Hall-effect-straintransducers [37, 38]. More recently, a robotic testing system has been introduced to
determine knee kinematics and in-situ forces in various ligaments [25, 39, 40].
A
--
Patella
Tibia
-
Femur
Anterior
cruciate
ligament
~
Figure 1.2: (A) The anteromedial (AM) and posterolateral (PL) bundles of the
anterior cruciate ligament; (B) Magnetic Resonance (MR) image of a healthy ACL
with its anatomical bundles.
Early investigations on in-vivo ACL biomechanics have used strain gauge
techniques to measure elongation of the ACL in living subjects [36, 38]. Direct
measurements of ACL surface strain in the anterior portion of the ligament using
Differential Variable Reluctance Transducer (DVRT) during various in-vivo activities of
the knee has been performed [38, 41]. Furthermore, the elongation patterns of the ACL
have been measured using a non-invasive imaging technique during a weightbearing
flexion of the knee [22, 42]. These studies indicated that the ACL may function in a more
complicated three-dimensional (3D) manner.
However, there are no reports on in-vivo forces of human knee ligaments due to
the technical difficulties associated with measuring ligament forces in living subjects.
This thesis provides a non-invasive technique to indirectly estimate the in-vivo forces
within the ACL. This knowledge is critical for understanding the in-vivo loading effect
on ACL function, ACL injury mechanisms, and further for optimizing the surgical
treatment of the injured ACL to restore the native ACL function.
The objective of this thesis was to determine the in-vivo biomechanics kinematics and forces - of the ACL by using advanced imaging techniques and a robotic
testing system. Dual fluoroscopic imaging and three-dimensional modeling techniques
were employed to gather the in-vivo data as an invasive method. Combined with the
force-elongation data measured from the robotic system, the in-vivo ACL data was used
to estimate the in-vivo tension of the ACL during functional activities. An improved
knowledge of in-vivo ligament function should improve our ability to treat the ACL
injuries.
1.3 Organization of the Thesis
This thesis is prepared in 8 chapters. Chapter 2 investigates the elongation
behavior of the healthy ACL under weightbearing conditions in living subjects. Due to
the complicated anatomic structure of the ACL, it was modeled using three detailed
anatomic approaches: I) a single central bundle, II) double functional bundles, and III)
multiple surface fiber bundles. A combined Dual Fluoroscopic and Magnetic Resonance
(MR) Imaging technique was used to determine relative elongations of the ACL bundles
under full weightbearing at different knee flexion angles. Chapter 3 discusses utilizing a
robotic testing system to determine the ACL force-elongation data in-vitro. The in-vivo
ACL elongation data were mapped to the in-vitro ACL force-elongation curve using a
statistical method to non-invasively estimate the in-vivo ACL forces in response to full
body weightbearing. As a gold standard, a robotic testing protocol was then implemented
to validate the proposed force estimation method in cadaveric specimens. Chapter 4
extends the methodology introduced in earlier chapter to determine the force-elongation
curves of each anatomic bundle of the ACL - i.e., anteromedial bundle and posterolateral
bundle - and estimate the in-vivo forces of each bundle at tested knee flexion angles.
Then, Chapter 5 investigates the in-situ forces of the anteromedial and posterolateral
bundles of the ACL under simulated functional loads such as simulated muscle loads,
anterior tibial load and combined rotational loads. Also, the contribution of each bundle
under different type of loading was determined.
Chapter 6 describes the findings regarding the in-vivo characterization of ACL
interaction with the femoral intercondylar notch at shallow knee flexion under
physiological loading. In this chapter, the impingement of 3D model of the ACL against
the intercondylar notch of femur was modeled. Chapter 7 extends the application of
combined dual fluoroscopy and MR imaging to investigate the time-dependent response
of the tibiofemoral joint cartilage under a constant bodyweight load (creep behavior) and
determine whether the medial and lateral compartments show differences in timedependent contact behavior. This is the first step to extend the force estimation method,
introduced in Chapter 3, to non-invasively determine the in-vivo stress distribution in the
tibiofemoral joint cartilage. Finally, Chapter 8 presents a summary of the findings of this
thesis and implications for future studies.
This work is based on the following publications:
i.
Hosseini A, Gill TJ, Li G: In vivo anterior cruciate ligament elongation in response
to axial tibial loads. J Orthop Sci 14:298-306, 2009.
ii.
Hosseini A, Gill TJ, Van de Velde SK, Li G. Estimation of in-vivo ACL force
change in response to increased weightbearing, Annals of Biomedical Engineering,
[under final review].
iii.
Wu JL, Seon JK, Gadikota HR, Hosseini A, Sutton KM, Gill TJ, Li G: In situ
forces in the anteromedial and posterolateral bundles of the anterior cruciate
ligament under simulated functional loading conditions. Am J Sports Med 38:55863, 2010.
iv.
Kozanek M, Hosseini A, Liu F, Van de Velde SK, Gill TJ, Rubash HE, Li G:
Tibiofemoral kinematics and condylar motion during the stance phase of gait. J
Biomech 42:1877-84, 2009.
v.
Van de Velde SK, Hosseini A, Kozanek M, Gill TJ, Rubash HE, Li G: Application
guidelines for dynamic knee joint analysis with a dual fluoroscopic imaging system.
Acta Orthop Belg 76:107-13, 2010.
vi.
Li G, Kozanek M, Hosseini A, Liu F, Van de Velde SK, Rubash HE: New
fluoroscopic imaging technique for investigation of 6DOF knee kinematics during
treadmill gait. J Orthop Surg Res 4:6, 2009.
vii. Hosseini A, Van de Velde SK, Kozanek M, Gill TJ, Grodzinsky AJ, Rubash HE, Li
G: In-vivo time-dependent articular cartilage contact behavior of the tibiofemoral
joint. Osteoarthritis Cartilage, 2010 [in press].
viii. Liu F, Kozanek M, Hosseini A, Van de Velde SK, Gill TJ, Rubash HE, Li G: In
vivo tibiofemoral cartilage deformation during the stance phase of gait. J Biomech
43:658-65, 2009.
ix.
Hosseini A, Lada K, Van de Velde SK, Kozanek M, Gill TJ, Li G: Impingement of
the anterior cruciate ligament against the femoral intercondylar notch during in-vivo
weight bearing. Am J Sports Med [under review].
x.
Van De Velde SK, Bingham JT, Hosseini A, Kozanek M, DeFrate LE, Gill TJ, Li
G: Increased tibiofemoral cartilage contact deformation in patients with anterior
cruciate ligament deficiency. Arthritis Rheum 60:3693-702, 2009.
xi.
Gill TJ, Van de Velde SK, Wing DW, Oh LS, Hosseini A, Li G: Tibiofemoral and
patellofemoral kinematics after reconstruction of an isolated posterior cruciate
ligament injury: in vivo analysis during lunge. Am J Sports Med 37:2377-85, 2009.
(Winner of the 2009 O'Donoghue Award)
xii. Kozanek M., Van de Velde SK, Hosseini A, Gill T, Li G. Book chapter entitled
"Biomechanics of ACL Deficiency and Contemporary Reconstruction Techniques",
Nova Science Publishers, Inc. [in press]
1.4 References
1.
Girgis FG, Marshall JL, Monajem A. The cruciate ligaments of the knee joint.
Anatomical, functional and experimental analysis. Clin Orthop Relat Res 1975:
216-231.
2.
Amis AA, Dawkins GP. Functional anatomy of the anterior cruciate ligament.
Fibre bundle actions related to ligament replacements and injuries. J Bone Joint
Surg Br 1991; 73: 260-267.
3.
Li G, DeFrate LE, Sun H, Gill TJ. In vivo elongation of the anterior cruciate
ligament and posterior cruciate ligament during knee flexion. Am J Sports Med
2004; 32: 1415-1420.
4.
Butler DL, Noyes FR, Grood ES. Ligamentous restraints to anterior-posterior
drawer in the human knee. A biomechanical study. J Bone Joint Surg Am 1980; 62:
259-270.
5.
Sakane M, Fox RJ, Woo SL, Livesay GA, Li G, Fu FH. In situ forces in the
anterior cruciate ligament and its bundles in response to anterior tibial loads. J
Orthop Res 1997; 15: 285-293.
6.
Feagin JA, Jr., Lambert KL, Cunningham RR, Anderson LM, Riegel J, King PH, et
al. Consideration of the anterior cruciate ligament injury in skiing. Clin Orthop
Relat Res 1987: 13-18.
7.
Hewett TE, Lindenfeld TN, Riccobene JV, Noyes FR. The effect of neuromuscular
training on the incidence of knee injury in female athletes. A prospective study. Am
J Sports Med 1999; 27: 699-706.
8.
Gottlob CA, Baker CL, Jr., Pellissier JM, Colvin L. Cost effectiveness of anterior
cruciate ligament reconstruction in young adults. Clin Orthop Relat Res 1999: 272282.
9.
Andriacchi TP, Mundermann A, Smith RL, Alexander EJ, Dyrby CO, Koo S. A
framework for the in vivo pathomechanics of osteoarthritis at the knee. Ann
Biomed Eng 2004; 32: 447-457.
10.
Kannus P, Jarvinen M. Posttraumatic anterior cruciate ligament insufficiency as a
cause of osteoarthritis in a knee joint. Clin Rheumatol 1989; 8: 251-260.
11.
Tandogan RN, Taser 0, Kayaalp A, Taskiran E, Pinar H, Alparslan B, et al.
Analysis of meniscal and chondral lesions accompanying anterior cruciate ligament
tears: relationship with age, time from injury, and level of sport. Knee Surg Sports
Traumatol Arthrosc 2004; 12: 262-270.
12.
Murrell GA, Maddali S, Horovitz L, Oakley SP, Warren RF. The effects of time
course after anterior cruciate ligament injury in correlation with meniscal and
cartilage loss. Am J Sports Med 2001; 29: 9-14.
13.
Defrate LE, Papannagari R, Gill TJ, Moses JM, Pathare NP, Li G. The 6 degrees of
freedom kinematics of the knee after anterior cruciate ligament deficiency: an in
vivo imaging analysis. Am J Sports Med 2006; 34: 1240-1246.
14.
Li G, Moses JM, Papannagari R, Pathare NP, DeFrate LE, Gill TJ. Anterior
cruciate ligament deficiency alters the in vivo motion of the tibiofemoral cartilage
contact points in both the anteroposterior and mediolateral directions. J Bone Joint
Surg Am 2006; 88: 1826-1834.
15.
Van De Velde SK, Bingham JT, Hosseini A, Kozanek M, DeFrate LE, Gill TJ, et
al. Increased tibiofemoral cartilage contact deformation in patients with anterior
cruciate ligament deficiency. Arthritis Rheum 2009; 60: 3693-3702.
16.
Fairclough JA, Graham GP, Dent CM. Radiological sign of chronic anterior
cruciate ligament deficiency. Injury 1990; 21: 401-402.
17.
Crawford C, Nyland J, Landes S, Jackson R, Chang HC, Nawab A, et al. Anatomic
double bundle ACL reconstruction:
a literature review. Knee Surg Sports
Traumatol Arthrosc 2007; 15: 946-964; discussion 945.
18.
Lewis PB, Parameswaran AD, Rue JP, Bach BR, Jr. Systematic review of singlebundle anterior cruciate ligament reconstruction outcomes: a baseline assessment
for consideration of double-bundle techniques. Am J Sports Med 2008; 36: 20282036.
19.
Pederzini L, Adriani E, Botticella C, Tosi M. Technical note: double tibial tunnel
using quadriceps tendon in anterior cruciate ligament reconstruction. Arthroscopy
2000; 16: E9.
20.
Takeuchi R, Saito T, Mituhashi S, Suzuki E, Yamada I, Koshino T. Double-bundle
anatomic anterior cruciate ligament reconstruction using bone-hamstring-bone
composite graft. Arthroscopy 2002; 18: 550-555.
21.
Williams RJ, 3rd, Hyman J, Petrigliano F, Rozental T, Wickiewicz TL. Anterior
cruciate ligament reconstruction with a four-strand hamstring tendon autograft.
Surgical technique. J Bone Joint Surg Am 2005; 87 Suppl 1: 51-66.
22.
Harner CD, Giffin JR, Dunteman RC, Annunziata CC, Friedman MJ. Evaluation
and treatment of recurrent instability after anterior cruciate ligament reconstruction.
Instr Course Lect 2001; 50: 463-474.
23.
Anderson AF, Snyder RB, Lipscomb AB, Jr. Anterior cruciate ligament
reconstruction. A prospective randomized study of three surgical methods. Am J
Sports Med 2001; 29: 272-279.
24.
Bach BR, Jr., Jones GT, Sweet FA, Hager CA. Arthroscopy-assisted anterior
cruciate ligament reconstruction using patellar tendon substitution. Two- to fouryear follow-up results. Am J Sports Med 1994; 22: 758-767.
25.
Yoo JD, Papannagari R, Park SE, DeFrate LE, Gill TJ, Li G. The effect of anterior
cruciate ligament reconstruction on knee joint kinematics under simulated muscle
loads. Am J Sports Med 2005; 33: 240-246.
26.
Tashman S, Collon D, Anderson K, Kolowich P, Anderst W. Abnormal rotational
knee motion during running after anterior cruciate ligament reconstruction. Am J
Sports Med 2004; 32: 975-983.
27.
Georgoulis AD, Papadonikolakis A, Papageorgiou CD, Mitsou A, Stergiou N.
Three-dimensional tibiofemoral kinematics of the anterior cruciate ligament-
deficient and reconstructed knee during walking. Am J Sports Med 2003; 31: 7579.
28.
Fox JA, Nedeff DD, Bach Jr BR, Spindler KP. Anterior cruciate ligament
reconstruction with patellar autograft tendon. Clin Orthop Relat Res 2002: 53-63.
29.
Thornton GM, Boorman RS, Shrive NG, Frank CB. Medial collateral ligament
autografts have increased creep response for at least two years and early
immobilization makes this worse. J Orthop Res 2002; 20: 346-352.
30.
Darcy SP, Kilger RH, Woo SL, Debski RE. Estimation of ACL forces by
reproducing knee kinematics between sets of knees: A novel non-invasive
methodology. J Biomech 2006; 39: 2371-2377.
31.
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.
32.
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.
33.
Butler DL, Guan Y, Kay MD, Cummings JF, Feder SM, Levy MS. Locationdependent variations in the material properties of the anterior cruciate ligament. J
Biomech 1992; 25: 511-518.
34.
Ahmed AM, Burke DL, Duncan NA, Chan KH. Ligament tension pattern in the
flexed knee in combined passive anterior translation and axial rotation. J Orthop
Res 1992; 10: 854-867.
35.
Lewis JL, Lew WD, Schmidt J. A note on the application and evaluation of the
buckle transducer for the knee ligament force measurement. J Biomech Eng 1982;
104: 125-128.
36.
Henning CE, Lynch MA, Glick KR, Jr. An in vivo strain gage study of elongation
of the anterior cruciate ligament. Am J Sports Med 1985; 13: 22-26.
37.
Fleming BC, Beynnon BD, Nichols CE, Renstrom PA, Johnson RJ, Pope MH. An
in vivo comparison between intraoperative isometric measurement and local
elongation of the graft after reconstruction of the anterior cruciate ligament. J Bone
Joint Surg Am 1994; 76: 511-519.
38.
Beynnon B, Howe JG, Pope MH, Johnson RJ, Fleming BC. The measurement of
anterior cruciate ligament strain in vivo. Int Orthop 1992; 16: 1-12.
39.
Li G, Rudy TW, Sakane M, Kanamori A, Ma CB, Woo SL. The importance of
quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in
the ACL. J Biomech 1999; 32: 395-400.
40.
Li G, Zayontz S, Most E, DeFrate LE, Suggs JF, Rubash HE. In situ forces of the
anterior and posterior cruciate ligaments in high knee flexion: an in vitro
investigation. J Orthop Res 2004; 22: 293-297.
41.
Beynnon BD, Fleming BC, Johnson RJ, Nichols CE, Renstrom PA, Pope MH.
Anterior cruciate ligament strain behavior during rehabilitation exercises in vivo.
Am J Sports Med 1995; 23: 24-34.
42.
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.
Chapter 2 - In-vivo Anterior Cruciate Ligament
Elongation in Response to Axial Tibial Loads
2.1 Introduction
The anterior cruciate ligament (ACL) is frequently injured in sports and strenuous
activities, especially in younger populations [1, 2]. The importance of ACL injury to
public health has led to numerous investigations in ACL material properties and
structural functions [3, 4]. Many investigations have reported on the force-elongation
relationship [4-6] and stress-strain behavior [3] of the ACL in order to understand the
biomechanical properties of the ligament. These studies were usually conducted using
uniaxial tensile tests on ACL specimens [3, 4, 7], where the ACL was considered in
different structural configurations such as a single tension element [4]; two bundle
elements [3]; or multi-bundle elements [3, 7]. Further, numerous in-vitro investigations
have also measured ACL forces in response to various loads applied to the knee in order
to understand the biomechanical function of the ligament in the knee joint [2, 8, 9]. These
investigations used various measurement techniques, such as a buckle transducer [10],
implantable pressure transducer [8], Hall Effect strain transducer [11, 12] and a robotic
technique [9, 13-15]. Among these various ACL biomechanical studies, most have
determined the ACL forces by applying an anterior tibial load [2, 15, 161. Few studies
also measured ACL forces under rotational moments [17, 18] or simulated muscle loads
[13, 19]. While these data have tremendously improved our knowledge of ACL
biomechanics,
quantitative
determination
of the ACL function
under in-vivo
physiological loading conditions is still a challenge in biomedical engineering research.
Early investigations on in-vivo ACL biomechanics have used strain gauge
techniques to measure the elongation of the ACL in living subjects [8]. Beynnon et al.
has extensively conducted direct measurements of ACL strains in the anterior portion of
the ligament using differential variable reluctance transducer (DVRT) during various in-
vivo activities of the knee [12]. Li et al. [20] and Jordan et al. [21] have measured the
elongation pattern of the ACL using a non-invasive imaging modality during a
weightbearing flexion of the knee. These studies indicated that the ACL may function in
a more complicated 3-dimensional (3D) manner. This knowledge is critical for
understanding the in-vivo loading effect on ACL function, ACL injury mechanisms, and
further for optimizing the surgical treatment of the injured ACL.
The objective of this study was to investigate the elongation behavior of the
healthy ACL under weightbearing conditions in living subjects. Due to the complicated
anatomic structure of the ACL and its 3D deformation in nature, an anatomic ACL
reconstruction needs to consider the ACL biomechanics in different regions of the
ligament. Therefore, we simulated the ACL using a more detailed anatomic approach i) a
single central bundle, ii) double functional bundles, and
iii) multiple surface fiber
bundles. A combined Dual Fluoroscopic and MR Imaging technique was used to
determine relative elongations of ACL bundles at different flexion angles when the tibia
was loaded from no load (< 10 N) to full body weight (BW).
2.2 Materials and Methods
Nine subjects (4 males, 5 females), aged 23 - 48 years old, were recruited with the
approval of the Institutional Review Board (IRB). All subjects had normal and healthy
knees with no history of injury or surgery (determined by both clinical examination and
MRI examination). Written informed consent was obtained from all subjects prior to
participating in this study.
2.2.1 Magnetic Resonance Imaging and 3D Knee Models
Each knee (chosen randomly, 5 right and 4 left knees) was scanned in a relaxed,
full extension position using a 3.0 Tesla MR Scanner (MAGNETOM Trio*, Siemens,
Malvern, PA, USA). The knee was scanned in both sagittal and coronal planes in 1 mm
slice thickness using a 3D double echo water excitation sequence [20, 22]. The size of the
MR Images was 160x160 mm with a resolution of 512x512 pixels. The series of the MR
images were imported into solid modeling software (Rhinoceros*, Robert McNeel &
Associates, Seattle, WA, USA) for construction of 3D models of the knee (Figure 2.1).
The bony contours were segmented in MR images and the 3D anatomic models of the
bones were created using the digitized contour data.
3D Model of the Knee
Femur
Tibial
Fibula
00-7
ro
110/44Z
ON
Figure 2.1: MR images of a knee in sagittal and coronal planes and construction of
3D knee model using Magnetic Resonance Imaging.
The attachment areas of the ACL on the femur and tibia were segmented on MR
images in both sagittal and coronal planes (Figure 2.2). Since the ACL insertion sites
were segmented in the same coordinate setup as that for segmentation of the femur and
tibia, these attachment areas were directly mapped onto the 3D anatomic model of the
knee. The attachment areas were further divided into two parts: anteromedial (AM) and
posterolateral (PL) bundle attachment areas of the ACL (Figure 2.3). This was done by an
orthopaedic surgeon since there are no distinct separations between the AM and PL
bundle insertion sites on the tibia and femur that could be specified from the MR images.
The geometric centers of the attachment areas of each bundle were determined similarly
as in previous studies [21]. The AM and PL attachment site geometry on both tibial and
femoral sides were then compared to previous anatomical studies to make sure that the
determination of the bundles was consistent with previous studies[21, 23-25].
In order to investigate the 3D elongation of the ACL, we further divided the
boundaries of the ACL insertion sites into 8 divisions (Figure 2.4). On the tibial
attachment site, points 1 through 4 have been chosen on the anteromedial section of the
ACL such that point 1 was always placed on the lateral border of the AM and PL bundles
and the numbers assigned to the points increased when moving medially (Figure 2.4.C).
Similarly, points 5 through 8 have been chosen on the posterolateral section of the ACL
attachment site such that point 5 was placed on the medial border of the AM and PL
bundles and the number assigned to the points increased by moving laterally (Figure
2.4.C). The points were evenly distributed along the ACL attachment boundaries. The
femoral insertion site has been treated in a similar way.
The arrangement of the points is the same for right and left knees. Each point on
the tibial attachment area has been connected to its corresponding point on the femoral
side and the resulting lines were defined as surface fiber bundles of the ACL and were
numbered the same as its end points for study of the non-homogeneous elongation of the
surface fiber bundles of the ACL (Figure 2.4.C). A cadaveric specimen was dissected to
qualitatively verify the reconstructed ACL model (Figure 2.4.B). The configuration of the
ACL was shown to twist externally in the tibial attachment relative to the femoral
attachment site in both the reconstructed 3D ACL model (Figure 2.4.A) and the cadaveric
ACL (Figure 2.4.B).
Sagittal Plane
Femoral Attachment
areas
Coronal Plane
Tibial Attachment
areas
Figure 2.2: Sagittal and coronal plane magnetic resonance images of the knee were
digitized and used to create the femoral and tibial attachment areas of the ACL
bundles.
PL Bundle
''
AM Bundle
Figure 2.3: The attachment areas were divided into two functional bundles. The
geometric centers of the attachment areas of each bundle were determined to model
the anteromedial (AM) and posterolateral (PL) bundles.
C4
PL Attachment
Center (Femoral)
5
6
3
2
AM Attachment
Center (Femoral)
7
Surface fiber
Lateral
Medial
Mda
Figure 2.4: (A) 3D Anterior Cruciate Ligament (ACL) model constructed from MR
Images; (B) ACL configuration of a cadaveric knee; and (C) Definition of ACL
surface fiber bundles.
2.2.2 Fluoroscopic Imaging of the Knee
A dual fluoroscopic system [26] has been used to capture the joint positions along
the flexion path of the knee (Figure 2.5.A). The system setup consists of two
fluoroscopes (BV Pulsera*, Philips, Bothell, WA, USA)
that were positioned
orthogonally to each other. A force plate constructed using a 6 degrees-of-freedom
(DOF) load sensor (JR3*, San Francisco, CA, USA) was installed on the top of the
platform and was connected to a monitor to simultaneously display the value of ground
reaction forces when the subject steps on the force plate (Figure 2.5.A).
The subject first stood on the force plate on both feet in a relaxing position for
measurement of the body weight. The subject then put only the testing leg on the force
plate. The body weight load applied on the testing leg could be controlled by the subject
through the force plate output that was displayed on the monitor. In this experiment, each
subject was tested under the no load condition (< 10 N) and the full body weight
condition, and at 4 flexion angles: 00, 150, 30*, and 45'.
At each target flexion angle, the subject was asked to step on the force plate using
the testing leg while the force plate measured a minimal load (< 10 N) to represent the no
load condition. The fluoroscopes imaged the knee position simultaneously. The subject
was then asked to apply full body weight on the testing leg while maintaining the same
flexion angle. The subject could reach the target load within 5 seconds. The fluoroscopes
imaged the new position again. After testing at one flexion angle, the subject was asked
to flex the knee to the next target flexion angle. The knee was tested in this manner at all
target flexion angles from low to high flexion angles. The flexion angle was controlled
using a goniometer by a single investigator throughout the experiment. The entire
experiment for each subject took approximately 10 minutes.
2.2.3 Reproducing In-vivo Knee Kinematics
A virtual dual fluoroscopic system based on the geometry of the actual
experimental system was created in the 3D solid modeling software (Figure 2.5.B). The
pair of fluoroscopic images of the knee position under a specific tibial load were
imported into the software and placed at the positions of the image intensifiers of the
virtual system. Two virtual cameras were positioned to represent the actual X-ray
sources.
The bony contours of both tibia and femur were outlined on both fluoroscopic
images to facilitate matching of the 3D anatomic model of the bones with their
fluoroscopic images. The 3D anatomic model of the knee was imported into the virtual
fluoroscopic system and projected onto the virtual image intensifiers by the virtual
cameras. Each bony model was individually manipulated in 6 DOF until the projection of
the 3D bony model matched with the outline of the bony contours on the fluoroscopic
images (Figure 2.5.B). The in-vivo position of the knee captured on the fluoroscopic
images was then reproduced using the matched 3D bony models. By repeating the same
procedure using the fluoroscopic image pairs taken at all flexion angles and under all
loading conditions, the kinematics of the knee of the subject during the experiment could
be reproduced using a series of matched bony models of the knee. Since the attachment
areas of the ACL are fixed to the corresponding bony surfaces of the tibia and femur, the
relative positions of these attachment areas of the ACL could be determined by using the
series of matched bony models under different loading conditions and flexion angles.
Therefore, the positions of both ends of each bundle of the ACL could be determined.
The accuracy of the above procedure in reproducing knee kinematics has been
extensively evaluated [22, 26]. Using standard geometries, the system has an accuracy of
0.1 mm in translation and 0.10 in rotation [26]. Using cadaveric human knee specimens,
the system has an accuracy of 0.1 mm in translation and a repeatability of 0.3* in rotation
[27]. The accuracy of determination of knee kinematics can directly affect the accuracy
of the ACL elongation data. If the translational accuracy in determination of femoral and
tibial position was 0.1 mm [26], the effect on the accuracy of the ACL bundle elongation
was maximally estimated to be 0.34 mm. The average ACL length was -26 mm over all
the subjects. Therefore, maximum error in relative ACL elongation was estimated to be
within a range of 0.026 or 2.6%.
Screen
Subiect
C-Arm
Platform
Force Plate
B
Intensifier (2)
Intensifier (1)
3D3 Model
Source (1)
Source (2)
Figure 2.5: (A) Schematic of the Dual Fluoroscopic Imaging System (DFIS) for
measurement of kinematics of the knee joint and a subject during a lunge activity;
(B) The virtual dual fluoroscopic system constructed for reproducing in-vivo knee
position in space.
2.2.4 Data Analysis
The results of this study were presented in three different portions. First, the ACL
was considered as a single ligament using its central bundle. Then, the kinematics of the
AM and PL bundles was determined. Finally, the elongations of 8 surface fiber bundles
of the ACL were presented. The length of the ACL central bundle was defined as the line
connecting the ACL attachment centers on the tibia and femur (this line was also defined
as the long axis of the ACL). The length of the AM bundle was defined as the line
connecting the AM bundle attachment centers on the tibia and femur, and the same was
done for the PL bundle. The lengths of the 8 lines, connecting each of the 8 points on the
tibia to their corresponding points on the femur represent the surface fiber bundles of the
ACL. To investigate the loading effect on ACL elongation, the length of the ACL
bundles under no load condition at each flexion angle (10) was used as a reference to
determine the relative elongation of the fiber bundles in response to increased tibial loads
at that flexion angle (e = (1-10)/lo ), where l was the length of the ACL bundle under
full body loading at that flexion angle.
A two-way repeated measures analysis of variance (ANOVA) and a post hoc
Student-Newman-Keuls test were used to compare the ACL deformation. The flexion
angle and body weight loading applied to the leg were considered as independent
variables and the lengths of ACL fiber bundles as the dependent variables. Statistical
significance was defined when p<0.05.
2.3 Results
2.3.1 Single Bundle
In general, the length of the ACL increased with tibial load (Figure 2.6). At full
extension, the length of the ligament increased from 27.1 ± 2.3 mm at the no load
condition to 27.5 ± 2.4 mm under full body weight. The increases of the ACL length
caused by the full body weight condition were significant at 150 and 300 of flexion
(p<0.05).
*
r-m
30-
r,
*
L
280=%
-m
26-
IT
fO BW
El BW
24-J
0 227
20-
I
I
15
30
45
Flexion (*)
Figure 2.6: Length of the ACL central bundle when the knee is under no load and
under full body load at different flexion angles.
The relative elongation of the ACL caused by full body weight loading peaked at
15* and 300 of flexion (Figure 2.7). At full extension, full body weight loading caused a
relative ACL elongation of 1.2 ± 2.2%. At 150 and 300 of flexion, full body weight
caused ACL relative elongations of 4.5 ± 3.2% and 4.6 ± 3.3%, respectively. The relative
ACL elongation dropped to 2.3 ±4%at 450 of flexion. The relative elongation at 15* and
300 were significantly higher than those at 0* and 45* of flexion.
*
*
II
II
870
6-
(U
0)
5-
0
4-
LI
(U
N1 BW
32-
a) 1 -
0-
-i
15
30
45
Flexion (*)
Figure 2.7: The relative elongation of the ACL central bundle in response to the full
body weight.
2.3.2 Double Bundles
The length patterns of the AM and PL bundles along the flexion path were similar
under no load and full body weight conditions (Figure 2.8.A, Figure 2.8.B). The AM
bundle increased in length with flexion angles and the PL bundle decreased in length with
flexion angles.
By increasing the load from no load (< 10 N) to full body weight, the length of
the AM bundle showed a peak relative elongation of 4.4 ± 3.4% at 30* of flexion (Figure
2.9). However, the PL bundle experienced a peak relative elongation of 5.9 ± 3.4% at 15*
of flexion. The relative elongations at 0' and 450 of flexion were significantly (p<0.05)
smaller than those at 150 and 30' of flexion in both AM and PL bundles.
34
-
3332OBW
31 -
01 BW
302928-
mmv
9
15
M"
30
Flexion (0)
28-
26-
-
E
S24-
U
MOBW
01BW
-2
13. 22 -
20+-
-r-
15
30
Flexion
(0)
Figure 2.8: Lengths of the (A) anteromedial (AM) bundle and (B) posterolateral
(PL) bundle when the knee is under no load and full body load at different flexion
angles.
41
*
*
0
CU
OAMB
E PLB
0
0
15
30
45
Flexion (*)
Figure 2.9: The relative elongation of the anteromedial bundle (AMB) and
posterolateral bundle (PLB) in response to the full body weight.
2.3.3 Multiple Surface Fiber Bundles
The lengths of the eight surface fiber bundles of the ACL under no load and full
body weight in all flexion angles have been listed in Table 2.1. In general the lengths of
posterior fiber bundles are shorter than anterior fiber bundles. This means that the AM
and PL bundles have different behavior in low flexion angles. Surface fiber bundle 4 at
the anteromedial portion of the ACL was the longest fiber among all surface fiber
bundles of the ACL at all flexion angles (Figure 2.1O.A, Figure 2.10.B). The maximum
length of this fiber under the no load condition was 34.9 ± 3.6 mm at full extension,
significantly longer compared to other flexion angles, and was 35.5 ± 3.3 mm at 300 of
flexion under full body weight. Surface bundle 7 on the posterolateral portion of the ACL
was the shortest fiber on the surface of ACL. The length of this fiber was 21.8 ± 3.8 mm
at full extension under the no load condition and 16.2 ± 2.4 mm at 30' of flexion.
Table 2.1: The lengths of the eight surface fiber bundles of the anterior cruciate
ligament (Mean + SD, N = 9)
Flexion
00
150
300
450
Angle:
Loading:
0 BW
1.0 BW
0 BW
1.0 BW
0 BW
1.0 BW
0 BW
1.0 BW
Fiber # 1
25.5+2.4
25.7±2.0
25.5+1.8
26.0+1.9
25.9+1.4
26.7+1.7
27.3+1.5
27.6+1.6
Fiber # 2
30.2±3.1
30.5+3.1
30.2+2.6
31.1+2.6
30.8+2.2
31.8+2.5
32.1t2.3
32.6±2.5
Fiber # 3
32.6+2.8
33.0+2.7
32.4+2.4
33.5+2.4
32.8+2.0
34.0±2.4
33.8+2.0
34.3±2.6
Fiber # 4
34.9+3.6
34.9+3.4
34.1±3.4
35.3+3.4
33.8+3.2
35.5+3.3
33.6+3.0
34.8+3.0
Fiber # 5
31.2±3.5
31.5±3.6
29.1+3.2
30.5+3.1
27.7+2.6
29.6+2.7
26.8±2.6
28.3+2.3
Fiber # 6
26.1+3.1
26.7+3.2
23.1±2.6
24.3±2.5
20.9+2.1
22.8+2.1
19.8±2.2
21.1+1.8
Fiber # 7
21.8+3.8
22.2+3.7
18.1+2.7
19.9+3.0
16.2±2.4
18.3+2.6
15.2+2.7
16.6+2.2
Fiber # 8
21.1 2.5
21.4+2.6
19.3+2.0
20.1+2.1
18.5+1.2
19.7+1.4
18.8+1.6
19.3+1.5
There was a dramatic difference between the relative elongations among the
surface fiber bundles (Figure 2.10.C). Surface fiber bundles at the anteromedial surface
showed shorter relative elongation values compared to those at the posterolateral surface.
The peak relative elongation of surface fiber bundle 4 was 5.0 ± 2.4% under the full body
weight at 300 of flexion. The peak relative elongation of surface fiber bundle 7 had a
value of 13.4 + 3.8% at 300 of flexion in response to full body weight loading. Except in
full extension, the relative elongation of this fiber bundle was significantly higher than all
other fiber bundles at other flexion angles.
*
*
A
B
*
(a)
40
40
35
C30
35
(a)
(a)
E
E25
1150
E
0 300
II
moo
30
0150
030 0
25
0450
*
>20
450
20
15
15
Fiber 4
Fiber 7
Fiber 4
Fiber 7
(a): Significantly different from all other flexion angles.
D Fiber 1
E Fiber 2
1 Fiber 3
0 Fiber 4
0 Fiber 5
0 Fiber 6
E Fiber 7
0 Fiber 8
0
15
30
45
Flexion(*)
(a): Significantly different from all other fibers. (b): Significantly different from fibers 1 to 4.
(c): Significantly different from fibers 1 to 3. (d): Significantly different from fibers 1 to 3 and 7.
(e): Significantly different from fibers 1 to 4 and 8. (All are comparing at the same flexion angle)
Figure 2.10: Lengths of the anterior surface bundle 4 and posterior surface bundle 7
when the knee is under (A) no load and (B) under full body load at different flexion
angles; (C) The relative elongation of the eight ACL surface fiber bundles in
response to the full body weight.
2.4 Discussion
This study investigated the elongation behavior of the ACL under increased axial
tibial load of the knee at different flexion angles. The data demonstrated that the ACL
elongated as the axial tibial load increased, as illustrated by previous studies [18, 20]. The
data also showed that the ACL deformed in a non-homogeneous manner. Each fiber
bundle responded to the axial tibial load differently.
The relative elongation of the overall ACL reached over 4.5% at 150 and 30' of
flexions when the tibial load increased from no load (< 10 N) to full body weight. Both
AM and PL bundles also showed increases in relative elongations as the tibial load
increased. The AM bundle showed peak relative elongation of 4.5% at 30*, while the PL
bundle showed a maximal relative elongation of 5.9% at 15' of flexion. The surface fiber
bundles showed a more dramatic variation in relative elongations under the body weight
loading applied to the tibia. In general, the bundles at the anteromedial surface showed
less relative elongation compared to those at the posterolateral surface of the ACL. At
30*, the posterolateral surface bundle 7 showed a relative elongation of over 13% from
no tibial load to full body weight tibial load while the surface fiber bundle 1 only had a
relative elongation of approximately 3%.
Our previous in-vivo studies indicated that the AM bundle of the ACL maintained
maximal length between full extension to 450 of flexion, and showed a reduction in
length at higher flexion angles [21]. The PL bundle showed maximal.length in full
extension and decreased in length as the knee flexed during a single leg lunge. In general,
the current study showed similar length patterns of the AM and PL bundles with flexion.
Our previous in-vitro studies also demonstrated that the ACL carried peak load and ACL
deficiency caused higher anterior tibial translation at low flexion angles when the knee is
subject to simulated muscle loads [28].
Beynnon and Fleming [11, 16, 18] measured the ACL strain in its anterior portion
using a DVRT that was installed on the ACL surface of living subjects. The strain was
shown to decrease with flexion from 15* of flexion. During the various activities such as
squatting, active flexion-extension, peak strain was shown to be around 4% at 150 of
flexion. Our data showed that on average, the relative elongations of the AM surface
bundle were above 3% under full body weight at both 15 and 300 flexion angles and
decreased at higher flexion angles. A direct comparison between these different studies is
difficult since the in-vivo loading conditions among these studies could not be controlled
to be the same. Further, the references for measurement of relative elongations between
these studies are also different. For example, Fleming et al. determined that the reference
length for measurement of an anterior ACL strain was at 30* of flexion with an 8.8 N
anterior shear load applied to tibia using cadaveric knees[11], while we used the length of
the ligament under no load at each flexion angle as a reference.
Our data indicated that each bundle behaved differently even under the same
loading conditions and at the same flexion angles. It may be necessary to determine a
reference length for each interested fiber bundle. However, due to the complicated 3D
geometry of the ACL, a unique reference length for each fiber bundle is difficult to
determine using contemporary technologies. The fiber bundle lengths of the ACL
changed with flexion angle even under the no load conditions. Therefore, the relative
elongation of this study at one flexion angle was calculated using the ligament length
under the no load condition (< 10 N) at the same flexion angle as a reference. If the ACL
bundle is slack under the no load condition (i.e. the reference length, l4, is shorter than
the actual reference length value), the relative elongation data calculated using the
formula e = (1-10)/l1
may overestimate the actual relative strain of the bundle. Vice
versa, if the ACL bundle is already in tension under the no load condition, the relative
elongation could be underestimated. Also, if any interaction of the ACL and the PCL
exists in the range of flexion of this study, then the reported values for relative elongation
of the surface fibers are underestimated. This is worth investigating in future studies.
The data demonstrated different behavior of the ACL at different flexion angles
even though the tibial load was controlled to be similar. While the overall ACL showed
peak relative elongation at 150 and 30' of flexion under full body weight, the AM bundle
showed peak relative elongation at 300 and the PL bundle at 15*. Similar patterns were
also seen among the 8 ACL surface bundles, where all bundles showed peak relative
elongations at 300 of flexion. Woo et al. demonstrated that in a uniaxial tensile test, the
ACL behaved differently when oriented in different flexion angles [4]. The ACL was
shown to be stiffer in tension at 30* of flexion. Different behavior of the ACL at different
flexion angles indicated that the fiber recruitment of the ACL vary with flexion angles. It
is interesting to note that on average, the ACL and all surface fiber bundles showed peak
relative elongation at around 300 of flexion, indicating that the ACL may experience
larger deformation around this flexion angle. Consequently, the ACL properties might
adapt to the loading conditions experienced at different flexion angles.
In general, the fiber bundles in the posterolateral portion of the ACL were shorter
(~30% shorter) compared to the anteromedial portion. However, the posterior portion
stretched more than the anterior portion and usually had higher relative elongations. This
phenomenon may have important implications to surgical ACL reconstruction.
Simulation of the ACL as a single bundle or double bundles may be insufficient to
describe the complicated functional behavior of the ACL. It also points out the difficulty
of determining truly "isometric" sites for tunnel placement using either single or double
bundle reconstruction techniques. DeFrate et al. [29] and Li et al. [30] have quantitatively
demonstrated that the length of the ligament has a profound effect on its stiffness. The
stiffness increases with the reduction of the ligament length. Surgical reconstruction of
the ACL should take into consideration the length effect of the anteromedial and
posterolateral portions of the ACL. Further, it might be critically important to simulate
the non-homogeneous deformation of the ACL bundles using graft materials in ACL
reconstruction.
There are several limitations in the current study that need to be improved in
future investigations. The ligament length was calculated using a straight line connecting
the two insertion points on the tibia and femur. This treatment might not be accurate to
account for ACL impingement with the femoral notch at full extension of the knee.
Further, interaction of the ACL and PCL was not considered in the current study.
Ignoring the impingement with femoral notch and interaction with the PCL would cause
underestimation of ACL elongation using the straight line model.
The ACL relative elongation was only measured under full body weight applied
to the tibia from full extension to 450 of flexion. Beyond 450, the subjects had difficulty
applying full body weight to one knee and maintaining the flexion angle at the same time.
Due to the experimental set up, these data only represented the quasi-static responses of
the ACL. The relative elongation of the ACL under functional dynamic loading
conditions, such as walking and stair-climbing, should be investigated in the future.
In summary, this study investigated the relative elongation of ACL when the knee
was loaded under full body weight in living subjects. The data demonstrated that different
ACL bundles behaved differently, but are not truly "reciprocal" in that one bundle does
not shorten while the other bundle lengthens. The fiber bundles at the posterior portion of
the ACL are shorter than those at the anterior portion. However, the posterior fiber
bundles experienced higher relative elongations than the anterior fiber bundles. Even
though the overall relative elongations of the ACL might not be high, the posterior
portion of the ACL might experience up to 13% relative elongation under the full body
weight. The data suggested that the ACL biomechanics should be investigated in a three
dimensional manner. The data might provide useful insight into improving ACL
reconstruction techniques that are aimed to reproduce the in-vivo function of the ACL,
and suggest that current reconstruction techniques using single bundle grafts or double
bundle grafts may not adequately restore the 3D deformation behavior of the ACL.
2.5 Acknowledgements
This
research
was
supported by National
Institutes
of Health
(grant
R21AR051078). The technical assistance of Ramprasad Papannagari, Jeff Bingham, Dr.
Samuel Van de Velde, Dr. Louis E. DeFrate, Dr. Kyung Wook Nha and Angela
Moynihan is greatly appreciated. Also, I would like to thank the volunteers who
participated in this study.
2.6 References
1.
Mommersteeg TJ, Huiskes R, Blankevoort L, Kooloos JG, Kauer JM. An inverse
dynamics modeling approach to determine the restraining function of human knee
ligament bundles. J. Biomechanics 1997; 30: 139-146.
2.
Sakane M, Fox RJ, Woo SL, Livesay GA, Li G, Fu FH. In situ forces in the
anterior cruciate ligament and its bundles in response to anterior tibial loads. J.
Orthop. Res. 1997; 15: 285-293.
3.
Butler DL, Guan Y, Kay MD, Cummings JF, Feder SM, Levy MS. Locationdependent variations in the material properties of the anterior cruciate ligament. J.
Biomech 1992; 25: 511-518.
4.
Woo SL, Hollis JM, Adams DJ, Lyon RM, Takai S. Tensile properties of the
human femur-anterior cruciate ligament-tibia complex. The effect of specimen age
and orientation. Am. J. Sports Med. 1991; 19: 217-225.
5.
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. Biomechanics 2004; 37: 383-390.
6.
Darcy SP, Kilger RH, Woo SL, Debski RE. Estimation of ACL forces by
reproducing knee kinematics between sets of knees: A novel non-invasive
methodology. J. Biomechanics 2006; 39: 2371-2377.
7.
Mommersteeg
TJ, Blankevoort L, Huiskes R, Kooloos
JG, Kauer JM.
Characterization of the mechanical behavior of human knee ligaments: a numericalexperimental approach. J. Biomech 1996; 29: 151-160.
8.
Henning CE, Lynch MA, Glick K.R. J. An in-vivo strain gage study of elongation
of the anterior cruciate ligament. Am. J. Sports Med. 1985; 13: 22-26.
9.
Woo SL, Wu C, Dede 0, Vercillo F, Noorani S. Biomechanics and anterior
cruciate ligament reconstruction. J Orthop Surg 2006; 1: 2.
10.
Ahmed AM, Burke DL, Duncan NA, Chan KH. Ligament tension pattern in the
flexed knee in combined passive anterior translation and axial rotation. J. Orthop.
Res. 1992; 10: 854-867.
11.
Fleming BC, Beynnon BD, Tohyama H, Johnson RJ, Nichols CE, Renst6m P, et al.
Determination of a zero strain reference for the anteromedial band of the anterior
cruciate ligament. Journal of Orthopaedic Research 1994; 12: 789-795.
12.
Beynnon BD, Johnson RJ, Fleming BC, Renstr6m PA, Nichols CE, Pope MH, et
al. The measurement of elongation of anterior cruciate-ligament grafts in-vivo. J
Bone Joint Surg Am. 1994; 76: 520-53 1.
13.
Li G, Rudy TW, Sakane M, Kanamori A, Ma CB, Woo SL. The importance of
quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in
the ACL. J. Biomechanics 1999; 32: 395-400.
14.
Rudy TW, Livesay GA, Woo SL, Fu FH. A combined robotic/universal force
sensor approach to determine in situ forces of knee ligaments. J. Biomech 1996; 29:
1357-1360.
15.
Li G, Zayontz S, Most E, DeFrate LE, Suggs JF, Rubash HE. In situ forces of the
anterior and posterior cruciate ligaments in high knee flexion: an in vitro
investigation. J Orthop Res 2004; 22: 293-297.
16.
Fleming BC, Beynonn BD, Nichols CE, Johnson RJ, Pope MH. An in vivo
comparison of anterior tibial translation and strain in the anteromedial band of the
anterior cruciate ligament. J. Biomech 1993; 26: 51-58.
17.
Kanamori A, Zeminski J, Rudy TW, Li G, Fu FH, Woo SL. The effect of axial
tibial torque on the function of the anterior cruciate ligament: a biomechanical
study of a simulated pivot shift test. Arthroscopy 2002; 18: 394-398.
18.
Fleming BC, Renstrom PA, Beynnon BD, Engstrom B, Peura GD, Badger GJ, et al.
The effect of weightbearing and external loading on anterior cruciate ligament
strain. J. Biomechanics 2001; 34: 163-170.
19.
Li G, Suggs J, Gill T. The effect of anterior cruciate ligament injury on knee joint
function under a simulated muscle load: a three-dimensional computational
simulation. Annals of Biomedical Engineering 2002; 30: 713-720.
20.
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.
21.
Jordan SS, DeFrate LE, Nha KW, Papannagari R, Gill TJ, Li G. The in vivo
kinematics of the anteromedial and posterolateral bundles of the anterior cruciate
ligament during weightbearing knee flexion. American Journal of Sports Medicine
2007; 35: 547-554.
22.
Bingham J, Li G. An optimized image matching method for determining in-vivo
TKA kinematics with a dual-orthogonal fluoroscopic imaging system. Journal of
Biomechanical Engineering 2006; 128: 588-595.
23.
Mochizuki T, Muneta T, Nagase T, Shirasawa S, Akita KI, Sekiya I. Cadaveric
knee observation study for describing anatomic femoral tunnel placement for twobundle anterior cruciate ligament reconstruction. Arthroscopy 2006; 22: 356-361.
24.
Harner CD, Baek GH, Vogrin TM, Carlin GJ, Kashiwaguchi S, Woo SL.
Quantitative analysis of human cruciate ligament insertions. Arthroscopy 1999; 15:
741-749.
25.
Buoncristiani AM, Tjoumakaris FP, Starman JS, Ferretti M, Fu FH. Anatomic
double-bundle anterior cruciate ligament reconstruction. Arthroscopy 2006; 22:
1000-1006.
26.
Li G, Wuerz TH, DeFrate LE. Feasibility of using orthogonal fluoroscopic images
to measure in vivo joint kinematics. Journal of Biomechanical Engineering 2004;
126: 314-318.
27.
DeFrate LE, Papannagari R, Gill TJ, Moses JM, Pathare NP, Li G. The 6 degrees of
freedom kinematics of the knee after anterior cruciate ligament deficiency: an in
vivo imaging analysis. American Journal of Sports Medicine 2006; 34: 1240-1246.
28.
Yoo JD, Papannagari R, Park SE, DeFrate LE, Gill TJ, Li G. The effect of anterior
cruciate ligament reconstruction on knee joint kinematics under simulated muscle
loads. American Journal of Sports Medicine 2005; 33: 240-246.
29.
DeFrate LE, van der Ven A, Gill TJ, Li G. The effect of length on the structural
properties of an Achilles tendon graft as used in posterior cruciate ligament
reconstruction. Am J Sports Med 2004; 32: 993-997.
30.
Li G, DeFrate L, Suggs J, Gill T. Determination of optimal graft lengths for
posterior cruciate ligament reconstruction--a theoretical analysis. Journal of
Biomechanical Engineering 2003; 125: 295-299.
Chapter 3 - Estimation of In-vivo Forces within
Anterior Cruciate Ligament in Response to
Weightbearing
3.1 Introduction
Accurate knowledge of anterior cruciate ligament (ACL) forces under functional
loading conditions is instrumental for understanding normal ACL function and improving
the surgical treatment of ACL injuries. Numerous studies have investigated the in-vitro
function of the ACL [1-5]. Different measurement techniques such as buckle transducers
[6-8], implantable pressure transducers [3, 9] and robotic techniques [10-13] have been
used to measure the ACL forces in-vitro. Most of these studies measured the ACL forces
by applying anterior tibial loads [10, 14, 15], simulated muscle loads [9, 13, 16] or
rotational moments to the knee joint [17-19]. However, the ACL might carry much
higher forces during in-vivo activities than the forces measured in in-vitro experiments
[20], because in-vivo loads can be much larger than those applied in in-vitro experiments
to simulate physiological loading conditions [15]. The estimation of in-vivo ACL forces
among non-diseased knees during functional joint loading conditions could be used to
provide norms for optimal tensioning of the graft during ACL reconstruction.
The assessment of ACL forces under in-vivo physiological loading conditions
remains challenging in biomechanical engineering. The in-vivo biomechanics of the ACL
has been investigated by measuring the anteromedial surface strains of the ACL using a
differential variable reluctance transducer [4, 21, 22] and by measuring ACL elongation
using a combined MR and dual fluoroscopic imaging system [23, 24]. While these
studies have improved our knowledge of the in-vivo ACL biomechanics considerably, the
knowledge of the in-vivo forces within the ACL under functional loading is limited.
Roberts et al, [25] have measured the forces in the human ACL in-vivo by using
Arthroscopic
Implantable
Force
Transducer
(AIFT)
during
passive
knee
flexion/extension. However, the data on ACL forces were obtained through a necessary
invasive - i.e. arthroscopic - procedure.
The objective of this study was to utilize force-elongation data obtained from
experimental testing of cadaveric knees and determine changes in in-vivo ACL forces
non-invasively utilizing previously published in-vivo knee joint kinematics data in
response to controlled weightbearing at discrete flexion angle [26].
3.2 Materials and Methods
3.2.1 Measurement of In-vivo Elongation of the ACL in Response to
Increased Weightbearing
The in-vivo ACL elongation data in response to increased weightbearing have
been discussed before. In short, nine healthy subjects (Table 3.1) were recruited under the
approval of the Institutional Review Board and consent forms were collected. One knee
of each subject (randomly chosen right or left) was scanned in full extension position
using a 3.0 Tesla MR scanner (MAGNETOM Trio®, Siemens, Malvern, PA, USA). The
MR images (size: 160x160 mm, resolution: 512x512 pixels) were imported into a solid
modeling software (Rhinoceros®, Robert McNeel & Associates, Seattle, WA, USA) for
the construction of 3D models of the knee, including the tibia, femur, and insertion sites
of the ACL on the tibia and femur [24].
The same knee was then imaged using a dual fluoroscopic imaging system (DFIS)
at 150, 30* and 450 of flexion (Figure 3.1). This system consists of two fluoroscopes (BV
Pulsera*, Philips, Bothell, WA, USA), with image intensifiers positioned orthogonally to
each other (exposure time: 8 msec, beam current: -0.4 mA, beam energy: -50 kVp,
source to intensifier distance: 950 mm, inter beam angle: 900). A force plate constructed
using a six degrees of freedom (DOF) force-moment sensor (JR3*, San Francisco, CA,
USA) was integrated into the dual fluoroscopic system. During the experiment, the
subject positioned the tested leg on the force plate with the tibia perpendicular to the
ground, and the ground reaction forces were displayed on a monitor in front of the subject
(Figure 3.1). The platform was equipped with handles to help the subject balance
him/herself and create the target external loading at each flexion angle, while the other
leg was in contact with the ground. Simultaneous fluoroscopic images of the knee were
taken at each target flexion angle under two in-vivo weightbearing conditions: zero load
(< 10 N) and 1.0 times body weight (BW). To represent the zero load condition at each
flexion angle, the subject was requested to place the testing leg on the force plate while
the force plate measured a minimum vertical ground reaction force (< 10 N). Full body
weight loading condition was defined when the force plate measured a vertical ground
reaction force equal to the full body weight of the subject. At each loading position, the
subject was asked to pause for two seconds while the fluoroscopic images were captured.
The flexion angles were controlled using a goniometer.
Screen
Subject
Handles
C-Arms
Force Plate -'
Figure 3.1: Schematic of the dual fluoroscopic imaging system.
A virtual dual fluoroscopic system based on the geometry of the actual
experimental system was created in the 3D modeling software [27] (Figure 3.2). The pair
of fluoroscopic images of the knee captured at each position as well as the bony models
were imported into the software and the in-vivo knee positions were reproduced by
matching the projections of 3D knee model to the images of the knee captured by the
fluoroscopes [27].
The relative positions of the ACL insertion sites could be determined by using the
series of matched knee models under different loading conditions and at different flexion
angles. The length of the ACL was measured as the distance between the centroids of the
ACL insertion site on the tibia and femur. At each flexion angle, the length of the ACL
under zero weightbearing was used as a reference for measuring the ACL elongation
under full body weight. In order to determine the ACL elongation at exact 150, 30' and
450 of knee flexion, the true flexion angles were obtained from the final matched
positions and the corresponding measured in-vivo elongations were interpolated for the
target flexion angles. In general, the difference of true measured flexion angles and the
target angles were less that 5'.
Table 3.1: Clinical data on the subjects tested.
Subject No.
Sex
Leg
Age
(Yr)
Height
(Cm)
Weight
(N)
BWI
(Kg/m2)
1
2
3
4
5
6
7
8
9
M
M
F
F
M
F
M
F
F
R
R
L
R
R
L
L
R
L
26
38
41
48
42
28
32
23
30
178
168
165
160
183
168
175
173
165
720
850
930
790
920
650
895
745
640
23.2
30.7
34.9
31.5
28.0
23.5
29.8
25.4
24.0
793.3 (111.8)
27.9 (4.1)
Mean (SD)
34.2 (8.4)
0:Sotoscole A
P
scope 2
Source 2
0 Source 1
Figure 3.2: Virtual dual fluoroscopic imaging system created based on the geometry
of the actual experimental system.
3.2.2 In-vitro Force-Elongation Relations of the ACL
Force-elongation curves of the ACL were determined using six human cadaveric
knee specimens (fresh frozen, Table 3.2) in a uniaxial tensile test performed on a robotic
testing system (Figure 3.3) at the same target flexion angles as used for the living
subjects. The testing system is composed of a 6 DOF manipulator (Kawasaki UZ150,
Kawasaki Heavy Industry, Japan), a 6 DOF force-moment sensor (JR3*, San Francisco,
CA, USA) and custom-made fixture and pedestal, which can operate in both
displacement and force control modes [10]. The knees were thawed 24 hours before
testing. The femur and tibia were cut approximately 20 cm from the joint line, and bone
ends were stripped of musculature, potted in bone cement, and secured in thick-walled
aluminum cylinders using metal screws (Figure 3.3). The passive flexion path of each
intact knee was defined as a set of flexion angles at which the forces and moments at the
knee joint were minimal (< 5 N and < 0.5 N.m) and determined by the robot in the force
control mode [10]. This was done in one degree increments (from full extension to 450 of
knee flexion).
Then, all the soft tissues of the knee were dissected away, except for the ACL.
The tibial and femoral insertion sites of the ACL were digitized using a 3D digitizer
(MicroScribe* G2LX, Amherst, VA, USA, Figure 3.4). The long axis of the ACL was
defined as the line connecting the centroids of the digitized insertion sites. The robotic
testing system was programmed to stretch the ACL along this longitudinal axis. All the
forces were transformed from the load cell coordinate system (attached to the endeffector of the robot's arm) to the knee joint coordinate system using the corresponding
Euler angles. At each target flexion angle (15', 30* and 45*), the knee was pre-stretched
five times along the long axis of the ACL at a rate of 12 mm/sec until 400N load was
reached (pre-conditioning of the soft tissue). Then the ACL was stretched along the same
path at the same rate up to 400 N and the in-vitro force-elongation data were recorded
(Figure 3.5). After pre-stretching as well as stretching at each flexion angle, the specimen
was allowed to recover for ten minutes in the relaxed (slack) condition before testing at
the next flexion angle (ten minutes relaxation time and 400 N loading were chosen based
on preliminary studies).
The specimen was constantly sprayed with saline solution to prevent dehydration.
The ACL was completely relaxed at start point (on the neutral path of the knee joint). By
stretching the ligament along its long axis, the ACL force was increasing with a delay
compared to the displacement which confirmed that the ACL was slack. In order to
capture the natural force-elongation characteristics of the ACL, no other measurement
instruments were attached to the fibers of the ACL during our in-vitro experiments. In
addition, it was not practically possible to check all the ACL fibers to make sure whether
all of them are taut during in-vitro elongation test. The force-elongation curves of the
ACL were determined for each specimen in the same way and the averaged forceelongation curves of the six specimens were calculated at each flexion angle.
Table 3.2: History of the cadaver donors.
Donor No.
1
2
3
4
5
6
Mean (SD)
Sex
Leg
Age
(Yr)
M
M
M
M
F
F
R
L
R
L
R
L
57
57
44
44
36
36
45.7 (9.5)
Robot
Load Cell
Figure 3.3: Robotic testing system with installed knee specimen (before removing
soft tissues).
Figure 3.4: MicroScribe* digitizer with six degrees-of-freedom.
Tibia
Femur
Figure 3.5: Stretching the ACL along its long axis using the robot arm; all the soft
tissues of the knee joint were dissected away, except for the ACL.
3.2.3 Estimation of In-vivo ACL Force Changes
The change in in-vivo force of the ACL in response to full body weightbearing
was determined by using a weighted mean statistical method [28]. At each target flexion
angle, the in-vivo ACL elongation data of each subject under full body weight was
matched to the in-vitro elongation data on the average force-elongation curves (shown
schematically in Figure 3.6.A and Figure 3.6.B). By mapping the in-vivo elongation data
of each subject to the elongation data on the in-vitro force-elongation curve (from the invitro tensile test) at each flexion angle, the in-vivo ACL force of each subject under the
full body weight was determined by a mean value F, and a standard deviation o-, (plotted
schematically in Figure 3.6.C). Thus in-vivo ACL force of all living knees can be
represented by their mean values and standard deviations (Fi± o-, i = 1, 2,..., 9) at each
target flexion angle.
(A)
(U
0
0>
.: - .
--
-
a(C)
(D)
In-vivo ACL elongation
(B)
Ai
of th
0
-
-
Weightbearing load
Fneesui
A
fo
i
v
--
Weightbearng load
(WB)
In vitro ACL elongation
Figure 3 6 Schematic diagram showing the methodology used for determination of
in-vivo ACL tension. (A) Weightbearing-elongation of the ACL from in-vivo
weightbearing, (B) Force-elongation of the ACL from in-vitro robotic test, (C)
Estimation of in-vivo
ACL tension for each individual as a function
of
weightbearing, (D) Average in-vivo ACL force-weightbearing data of al living
knees using weighted mean statistical method. (figures are only conceptual and are
not presenting experimental results, BW: Body Weight)
It should be noted that since the in-vivo ACL elongation was measured using its
length at zero loading as a reference, the ACL force determined using this elongation
actually represented the ACL force change or increase when the weightbearing increased
from zero to full body weight. To estimate the average in-vivo ACL force increase of all
living knees, a weighted mean statistical method was used [28]. This method weighs each
living knee force in proportion to its error or standard deviation. If the ACL force of the
i-th subject is expressed as Fi ± ai, the weighted mean of in-vivo ACL force and its
corresponding standard error, denoted as F ± a, can be calculated using the following
equations [28]:
oa
tT
(N: total number of the living subjects)
22___
F~
and
F =
U=
2
2
i1
i
i=
I
This method has been widely used in both engineering and physics when
processing experimental data. The above procedure determined the mean in-vivo ACL
force increase caused by full body weight at all target flexion angles (schematic Figure
3.6.D).
3.2.4 Effect of Assumed Tension in the ACL under Zero Weightbearing
on In-vivo ACL Force Estimation
The above procedure for estimation of in-vivo ACL forces assumed that the ACL
forces were zero when the weightbearing load was zero. The determined ACL forces
represent the ACL force change when the weightbearing increased from zero to full body
weight.
If the ACL was initially tensioned under the zero weightbearing condition,
matching of the in-vivo ACL elongation should be initiated from the corresponding force
level on the in-vitro force-elongation curves. Due to the nonlinearity of the ACL forceelongation curve at low force levels, a change in the initial point of matching affects the
evaluation of the increase in the ACL force. Therefore, we evaluated the effect of
different values of assumed tension in the ACL under zero weightbearing (every 10 N up
to 50 N) on the evaluation of in-vivo ACL force changes caused when a full body weight
was applied to the tibia. By elevating the assumed ACL tension under zero weightbearing
and entering the linear part of the force-elongation curve, the initial ACL tension will not
have any effect on the estimated ACL force increase. The in-vivo ACL forces at each
assumed ACL tension under zero weightbearing was estimated as the summation of that
assumed ACL tension under zero weightbearing and the increase in the ACL force due to
full body weight. If the ACL was slack at the zero weightbearing, the actual ACL force
would be lower than the values obtained in this study by assuming no ACL tension under
zero weightbearing.
3.2.5 Sensitivity Study
The accurate identification of the centroid of the ACL insertions on the femur and
tibia is critical, as a shift in the location of the centroid could have an impact on the
estimated ACL forces. A previous study showed that the effect of the position of the
centroid of the ACL insertions on the elongation of the ACL was maximally 0.34 mm
[26]. Depending on different flexion angles and the assumed tension in the ACL, this can
cause variations in the estimated changes in the ACL force. A sensitivity study was
performed to determine the effect of the position of the ACL insertions centroid on the
estimated ACL force in different flexion angles.
3.2.6 Statistical Analysis
In this study, the in-vivo ACL force increase was estimated as a function of
assumed ACL tension under zero weightbearing and knee flexion angle. A two-way
repeated measures analysis of variance (ANOVA) and a post hoc Student-NewmanKeuls test were used to determine the statistically significant differences in the force
increase among different flexion angles as a function of assumed ACL tension under zero
weightbearing (Statistica* StatSoft, Inc., Tulsa, OK, USA). The independent variables
were: flexion angle and the assumed ACL tension under zero weightbearing. The
dependent variable was increase in the ACL force due to full body weightbearing. Level
of significance was set at p<0.05.
3.3 Results
3.3.1 In-vivo ACL Elongation Due to Full Body Weight
The mean values of the in-vivo ACL elongation of living subjects at tested flexion
angles are shown in Figure 3.7. The data demonstrated that the ACL elongated as the
weightbearing increased. Due to full body weight, elongation of the ACL was 1.3 ± 0.9
mm, 1.5 + 0.8 mm and 1.1 ± 0.9 mm at 15*, 300 and 450 of flexion, respectively.
2.5
-
21.5
-
10.5
-
0150
300
450
Flexion Angle
Figure 3.7: In-vivo weightbearing-elongation behavior of the ACL at 15*, 30* and
45* of flexion.
3.3.2 In-vitro Force-Elongation Behavior of the ACL
The averaged in-vitro force-elongation behavior of the ACL at different flexion
angles are presented in Figure 3.8. The in-vitro data showed that the structural properties
of the ACL under loading were dependent on the flexion angle. The amount of the forces
experienced by the ACL due to a fixed amount of elongation was greater at 150 and 30*
of flexion compared to 450 of flexion. The stiffness of the ACL in the linear region of the
force-elongation curves was 122.4 ± 11.4 N/mm at 15* of flexion, 117.7 ± 11.3 N/mm at
30* and finally 111.7 ± 8.9 N/mm at 450 of flexion. The change in the stiffness from 150
to 300 of flexion was not statistically significant (p> 0 .1); however the stiffness at 450 of
flexion was significantly less than that at 150 and 300 (p<0.04).
300
250
200
4+15*
-=30*
-e45*
150
100
0
1
2
3
Elongation (mm)
Figure 3.8: In-vitro force-elongation curves of the ACL at 150, 300 and 450 of flexion
(Standard deviation bars for 300 are not shown for figure clarity purposes).
3.3.3 In-vivo ACL Force Increase Due to Full Body Weight
In-vivo ACL force increases due to full body weight were calculated by assuming
various assumed ACL tensions under zero weightbearing (Figure 3.9). The patterns of the
forces showed that the estimated in-vivo ACL force increase approached an asymptote at
each flexion angle when the assumed ACL tension under zero weightbearing increased
over 20 N. When the assumed ACL tension under zero weightbearing was beyond 20 N,
the variations of force increase in the ACL due to the applied load were not significant in
all tested knee flexion angles (p>0.13). Therefore, the asymptotic value might represent
an upper bound of the increase in ACL force as the weightbearing increased from zero to
full body weight. Percentage of change in the ACL force increase under full body weight,
due to 10 N increase in assumed ACL tension under zero weightbearing was shown in
Table 3.3. At an assumed ACL tension of 40 N under zero weightbearing, the increase in
the ACL force changed by less than 5% when an assumed ACL tension of 50 N was used
under zero weightbearing. This percentage of change in the ACL force increase would
approach to zero by entering the linear region of the ACL force-elongation curves (Figure
3.8).
Table 3.3: Percentage of change in the ACL force increase under full body weight,
due to 10 N increase in the ACL tension under zero body weight.
Flexion Angle
ACL Tension under
zero weightbearing
(N)
150
30*
450
10
20
30
40
50
28.4
9.7
5.6
3.7
3.3
36.4
11.9
7.5
5.5
4.7
91.7
20.3
14.9
7.4
4.9
Assuming the ACL tension was 0 N under zero weightbearing, the increase in invivo ACL forces caused by full body weight were 131.4 ± 16.8 N at 150, 106.7 ± 11.2 N
at 300, and 34.6 ± 4.5 N at 450 of flexion (Figure 3.9). The increase in the in-vivo ACL
forces due to full body weight were 202.7 ± 27.6, 184.9 ± 22.5 and 98.6
+
11.7 N,
respectively at 150, 300 and 450 of flexion with an assumed ACL tension of 40 N under
zero weightbearing (Figure 3.9). In general, the ACL force increases at 150 and 300 of
knee flexion were significantly greater than those at 450 of flexion (p<0.0001). However,
the ACL force increases at 150 and 300 of flexion were not significantly different
(p>0 .08 ).
G-15 0
-+ - 300 -
450
250
0.3
z
200
.- -
S .150
U)
*E
C
~0.2 *-..
2100
0
LL..---J
u.
0.1 zo
50 0
0
0
10
20
30
40
50
Initial ACL Tension (N)
Figure 3.9: The increase in ACL force when the knee was under full body
weightbearing and different ACL tensions under zero weightbearing were assumed.
3.3.4 Estimation of In-vivo ACL Force
At each assumed ACL tension under zero weightbearing, the in-vivo ACL forces
were estimated as the summation of that assumed ACL tension and the increase in the
ACL force caused by full body weight, which was estimated at that assumed ACL
tension. With an ACL tension of 0 N at zero weightbearing, the in-vivo ACL force would
be the same as the increase in the ACL force. When the ACL tension under zero
weightbearing was 40 N, the estimated ACL forces under full weightbearing were 242.7
± 27.6 N at 150, 224.9
± 22.5 N at 300, and 138.6 ± 11.7 N at 450 of flexion. At 15* and
300, the ACL forces were not significantly different. These forces were significantly less
in 450 than those in 150 and 30* of flexion.
3.3.5 Sensitivity Study
Depending on different flexion angles and the assumed ACL tension under zero
weightbearing, a maximum ACL elongation error of 0.34 mm [26] caused variations in
the estimated changes in the ACL force. At 150 of flexion, the variation in the position of
the centroid of the ACL insertions caused a maximum force variation of 37.7 N at 0 N of
ACL tension under zero weightbearing (42.4 N at 40 N of ACL tension under zero
weightbearing). At 450 of flexion, this force variation was maximally 22.3 N at 0 N of
ACL tension under zero weightbearing (34.4 N at 40 N of ACL tension under zero
weightbearing).
3.4 Discussion
This study estimated the changes in in-vivo forces of the ACL at three discrete
flexion angles with zero and full body weight applied to the tibia. A combined MR and
dual fluoroscopic imaging system was used to obtain the in-vivo ACL elongation data
[26] and a robotic testing system [29] was employed to measure the in-vitro force-
elongation data of the ACL at the different flexion angles. Finally, a weighted mean
statistical method was used to estimate the in-vivo ACL force increases. The results
showed that by applying full body weightbearing, the ACL would experience a mild
force increase (below 250 N) when compared to the ACL failure tension of about 1500 N
[5]. The ACL force increase was significantly higher at 150 and 30' compared to 45'.
Numerous studies have reported on in-situ forces in the ACL using in-vitro
experimental setups and ACL forces have been reported to be higher at low flexion
angles [10, 17, 30]. For example, the in-vitro force in the ACL was found to peak
between 15' and 30' of flexion in response to various simulated muscle loads [10]. The
value of ACL force under 400 N quadriceps loading was reported 63.9 ± 33.4 N and 71.7
± 27.9 N at full extension and 30* of knee flexion respectively [10]. Also, the ACL
experienced a maximum force of 131 N at 300 flexion under anterior tibial load of 130 N
[31]. However, it has always been challenging to determine the ACL forces in-vivo.
Fleming et al. and Beynnon et al. [17, 30] studied the ACL strain on the anterior part of
the ACL surface of living subjects using a differential variable reluctance transducer.
They similarly reported that the ACL strain decreased with flexion beyond 15'. Under
Isometric quadriceps contraction (30 N.m of extension torque) the peak strain was
reported 4.4 ± 0.6 % at 150 of flexion [30]. Previous in-vivo studies showed that the ACL
has a larger elongation at low flexion angles [23, 24] (Figure 3.7). A direct comparison
between these studies is difficult though, since the loading conditions among these
studies were not the same. However, all these reports were consistent in that the ACL
was found to be more functional at lower flexion angles.
In general, the increases in in-vivo ACL forces in response to controlled
weightbearing were greater in all tested flexion angles compared to the ACL forces
reported in previous in-vitro studies. (e.g., 131 N under anterior tibial load [31], 71.7 ±
27.9 N under quadriceps load [10] in in-vitro studies and 184.9 ± 22.5 N under in-vivo
increased weightbearing with 40 N of assumed ACL tension under zero weightbearing,
all at 300 of knee flexion). This observation suggests that the ACL might carry much
higher forces during in-vivo weightbearing than the forces measured during in-vitro
experiments.
In this study, the in-vitro force-elongation of the ACL was determined using a
tensile test at different knee flexion angles. The ACL tensile behavior at different flexion
angles has been extensively studied by Woo et al. [51. In their study, anterior-posterior
displacement tests with the intact knee at 300 and 900 of flexion revealed a significant
effect of knee flexion angle [5]. Our data described a similar dependence of the ACL
tensile behavior on the flexion angle. When determining in-vivo ACL forces, it is always
difficult to determine an initial reference length of the ACL [22-24]. In the present study,
we used the ACL length measured at zero weightbearing condition at each flexion angle
as a reference. Consequently, the estimated forces in our study - before adding the
assumed ACL tension under zero weightbearing - represented the ACL force increases,
when weightbearing increased from zero to full body weight.
Since the in-vivo ACL tension under zero weightbearing could not be determined,
we evaluated the effect of different values of ACL tensions under zero weightbearing on
the estimated increases in ACL force when the weightbearing increased from zero to full
body weight. The data indicated that when the assumed ACL tension under zero
weightbearing was over 20 N, the change in the estimated ACL force approached an
asymptotic value. This may be due to the decrease in nonlinearity of the force-elongation
curve as the force level increased (Figure 3.8). Therefore, the asymptotic value might
represent an upper bound of the increase in ACL force as the weightbearing increased
from zero to full body weight. This upper bound corresponds to the constant slope of
force-elongation curve in its linear region. In this study, an assumed 40 N of ACL tension
under zero weightbearing was used to estimate the ACL force changes.
Using a uniaxial tensile test to obtain the in-vitro force-elongation data and
stretching the ACL along its longitudinal axis can recruit a higher number of fibers under
tension, whereas in the in-vivo study, the ACL elongation data were obtained from the
six DOF knee motion, which may or may not use all the fibers of the ACL [26]. Mapping
such in-vivo ACL elongation to the uniaxial force-elongation curve may have
overestimated the in-vivo ACL force changes. On the other hand, the force estimation
was based on the ACL elongation and the ACL torsion was not evaluated, even though
the ACL may experience torsion during functional activities. If any interaction between
ACL and PCL happened in the range of flexion of this study, the measured in-vivo
elongations would be underestimated [26].
The current technique for estimating the in-vivo ACL forces has several
limitations. First, due to the difficulty in obtaining knee specimens from healthy younger
donors, the in-vitro force-elongation data were determined using six relatively older
cadaveric knee specimens, inhibiting age matching. Furthermore, ACL elongation data
were only obtained at 150, 300, and 450 of flexion, as the ACL was found to be more
functional at lower flexion angles. A complete understanding of ACL forces under invivo loading conditions requires an examination of a full spectrum of functional
activities, such as gait, stair climbing, etc. The in-vivo ACL force increase was indirectly
estimated using in-vitro ACL force-elongation data and the in-vivo ACL elongation data.
Direct measurement of in-vivo ACL force is not possible at present time. Since the
tension of the ACL was not known when the knee was subjected to zero weightbearing,
the estimated force only represented the ACL force change when the weightbearing
increased from zero to full body weight. The estimation of the overall in-vivo ACL force
depends on the value of ACL tension under zero weightbearing, which could not be
determined at the present time. Therefore, we estimated the ACL force by using different
ACL tensions under zero weightbearing. Finally, the loading rates in in-vitro and in-vivo
studies were not the same, even though effort has been made to control the in-vitro
loading in a similar time range as the in-vivo loading. Despite these technical challenges,
the data revealed that the ACL force only changed by less than 250 N when the knee was
loaded from zero to full body weight, which accounts for less than 20% of the ultimate
strength of the ACL [5].
The present in-vivo ACL force values were estimated during only weightbearing
and evaluated at 15, 30, and 45 degrees of flexion. Therefore, caution is advised when
extrapolating the data to functional activities. Nevertheless, we believe that the clinical
implication of this study is considerable. This study presents the first non-invasive
estimation of in-vivo forces transmitted by the ACL - data critical for the optimal
restoration of the ligament's mechanical function. In future studies, the same
methodology could be applied to compare the in-vivo ACL/graft forces before and after
various reconstruction techniques.
In conclusion, the previously described combined MR and dual fluoroscopic
imaging system and a robotic testing system were utilized to investigate non-invasively
the in-vivo ACL force increases in response to a change in weightbearing from zero to
full body weight. The data demonstrated that the increase in the ACL force was
dependent on the flexion angle, with a larger increase in ACL force at low flexions. The
estimated in-vivo ACL force increase represented an overestimated value, which
indicated that under full body weight, the ACL might experience less than 250 N of
tensile force. This study presents an insight into the biomechanical behavior of the ACL
under a functional in-vivo loading condition.
3.5 Validation Study
3.5.1 Validation of the In-vivo ACL Force Estimation Method
In this validation study, a robotic testing system was used to apply external load
on cadaveric knee specimen and measure the corresponding ACL force as the gold
standard. These force values were compared to those estimated by the method introduced
in this study. The magnitude and direction of the forces measured by the robotic testing
system has been validated before [32].
One fresh-frozen cadaveric knee specimen (left knee, 48 years old man) was used.
MR images of the knee were acquired while all soft tissues of the knee were intact. The
3D surface model of knee, including tibia, femur and the insertion sites of the ACL on
each bone were created using the protocol described in the Methods section. Then, the
knee specimen was installed in the robot testing system and its passive flexion path was
determined in 1 increments in the same way descried in Methods section. Next, the dual
fluoroscopic testing system was set up orthogonally, in such a way that the installed knee
specimen was in the filed of view of both intensifiers (Figure 3.10).
Following setting up both robotic and fluoroscopic systems, the intact knee was
tested under 130 N anterior tibial load at 15*, 300 and 450 of knee flexions on the passive
path by using a published protocol [10] (A force applied anteriorly -towards front of the
body- to the proximal tibia). First, at each target flexion angle, the knee was imaged by
the fluoroscopes on the passive path. Then, the anterior tibial load was applied to the
knee specimen by the robot arm and the forces transmitted through the joint as well as the
corresponding kinematics response of the knee to the applied load were recorded.
Simultaneously, a pair of fluoroscopic images of the knee joint was captured. After
recording data at all aimed flexion angles, the ACL was resected via a small arthrotomy
with the knee in 300 of flexion. Then, the arthrotomy and skin were closed in layers. At
each flexion angle, the recorded kinematics of the intact knee under anterior tibial load
was replayed by the robot and the force transmitted through the joint was measured.
Using the principle of superposition, the difference between the forces measured in the
ACL deficient knee and the intact ACL knee represents the in-vitro ACL force under
anterior tibial load [13].
At the next step, the 3D knee models were matched to the corresponding pair of
fluoroscopic images in a virtual dual fluoroscopic imaging system using the protocol
explained in the Methods section. Then, the elongation of the ACL at each flexion angle
was measured. The length of the ACL with the knee under no load (passive path) was
chosen as the reference length. ACL tensions under zero load bearing were considered
from 0 to 50 N in 10 N increments.
At each target flexion angle, by mapping the
elongation of the ACL under anterior tibial load to the elongation data from in-vitro
force-elongation curve, the ACL force increases for different assumed ACL tension at
zero load bearing were estimated. Finally, the absolute values of the ACL force were
calculated by adding the ACL tension under zero load bearing to the estimated force
increase in the ACL. The estimated absolute values of the ACL force at different ACL
tensions at zero load bearing were compared with the in-vitro ACL force measured by the
robotic testing system (Figure 3.11).
Robot Arm
Fluoroscopes
Robot Arm
Load Cell
I
Knee Specimen
V
Fluoroscopes
Figure 3.10: (A) Set up of the Dual Fluoroscopic Imaging System around the robotic
testing system for validation study. (B) A knee specimen installed on the robotic
testing system with the fluoroscopes to image the knee joint during applying load.
The in-vitro ACL forces, measured by the robot, were 86.5 N, 146.3 N and 162.2
N at 15*, 300 and 450 of flexion, respectively. Using the method introduced in this study
for estimation of in-vivo ACL forces, the estimated ACL forces (force increase + ACL
tension under zero load bearing) with 40 N of ACL tension at zero load bearing, were
123.8 N, 151.1 N and 171.2 N at 150, 300 and 450 of flexion, respectively. At all three
different flexion angles, the actual ACL forces were less than the estimated ACL force
with an ACL tension of 40 N under zero load bearing, by 43.1% at 15*, 3.3% at 300 and
5.5% at 450*. In other words, the estimated ACL forces by using 40 N of ACL tension
under zero loading was a reasonable overestimation of the real ACL force at all flexions.
Variable ACL tension at zero load bearing condition might be the reason of greater
difference percentage at 150 of flexion. Because of lack of knowledge about the ACL
tension at zero loading, we can not predict the exact ACL force.
150
200 -
- ---
--
-
-
160 -
0
--
o
16
U_
0
40
--
Est. ACL
(N)
Force (N)
- - - --
-
50
10
0
20
40
30
50
In Vitro
300
0
8-
U
4
--
-
160--
120
--
---
-
40
0
10
20
30
40
50
In Vitro
450
160
120
S0
U
40
0
0
10
20
137.9
86.5
Ini. Tension
Est. ACL
(N)
Force (N)
30
40
Initial Tension (N)
0
10
20
30
40
50
In Vitro
50.9
92.1
115.6
134.4
151.1
166.8
146.3
(from robot)
Initial Tension (N)
200
..
-
-
0
In Vitro
(from robot)
Initial Tension (N)
200 --
38.4
71.6
92.2
109.4
123.8
0
10
20
30
40
--
120
Ini. Tension
50
In Vitro
Ini. Tension
Est. ACL
(N)
Force (N)
0
10
20
30
40
50
in Vitro
62.1
108.2
134.1
153.8
171.2
186.9
162.2
(from robot)
Figure 3.11: The in-vitro ACL force due to 130 N anterior tibial load and the
corresponding estimation of the ACL forces with different ACL tensions under zero
weightbearing at 15*, 300 and 450 of knee flexion. At all three different flexion
angles, the actual ACL forces (labeled as in-vitro) were less than the estimated ACL
force with an ACL tension of 40 N under zero load bearing.
3.6 Acknowledgements
This study was made possible through grants received from the National Institutes
of Health (R21 AR051078 and R01 AR055612) and the Department of Orthopaedic
Surgery at the Massachusetts General Hospital. The technical assistance of Michal
Kozanek is greatly appreciated.
3.7 References
1.
Butler DL, Guan Y, Kay MD, Cummings JF, Feder SM, Levy MS. Locationdependent variations in the material properties of the anterior cruciate ligament. J.
Biomech 1992; 25: 511-518.
2.
Chandrashekar N, Mansouri H, Slauterbeck J, Hashemi J. Sex-based differences in
the tensile properties of the human anterior cruciate ligament. J Biomech 2006; 39:
2943-2950.
3.
Henning CE, Lynch MA, Glick KR, Jr. An in-vivo strain gage study of elongation
of the anterior cruciate ligament. Am. J. Sports Med. 1985; 13: 22-26.
4.
Fleming BC, Beynnon BD, Tohyama H, Johnson RJ, Nichols CE, Renst6m P, et al.
Determination of a zero strain reference for the anteromedial band of the anterior
cruciate ligament. J Orthop Res 1994; 12: 789-795.
5.
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.
6.
Ahmed AM, Burke DL, Duncan NA, Chan KH. Ligament tension pattern in the
flexed knee in combined passive anterior translation and axial rotation. J. Orthop.
Res. 1992; 10: 854-867.
7.
Jasty M, Lew WD, Lewis JL. In-vitro ligament forces in the normal knee using
buckle transducers. Trans ORS 1982; 7: 241.
8.
Lewis JL, Lew WD, Schmidt J. A note on the application and evaluation of the
buckle transducer for knee ligament force measurement. J. Biomech. Eng. 1982;
104: 125-128.
9.
Claes LE, Diirselen L, Kiefer H. Influence of load, flexion and muscle-forces on
the stress and strain of knee ligaments. Trans ORS 1986; 11: 238.
10.
Li G, Zayontz S, Most E, DeFrate LE, Suggs JF, Rubash HE. In situ forces of the
anterior and posterior cruciate ligaments in high knee flexion: an in vitro
investigation. J Orthop Res 2004; 22: 293-297.
11.
Rudy TW, Livesay GA, Woo SL, Fu FH. A combined robotic/universal force
sensor approach to determine in situ forces of knee ligaments. J. Biomech 1996; 29:
1357-1360.
12.
Woo SL, Wu C, Dede 0, Vercillo F, Noorani S. Biomechanics and anterior
cruciate ligament reconstruction. J Orthop Surg 2006; 1: 2.
13.
Li G, Rudy TW, Sakane M, Kanamori A, Ma CB, Woo SL. The importance of
quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in
the ACL. J Biomech 1999; 32: 395-400.
14.
Fleming BC, Beynnon BD, Nichols CE, Johnson RJ, Pope MH. An in vivo
comparison of anterior tibial translation and strain in the anteromedial band of the
anterior cruciate ligament. J. Biomech 1993; 26: 51-58.
15.
Sakane M, Fox RJ, Woo SL, Livesay GA, Li G, Fu FH. In situ forces in the
anterior cruciate ligament and its bundles in response to anterior tibial loads. J
Orthop Res 1997; 15: 285-293.
16.
Li G, Suggs J, Gill T. Investigation of the effect of ACL injury on knee joint
function -a computational simulation. Annals Biomed Eng 2002; 30: 713-720.
17.
Fleming BC, Renstrom PA, Beynnon BD, Engstrom B, Peura GD, Badger GJ, et al.
The effect of weightbearing and external loading on anterior cruciate ligament
strain. J Biomech 2001; 34: 163-170.
18.
Fukubayashi T, Torzilli PA, Sherman MF, Warren RF. An in-vitro biomechanical
evaluation of anterior-posterior motion of the knee. J. Bone Joint Surg. 1982; 64A:
258-264.
19.
Kanamori A, Zeminski J, Rudy TW, Li G, Fu FH, Woo SL. The effect of axial
tibial torque on the function of the anterior cruciate ligament: a biomechanical
study of a simulated pivot shift test. Arthroscopy 2002; 18: 394-398.
20.
Nagura T, Dyrby C, Alexander E, Andriacchi T. Mechanical loads at the knee joint
during deep flexion. J Ortho Res 2002; 20: 881-886.
21.
Beynnon BD, Fleming BC, Johnson RJ, Nichols CE, Renstr6m PA, Pope MH.
Anterior cruciate ligament strain behavior during rehabilitation exercises in vivo.
Am. J. Sports Med. 1995; 23: 24-34.
22.
Beynnon BD, Johnson RJ, Fleming BC, Renstr6m PA, Nichols CE, Pope MH, et
al. The measurement of elongation of anterior cruciate-ligament grafts in-vivo. J
Bone Joint Surg Am. 1994; 76: 520-531.
23.
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.
24.
Jordan SS, DeFrate LE, Nha KW, Papannagari R, Gill TJ, Li G. The in vivo
kinematics of the anteromedial and posterolateral bundles of the anterior cruciate
ligament during weightbearing knee flexion. Am J Sports Med 2007; 35: 547-554.
25.
Roberts CS, Cumming JF, Grood ES, Noyes FR. In vivo measurement of human
anterior cruciate ligament forces during knee extension exercises. Trans. Orthop.
Res. Soc. 1994: 19:84.
26.
Hosseini A, Gill TJ, Li G. In vivo anterior cruciate ligament elongation in response
to axial tibial loads. J Orthop Sci 2009; 14: 298-306.
27.
Li G, Wuerz TH, DeFrate LE. Feasibility of using orthogonal fluoroscopic images
to measure in vivo joint kinematics. J Biomech Eng 2004; 126: 314-318.
28.
Leo WR. Techniques for Nuclear and Particle Physics Experiments. London,
Springer-Verlag 1992.
29.
Most E, Li G, Schule S, Sultan P, Park SE, Zayontz S, et al. The kinematics of
fixed- and mobile-bearing total knee arthroplasty. Clin Orthop Relat Res 2003:
197-207.
30.
Fleming BC, Beynnon BD, Renstrom PA, Johnson RJ, Nichols CE, Peura GD, et
al. The strain behavior of the anterior cruciate ligament during stair climbing: an in
vivo study. Arthroscopy 1999; 15: 185-191.
31.
Li G, Papannagari R, DeFrate LE, Yoo JD, Park SE, Gill TJ. Comparison of the
ACL and ACL graft forces before and after ACL reconstruction: an in-vitro robotic
investigation. Acta Orthop 2006; 77: 267-274.
32.
Fujie H, Livesay GA, Woo SL, Kashiwaguchi S, Blomstrom G. The use of a
universal force-moment sensor to determine in-situ forces in ligaments: a new
methodology. J Biomech Eng 1995; 117: 1-7.
Chapter 4 - Estimation of In-vivo Forces within the
Anteromedial and Posterolateral Bundles of the
Anterior Cruciate Ligament under Weightbearing
4.1 Introduction
It is known that the Anterior Cruciate Ligament (ACL) consists of two anatomical
bundles, i.e., the anteromedial (AM) and posterolateral (PL) bundles [1, 2]. Earlier
studies have also differentiated between the action of the anterior and posterior part of the
ACL with a reciprocal tightening and slackening of the anterior and posterior fibers of the
ACL in flexion and extension of the knee [2, 3]. During passive knee motion, the AM
bundle was reported being tight in flexion and the PL bundle being tight in extension [1,
3]. Applying anterior tibial load to the knee joint also caused reciprocal force pattern in
the anatomical bundles of the ACL in-situ with higher tensions in the PL bundle compared to the AM bundle - near full extension [4-6].
Interestingly, the in-vivo elongation patterns of the AM and PL bundles of the
ACL have been found to be similar. Both bundles were described to have their maximum
length near full extension and then shorten with flexion [7]. This implies that under
physiological loading conditions, the ACL bundles might function in a different way
compared to passive knee motion. However, the load carrying contribution of the AM
and PL bundles of the ACL under physiological activities is unknown. In order to
develop an optimal ACL reconstruction technique that adequately restores the natural
behavior of the two functional bundles of the ACL, it is substantial to understand the
contributions of the AM and PL bundles under physiological loads.
The objective of this study was to estimate the in-vivo forces of the anteromedial
and posterolateral bundles of the ACL under controlled weightbearing using a noninvasive technique (as described in previous chapter). A combination of MR and dual
fluoroscopic imaging system was used to determine the elongation of the ACL bundles
in-vivo, and a robotic testing system was utilized to determine the in-vitro forceelongation data of the bundles. For each bundle, the in-vivo elongation data were mapped
to the corresponding in-vitro force-elongation curves to estimate the in-vivo forces of
AM and PL bundles in response to a controlled weightbearing.
4.2 Materials and Methods
This study was planned in three main parts. First, at each tested flexion angle of
the knee, the in-vivo elongations of the AM and PL bundles under the weightbearing load
was accurately determined using a dual fluoroscopic imaging technique. Second, the insitu force-elongation curves of those bundles were determined at the same flexion angles
using cadaveric knee specimens. Finally, by matching the data from the first and second
steps, the in-vivo forces of each bundle under the weightbearing activity were estimated.
4.2.1 In-vivo Elongation of the AM and PL Bundles in Response to
Increased Weightbearing
The measurement of the in-vivo ACL elongation as well as its anatomical bundles
in response to increased weightbearing has been explained in details in Chapter 2.2.
Briefly, nine healthy subjects were recruited under the approval of the Institutional
Review Board and consent forms were collected. All the knees were imaged with a 3.0
Tesla scanner (MAGNETOM Trio*, Siemens, Malvern, PA, USA) in both sagittal and
coronal planes. The 3D anatomic models of the bones and the insertion sites of the AM
and PL bundles on the femur and tibia were created using these MR images [8].
Next, the kinematics of the same knees was determined using the previously
described dual fluoroscopic imaging technique [8, 9]. The system consists of two
fluoroscopes (BV Pulsera*, Philips, Bothell, WA, USA), with image intensifiers
positioned orthogonally to each other. A force plate constructed using a six degrees-of-
freedom (DOF) load sensor (JR3*, San Francisco, CA, USA) was installed on the top of
a platform and was connected to a monitor to simultaneously display the value of ground
reaction forces when the subject stepped on the force plate (Figure 2.5.A). The
kinematics data was collected during a single-legged quasi-static lunge activity (at 150,
300 and 450 of flexion) under different controlled weightbearing: zero load (< 10 N), and
1.0 times body weight (BW). Then based on the geometry of the actual experimental
system, a virtual dual fluoroscopic system was created in the 3D modeling software
(Figure 2.5.B). The 3D knee models and the fluoroscopic images were used to reproduce
the in-vivo kinematics of the tested knee at each imaged position. Also, the insertions of
both the AM and PL bundles of the ACL were mapped on to the matched positions of
knee models. The length of the AM (PL) at each matched position was measured as the
length of a straight line connecting the AM (PL) insertions on tibial and femoral sides. At
each flexion angle, the elongation of each bundle with respect to its length under minimal
load was measured. The curves of ACL elongation-weightbearing were obtained for each
subject.
4.2.2 In-vitro Force-Elongation Relations of the AM and PL Bundles
Determining the force-elongation curves of the ACL was described in details in
Chapter 3.2.2. A similar experiment was set up to determine the force-elongation
relations of the AM and PL bundles. A robotic testing system (Figure 3.3) was
programmed to perform a uniaxial tensile test for each bundle. The testing system is
made of a 6 DOF manipulator (Kawasaki UZ150, Kawasaki Heavy Industry, Japan), with
a 6 DOF force-moment sensor (JR3*, San Francisco, CA, USA) mounted on the endeffector of the robot. This system is equipped with a custom-made fixture and pedestal to
facilitate the installation of a knee specimen [10]. The force-elongation curves of the AM
and PL bundles were determined using six human cadaveric knee specimens (Table 3.2).
Each specimen was stored at -20*C before the experiment and was thawed at
room temperature for 24 hours prior to experiment. Both tibial and femoral bones were
stripped of musculature about 10 cm away from the joint, potted in bone cement, and
installed on the pedestal and fixture of the robotic system. Then, the passive flexion path
of the knee was determined with a minimum load in the knee joint (< 5 N and < 0.5 N.m)
in one degree increments [10]. All the soft tissues of the knee were dissected away,
except for the ACL. To determine the long axis of the ligament, the insertion sites of the
ACL were determined using a digitizer (MicroScribe* G2LX, Amherst, VA, USA). The
robot was programmed to transfer the forces from the load cell coordinate system
(attached to the end-effector of the robot's arm) to the knee joint coordinate system using
the corresponding Euler angles.
Next, the AM and PL bundles were identified and dissected by an orthopaedic
surgeon (Figure 4.1). After bundle separation, the combination of AM+PL bundles was
stretched along the long axis of the ACL at a rate of 12 mm/sec up to 400 N and the
force-elongation curves were determined at each flexion angle (15*, 30* and 450). Then,
the PL bundle was cut at its femoral insertion, while the AM bundle was intact. At each
tested flexion angle, the AM bundle was stretched again along corresponding recorded
path and the in-vitro force-elongation data of the AM bundle was determined. Finally, to
find out the in-vitro force-elongation data of the PL bundle, the principle of superposition
was used. After each stretching, the tissue was allowed to recover for ten minutes in the
relaxed position on the determined passive path of the knee.
Figure 4.1: The Anteromedial (AM) bundle and Posterolateral (PL) bundle of ACL
were identified and separated for tensile test. The bundles are hold separately using
sutures at 450 of knee flexion (anterior view).
4.2.3 Estimation of In-vivo AM and PL Forces
The changes in in-vivo forces of the AM and PL bundles in response to full body
weightbearing were determined by using a weighted mean statistical method [11], as
fully discussed in Chapter 3.2.3 and demonstrated in Figure 3.6.
For each bundle of the ACL, the in-vivo elongation data were mapped to in-vitro
force-elongation curves at the corresponding flexion angles and the changes in the invivo forces were statistically estimated (Figure 3.6). Since the tension of each bundle
under zero weightbearing was unknown, the force estimation was done with different
values of assumed tension in ACL bundles under zero weightbearing (every 10 N up to
50 N).
4.2.4 Statistical Analysis
In this study, the changes in in-vivo forces of the AM and PL bundles were
estimated as a function of knee flexion angle and assumed initial tension under zero
weightbearing. A two-way repeated measures analysis of variance (ANOVA) and a post
hoc Student-Newman-Keuls test were used to determine the statistically significant
differences in the force increase among different flexion angles as a function of assumed
ACL tension under zero weightbearing (Statistica* StatSoft, Inc., Tulsa, OK, USA). The
independent variables were: flexion angle and the bundles of the ACL. The dependent
variables were increase in the ACL force due to full body weightbearing and the stiffness
of the bundles in the linear region of force-elongation curves. Level of significance was
set at p<0.05.
4.3 Results
4.3.1 In-vitro Force-Elongation Behavior of the AM and PL Bundles of
the ACL
The averaged in-vitro force-elongation behavior of the anteromedial and
posterolateral bundles of the ACL at different flexion angles are shown in Figure 4.2. The
stiffness of the AM in the linear region of the force-elongation curves was 98.0 ± 44.7
N/mm at 150 of flexion, 111.0 ± 17.2 N/mm at 30* and finally 105.1 ± 13.9 N/mm at 450
of flexion. The flexion angle did not have a significant effect on the stiffness of the AM
bundle (p>0.74). The stiffness of the PL in the linear region of the force-elongation
curves was 39.4 + 43.0 N/mm, 18.2 ± 18.6 N/mm and 17.1 ± 21.2 N/mm at 150, 30* and
450 of knee flexion, respectively. The stiffness of the PL bundle was not also
significantly different at 150, 300 and 450 of flexion (p>0.34). However, at all tested
flexion angles, the stiffness (N/mm) of the AM bundle was significantly higher than that
of PL bundle (p<0.002).
4.3.2 In-vivo Force Increase in the AM and PL Bundles of the ACL Due
to Full Body Weight
In-vivo force increases of the anteromedial and posterolateral bundles due to full
body weight were calculated by considering various assumed tensions under zero
weightbearing (Figure 4.3). In general, the mean values of the AM bundle force increases
were the highest at 300 of flexion. The patterns of the forces showed that by increasing
the assumed AM tension under zero weightbearing, the estimated increase in in-vivo AM
force approached an asymptote at each flexion angle. Assuming the AM tension was 0 N
under zero weightbearing, the increase in in-vivo AM forces caused by full body weight
were 94.6 ± 44.2 N at 150, 107.0 ± 31.0 N at 300, and 36.8 ± 13.7 N at 450 of flexion
(Figure 4.3.A). The increase in the in-vivo AM forces due to full body weight were 145.3
± 81.8, 167.3
± 47.4 and 109.6 ± 29.2 N, respectively at 150, 30* and 450 of flexion with
an assumed tension of 40 N under zero weightbearing (Figure 4.3.A). However, the
changes in AM force at 15*, 30' and 450 of flexion were not significantly different
(p>0.45).
With regard to the changes in PL bundle force, the same asymptotic behavior was
observed (Figure 4.3.B). The mean values of the changes in PL bundle force were the
highest at 150 and lowest at 45' of flexion, although not significantly different. Assuming
the PL tension was 0 N under zero weightbearing, the increase in in-vivo PL forces
caused by full body weight were 81.3 ± 62.3 N at 150, 45.4 ± 36.5 N at 30*, and 14.0 ±
14.9 N at 45* of flexion (Figure 4.3.B). The increase in the in-vivo PL forces due to full
body weight were 82.2 ± 107.0, 38.9
+
69.2 and 23.7 ± 58.6 N, respectively at 150, 300
and 45* of flexion with an assumed PL tension of 40 N under zero weightbearing (Figure
4.3.B). The effect of bundle was statistically significant different (p<0.008) with higher
force increase in the AM bundle.
4.3.3 Estimation of In-vivo Forces within the AM and PL Bundles
At each assumed bundle tension under zero weightbearing, the in-vivo AM (PL)
forces were estimated as the summation of that assumed AM (PL) tension and the
increase in the AM (PL) force caused by full body weight, which was estimated at that
assumed initial tension.
With an initial tension of 0 N at zero weightbearing, the in-vivo AM (PL) forces
would be the same as the increase in the AM (PL) forces. When the AM (PL) tension
under zero weightbearing was 40 N, the estimated AM (PL) forces under full
weightbearing were 185.3 ± 81.8 (122.2 ± 107.0) N at 15*, 207.3 ± 47.4 (78.9 ± 69.2) at
30 , and 149.6 ± 29.2 (63.7 ± 58.6) N at 450 of flexion. At 150 and 300, the ACL forces
were not significantly different. These forces were significantly less in 450 than those in
150 and 300 of flexion.
A
300
250
200
-*15*
-"-30*
150
--
100
0
1
2
450
3
Elongation (mm)
B
300 .
250200 150-
I---
15*
-+*-30*1
-+&-45*
100 -
0
1
2
3
Elongation (mm)
Figure 4.2: In-vitro force-elongation curves of bundles of the ACL at 15*, 300 and
450 of flexion: (A) Anteromedial (AM) and (B) Posterolateral (PL). (Standard
deviation bars for 300 are not shown for figure clarity purposes)
A
-4-15* -
z
450
-30*-
250
0.3
g 200 -
150
0100
AF
-0.1
e o--
o
UL50
0
20
40
Initial AM Bundle Tension (N)
I
B
-G-150
-1-
-+30
450
250 -
0.3
2
200-
:-
!
150 -.
tn
100 u- 5010
0.1
0
0
OE
0
0
10
20
30
40
50
Initial PL Bundle Tension (N)
Figure 4.3: The increase in bundle forces when the knee was under full body
weightbearing and different bundle tensions under zero weightbearing were
assumed: (A) Anteromedial (AM) and (B) Posterolateral (PL).
4.4 Discussion
In this study, the changes in in-vivo forces of the anteromedial and posterolateral
bundles of the ACL in response to full body weight were estimated. The in-vivo
elongation of the AM and PL bundles of the ACL was obtained using a combined MR
and dual fluoroscopic imaging system (DFIS) [8]. A robotic testing system [12] was used
to extract the in-vitro force-elongation data of the bundles of the ACL. By mapping the
in-vivo elongation data of each bundle to the corresponding in-vitro force-elongation
curves, the in-vivo force increases of AM and PL bundles of the ACL in response to
applied full body weight were statistically determined. Since the tension of neither ACL
nor its anatomical bundles under zero weightbearing condition was known, the force
increase was estimated by assuming different values of initial tension. Three discrete
flexion angles (150, 300 and 450) were included in this study.
The results showed that both the AM and PL bundles shared the ACL tension
during the full body weightbearing. In general, the mean values of the force increase
within the AM bundle in response to full body weightbearing throughout the tested range
of knee flexion was more than 50% of that in the PL bundle. The mean value of the force
increase in the AM bundle due to full body weightbearing was the highest at 300 of
flexion, even though not statistically significant. This pattern is slightly different from
those of the PL bundle and the ACL (described in Chapter 3), with the greatest force
increase at 15' of knee flexion.
Our data indicates that The AM and PL bundles support each other under various
loading conditions rather than function independently. This is in agreement with our
recent in-situ study in which the load sharing patterns of both bundles were
complementary rather than reciprocal under simulated muscle loads [13]. In previous invitro studies, it was reported that the two bundles function in a reciprocal manner during
passive knee motion, with the PL bundle being tight in extension and the AM bundle
being tight in flexion [1, 3]. However, the in-vivo elongation patterns of the AM and PL
bundles during single lunge activity were found to be complimentary with the maximum
lengths at near full extension. This indicates that under physiological loading, the bundles
of the ACL might function differently.
The contribution of the AM and PL bundles in sharing the ACL loads is clinically
important in ACL reconstruction. The initial tension of the ACL graft and the specific
angle for graft fixation are very important parameters, which could directly affect the
surgical outcomes. These parameters are more controversial in double-bundle ACL
reconstruction. It has been considered to fix the AM and PL grafts either at two different
knee flexion angles at which each bundle carried the highest force, or at the same flexion
angle [14-16]. However, the fixation angle remains controversial and varies between 100
to 900 of knee flexion [14, 17-19]. According to findings of this study, both AM and PL
bundles carried maximum load at 150 and 30* of flexion angle and might be fixed within
this range of flexion. More physiological activates should be considered and the effect of
different loadings should be further investigated.
In this study, the AM bundle was found to be significantly stiffer that PL bundle.
Similar results were reported by previous investigators. Butler et al. extensively
investigated the location-dependent variations in the material properties of the ACL [20].
They reported that AM bundle had higher load-related material properties (such as
modulus, maximum strain and strain energy density) than PL bundle [20, 21]. Moreover,
Woo et al. showed the effect of specimen orientation on the tensile properties of the
human femur-ACL-tibia complex [22]. The linear stiffness of the ACL in the anatomical
orientation was 11-45% higher than those tested in tibial orientation, although no
statistical significance was reported [22]. In the current study, the flexion angle did not
have any significant effect on the stiffness of the bundles. However, it was discussed in
the previous chapter that the stiffness of the ACL was dependent of the flexion angle,
which indicated that the complex anatomy of the ACL might adopt itself for an optimal
functionality at different flexion angle.
The current methodology for estimating of the in-vivo forces within the ACL
bundles has its limitations. The difficulty in obtaining knee specimens from healthy
younger donors, force estimation in limited discrete flexion angles (150, 30*, and 450)
and assuming different tension for the bundles when the knee was subjected to zero
weightbearing have been discussed in Chapter 3.4. Also, stretching the ACL bundles
along their longitudinal axis to obtain the in-vitro force-elongation data can recruit a
higher number of fibers under tension, whereas in the in-vivo study, all the fibers of the
ACL may or may not be used. Therefore, mapping such in-vivo elongation data to the
uniaxial force-elongation curve may have overestimated the changes in in-vivo bundle
force. The in-vivo bundle forces of the ACL were measured under a quasi-static
condition. A complete understanding of the forces within the ACL bundles under in-vivo
loading conditions requires an investigation of a full spectrum of dynamic loading
conditions.
In conclusion, the in-vivo force increases of the ACL bundles in response to a
change in weightbearing from zero to full body weight were non-invasively investigated
utilizing a combined MR and dual fluoroscopic imaging system and a robotic testing
system. The findings support this concept that both bundles function in a complementary
manner. The results demonstrated that the AM bundle carried greater portion of the
tension within the ACL in response to full body weightbearing at all tested flexion
angles. Further investigations are needed to determine the tension of the ligament/bundles
under no weightbearing. The function of each bundle should be studied in a wide variety
of dynamic activities. These data might be useful to restore the function of each bundle in
ACL reconstruction.
4.5 Acknowledgements
The financial support of the National Institutes of Health (R21 AR051078 and
ROl AR055612) and the Department of Orthopaedic Surgery at the Massachusetts
General Hospital are gratefully acknowledged. Also, the technical assistance of Drs.
Jong-Keun Seon and Michal Kozanek is greatly appreciated.
4.6 References
1.
Amis AA, Dawkins GP. Functional anatomy of the anterior cruciate ligament.
Fibre bundle actions related to ligament replacements and injuries. J Bone Joint
Surg Br 1991; 73: 260-267.
2.
Girgis FG, Marshall JL, Monajem A. The cruciate ligaments of the knee joint.
Anatomical, functional and experimental analysis. Clin Orthop Relat Res 1975:
216-231.
3.
Bach JM, Hull ML, Patterson HA. Direct measurement of strain in the
posterolateral bundle of the anterior cruciate ligament. J Biomech 1997; 30: 281283.
4.
Sakane M, Fox RJ, Woo SL, Livesay GA, Li G, Fu FH. In situ forces in the
anterior cruciate ligament and its bundles in response to anterior tibial loads. J
Orthop Res 1997; 15: 285-293.
5.
Vercillo F, Woo SL, Noorani SY, Dede 0. 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.
6.
Gabriel MT, Wong EK, Woo SL, Yagi M, Debski RE. Distribution of in situ forces
in the anterior cruciate ligament in response to rotatory loads. J Orthop Res 2004;
22: 85-89.
7.
Jordan SS, DeFrate LE, Nha KW, Papannagari R, Gill TJ, Li G. The in vivo
kinematics of the anteromedial and posterolateral bundles of the anterior cruciate
ligament during weightbearing knee flexion. Am J Sports Med 2007; 35: 547-554.
8.
Hosseini A, Gill TJ, Li G. In vivo anterior cruciate ligament elongation in response
to axial tibial loads. J Orthop Sci 2009; 14: 298-306.
9.
Li G, Wuerz TH, DeFrate LE. Feasibility of using orthogonal fluoroscopic images
to measure in vivo joint kinematics. J Biomech Eng 2004; 126: 314-318.
10.
Li G, Zayontz S, Most E, DeFrate LE, Suggs JF, Rubash HE. In situ forces of the
anterior and posterior cruciate ligaments in high knee flexion: an in vitro
investigation. J Orthop Res 2004; 22: 293-297.
11.
Leo WR. Techniques for Nuclear and Particle Physics Experiments. London,
Springer-Verlag 1992.
12.
Most E, Li G, Schule S, Sultan P, Park SE, Zayontz S, et al. The kinematics of
fixed- and mobile-bearing total knee arthroplasty. Clin Orthop Relat Res 2003:
197-207.
13.
Wu JL, Seon JK, Gadikota HR, Hosseini A, Sutton KM, Gill TJ, et al. In situ forces
in the anteromedial and posterolateral bundles of the anterior cruciate ligament
under simulated functional loading conditions. Am J Sports Med 2010; 38: 558563.
14.
Fu FH, Shen W, Starman JS, Okeke N, Irrgang JJ. Primary anatomic double-bundle
anterior cruciate ligament reconstruction: a preliminary 2-year prospective study.
Am J Sports Med 2008; 36: 1263-1274.
15.
Kondo E, Yasuda K, Azuma H, Tanabe Y, Yagi T. Prospective clinical
comparisons of anatomic double-bundle versus single-bundle anterior cruciate
ligament reconstruction procedures in 328 consecutive patients. Am J Sports Med
2008; 36: 1675-1687.
16.
Yasuda K, Kondo E, Ichiyama H, Tanabe Y, Tohyama H. Clinical evaluation of
anatomic double-bundle anterior cruciate ligament reconstruction procedure using
hamstring tendon grafts: comparisons among 3 different procedures. Arthroscopy
2006; 22: 240-251.
17.
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.
18.
Aglietti P, Giron F, Cuomo P, Losco M, Mondanelli N. Single-and double-incision
double-bundle ACL reconstruction. Clin Orthop Relat Res 2007; 454: 108-113.
19.
Yasuda K, Ichiyama H, Kondo E, Miyatake S, Inoue M, Tanabe Y. An in vivo
biomechanical study on the tension-versus-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.
20.
Butler DL, Guan Y, Kay MD, Cummings JF, Feder SM, Levy MS. Locationdependent variations in the material properties of the anterior cruciate ligament. J
Biomech 1992; 25: 511-518.
21.
Butler DL, Kay MD, Stouffer DC. Comparison of material properties in fasciclebone units from human patellar tendon and knee ligaments. J Biomech 1986; 19:
425-432.
22.
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.
Chapter 5 - In-Situ Forces within the Anteromedial and
Posterolateral Bundles of the Anterior Cruciate
Ligament under Simulated Functional Loading
Conditions
5.1 Introduction
It has been generally accepted in literature that the anterior cruciate ligament
(ACL) consists of two major functionalI components, the anteromedial (AM) and
posterolateral (PL) bundles [1-4]. Previous anatomic studies have shown that the two
bundles function in a reciprocal manner during passive knee motion, with the PL bundle
being tight in extension and the AM bundle being tight in flexion [1, 3, 5, 6]. In response
to an anterior tibial load, the two functional bundles of the ACL were shown to carry
inversely related in-situ forces through the flexion-extension path of the knee, especially
at near full extension, where the in-situ force of the PL bundle was shown higher than the
AM bundle [7-10]. Under the combined rotational loads, the two bundles shared the load
at the selected flexion angles [3, 8, 10].
Recent in-vivo studies revealed that the AM and PL bundles of the ACL have a
more complementary, as opposed to reciprocal, lengthening pattern during weightbearing flexion, especially at low flexion angles [11, 12]. Both bundles were observed to
reach maximum length at near extension and then shorten with flexion, indicating that the
ACL bundles may function differently under physiological loading conditions when
compared to passive loading conditions. A similar result was obtained using a surgical
navigation system to evaluate the length change and orientation of the two bundles in
cadaveric knees [13]. Our in-vitro studies also found that the ACL force diminished
beyond 300 of flexion under simulated muscle loads, implying that both bundles may not
function at high flexion [14, 15]. However, no data has been reported on the AM and PL
bundle forces when the knee is subjected to muscle loads. A quantitative knowledge on
the in-situ forces of the AM and PL bundles under physiological loads could be
instrumental for understanding the ACL function and developing anatomic ACL
reconstruction techniques that are aimed to reproduce the two functional bundles of the
ACL.
The objective of this study was to measure the in-situ forces of the AM and PL
bundles of the ACL under simulated quadriceps muscle loads. The forces of the two
bundles under an anterior tibial load and combined rotational loads were also examined
in the study. We hypothesized that the load sharing patterns of the AM and PL bundles
would be complementary under simulated muscle loads.
5.2 Materials and Methods
5.2.1 Specimen Preparation
In-situ forces of the AM and PL bundles were studies in eight fresh-frozen
cadaveric knee specimens with an average age of 55 years (47 to 60 years) and with one
female and seven male donors. Prior to the experiment, all specimens were stored at 20*C and were thawed at room temperature for 24 hours before the experiment. Each of
the specimens was examined after it was completely thawed for osteoarthritis and ACL
injury by fluoroscopy and manual stability evaluation. Specimens with either of these
conditions were excluded from this study. The femur and tibia were truncated
approximately 25 cm from the joint line, with all the soft tissues around the knee intact
and a bone screw was used to firmly secure the fibula to the tibia in its anatomical
position. Each specimen was manually pre-conditioned by flexing the knee joint ten
times before it was installed on the robotic testing system.
5.2.2 In-situ Forces within the AM and PL Bundles
A robotic testing system (Figure 3.3) was used to investigate the knee joint
biomechanics. This testing system has been previously described in the literature [14-20].
After the specimen was installed on the robotic testing system, a passive flexion path of
the ACL intact knee was determined from 0' to 900 of flexion in 1 increment of knee
flexion. A passive position along the passive flexion path was described as a position of
the knee at which all resultant forces and moments at the knee center were minimal (< 5
N and < 0.5 N.m, respectively). The kinematic responses of each knee were then
determined under three different subphysiologic loading conditions: an anterior tibial
load of 134 N, combined torques of 10 N.m valgus and 5 N.m internal tibial torque and a
simulated quadriceps load of 400 N at selected flexion angles of 00, 150, 300, 600, and
900. The simulated quadriceps loads were applied to the knee joint by hanging weights
from a rope passing through a pulley system at each of the selected flexion angles [14,
15]. Under each loading condition, the robotic testing system recorded the kinematic
responses of the knee joint.
After the kinematics of the ACL intact knee were determined under the external
loads at the selected flexion angles, the AM and PL bundles were identified via a medial
miniarthrotomy with the knee flexed to 90* by one orthopaedic surgeon and verified by
another surgeon (Figure 5.1). The AM or the PL bundle were cut in an alternative fashion
at their femoral insertion using a No. 15 scalpel during the testing of the eight specimens.
Careful attention was paid to avoid any damage to other structures. After resection of one
bundle, the miniarthrotomy and skin were repaired through a layered closure. Following
the repair, the kinematics of the intact knee was replayed at each of the selected flexion
angles and the forces transferred through the knee joint were recorded. To determine the
amount of force experienced by the resected bundle under the external loads, the
principle of superposition was used [7-10]. The force within each ACL bundle was
determined as the difference of the forces measured before and after transection of the
bundle [14, 15]. A similar process was followed to resect the second bundle of the ACL
and the intact knee kinematics were again replayed to determine the forces experienced
100
by the second bundle under the three external loads at each of the selected flexion angles
using the principle of superposition.
Figure 5.1: The anteromedial (AM) bundle and posterolateral (PL) bundle of ACL
viewed from the anterior arthrotomy of the knee.
5.2.3 Statistical Analysis
In this experiment, each specimen was tested to determine the in-situ forces
experienced by each of the ACL bundles under three external loading conditions at the
selected flexion angles. A two-way repeated measures analysis of variance (ANOVA)
was used to detect statistically significant differences in the forces experienced by the
two bundles at the selected flexion angles under the three external loads. When
significant differences were found, post-hoc comparisons were made using the StudentNewman-Keuls test. Differences were considered statistically significant at p<0.05.
101
5.3 Results
5.3.1 In-situ Forces under 134 N Anterior Tibial Load
The in-situ force of the AM bundle was relative constant throughout the range of
flexion tested (Figure 5.2). The peak of the in-situ force of the AM bundle was 123.7 ±
26.3 N at 300 of knee flexion and minimum of 80.2 ± 24.0 N at 900 of knee flexion. The
in-situ force of the AM bundle at 30* of knee flexion was significant higher than that at
600 and 90* of flexion (p<0.05).
The magnitude of the in-situ force of the PL bundle in response to the anterior
tibial load decreased with increasing knee flexion (Figure 5.2). The peak of the in-situ
force of PL bundle was 51.3 ± 19.5 N at 00 of knee flexion and minimum of 7.1 ± 4.8 N
at 900 of flexion. Statistically significant changes in the magnitude of the in-situ force of
PL bundle were seen at 60* and 900 of flexion compared to those at 00 and 150 of flexion
(p<0.05).
E AMB
E PLB
*
*
r__N
150
*
120
90
.
0
60-
U.
300
0
15
30
Flexion Angle
60
90
(0)
Figure 5.2: The in-situ forces in the anteromedial bundle (AMB) and posterolateral
bundle (PLB) in response to 134 N anterior tibial load. The PL bundle carried
significantly lower in-situ force than the AM bundle at all flexion angles (p<0.05).
102
Comparison of the in-situ forces of the AM and PL bundles revealed that the PL
bundle carried significantly lower in-situ force than the AM bundle at all flexion angles
(p<0.05). At O0 of flexion, the in-situ force of the PL bundle was 53% of the AM bundle
force. At 300, the in-situ force of the PL bundle decreased to 23% of the AM bundle. At
900 , the in-situ force of the PL bundle was only 9% of the AM bundle.
5.3.2 In-situ Forces under Combined Valgus and Internal Tibial
Torques
Under combined rotational loads of 10 N.m valgus and 5 N.m internal tibial
torques, the in-situ forces of the AM bundle were 59.9 ± 27.5 N and 75.5 ± 42.5 N at 0*
and 30* of knee flexion, respectively. The forces of the PL bundle were 40.9 ± 23.7 N
and 35.9 ± 31.4 N, respectively at the two flexion angles (Figure 5.3). However, there
was no significant difference between the two bundles at 0* of flexion, whereas the insitu force of the PL bundle was significantly lower than that of the AM bundle at 300 of
flexion (p<0.05).
5.3.3 In-situ Forces under 400 N Quadriceps Muscle Load
In response to the quadriceps muscle load, the magnitude of the in-situ force of
the AM bundle was a maximum of 75.2 E 48.7 N at 15' of flexion and a minimum of
12.5 ± 10.7 N at 90' of flexion. The magnitude of the in-situ force for the PL bundle was
a maximum of 51.5 ± 41.6 N at 300 of knee flexion and a minimum of 8.2 ± 4.8 N at 900
of flexion. There was also no significant difference between two bundle forces at all
flexion angles (Figure 5.4). At 600 and 900, both bundles carried similar load less than 25
N.
103
E PLB
*AMB
150
*
I
120
-
90
-
60
-
I
30 0-1
-- I
Flexion Angle (*)
Figure 5.3: The in-situ forces in the anteromedial bundle (AMB) and posterolateral
bundle (PLB) in response to combined 10 N.m valgus and 5 N.m internal tibial
torques. There was no significant difference between the two bundles at 00 of
flexion, but the PL bundle shared significantly lower force than the AM bundle at
30* of flexion (p<0.05).
MPLB
*AMB
150
-
120
-
90 -
60
-
L*T
i01
LI
30
Flexion Angle
60
90
(0)
Figure 5.4: The in-situ forces in the anteromedial bundle (AMB) and posterolateral
bundle (PLB) in response to 400 N quadriceps muscle load. There was also no
significant difference between two bundle forces at all flexion angles (p> 0.05).
104
5.4 Discussion
This study investigated the in-situ forces of the two functional bundles of the
ACL in human knees under simulated muscle loads and passive tibial loads using
cadaveric knee specimens. The data under simulated muscle loads indicated that the AM
and PL bundles carried similar loads, even though on average, the loads of the AM
bundle were higher than PL bundle. It is interesting to note that under an anterior tibial
load, both bundles carried peak loads at low flexion angles (0* to 300), whereas the PL
bundle carried diminishing loads with increasing knee flexion. The PL bundle carried
approximately less than 50% of the load carried by the AM bundle throughout the range
of knee flexion. Under combined torque loads, the PL bundle also carried lower loads
than the AM bundle and the forces of the PL bundle decreased as flexion angle increased.
Our data indicated that the AM and PL bundles function in a complementary manner.
The AM and PL bundles supplement each other under various loading conditions rather
than function independently. The data supported our hypothesis that the load sharing
patterns of both bundles are complementary rather than reciprocal under simulated
muscle loads.
The function of the AM and PL bundles of the ACL with applying various tibial
loads has been reported in various studies [7-10]. In a pioneer work, Girgis et al. [3]
found that the AM bundle was tight in flexion while the PL bundle was tight in low
flexion by using palpation during passive flexion, indicating a reciprocal function of the
two ACL bundles along the flexion path of the knee. Later, Sakane et al. [9] and Gabriel
et al. [7] found that under an anterior tibial load, the PL bundle carried a higher load at
low flexion and lower load at high flexion compared to the AM bundle. In general, our
data showed a similar trend in the change of force magnitude with flexion of the two
bundles, but the reciprocal function of the two bundles was not shown in our data under
both the anterior tibial load and the simulated muscle loads. However, the load sharing
pattern in our study under combined rotational loads at 30" of flexion was similar to that
of Gabriel et al [7]. Markolf et al. [21] found that the PL bundle carried peak loads at full
extension under an anterior tibial load and the PL bundle force sharply decreased with
105
flexion as well. Our data on the PL bundle forces under an anterior tibial load showed a
similar trend as that of Markolf et al [21].
In our previous studies of the in-situ force of the ACL under simulated muscle
loads, the ACL was shown to carry minimal loads at high flexion angles [14, 15], which
implied that under muscles loads, the two bundles did not function at high flexion angles.
This conclusion was confirmed by our data on ACL elongation during an in-vivo single
legged lunge activity [11, 12], where the two bundles were shown to decrease in length as
flexion angle increased. In the present study, the two bundles under muscle loads were
shown to carry high loads between 00 to 300 of knee flexion and minimal loads at 60* and
90'. The in-vivo AM and PL bundle elongation patterns and the in-vitro AM and PL
bundle forces along flexion path demonstrated consistent functional behavior.
The load sharing of the AM and PL bundles may have important clinical
relevance in ACL reconstruction. The specific flexion angle for graft fixation is one of
the most controversial problems surgeons face during double-bundle ACL reconstruction.
There is no general consensus on the range of angles of knee flexion for graft fixation. In
literature, the two bundle grafts were either fixed at the same knee flexion angle or at two
different knee flexion angles where each bundle carried the highest force [22-28]. While
recent literature suggested that the PL bundle should be fixed at or near full extension to
avoid overloading the graft [8, 11-13, 22, 24, 25, 29], the fixation angle of the AM bundle
graft has been varied from 90* to 10' of knee flexion [8, 10, 22-24, 30-33]. Our data
indicated that the AM and PL bundle carried maximal loads between 0* to 300 of flexion
under various applied loads. The two bundles might be fixed within this range of flexion.
More studies should be carried out to examine the effect of flexion angles for graft
fixation on knee stability after ACL reconstruction. The clinical outcome of various graft
fixation angles should also be further investigated.
Several limitations of our study should be noted. The 400 N quadriceps muscle
load, half of total body weight, is less than that experienced during daily activities. Lower
muscle loads would mechanically cause less in-situ forces in the ACL. Ground reaction
forces were not simulated in this study. Future investigation should focus on the
improvement of the loading levels and include the simulation of ground reaction forces to
simulate more realistic knee joint function. It should be noted that the variation in the
106
force data has been indicated by the large standard deviations which may be due to the
inter-specimen variation. In order to eliminate the methodological variation, the two
bundles were transected in an alternative way. The AM and PL bundles were specified by
one orthopaedic surgeon first and then verified by another surgeon. The bundle
separation method was similar to that used by Girgis et al [3]. Finally, the in-situ bundle
forces of the ACL were measured under a quasi-static condition. The investigation of the
bundle function of ACL under dynamic loading conditions might be necessary.
In conclusion, our study evaluated the load sharing between the AM and the PL
bundles of the ACL under three different loading conditions. Our findings demonstrate
that the AM bundle carried greater portion of the load within the ACL at all flexion
angles under externally applied loads, whereas the PL bundle only shared the load of the
ACL at low flexion angles. The data appear to support the concept that both bundles
function in a complementary rather than reciprocal manner. Thus, how to recreate the two
bundle functions in a single or double-bundle ACL reconstruction should be further
investigated.
5.5 Acknowledgements
This study was made possible through grants received from the National Institutes
of Health (R01 AR055612 & R01 AR051078).
107
5.6 References
1.
Amis AA, Dawkins GP. Functional anatomy of the anterior cruciate ligament.
Fibre bundle actions related to ligament replacements and injuries. J Bone Joint
Surg Br 1991; 73: 260-267.
2.
Arnoczky SP. Anatomy of the anterior cruciate ligament. Clin Orthop Relat Res
1983: 19-25.
3.
Girgis FG, Marshall JL, Monajem A. The cruciate ligaments of the knee joint.
Anatomical, functional and experimental analysis. Clin Orthop Relat Res 1975:
216-231.
4.
Muneta T, Sekiya I, Yagishita K, Ogiuchi T, Yamamoto H, Shinomiya K. Twobundle reconstruction of the anterior cruciate ligament using semitendinosus tendon
with endobuttons: operative technique and preliminary results. Arthroscopy 1999;
15: 618-624.
5.
Bach JM, Hull ML, Patterson HA. Direct measurement of strain in the
posterolateral bundle of the anterior cruciate ligament. J Biomech 1997; 30: 281283.
6.
Kurosawa H, Yamakoshi K, Yasuda K, Sasaki T. Simultaneous measurement of
changes in length of the cruciate ligaments during knee motion. Clin Orthop Relat
Res 1991: 233-240.
7.
Gabriel MT, Wong EK, Woo SL, Yagi M, Debski RE. Distribution of in situ forces
in the anterior cruciate ligament in response to rotatory loads. J Orthop Res 2004;
22: 85-89.
8.
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.
108
9.
Sakane M, Fox RJ, Woo SL, Livesay GA, Li G, Fu FH. In situ forces in the
anterior cruciate ligament and its bundles in response to anterior tibial loads. J
Orthop Res 1997; 15: 285-293.
10.
Vercillo F, Woo SL, Noorani SY, Dede 0. 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.
11.
Jordan SS, DeFrate LE, Nha KW, Papannagari R, Gill TJ, Li G. The in vivo
kinematics of the anteromedial and posterolateral bundles of the anterior cruciate
ligament during weightbearing knee flexion. Am J Sports Med 2007; 35: 547-554.
12.
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.
13.
Pearle AD, Shannon FJ, Granchi C, Wickiewicz TL, Warren RF. Comparison of 3dimensional obliquity and anisometric characteristics of anterior cruciate ligament
graft positions using surgical navigation. Am J Sports Med 2008; 36: 1534-1541.
14.
Li G, Rudy TW, Sakane M, Kanamori A, Ma CB, Woo SL. The importance of
quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in
the ACL. J Biomech 1999; 32: 395-400.
15.
Li G, Zayontz S, Most E, DeFrate LE, Suggs JF, Rubash HE. In situ forces of the
anterior and posterior cruciate ligaments in high knee flexion: an in vitro
investigation. J Orthop Res 2004; 22: 293-297.
16.
Fujie H, Mabuchi K, Woo SL, Livesay GA, Arai S, Tsukamoto Y. The use of
robotics technology to study human joint kinematics: a new methodology. J
Biomech Eng 1993; 115: 211-217.
17.
Li G, Papannagari R, DeFrate LE, Yoo JD, Park SE, Gill TJ. The effects of ACL
deficiency on mediolateral translation and varus-valgus rotation. Acta Orthop 2007;
78: 355-360.
18.
Li G, Zayontz S, DeFrate LE, Most E, Suggs JF, Rubash HE. Kinematics of the
knee at high flexion angles: an in vitro investigation. J Orthop Res 2004; 22: 90-95.
109
19.
Rudy TW, Livesay GA, Woo SL, Fu FH. A combined robotic/universal force
sensor approach to determine in situ forces of knee ligaments. J Biomech 1996; 29:
1357-1360.
20.
Woo SL, Fisher MB. Evaluation of knee stability with use of a robotic system. J
Bone Joint Surg Am 2009; 91 Suppl 1: 78-84.
21.
Markolf KL, Park S, Jackson SR, McAllister DR. Contributions of the
posterolateral bundle of the anterior cruciate ligament to anterior-posterior knee
laxity and ligament forces. Arthroscopy 2008; 24: 805-809.
22.
Aglietti P, Giron F, Cuomo P, Losco M, Mondanelli N. Single-and double-incision
double-bundle ACL reconstruction. Clin Orthop Relat Res 2007; 454: 108-113.
23.
Colombet P, Robinson J, Jambou S, Allard M, Bousquet V, de Lavigne C. Twobundle, four-tunnel anterior cruciate ligament reconstruction. Knee Surg Sports
Traumatol Arthrosc 2006; 14: 629-636.
24.
Fu FH, Shen W, Starman JS, Okeke N, Irrgang JJ. Primary anatomic double-bundle
anterior cruciate ligament reconstruction: a preliminary 2-year prospective study.
Am J Sports. Med 2008; 36: 1263-1274.
25.
Ishibashi Y, Tsuda E, Tazawa K, Sato H, Toh S. Intraoperative evaluation of the
anatomical double-bundle anterior cruciate ligament reconstruction with the
OrthoPilot navigation system. Orthopedics 2005; 28: s1277-1282.
26.
Kondo E, Yasuda K, Azuma H, Tanabe Y, Yagi T. Prospective clinical
comparisons of anatomic double-bundle versus single-bundle anterior cruciate
ligament reconstruction procedures in 328 consecutive patients. Am J Sports Med
2008; 36: 1675-1687.
27.
Muneta T, Koga H, Morito T, Yagishita K, Sekiya I. A retrospective study of the
midterm outcome of two-bundle anterior cruciate ligament reconstruction using
quadrupled semitendinosus tendon in comparison with one-bundle reconstruction.
Arthroscopy 2006; 22: 252-258.
28.
Yasuda K, Kondo E, Ichiyama H, Tanabe Y, Tohyama H. Clinical evaluation of
anatomic double-bundle anterior cruciate ligament reconstruction procedure using
110
hamstring tendon grafts: comparisons among 3 different procedures. Arthroscopy
2006; 22: 240-251.
29.
Yasuda K, Ichiyama H, Kondo E, Miyatake S, Inoue M, Tanabe Y. An in vivo
biomechanical study on the tension-versus-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.
30.
Mae T, Shino K, Matsumoto N, Nakata K, Nakamura N, Iwahashi T. Force sharing
between two grafts in the anatomical two-bundle anterior cruciate ligament
reconstruction. Knee Surg Sports Traumatol Arthrosc 2006; 14: 505-509.
31.
Markolf KL, Park S, Jackson SR, McAllister DR. Anterior-posterior and rotatory
stability of single and double-bundle anterior cruciate ligament reconstructions. J
Bone Joint Surg Am 2009; 91: 107-118.
32.
Siebold R, Dehler C, Ellert T. Prospective randomized comparison of doublebundle versus single-bundle anterior cruciate ligament reconstruction. Arthroscopy
2008; 24: 137-145.
33.
Streich NA, Friedrich K, Gotterbarm T, Schmitt H. Reconstruction of the ACL
with a semitendinosus tendon graft: a prospective randomized single blinded
comparison of double-bundle versus single-bundle technique in male athletes. Knee
Surg Sports Traumatol Arthrosc 2008; 16: 232-238.
111
Chapter 6 - Impingement of the Anterior Cruciate
Ligament against the Femoral Intercondylar Notch
during In-Vivo Weight Bearing
6.1 Introduction
Impingement of the anterior cruciate ligament (ACL) against the femoral
intercondylar notch is believed to be one of the potential mechanisms of ACL injury [1,
2]. Hyperextension [3, 4] and external tibial rotation combined with valgus motion at low
flexion angles [2], may cause the ACL to impinge against the intercondylar notch, and
this specific combination of motions has often been observed during non-contact ACL
injury [1, 5].
In ACL reconstruction, the graft can impinge against the intercondylar notch of
the femur at shallow flexion [6, 7]. Graft impingement is believed to be harmful and
cause graft deterioration [7, 8], postoperative pain and loss of extension [9-12].
Therefore, many studies have emphasized the importance of avoiding impingement in
ACL reconstruction [12-14], by determining the optimal location of the tibial tunnel [6]
and femoral tunnel [15] or by performing a notchplasty [15, 16].
Knowledge of the biomechanical stress of the ACL is crucial for understanding
the normal function of the ACL and improving ACL reconstruction techniques.
Therefore, ACL tension [17-20] and ACL strain [21, 22] have been investigated in great
detail both in-vitro and in-vivo. Various computational models of the ACL have been
developed to evaluate the ACL tensile behavior [23-26]. The biomechanical behavior of
the ACL near full extension, however, has not been investigated to the same extent,
mainly because of the complicated lateral interaction of the ligament with the femoral
bone surface. Jagodzinski et al. measured the in-vitro contact pressure caused by ACL
impingement during passive full extension and passive hyperextension using a miniature
112
pressure sensor [27]. An increase in impingement pressure was reported for flexion
angles less that ~10*.
Even though the previous in-vitro studies have confirmed the ACL impingement
against the intercondylar notch, the in-vivo characterization of ACL interaction with the
femoral notch under physiological loading remains obscure. To determine the possible
role of impingement before and after ACL injuries, it is necessary to quantify the
interaction between the intercondylar notch and the ACL in-vivo. This knowledge could
be useful for the estimation of the tension in the ACL during impingement and could
provide better understanding of the mechanisms of ACL injury and effects of ACL
reconstruction on graft impingement. In this study, the impingement of the ACL against
the intercondylar notch under increasing weightbearing was investigated using a
combined MR and dual fluoroscopic imaging system.
6.2 Materials and Methods
6.2.1 Subject Selection
Eight healthy subjects, five women and three men, aged 23 - 48 years old, with an
average ± SD body mass index (BMI) of 27.9 ± 4.1 were recruited for this study. The
subjects had no history of knee injury or knee disease confirmed by clinical examination
and MRI examination. The study was approved by our Institutional Review Board and
written informed consent was obtained from all subjects. One knee of each subject was
randomly chosen (five right and four left knees) for the experiment. The subjects were
included in our previous study of the in-vivo ACL elongation in response to axial tibial
loads [28].
113
6.2.2 Magnetic Resonance Imaging and Three-Dimensional Model of
Knee
First, each knee was scanned in a relaxed, fully extended position using a 3.0
Tesla MR Scanner (MAGNETOM Trio*, Siemens, Malvern, PA, USA), with the
subjects lying in a supine position. The knee was scanned in both sagittal and coronal
planes with 1 mm slice thickness using a three-dimensional (3D) double echo water
excitation sequence (images size: 160 mm x 160 mm, image resolution: 512x512 pixels,
time of repetition: 24 ms, time of echo: 6.5 ms and flip angle: 25*) [29, 30]. The entire
MRI scan lasted approximately 25 minutes. To create the 3D model of the knee, the
series of the MR images were imported into a modeling software (Rhinoceros*, Robert
McNeel & Associates, Seattle, WA, USA) and placed in parallel planes separated 1 mm
apart. The bony contours were digitized in MR images and the 3D anatomic models of
the tibial and femoral bones were created using the digitized contour data. Also, the
femoral and tibial insertion sites of the ACL were determined on the MR Images of the
knee in both sagittal and coronal planes. This method of construction of ACL attachments
on the femur and tibia has been extensively used and validated in previous studies [3033].
Then, these attachment areas were directly mapped onto the 3D anatomic model
of the knee. The attachment areas were further divided into two functional bundles - an
anteromedial (AM) and a posterolateral (PL) bundle - using an established protocol [28,
30, 34].
6.2.3 Fluoroscopic Imaging of the Knee
To determine the joint kinematics under body weightbearing at different knee
flexion angles, a dual fluoroscopic imaging system (DFIS) was used. The system setup
consisted of two fluoroscopes (BV Pulsera*, Philips, Bothell, WA, USA) around a
platform with their intensifiers positioned in orthogonal planes providing an image space
of - 300 mm x 300 mm x 300 mm . The resolution of fluoroscopic images is 1024 x 1024
114
pixels. A force plate constructed of a six degrees-of-freedom (DOF) load sensor (JR3*,
San Francisco, CA, USA) was installed on the platform. The force plate was connected to
a monitor in order to display the instantaneous ground reaction force when the subject
stepped on the force plate.
First the subject positioned the studied leg on the force plate. Using the force plate
output, which was displayed on the monitor, the applied force on the studied leg could be
controlled by the subject. In this study, two different loading conditions were defined and
used: no (zero) weightbearing condition with a ground reaction force less than 10 N and
full body weightbearing condition. The loading conditions were applied at four knee
flexion angles: 00, 150, 300, and 45*.
At each flexion angle the subject positioned the studied leg on the force plate
while keeping the knee joint in the view field of both intensifiers. The subject looked at
the monitor while applying a minimum touching load (< 10 N) to represent the zero
weightbearing condition. When the subject reached the desired value of the force and the
knee was still, both fluoroscopes shot simultaneously and the load from the force plate
was recorded. Then the subject was asked to apply full bodyweight on the studied leg,
while maintaining the same flexion angle. The new position of the knee and the ground
reaction force were recorded again by the fluoroscopes and force plate. The knee was
imaged in the same manner at all target flexion angles under zero and full bodyweight.
The target flexion angles were measured with a goniometer and actual flexion angles
were calculated in the modeling software. The entire fluoroscopic experiment took about
10 minutes.
6.2.4 In-vivo Knee Positions and ACL Impingement
A virtual dual fluoroscopic system was created in the modeling software based on
the relative position and orientation of the sources and intensifiers of two fluoroscopes.
Each pair of fluoroscopic images of the knee, which corresponded with a specific
position and tibial load, were imported into the software and placed in the position of the
intensifiers. The 3D bony models of the knee along with the ACL insertions were
115
imported into the virtual dual fluoroscopic system and were rotated and translated in 6
DOF until the projections of each bone matched the outlined silhouettes of the bones on
the pair fluoroscopic images. This procedure was repeated at every flexion angle and
under all loading conditions until the series of the matched bony models reproduced the
in-vivo position of the subject's knee during the entire experiment. The relative positions
of tibial and femoral insertions of the ACL could also be determined by using the series
of matched bony models under different loading conditions and flexion angles. The
accuracy of the abovementioned method in reproducing knee kinematics using a
combined MRI and dual fluoroscopic imaging system was investigated and reported <
0.1 mm in translation and < 0.3' in rotation, respectively [35].
In order to investigate the impingement of the ACL against the intercondylar
femoral notch, a 3D model of the ACL was created (Figure 6.1). At each matched
position, a loft surface was created by using the AM portion of the ACL insertions on
both tibial and femoral sides as the boundary curves. This surface introduced the exterior
surface of the AM bundle. The PL surface was created in the same way by using the PL
portion of the ACL insertions. The reconstructed ACL model was verified qualitatively
by dissecting a cadaveric specimen. In both reconstructed ACL model and cadaveric
ACL, the configuration of the ACL was shown to twist externally in the tibial insertion
site relative to the femoral insertion site [28].
The impingement of the ACL was defined as the penetration of the surface of the
ACL into the 3D surface model of the femur (Figure 6.2.A). At each matched position,
the location of the maximum impingement (t) was determined and the value of maximum
impingement was measured. At the location of maximum impingement, the impingement
ratio was defined as the ratio of maximum impingement (t) over the diameter of the ACL
(D) at the same location (Figure 6.2.B).
Furthermore, a clock coordinate system was defined in the notch view of the
femur to study the position of maximum impingement (Figure 6.3). Impingement angle so
was defined and measured as the angle between the vertical (anterior-posterior) axis in
the notch view and the axis connecting the origin of the clock to the location of maximum
impingement in the notch view.
116
Femur
Intercondylar
notch of the femur
AM
bundle
PL
bundle
Tibia
Figure 6.1: 3D model of the Anterior Cruciate Ligament (ACL) built based on the
series of MR images.
117
A
Impinged
ACL
Intersection Plane
(at the location of
maximum impingement)
Tibia
/
O
/
\
Intersection
Plane
\
t
\D
Figure 6.2: (A) Impingement of the ACL against the intercondylar notch of the
femur (medial view, full extension), (B) intersection plane at the location of
maximum impingement; D: diameter on the ACL at the location of maximum
impingement; t: maximum impingement of the ACL.
118
'~i1
Anterior-Posterior Axis
(Lateral)
(Medial)
Impinged
Area
Clock Coordinate System
Figure 6.3: Definition of impingement angle (<p) in the clock coordinate system at
notch view.
6.2.5 Statistical Analysis
The maximum impingement, impingement ratio, and impingement angle
(dependent variables) were measure at each flexion angle and weightbearing condition
(independent variables). A two-way repeated measures analysis of variance (ANOVA)
was used to detect statistically significant differences in the impingement data at different
knee conditions. When significant differences were found, post hoc comparisons were
made using the Student-Newman-Keuls test. Differences were considered statistically
significant at p<0.05. The statistical analysis was performed in STATISTICA (StatSoft,
Inc, Tulsa, OK, USA).
119
6.3 Results
No ACL impingement was observed at 300 and 450 of flexion. However, the ACL
had anterior impingement against the femoral intercondylar notch at 0* and 150 of
flexion, both under zero and full bodyweight loading.
6.3.1 Maximum Impingement (t)
At full extension, the maximum impingement was 1.7 ± 0.7 mm under no
weightbearing (< 10 N), and significantly increased to 2.1 ± 0.9 mm under full
bodyweight loading (p<0.05; Figure 6.4). The maximum ACL impingement against the
femoral notch significantly decreased at 150 of knee flexion. It was 0.7 ± 0.3 mm under
no weightbearing and 0.9 ± 0.3 mm under full bodyweight loading (p<0.05).
*
Ei
E
E
E
-E
3.532.521.510.50-
a
OBW
S1BW
g
150
00
Flexion
Figure 6.4: Maximum impingement during weight bearing from minimum
bodyweight (OBW) to full bodyweight (1BW) at low flexion, (p<0.05).
120
6.3.2 Impingement Ratio (t/D)
The ratio of impingement was ~ 30% at full extension and ~ 15% at 150 of flexion
(Figure 6.5). By applying full bodyweight, the impingement ratio significantly increased
from 26.6 ± 9.0% (under no weightbearing) to 32.5 ± 9.4% (under full bodyweight) at
full extension (p<0.05). This ratio significantly decreased at 15* of flexion compared to
full extension with a change from 10.9 ± 6.7% (under no weightbearing) to 15.3 + 6.1%
(under full bodyweight) (p<0.05).
*
50-
-~Th
*
m
0
40IMOBW
30E
0-
E
N 1B3W
20100-
-,
0
150
Flexion
Figure 6.5: Percentage of impingement ratio (t/D) during weight bearing from
minimum bodyweight (OBW) to full bodyweight (1BW) at low flexion, (p<0.05).
6.3.3 Impingement angle <p
Generally, applying body weight load caused a reduction in angle <p (Figure 6.6).
At full extension, the location of the maximum impingement with respect to the clock
coordinates in the notch view was 32.40
9.4' under no weightbearing. With applying
121
under full bodyweight load, the impingement angle decreased to 30.50*
9.4*. However,
at 15* of flexion, angle <p was 46.00 + 10.0' and 42.70 ± 10.6* under no weightbearing
and full bodyweight, respectively. These data imply that full bodyweight loading changed
the location of the maximum ACL impingement medially (towards the center of the
notch) at both 00 and 150 of flexion. This medial displacement was significant only at 150
of knee flexion (p<0.05).
*
0
E
0.
E2
*
6055504540-
-m
E OBW
N 1BW
35
-
30
-
2520
-
150
Flexion
Figure 6.6: The location of maximum impingement during weight bearing from
minimum bodyweight (OBW) to full bodyweight (1BW) in low flexion, (p<0.05).
6.4 Discussion
The impingement of the ACL against the femoral intercondylar notch was studied
in-vivo. By using MR imaging and a dual fluoroscopic technique, the kinematics of the
knee joint as well as the ACL were captured under weight bearing and then regenerated.
122
The impingement of the ACL against the femoral notch was modeled as the penetration
of the 3D surface of the ACL through the 3D surface of the femur.
The ACL impingement was greatest at full extension and decreased at 150 of
flexion. No impingement was observed at 300 and 450 of flexion. At both full extension
and 150 of flexion, applying body weight load caused the impingement to increase. This
increase due to loading was significantly greater at full extension compared with that at
15' of flexion (0.4 mm compared with 0.2 mm on average). Similarly, the impingement
ratio (percent of impingement) was greater at full extension, and decreased at 15* of
flexion. Applying body weight load significantly increased the impingement ratio on
average 5.9 % at full extension and 4.4 % at 15' of flexion. These data imply that the
ACL is tighter and likely under more tension (due to impingent) under full body weight
at full extension compared to 150 of flexion.
The location of maximum impingement with respect to the clock coordinates in
the notch view (angle p, Figure 6.6) moved medially due to applied full bodyweight.
Based on the slope of the notch, such medial shift of the location of maximum
impingement could be anticipated with the tibia translating anteriorly in response to
weightbearing and thereby pulling the impinged ligament towards the center of the notch.
This study demonstrated that during physiological loading, impingement of the
ACL against the femoral bone surface occurs in-vivo. The implications of these data are
complicated though. On the one hand, the data showed that, similar to in-vitro
observations [27], in-vivo impingement occurs at full extension and shallow knee
flexions. Even though this ACL impingement is the result of the geometric constraint of
the intercondylar notch surface and the relative position of tibial plateau and femoral
condyles, impingement of the ACL might thus play a considerable role in providing knee
stability at full extension in the healthy joint. On the other hand, hyperextension or
external tibial rotation combined with abduction (valgus motion) in shallow flexions have
been considered as the main mechanisms of ACL injury [2-4] - motions that are
associated with ACL impingement. Even though the type of physiological loading in the
current study was not the same as either tibial rotation combined with abduction, or
hyperextension, the data showed that ACL does impinge against the femoral
intercondylar notch in-vivo. Applying above-mentioned loads during dynamic activities
123
could therefore lead to the so-called "position of no return" and a consequent rupture of
the ACL.
Theoretically, it could be hypothesized based on the present data that to restore
the stability of an ACL deficient knee near full extension to that of the healthy knee,
normal in-vivo ACL impingement should be maintained in ACL reconstruction. If an
optimal tunnel placement combined with an optimal graft material were designed which
would replicate the exact mechanical function of the native ACL, then the normal in-vivo
impingement with its inherent stability could be maintained. Obviously though, the
material properties and twisting behavior of an ACL graft do not mimic entirely those of
the native ACL and postoperative clinical outcomes revealed serious concerns about
maintaining graft impingement.
Based on our data, it could be conjectured that if the ACL graft were placed in the
anatomic position of the native ACL, impingement of the graft could be anticipated under
weightbearing conditions at low flexion angles. It has been documented that impingement
of the ACL graft leads to graft deterioration [7, 8], Cyclops syndrome [8] and loss of full
extension [9-11]. Impingement of the ACL could also be harmful for the graft fixation
after surgery. Impingement is considered deleterious when it excessively stretches the
ligament substitute or causes abrasion [36]. Biologically, it has been shown that large
lateral compressive stresses applied to tendons induced a fibrocartilaginous remodeling
[37].
This remodeling response
includes an increase in proteoglycan
content.
Furthermore, radiographic changes have been reported in the ACL grafts which impinged
against the roof of the intercondylar notch [38].
Thus, instead of replicating the impingement behavior of the native ACL,
impingement-free ACL reconstruction techniques - such as modifying the tunnel
placement and reshaping the roof of the femoral intercondylar notch - have been
suggested to avoid deleterious impingement of the graft with the bone. For instance, a
tibial tunnel placement that is far enough posterior to avoid anterior or lateral
impingement has been suggested [6, 13]. Miller et al. reported that there was no graft
impingement when the tibial tunnel was located in the posterior one-third of the ACL
footprint and recommended using this position [6]. However, this might not be able to
restore the A-P stability of the knee because of the more vertical orientation of the graft
124
in sagittal plane, and also might cause the impingement of ACL graft with posterior
cruciate ligament. Other studies discussed tunnel placement on the femoral side, since the
femoral attachment of the ACL has a greater effect on the graft length changed during
knee flexion and extension, than does the tibial attachment [13] and the femoral tunnel
placement is believed to be am important factor in failure of ACL reconstructions [15,
39]. Currently, a point located 6-7 mm anterior to the over the top position at 11 o'clock
(1-o'clock) position for a right knee (left knee) is recommended for the femoral tunnel
placement [15, 39]. Also, reshaping the intercondylar notch during a notchplasty is
commonly performed in conjunction with ACL reconstruction to prevent the graft
impingement [13, 15].
The ACL graft impingement could be also dependent on the amount of pretension
applied and the tensioning angle at which the graft is fixed. The tissue used as a graft also
affected the pretension [40] and the graft impingement, consequently. Burks and Lenand
reported that the stiffest tissue used, bone patellar tendon bone, required the least
pretention (16 N), whereas the least stiff tissue used, iliotibial band, required the greatest
pretention (60 N) to obtain a normal 90 N K-1000 test in a cadaveric study [40]. A recent
study showed that a graft pretension more than 40 N leads to over constrained joint using
hamstring tendon graft [41].
However, the amount of bone removal during notchplasty remains controversial.
Performing a notchplasty - if any - to mimic the normal knee (restoring full extension
while maintaining stability) is demanding. Postoperative patellofemoral joint problems
have been reported [42]. La prade et al. [43] discussed the effect of aggressive
notchplasty on the articular cartilage histopathology which is consistent with early
degenerative disease. It has been shown that notchplasty adversely affects the tension
pattern in the graft and the anterior knee laxity [15]. Also, both notch expansion [42] and
regrowth of the notch [43-45] have been reported. These data may suggest that reshaping
the notch should be avoided as much as possible. Instead, focusing on the tibial and
femoral tunnel placement - during the surgery - and improving the rehabilitation
protocols - after the surgery - would be able to prevent the notchplasty.
In the literature, hyperextension or external tibial rotation combined with
abduction (valgus motion) in shallow flexions have been considered as the main
125
mechanisms of ACL injury [2-4]. Our data supports this suggestion. Even though the
type of physiological loading it the current study is not the same as either tibial rotation
combined with abduction, or hyperextension; the data showed that ACL does impinge
against the femoral intercondylar notch in-vivo. Applying above-mentioned loads during
dynamic activities can lead to the so-called "position of no return" and consequently the
ACL torn.
In conclusion, this study investigated the in-vivo impingement of the ACL against
the femoral intercondylar notch under full weight bearing load. The ACL impinged
against the bone surface at full extension and 150 of knee flexion under both zero and full
bodyweight. By increasing the load at full extension, the magnitude of maximum
impingement significantly increased. These data suggest that at full extension
impingement of the ACL may play an important role in providing stability of the knee.
Focusing on modifying the position of tibial and femoral tunnels is promising to prevent
notchplasty. The data of this study could provide insight into the mechanism of ACL
injury and present a method to validate 3D computational results which are used to
predict the ACL impingement and ACL injury. Further studies should focus on
quantifying of impingement force of the ACL using either in-vitro experiments or 3D
finite element modeling, especially under simulated muscle loading.
6.5 Acknowledgements
The financial support of the National Institutes of Health (R21AR051078) and the
department of Orthopaedic Surgery at the Massachusetts General Hospital are gratefully
acknowledged. The technical assistance of Kevin Lada and Bijoy Thomas is greatly
appreciated. Also, I would like to thank the volunteers who participated in this study.
126
6.6 References
1.
Shimokochi Y, Shultz SJ. Mechanisms of noncontact anterior cruciate ligament
injury. J Athl Train 2008; 43: 396-408.
2.
Fung DT, Zhang LQ. Modeling of ACL impingement against the intercondylar
notch. Clin Biomech (Bristol, Avon) 2003; 18: 933-941.
3.
Olsen OE, Myklebust G, Engebretsen L, Bahr R. Injury mechanisms for anterior
cruciate ligament injuries in team handball: a systematic video analysis. Am J
Sports Med 2004; 32: 1002-1012.
4.
Friedman RL, Feagin JA, Jr. Topographical anatomy of the intercondylar roof. A
pilot study. Clin Orthop Relat Res 1994: 163-170.
5.
Boden BP, Dean GS, Feagin JA, Jr., Garrett WE, Jr. Mechanisms of anterior
cruciate ligament injury. Orthopedics 2000; 23: 573-578.
6.
Miller MD, Olszewski AD. Posterior tibial tunnel placement to avoid anterior
cruciate ligament graft impingement by the intercondylar roof. An in vitro and in
vivo study. Am J Sports Med 1997; 25: 818-822.
7.
Howell SM. Arthroscopic roofplasty: a method for correcting an extension deficit
caused by roof impingement of an anterior cruciate ligament graft. Arthroscopy
1992; 8: 375-379.
8.
Watanabe BM, Howell
SM.
Arthroscopic
findings associated with
roof
impingement of an anterior cruciate ligament graft. Am J Sports Med 1995; 23:
616-625.
9.
Jagodzinski M, Richter GM, Passler HH. Biomechanical analysis of knee
hyperextension and of the impingement of the anterior cruciate ligament: a
cinematographic MRI study with impact on tibial tunnel positioning in anterior
cruciate ligament reconstruction. Knee Surg Sports Traumatol Arthrosc 2000; 8:
11-19.
127
10.
Kartus J, Magnusson L, Stener S, Brandsson S, Eriksson BI, Karlsson J.
Complications following arthroscopic anterior cruciate ligament reconstruction. A
2-5-year follow-up of 604 patients with special emphasis on anterior knee pain.
Knee Surg Sports Traumatol Arthrosc 1999; 7: 2-8.
11.
Muneta T, Ezura Y, Sekiya I, Yamamoto H. Anterior knee laxity and loss of
extension after anterior cruciate ligament injury. Am J Sports Med 1996; 24: 603607.
12.
Shelbourne KD, Trumper RV. Preventing anterior knee pain after anterior cruciate
ligament reconstruction. Am J Sports Med 1997; 25: 41-47.
13.
Amis AA, Jakob RP. Anterior cruciate ligament graft positioning, tensioning and
twisting. Knee Surg Sports Traumatol Arthrosc 1998; 6 Suppl 1: S2-12.
14.
Howell SM, Clark JA. Tibial tunnel placement in anterior cruciate ligament
reconstructions and graft impingement. Clin Orthop Relat Res 1992: 187-195.
15.
Hame SL, Markolf KL, Hunter DM, Oakes DA, Zoric B. Effects of notchplasty and
femoral tunnel position on excursion patterns of an anterior cruciate ligament graft.
Arthroscopy 2003; 19: 340-345.
16.
Markolf KL, Hame SL, Hunter DM, Oakes D, Gause P. Biomechanical effects of
femoral notchplasty in anterior cruciate ligament reconstruction. Am J Sports Med
2002; 30: 83-89.
17.
Li G, Zayontz S, Most E, DeFrate LE, Suggs JF, Rubash HE. In situ forces of the
anterior and posterior cruciate ligaments in high knee flexion: an in vitro
investigation. J Orthop Res 2004; 22: 293-297.
18.
Rudy TW, Livesay GA, Woo SL, Fu FH. A combined robotic/universal force
sensor approach to determine in situ forces of knee ligaments. J Biomech 1996; 29:
1357-1360.
19.
Henning CE, Lynch MA, Glick KR, Jr. An in vivo strain gage study of elongation
of the anterior cruciate ligament. Am J Sports Med 1985; 13: 22-26.
128
20.
Markolf KL, Gorek JF, Kabo JM, Shapiro MS. Direct measurement of resultant
forces in the anterior cruciate ligament. An in vitro study performed with a new
experimental technique. J Bone Joint Surg Am 1990; 72: 557-567.
21.
Fleming BC, Renstrom PA, Beynnon BD, Engstrom B, Peura GD, Badger GJ, et al.
The effect of weightbearing and external loading on anterior cruciate ligament
strain. J Biomech 2001; 34: 163-170.
22.
Beynnon BD, Johnson RJ, Fleming BC, Renstrom PA, Nichols CE, Pope MH, et
al. The measurement of elongation of anterior cruciate-ligament grafts in vivo. J
Bone Joint Surg Am 1994; 76: 520-53 1.
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.
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.
25.
Limbert G, Taylor M, Middleton J. Three-dimensional finite element modelling of
the human ACL: simulation of passive knee flexion with a stressed and stress-free
ACL. J Biomech 2004; 37: 1723-1731.
26.
Kwan MK, Lin TH, Woo SL. On the viscoelastic properties of the anteromedial
bundle of the anterior cruciate ligament. J Biomech 1993; 26: 447-452.
27.
Jagodzinski M, Leis A, Iselborn KW, Mall G, Nerlich M, Bosch U. Impingement
pressure and tension forces of the anterior cruciate ligament. Knee Surg Sports
Traumatol Arthrosc 2003; 11: 85-90.
28.
Hosseini A, Gill TJ, Li G. In vivo anterior cruciate ligament elongation in response
to axial tibial loads. J Orthop Sci 2009; 14: 298-306.
29.
Bingham J, Li G. An optimized image matching method for determining in-vivo
TKA kinematics with a dual-orthogonal fluoroscopic imaging system. J Biomech
Eng 2006; 128: 588-595.
129
30.
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.
31.
Edwards A, Bull AM, Amis AA. The attachments of the anteromedial and
posterolateral fibre bundles of the anterior cruciate ligament. Part 2: femoral
attachment. Knee Surg Sports Traumatol Arthrosc 2008; 16: 29-36.
32.
Kopf S, Musahl V, Tashman S, Szczodry M, Shen W, Fu FH. A systematic review
of the femoral origin and tibial insertion morphology of the ACL. Knee Surg Sports
Traumatol Arthrosc 2009; 17: 213-219.
33.
Siebold R, Ellert T, Metz S, Metz J. Tibial insertions of the anteromedial and
posterolateral bundles of the anterior cruciate ligament: morphometry, arthroscopic
landmarks, and orientation model for bone tunnel placement. Arthroscopy 2008;
24: 154-161.
34.
Jordan SS, DeFrate LE, Nha KW, Papannagari R, Gill TJ, Li G. The in vivo
kinematics of the anteromedial and posterolateral bundles of the anterior cruciate
ligament during weightbearing knee flexion. Am J Sports Med 2007; 35: 547-554.
35.
Defrate LE, Papannagari R, Gill TJ, Moses JM, Pathare NP, Li G. The 6 degrees of
freedom kinematics of the knee after anterior cruciate ligament deficiency: an in
vivo imaging analysis. Am J Sports Med 2006; 34: 1240-1246.
36.
Aichroth P, Cannon WD, Patel DV. Knee surgery: current practice. New York,
NY, Raven Press 1992.
37.
Gillard GC, Reilly HC, Bell-Booth PG, Flint MH. The influence of mechanical
forces on the glycosaminoglycan content of the rabbit flexor digitorum profundus
tendon. Connect Tissue Res 1979; 7: 37-46.
38.
Howell SM, Berns GS, Farley TE. Unimpinged and impinged anterior cruciate
ligament grafts: MR signal intensity measurements. Radiology 1991; 179: 639-643.
39.
Fu FH, Bennett CH, Ma CB, Menetrey J, Lattermann C. Current trends in anterior
cruciate ligament reconstruction. Part II. Operative procedures and clinical
correlations. Am J Sports Med 2000; 28: 124-130.
130
40.
Burks RT, Leland R. Determination of graft tension before fixation in anterior
cruciate ligament reconstruction. Arthroscopy 1988; 4: 260-266.
41.
Gadikota HR, Wu JL, Seon JK, Sutton K, Gill TJ, Li G. Single-tunnel doublebundle anterior cruciate ligament reconstruction with anatomical placement of
hamstring tendon graft: can it restore normal knee joint kinematics? Am J Sports
Med 2010; 38: 713-720.
42.
Howell SM, Barad SJ. Knee extension and its relationship to the slope of the
intercondylar roof. Implications for positioning the tibial tunnel in anterior cruciate
ligament reconstructions. Am J Sports Med 1995; 23: 288-294.
43.
LaPrade RF, Terry GC, Montgomery RD, Curd D, Simmons DJ. Winner of the
AlbertTrillat Young Investigator Award. The effects of aggressive notchplasty on
the normal knee in dogs. Am J Sports Med 1998; 26: 193-200.
44.
Bents RT, Jones RC, May DA, Snearly WS. Intercondylar notch encroachment
following anterior cruciate ligament reconstruction: a prospective study. Am J
Knee Surg 1998; 11: 81-88.
45.
Berg EE. Assessing arthroscopic notchplasty. Arthroscopy 1991; 7: 275-277.
131
Chapter 7 - In-Vivo Time-Dependent Articular
Cartilage Contact Behavior of the Tibiofemoral Joint
7.1 Introduction
The proposed force estimation method discussed in Chapter 4, can be generalized
to measure the contact pressure distribution of the tibiofemoral cartilage. By knowing the
tibiofemoral cartilage deformation data in-vivo, and mapping them to in-vitro material
property data, it is possible to determine the in-vivo contact pressure in the tibiofemoral
cartilage. As the first step of application, the DFIS was employed to investigate the timedependent responses of the tibiofemoral cartilage under a constant bodyweight load (invivo creep).
Numerous studies have investigated articular cartilage contact in order to
understand the intrinsic biomechanical characteristics of cartilage and its associated
pathologies such as cartilage degeneration in medial and lateral compartments.
Biomechanically, articular cartilage has been viewed as a biphasic material [1]. The invitro response of articular cartilage to various simulated loading conditions has been
studied using pressure sensors [2-4], imaging techniques [5], and finite element methods
[6]. For example, in most in-vitro studies that employed MRI to investigate the cartilage,
the tibiofemoral joint was first loaded for a certain amount of time to deform as desired
and then scanned [7]. Analogously, the biphasic nature of cartilage tissue under various
loading
conditions
has
been
analyzed
extensively
using
indentation
and
confined/unconfined compression tests [1, 8-10]. However, due to the complexity of the
in-vivo loading conditions, it is a challenge to simulate in-vivo physiological cartilage
responses in an in-vitro experimental setup.
In-vivo studies have also described changes in the thickness and volume of the
knee joint cartilage after dynamic activities such as bending, running, normal gait and
squatting [11]. Although the studies based on this type of pre-loading protocol could
132
provide long-term cartilage contact data, the time-dependent response of tibiofemoral
cartilage to an external load remains unclear, especially the short-term response of
tibiofemoral cartilage. In addition, No data have been reported on the specific contact
behavior of the medial and lateral compartments of the knee, even though varying
degrees of osteoarthritis (OA) have been described in the knee hemi-joints [12]. These
data would be critical for understanding the function of cartilage and investigating
pathologies of the cartilage.
Recently, a combined Dual Fluoroscopic Imaging System (DFIS) and MRI
technique has been used to study the in-vivo cartilage contact location [13]. Furthermore,
the instantaneous tibiofemoral cartilage contact deformation during in-vivo physiological
activities such as lunge and gait has been investigated using this technique [14-16]. The
objective of this study was to investigate the time-dependent response of the tibiofemoral
cartilage under a constant bodyweight load and determine whether the medial and lateral
compartments show differences in time-dependent contact behavior. The combined DFIS
and MRI technique was employed to measure the real-time tibiofemoral cartilage contact
deformation as well as the contact area, as the characteristics of the cartilage contact
behavior, in the medial and lateral compartments of the knee joint.
7.2 Materials and Methods
7.2.1 Subject selection
Six human knees, with no history of injury or proprioceptive defects upon
physical and radiographic (MRI and X-ray) examination, were investigated in this study.
All knees were from healthy males aged between 30-45 years and with average body
mass index (BMI) of 24.8 kg/m 2 . The study was approved by our institutional review
board and written consent was obtained from all the participants. All the subjects were
asked to refrain from any strenuous activities such as running, lifting, stair climbing for at
least four hours prior to their visit and to remain seated (non-weightbearing position) for
133
two hours prior to the MRI scan of the knee to reduce the effect of residual cartilage
deformation[ 14].
7.2.2 Magnetic Resonance Imaging and 3D Model of Knee
Each knee was scanned in sagittal, coronal and transverse planes using a 3T MR
scanner (MAGNETOM Trio*, Siemens, Malvern, PA, USA) with the subject supine and
the knee in a relaxed, extended position (Figure 7.1). The MRI scanner was equipped
with a surface coil and a 3D double echo water excitation sequence (field of view: 160
mm x 160 mm x 120 mm, image resolution: 512 x 512 pixels, voxel resolution: 0.31 mm
x 0.31 mm x 1.00 mm, time of repetition: 24 ms, time of echo: 6.5 ms and flip angle: 250)
[14]. The MR images were imported into a solid modeling software package
(Rhinoceros*, Robert McNeel & Associates, Seattle, WA, USA) to construct the 3D
surface mesh models of the tibia, femur, fibula, and articulating cartilage using a protocol
established in our laboratory [17]. The meshes were assembled using a point density of
80 vertices/cm 2 and triangular facets, with an average aspect ratio of 2. A typical 3D knee
joint model is shown in Figure 7.2.
Figure 7.1: A 3-Tesla Magnetic Resonance scanner was used to construct the threedimensional (3D) knee models in a relaxed, extended position.
134
Femoral Cartilage
Lateral Tibial
Cartilage
Medial Tibial
Cartilage
Fibula
Tibia
Figure 7.2: A 3D knee model constructed using the series of MR images of a
subject's knee.
7.2.3 Dual Fluoroscopic Imaging and Reproduction of Knee Kinematics
A Dual Fluoroscopic Imaging System (DFIS) was used to capture the in-vivo
kinematics of the knee joints (Figure 7.3). The DFIS was constructed using two
fluoroscopes (BV Pulsera*, Philips, Bothell, WA, USA) with their intensifiers positioned
in orthogonal planes providing a cubic imaging space of ~ 300 mm x 300 mm x 300 mm
and image resolution of 1024 x 1024 pixels (0.29 mm x 0.29 mm). A force plate with a
six degrees-of-freedom (6DOF) load cell (JR3*, Inc., Woodland, CA, USA) was
incorporated into the DFIS to simultaneously record the ground reaction forces during
loading. The load cell had a resolution of 0.5 N with data acquisition rate of 1 kHz. Each
knee joint was imaged for 300 seconds (timing and recording were started at the moment
of foot-force plate contact) while the subject stood still on the testing leg under full body
weight. Two supporting bars were incorporated into the DFIS to help stabilize the subject
during the single-leg upright standing for 300 seconds. For the first five seconds, the knee
135
was imaged at a rate of 15 frames per second. Then, the images were captured every 5
seconds up to 50 seconds, and finally every 20 seconds up to 300 seconds.
Figure 7.3: Subject performing single leg weight-bearing on a force plate while
being imaged by two orthogonally placed fluoroscopes. The pairs of fluoroscopic
images were imported into modeling software to reproduce the kinematics of the
tested knee joint in a virtual dual fluoroscopic imaging system.
The pairs of fluoroscopic images were imported into the solid modeling software
and placed in orthogonal planes based on the geometry of the fluoroscopes (the relative
positions of the intensifiers and the X-ray sources) during the experiment to create a
'virtual' DFIS [18]. The 3D MRI-based bony models of the knee joint were then imported
into the virtual DFIS, viewed from two orthogonal directions corresponding to the setup
of the fluoroscopes' X-ray sources. The knee models were translated and rotated
independently in 6-DOF until the projection of the model matched the outlines of
corresponding bones on the imported images obtained at each time point. When the
projections matched with the pair of orthogonal images taken in-vivo, the models
reproduced the in-vivo positions of the knee bones inside the software. The matching
process was done manually in this study. The mesh models of the femoral and tibial
136
cartilages (built from the relaxed position of the knee during MRI) were then imported
and mapped onto the bony models at each time point. The accuracy of the system in
reproducing knee kinematics using the above technique was reported < 0.1 mm and
< 0.3* in translation and rotation respectively [19].
7.2.4 In-vivo Cartilage Contact Behavior
At each reproduced in-vivo position of the knee joint, cartilage contact was
defined as the overlap of the tibial and femoral cartilage surface meshes (Figure 7.4.A).
Contact area (mm 2 ) was defined as the area of a patch surface which was fitted to the
curve made from the intersection of the overlapped cartilage meshes.
Cartilagecontact deformation (%) was calculated at each vertex of the articular
surface mesh as the amount of penetration (mm) divided by the sum of the tibial and
femoral cartilage surface thicknesses (mm) at the same place, multiplied by 100 [14, 15].
Penetration was calculated as the minimum Euclidian distance connecting a vertex of the
reference cartilage mesh to the opposite intersecting cartilage mesh (Figure 7.4.B). At
each time point, the peak contact deformation was determined as the maximum contact
deformation inside the cartilage contact area (Figure 7.5). The rate of change of the
cartilage contact deformation (%/s) was defined and calculated as the change in the
cartilage contact deformation at two consecutive time points divided by the time interval
over which it occurred. Similarly, the rate of change of contact area (mm2 /s) was
calculated.
A previous validation study showed an accuracy of 4% when this technique was
used to measure the cartilage contact deformation in human ankle joint [20].
Furthermore, the accuracy of cartilage thickness measurement using MRI-based model of
the knee joint has been validated and reported to be 0.04 ± 0.01 mm (mean ± SD) [15].
137
Measured
surface
B
Nearest
distance
Reference
vertex
Figure 7.4: (A) Sagittal section of a typical knee showing the definition of contact
area and cartilage penetration. (B) Method of measuring cartilage thickness and
penetration depth from meshed surfaces.
7.2.5 Statistical Analysis
To study the time-dependent contact behavior of tibiofemoral cartilage, the peak
contact deformation at medial and lateral compartments was reported as a function of
time. In addition, the cartilage contact area change with time was determined. A two-way
repeated measures analysis of variance and a post hoc Student-Newman-Keuls test were
used to determine the statistically significant differences in contact area and cartilage
contact deformation between the medial and lateral compartments as a function of time
(Statistica* StatSoft, Inc, Tulsa, OK, USA). Level of significance was set at p<0.05.
138
3D surface model
of femoral cartilage
Peak contact deformation
4i
/I
3D surface
model of
tibial cartilage
Figure 7.5: The peak contact deformation was determined as the maximum contact
deformation in the cartilage contact area.
7.3 Results
The peak cartilage contact deformation, as well as the cartilage contact area of
both the medial and lateral compartments of the individual knee joints are presented in
Table 7.1 and Table 7.2. The average peak cartilage contact deformation over time as
well as the rate of change of the cartilage contact deformation (mean ± SD) are shown in
Figure 7.6 for the medial and lateral tibial compartments. Figure 7.7 presents the average
cartilage contact area as well as its rate of change for both compartments. In all of the
cases, the vertical component of the ground reaction force - measured with the load
platform - reached the full body weight of the subject within approximately one second.
139
Lateral ---
Medial -*-
Ground Reaction
!el
20
-1 -he
---------- ------- - - - - -0.7
--- ------
15 -------CC
1e-1W1)
0
05
-1-0
0
- --0
-- -- ---
50
100
--- -- - --- -- -- 1-- -- --
150
200
-- - --- -- ---- 0.25
250
U
300
Time(s)
B
3.5
S 3
-
--- --------
2.5
-----
cc 2
1.5
1
----
-
--- ---------- --- ----------
- ---
----
---
--- ----
- -- -----
---
----
----- ------- ------------------------ --- ------- ---
- ---
--, -Medial
E
0
-0.5
0
50
100
150
200
250
300
Time(s)
Figure 7.6: (A) The variation of the peak cartilage contact deformation over time
(mean ± standard deviation) and the corresponding ground reaction force
(normalized for body weight). (B) Mean values of the rate of change of the peak
cartilage deformation in tibial compartments.
140
-+- Lateral -r-Medial
-*-Ground Reaction
300
- - - ----
250
200
- - -
- -
- -
0
---------------------- ------------------ ------- --
150
------ - - - - - - -- -- - ---- --- - -1- T - - - -
0.75
0.5
-o
100
o
0 1L
-------------------------------------------------- 0.25 c
50
I
0
50
100
150
200
250
0
30C
Time(s)
Rate of Area
45
40 1
35
30
2520
15
-
10
-
-
---------------------------------------
501
-5
-
SA
-&
.A
-W
100
---
-
-A
150
-------------&
200
--Lateral
-AMedial
@
250
300
Time(s)
Figure 7.7: (A) The variation of cartilage contact area over time (mean ± standard
deviation) and the corresponding ground reaction force (normalized for body
weight). (B) Mean values of the rate of change of the cartilage contact area in tibial
compartments.
141
7.3.1 Cartilage Contact Deformation and Contact Area with Time
Medial compartment: The peak contact deformation was measured 4.0 ± 1.3%
when the tested leg contacted with the ground (time zero). The corresponding cartilage
contact area was 47.0 ± 21.2 mm2. At the first second of loading, the peak values of
cartilage contact deformation and the cartilage contact area were 5.4 ± 1.7% and 87.6 ±
33.1 mm2. At this moment, the loading had reached 89.7% of full body weight. At 10
seconds of loading, the peak cartilage contact deformation sharply increased to 8.3 ±
1.2%, representing a 105.4% increase in the magnitude compared to that at the beginning
of the loading. The corresponding cartilage contact area was 174.2 ± 19.7 mm 2 . The peak
contact deformation further increased to 10.5
+
0.8 %, with a contact area of 223.9 ± 14.8
mm 2 at 50 seconds of loading. Thereafter, the peak cartilage contact deformation was
relatively constant and reached 12.1 ± 1.4 % at 300 seconds of loading with a
corresponding contact area of 263.2 ± 19.6 mm2. The contours of contact deformation
distribution of a typical subject in the sagittal cross-section of medial compartment are
shown in Figure 7.8.A.
Lateral compartment: At time zero, the peak cartilage contact deformation was
2.6 ± 2.4 % with a corresponding contact area of 20.3
20.3 mm 2 . At 10 seconds of
loading, the peak cartilage contact deformation was 9.9
3.2 %, representing 19.2 %
more deformation in comparison with that measured in medial compartment. The contact
area increased to 94.8 ± 24.9 mm 2, representing a 45.6 % decrease in contact area with
respect to the medial compartment. After 50 seconds, the magnitude of the peak cartilage
contact deformation reached 12.6 ± 3.4 % and a contact area of 123.0 ± 22.8 mm2 .
Thereafter, both the peak contact deformation and contact area remained relatively
constant and were 14.6 t 3.9 % and 135.6 ± 20.8 mm2 at 300 seconds, respectively. At
this time point, the peak deformation in the lateral compartment was 21 % greater than
that in the medial compartment, whereas the contact area was 48.5 % less than that in the
medial side. The contours of contact deformation distribution of a typical subject in the
sagittal cross-section of the lateral compartment are shown in Figure 7.8.B.
142
7.3.2 Rate of Change
Medial compartment: the deformation rate reached its peak of 1.4 ± 0.9 %/s at the
first second of loading. The rate of change of the contact area also experienced its peak
value of 40.6 ± 20.8 mm 2 /s at this time point. The rate of change in the peak deformation
and contact area quickly decreased to 0.1 ± 0.0 %/s and 4.2 ± 1.3 mm 2 /s, respectively at
the 10th second of loading. Beyond about 50 seconds, no changes in rate of peak
deformation and contact area were detectable within the measurement accuracy of our
system.
Lateral compartment: Peak rate of change of the contact deformation and contact
area (3.1 ± 2.5 %/s and 24.0 ± 11.4 mm 2 /s, respectively) was observed in first second of
loading. These values represent that at the beginning of loading, the rate of change of the
peak deformation curve was 2.2 times faster in the lateral compartment. However, the
rate of change of the contact area was 1.7 times faster in the medial compartment.
Thereafter, the rate of change of both deformation and contact area decreased quickly and
after about 50 seconds of loading, no changes in the rate of peak deformation and contact
area were detectable within the measurement accuracy our system.
143
Medial
Lateral
15%
-
12%
300 s
50s
x-- 15 s
9%
6%
:*:
-
3%
-
I
s
Thickness (mm)
0%
(2.3 mm)
3.5
20
3.5
3
3.0
2.5
.2
.
0
10
1.5
15
2
2.5w
2.0
o0
u10
E
e
1.5
1.0 i-
5
5
0.5
0.5
0
Distance (mm)
-10
5
0
-5
Distance (mm) A
10
Anterior
Posterior
0.0
0
0
100
0
Anterior
Posterior
Peak Deformation
Peak Deformation
(B) Lateral Compartment
(A) Medial Compartment
Figure 7.8: Contours of contact deformation distribution of a typical subject in the course of time
in the sagittal cross-sections (dashed lines) in medial and lateral compartments.
144
Table 7.1: Cartilage contact deformation (%) as a function of time under full body weight.
Time (sec)
Knee 1
Knee 2
Knee 3
Knee 4
Knee 5
Medial Lateral
Medial Lateral
Medial Lateral
Medial Lateral
Medial Lateral
0.1
11.3
13.0
8.9
5.3
11.0
9.1
5.4
9.3
5.4
9.2
9.7
12.4
13.3
4.6
7.4
7.9
8.2
9.9
5.8
9.8
14.5
8.8
14.1
7.3
9.7
6.1
9.7
15.0
8.4
13.7
10.2
6.9
10.5
15.6
13.5
14.7
15.0
0.7
4.9
8.6
10.0
5.1
9.0
8.2
5.6
10
8.9
13.4
6.0
8.8
15
20
9.1
9.5
14.7
14.9
8.9
9.8
8.7
9.3
6.3
6.7
8.8
10.6
9.2
7.2
25
10.0
15.3
9.2
11.6
9.4
5
Lateral
3.4
8.8
1.7
5.0
Medial
1.6
5.2
1.9
5.8
0
Knee 6
4.6
13.0
30
10.8
15.9
9.5
12.0
10.2
7.6
50
70
11.5
11.4
16.4
16.5
10.7
11.7
12.4
13.1
10.7
11.5
9.4
9.9
10.5
11.2
7.9
9.0
10.8
11.5
15.0
14.8
8.7
8.9
9.8
90
110
11.2
10.9
16.5
16.6
12.7
12.1
15.4
16.0
11.8
12.7
10.1
9.9
10.8
11.2
8.6
8.8
11.5
12.0
15.2
15.6
10.5
9.3
13.9
14.3
150
190
10.9
11.2
17.4
17.5
12.4
13.2
15.7
17.1
12.8
12.1
9.8
10.2
10.4
11.1
7.9
8.3
11.5
11.9
14.7
14.7
10.8
10.2
14.3
15.0
210
11.2
17.3
11.8
17.5
12.3
10.3
10.9
8.1
11.5
15.4
10.4
16.0
250
11.9
17.4
11.9
18.6
12.6
10.9
11.5
13.0
290
12.2
17.8
12.8
18.5
13.2
10.9
11.6
8.5
8.7
12.3
14.6
15.3
11.2
9.9
16.3
15.9
300
12.6
18.4
13.4
18.2
13.1
10.8
11.5
8.9
12.5
15.6
9.5
16.0
145
Table 7.2: Contact area (mm 2) as a function of time under full body weight.
Knee 1
Knee 2
Knee 3
Knee 4
Knee 5
Knee 6
Time (sec)
Medial
Lateral
Medial
Lateral
Medial
Lateral
Medial
Lateral
Medial
Lateral
Medial
Lateral
0
37.5
24.3
12.0
5.0
5
10
155.1
167.4
85.9
99.0
103.7
147.1
99.8
105.8
174.9
175.5
106.9
110.8
175.4
181.6
110.8
118.0
20.0
50.0
59.0
63.6
66.9
76.1
172.4
179.0
15
20
52.8
149.3
161.8
173.4
190.9
187.4
196.2
21.1
69.3
70.8
72.6
77.2
50.0
162.9
187.3
197.1
200.4
53.8
176.2
202.8
213.4
224.5
20.0
110.8
124.6
127.2
135.4
25
187.8
120.4
202.4
123.9
195.8
69.2
194.5
81.8
200.0
31.2
100.0
109.6
120.5
127.4
134.4
225.9
142.2
30
192.2
120.0
204.8
126.8
200.0
74.0
207.2
89.7
207.4
135.8
231.0
140.6
50
207.1
127.1
212.9
130.0
231.1
91.0
218.2
99.7
225.5
144.5
248.4
145.5
70
211.5
128.0
213.0
240.0
90
110
212.4
208.8
125.5
123.5
228.9
232.1
131.3
136.6
142.3
95.4
97.9
97.7
107.4
106.7
144.3
152.8
154.6
150
190
210
213.2
233.1
234.7
126.8
128.2
122.5
238.2
230.0
237.3
250
238.7
124.5
106.4
241.6
245.4
252.9
262.0
263.1
264.6
267.9
152.0
151.8
157.1
154.6
255.3
259.1
257.2
252.2
260.0
256.0
261.6
148.6
150.4
153.0
154.6
150.7
152.9
155.6
290
231.5
300
241.1
150.7
142.2
142.5
262.0
277.8
273.1
269.5
270.9
100.0
100.5
100.3
230.4
145.2
284.0
103.1
230.9
237.8
246.1
248.7
265.5
265.5
267.2
131.2
230.9
149.1
291.0
106.4
272.3
113.3
266.2
156.7
262.9
151.7
133.1
242.7
147.5
292.6
106.9
273.9
115.5
268.4
156.0
260.4
154.7
146
110.6
106.2
106.7
106.2
7.4 Discussion
This study investigated the time-dependent contact of the articular cartilage of the
human knee under constant full bodyweight loading during a single leg standing using a
combined dual fluoroscopic and MR imaging technique [18]. The peak cartilage contact
deformation and the cartilage contact area as functions of time were determined. Both
medial and lateral compartments of the tibial plateau were considered and compared to
determine whether the hemi-joints show differences in contact behavior.
The cartilage contact deformation and contact area during the measured time
interval (300 seconds) were found to sharply increase in the first 20 seconds even though
the body weight reached constant within 1 second during the single leg standing, and
beyond 50 seconds, the cartilage contact deformation and contact area changed in a much
lower rate. Generally, during the measured time interval, the lateral cartilage had greater
peak contact deformation compared to medial side, while the cartilage contact area was
greater in the medial compartment. The location of cartilage-cartilage contact indicated
that the contact deformation occurred in the concave (conforming) surface in the medial
compartment of tibia, while in the lateral compartment, the cartilage contact occurred at
the convex surface of tibial cartilage (Figure 7.9).
Previous studies have documented that tibial cartilage is thicker on the lateral
plateau compared to that of the medial plateau [11, 14]. The same pattern was observed
in the current study (Table 7.3). In reported in-vivo studies of the knee during lunge [14],
the peak contact deformation of the medial compartment was reported to be greater than
that in the lateral compartment (25 + 9 % and 22 ± 10 %, respectively; at full extension).
Also, during the stance phase of gait [16], the peak contact deformation of the medial
compartment (ranging from 8 ± 5 %, at the beginning of stance, to 23 ± 6 %, at 30% of
stance) was reported to be greater than that in the lateral compartment (ranging from 7 ±
3 %, at the beginning of stance, to 16 ± 4 %, at 30% of stance corresponding to full
extension). Our data show that the in-vivo biomechanics of loading during single leg
standing is different. During the single leg standing, the body is likely laterally inclined
147
(body weight center shifts laterally) to keep stability, which may explain the higher
contact deformation at the lateral compartment. Future studies should quantify the body
weight center location with respect to the knee joint.
(A) Medial Compartment
(B) Lateral Compartment
Sagittal cross-sectional planes
Figure 7.9: Patterns of contact deformation in the tibiofemoral cartilage. (A) Medial
compartment: contact is occurring on the concave (conforming) surface of medial
tibial cartilage, (B) Lateral compartment: contact is occurring on the convex surface
of lateral tibial cartilage.
The peak deformation of knee cartilage (peak cartilage surface overlapping
normalized by cartilage thickness) was less than the peak deformation that was measured
in the ankle joint (32.3% at 300 seconds.) during the single leg standing [21]. Also, the
rate of change of cartilage contact deformation was less than that previously measured in
the ankle joint (1.4-3.1% versus 18.7%/s, respectively; at 1 second.). However, it is
148
interesting to note that the summation of medial and lateral contact areas in articular
cartilage of the knee was close to that of the human ankle. Ankle cartilage is much
thinner than knee cartilage [20, 22]. The average cartilage thickness was reported to be
1.4 ± 0.2 mm in the proximal talar cartilage [20], whereas in our study, it was 2.7 ± 0.5
mm and 3.2 ± 0.6 mm in the medial and lateral tibial compartments, respectively.
Further, it is worth noting that in this study only cartilage-cartilage contact was
investigated and meniscus-cartilage contact was not included. This might explain why the
deformation in the knee joint was less than that of the ankle joint.
Table 7.3: The thickness of tibial cartilage (mm) at the location of peak cartilage
contact deformation.
Thickness (mm)
Knee
Medial
Lateral
1
2.7
2.3
2
2.3
3.4
3
2.3
3.6
4
3.5
3.9
5
6
2.3
2.9
3.0
3.2
Mean A SD
2.7 + 0.5
3.2 ± 0.6
MR imaging techniques have been extensively used to study the effect of loading
on the cartilage morphology [7, 11]. However, due to the limitations such as long data
acquisition time during MRI scanning and the time dependent behavior of the cartilage
itself, capturing the real-time deformation of the cartilage under a physiological loading
presents a challenge. In most ex-vivo joint studies, the joint was first loaded for a certain
amount of time to deform as desired and then scanned using MRI [7, 23]. Thus, the MR
imaging techniques might be adequate only for studying the long-term response of the
cartilage to loadings [21]. Nevertheless, critical data have been reported on the volume
and average thickness changes of the human knee cartilage after bending, squatting,
running [11, 24, 25]. For example, Eckstein et al. have reported a 3.1 ± 4.5% and 2.4 ±
149
5.2% cartilage volume change in the medial and lateral tibial compartments, respectively,
after two minutes of static loading (squatting) on one leg at 15
0 of
flexion with 200%
body weight [11]. Additionally, Herberhold et al., measured the cartilage deformation in
a selected central 2D slice within the contact area and reported a 1.3% femoral cartilage
deformation in the first minute of loading of 150% body weight (3% patellar cartilage
deformation) [23]. Due to difference in the targeted joint, the measured deformation
quantity (thickness, volume, etc.), as well as the type of loading and boundary conditions,
it is difficult to compare those studies directly with the current study. In general, the
cartilage deformations measured in the current study were relatively higher than those
previously reported in the literature. Nevertheless, a significant difference in cartilage
volumetric deformation between medial and lateral compartment has been similarly
observed by Eckstein et al. [11].
While the determination of in-vivo cartilage contact deformation of the knee has
been a challenge in biomechanical engineering, in in-vitro studies using bone-cartilage
surfaces or cartilage explants, indentation tests and confined/unconfined compression
tests have been widely employed to apply a constant force to investigate the creep
behavior of the cartilage [1, 26-30]. This phenomenon is similar to that observed in our
data. Usually, a sharp increase in the deformation was observed in the initial seconds
after applying the load, followed by a continuous creep for a long term. However, the
physiological and biomechanical conditions in living tissue within intact joints differ
substantially from those in experiments involving post-mortem specimens of cartilage or
cartilage-bone plugs because of the influence of different boundary conditions and the
fact that the integrity of the matrix has been changed at the edges of the tissue [25]. In
reality, neither confined nor unconfined compression precisely mimics deformation of
cartilage within intact (living) articular joints. Furthermore, in most in-vitro experiments
(except during unconfined compression) the contact area is held constant. This type of
experimental setup represents different biomechanical contact conditions compared to
physiological conditions in which the contact area varies with time as shown in the
present data (Figure 7.7).
The data obtained in this study may have important implications in biomechanical
studies of human cartilage. Different rates of OA in medial and lateral compartments
150
have been reported in various studies [12]. By distinguishing the contact behavior of the
two compartments during functional loading conditions, it may provide insights into the
biomechanical factors that might be related to OA development. Clinically, numerous
cartilage repair techniques have been proposed [31]. Our data might provide guidelines to
evaluate the time-dependent behavior of the repaired cartilage. Further, in ex-vivo tests of
time-dependent cartilage behavior, a selected load or deformation was applied to the
specimen. Our data may provide useful information on the loading conditions to design
ex-vivo experiments of cartilage specimens in order to simulate physiological responses
of the cartilage. Finally, the in-vivo time-dependent contact responses of the cartilage can
provide a physiological objective function to validate 3D finite element models that are
established to simulate human knee joint functions.
Certain limitations of this study should be noted. Since the menisci deform and
move in response to joint loading, and are invisible on current fluoroscopic images, the
deformation of the menisci cannot be computed with the present methodology. Therefore,
the meniscus-cartilage contact was not included in this study. Cartilage contact
deformation was calculated based on the overlapping of the 3D models of tibial and
femoral cartilages, and the deformation of the individual cartilage layers could not be
determined. Using the overlap of the cartilage surface models to determine the cartilage
contact area might overestimate the actual cartilage contact area, since the true cartilage
is not penetrating through the contact, and therefore will deform and expand beyond the
edge of the overlapping contact area. Another limitation was that the in-vivo forces in the
medial and lateral compartments of the knee joint were not measured. Despite the abovementioned limitations, the data on time-dependent contact behavior of human knee joint
was determined under in-vivo physiological loading conditions.
In conclusion, this study investigated the in-vivo time-dependent contact behavior
of human tibiofemoral articular cartilage under a constant full bodyweight. The cartilage
deformation was found to sharply increase after loading. The contact area was greater in
the medial than in the lateral compartment, while the peak contact deformation was
greater in the lateral compartment. These data could provide insight into normal in-vivo
cartilage function, and may be instrumental for the design of relevant ex-vivo
experiments
that
are
aimed
to
investigate,
151
for
instance,
the
chondrocyte
mechanotransduction under physiological loading conditions. Further, in-vivo cartilage
contact data are necessary for validation of 3D computational models which are used to
predict the intrinsic biomechanical responses of the articular joints.
7.5 Acknowledgements
This study was made possible through grants received from the National Institutes
of Health (ROl AR055612, F32 AR056451). Also, I would like to thank the volunteers
who participated in this study and Bijoy Thomas for his technical assistance.
152
7.6 References
1.
Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation
of articular cartilage in compression? Theory and experiments. J Biomech Eng
1980; 102: 73-84.
2.
Guettler JH, Demetropoulos CK, Yang KH, Jurist KA. Dynamic evaluation of
contact pressure and the effects of graft harvest with subsequent lateral release at
osteochondral donor sites in the knee. Arthroscopy 2005; 21: 715-720.
3.
D'Agata SD, Pearsall AW, Reider B, Draganich LF. An in vitro analysis of
patellofemoral contact areas and pressures following procurement of the central
one-third patellar tendon. Am J Sports Med 1993; 21: 212-219.
4.
Hsieh YF, Draganich LF, Ho SH, Reider B. The effects of removal and
reconstruction of the anterior cruciate ligament on the contact characteristics of the
patellofemoral joint. Am J Sports Med 2002; 30: 121-127.
5.
Neu CP, Hull ML, Walton JH, Buonocore MH. MRI-based technique for
determining nonuniform deformations throughout the volume of articular cartilage
explants. Magn Reson Med 2005; 53: 321-328.
6.
Haut Donahue TL, Hull ML, Rashid MM, Jacobs CR. The sensitivity of
tibiofemoral contact pressure to the size and shape of the lateral and medial
menisci. J Orthop Res 2004; 22: 807-814.
7.
Naish JH, Xanthopoulos E, Hutchinson CE, Waterton JC, Taylor CJ. MR
measurement of articular cartilage thickness distribution in the hip. Osteoarthritis
Cartilage 2006; 14: 967-973.
8.
Ateshian GA, Warden WH, Kim JJ, Grelsamer RP, Mow VC. Finite deformation
biphasic
material properties
of bovine
articular
cartilage
compression experiments. J Biomech 1997; 30: 1157-1164.
153
from confined
9.
Lee RC, Frank EH, Grodzinsky AJ, Roylance DK. Oscillatory compressional
behavior of articular cartilage and its associated electromechanical properties. J
Biomech Eng 1981; 103: 280-292.
10.
Treppo S, Koepp H, Quan EC, Cole AA, Kuettner KE, Grodzinsky AJ.
Comparison of biomechanical and biochemical properties of cartilage from human
knee and ankle pairs. J Orthop Res 2000; 18: 739-748.
11.
Eckstein F, Lemberger B, Gratzke C, Hudelmaier M, Glaser C, Englmeier KH, et
al. In vivo cartilage deformation after different types of activity and its dependence
on physical training status. Ann Rheum Dis 2005; 64: 291-295.
12.
Felson DT, Nevitt MC, Zhang Y, Aliabadi P, Baumer B, Gale D, et al. High
prevalence of lateral knee osteoarthritis in Beijing Chinese compared with
Framingham Caucasian subjects. Arthritis Rheum 2002; 46: 1217-1222.
13.
Li G, Park SE, DeFrate LE, Schutzer ME, Ji L, Gill TJ, et al. The cartilage
thickness distribution in the tibiofemoral joint and its correlation with cartilage-tocartilage contact. Clin Biomech (Bristol, Avon) 2005; 20: 736-744.
14.
Bingham JT, Papannagari R, Van de Velde SK, Gross C, Gill TJ, Felson DT, et al.
In vivo cartilage contact deformation in the healthy human tibiofemoral joint.
Rheumatology (Oxford) 2008; 47: 1622-1627.
15.
Van de Velde SK, Bingham JT, Hosseini A, Kozanek M, Defrate LE, Gill TJ, et al.
Increased tibiofemoral cartilage contact deformation in patients with anterior
cruciate ligament deficiency. Arthritis Rheum 2009; 60: 3693-3702.
16.
Liu F, Kozanek M, Hosseini A, Van de Velde SK, Gill TJ, Rubash HE, et al. In
vivo tibiofemoral cartilage deformation during the stance phase of gait. J Biomech
2009.
17.
Li G, DeFrate LE, Park SE, Gill TJ, Rubash HE. In vivo articular cartilage contact
kinematics of the knee: an investigation using dual-orthogonal fluoroscopy and
magnetic resonance image-based computer models. Am J Sports Med 2005; 33:
102-107.
154
18.
Li G, Wuerz TH, DeFrate LE. Feasibility of using orthogonal fluoroscopic images
to measure in vivo joint kinematics. J Biomech Eng 2004; 126: 314-318.
19.
Li G, Van de Velde SK, Bingham JT. Validation of a non-invasive fluoroscopic
imaging technique for the measurement of dynamic knee joint motion. J Biomech
2008; 41: 1616-1622.
20.
Wan L, de Asla RJ, Rubash HE, Li G. In vivo cartilage contact deformation of
human ankle joints under full body weight. J Orthop Res 2008; 26: 1081-1089.
21.
Li G, Wan L, Kozanek M. Determination of real-time in-vivo cartilage contact
deformation in the ankle joint. J Biomech 2008; 41: 128-136.
22.
Athanasiou KA, Niederauer GG, Schenck RC, Jr. Biomechanical topography of
human ankle cartilage. Ann Biomed Eng 1995; 23: 697-704.
23.
Herberhold C, Faber S, Stammberger T, Steinlechner M, Putz R, Englmeier KH, et
al. In situ measurement of articular cartilage deformation in intact femoropatellar
joints under static loading. J Biomech 1999; 32: 1287-1295.
24.
Eckstein F, Tieschky M, Faber SC, Haubner M, Kolem H, Englmeier KH, et al.
Effect of physical exercise on cartilage volume and thickness in vivo: MR imaging
study. Radiology 1998; 207: 243-248.
25.
Eckstein F, Tieschky M, Faber S, Englmeier KH, Reiser M. Functional analysis of
articular cartilage deformation, recovery, and fluid flow following dynamic
exercise in vivo. Anat Embryol (Berl) 1999; 200: 419-424.
26.
Frank
EH,
Grodzinsky
AJ.
Cartilage
electromechanics--I.
Electrokinetic
transduction and the effects of electrolyte pH and ionic strength. J Biomech 1987;
20: 615-627.
27.
Frank EH, Grodzinsky AJ. Cartilage electromechanics--II. A continuum model of
cartilage electrokinetics and correlation with experiments. J Biomech 1987; 20:
629-639.
155
28.
Mow VC, Gibbs MC, Lai WM, Zhu WB, Athanasiou KA. Biphasic indentation of
articular cartilage--II. A numerical algorithm and an experimental study. J Biomech
1989; 22: 853-861.
29.
Armstrong CG, Lai WM, Mow VC. An analysis of the unconfined compression of
articular cartilage. J Biomech Eng 1984; 106: 165-173.
30.
Boschetti F, Pennati G, Gervaso F, Peretti GM, Dubini G. Biomechanical
properties of human articular cartilage under compressive loads. Biorheology 2004;
41: 159-166.
31.
Bedi A, Feeley BT, Williams RJ, 3rd. Management of articular cartilage defects of
the knee. J Bone Joint Surg Am 2010; 92: 994-1009.
156
Chapter 8 - Conclusions
8.1 Summary
The main purpose of this thesis was to study the biomechanical behavior of the
normal Anterior Cruciate Ligament (ACL), and specifically to determine the ACL force
in living subjects. A Dual Fluoroscopic Imaging System (DFIS) combined with Magnetic
Resonance Imaging (MRI) has been introduced and used to study the ACL biomechanics.
The main advantage of using this accurate and non-invasive methodology is that it
captures the kinematics of the knee joint indirectly, without attaching any measurement
devices to the testing subject (or the ligament). First, the in-vivo kinematics of healthy
ACL due to weightbearing conditions was extensively studied. It was shown that the
ACL has its maximum length at low knee flexion angles, indicating that ACL might be
functional mostly at low flexion angles. The data demonstrated that functional bundles of
the ACL - i.e., the anteromedial (AM) and Posterolateral (PL) bundles - behaved
differently, but are not truly "reciprocal" in that one bundle does not shorten while the
other bundle lengthens. Both bundles were at their maximum length at low flexion
angles. In general the AM bundle is longer than PL bundle. However due to full body
weightbearing, the PL bundle has experienced a greater relative elongation. The surface
fiber bundles elongation showed that even though the overall relative elongations of the
ACL might not be high (about 5 %), the posterior portion of the ACL might experience
up to 13 % relative elongation under the full body weight. The data suggested that the
ACL biomechanics should be investigated in a three dimensional manner and the current
reconstruction techniques using single bundle grafts may not adequately restore the 3D
deformation behavior of the ACL.
Next, the structural behavior of the normal ACL was determined using a robotic
testing system. The force-elongation behavior of the ACL in different flexion angles
revealed that the material property of the ACL is dependent on the flexion angle. The
157
ACL was stiffer at lower flexion angles, which again indicates that the ACL is functional
mostly in low flexion angles. Then, the changes in in-vivo ACL forces due to full body
weightbearing were indirectly determined utilizing the in-vivo knee joint kinematics and
the in-vitro force-elongation data. The estimation of the overall in-vivo ACL force
depends on the value of ACL tension under zero weightbearing, which could not be
determined at the present time and current technology. Therefore, we estimated the ACL
force by assuming different ACL tensions under zero weightbearing. Since the tension of
the ACL was not known when the knee was subjected to zero weightbearing, the
estimated force only represented the change in the ACL force when the weightbearing
increased from zero to full body weight. The results described that the increase in the
ACL force was dependent on the flexion angle, with a larger increase in ACL force at
low flexions. By applying full body weight, the ACL experienced a mild force increase
(below 250 N) when compared to the ACL failure tension of about 1500 N. The tension
contribution of each bundle of the ACL in response to physiological weightbearing was
considered next.
The biomechanical response of the anteromedial and posterolateral bundles was
further investigated using simulated functional loads such as muscle loading, anterior
tibial loads and combined rotational loads, applied on cadaveric knees. The findings
demonstrated that the AM bundle carried greater portion of the load within the ACL at all
flexion angles under externally applied loads, whereas the PL bundle only shared the load
of the ACL at low flexion angles. The data supported this concept that both bundles
function in a complementary rather than reciprocal manner. The results were in
agreement with earlier data on ACL elongation during an in-vivo single legged lunge
activity, where the two bundles were shown to decrease in length as flexion angle
increased. In the present study, the two bundles under muscle loads were shown to carry
high loads between 0* to 30* of knee flexion and minimal loads at 600 and 900. The invivo AM and PL bundle elongation patterns and the in-vitro AM and PL bundle forces
along flexion path demonstrated consistent functional behavior. These findings indicate
that if a double bundle ACL reconstruction is considered, the two bundles might be fixed
within 0* to 300 of knee flexion.
158
Then, it was demonstrated that near full extension, the ACL impinged against the
femoral intercondylar notch. This impingement exerts lateral contact pressure on the midsubstance of the ACL. During sport or rigorous activities, the impingement pressure
could be high enough to cause ACL injury. Therefore, the in-vivo impingement of the
ACL against the femoral intercondylar notch under full weight bearing load was
investigated. The ACL impingement was greatest at full extension and decreased at 150
of flexion. No impingement was observed at 30* and 450 of flexion. At both full
extension and 150 of flexion, applying body weight load caused the impingement to
increase (0.2 - 0.4 mm). Also, due to applied full bodyweight, the location of maximum
impingement inside the femoral notch moved medially. These data could provide insight
into the mechanism of ACL injury and present a method to validate 3D computational
results, which are used to predict the ACL impingement and ACL injury. Clinically, it
has been documented that after ACL reconstruction, impingement of the ACL graft leads
to graft deterioration and loss of full extension. Some surgeons recommend reshaping the
roof of the femoral intercondylar notch during ACL reconstruction surgery (notchplasty)
to avoid graft impingement. However, notchplasty has generated some controversy that it
might not be able to restore the AP stability of the knee. Therefore, an optimal design of
ACL reconstruction seems necessary.
The proposed methodology to determine the in-vivo forces within the ACL can be
generalized to cartilage. By knowing the tibiofemoral cartilage deformation data in-vivo,
and mapping them to in-vitro material property data, it is possible to determine the invivo contact pressure inside the tibiofemoral joint cartilage. As the first step of this
application, the DFIS was used to study the time-dependent responses of the tibiofemoral
cartilage under a constant bodyweight load and determine whether the medial and lateral
compartments show differences in time-dependent contact behavior. The cartilage
deformation was found to sharply increase after loading (in about 50 seconds). The
contact area was greater in the medial than in the lateral compartment, while the peak
contact deformation was greater in the lateral compartment of the knee. Not only the
value of peak contact deformation was different in the knee compartments, but also the
geometry of the contact was found to be different in the compartments of the knee. The
location of cartilage-cartilage contact indicated that the contact deformation occurred in
159
the concave (conforming) surface in the medial compartment of tibia, while in the lateral
compartment, the cartilage contact occurred at the convex surface of tibial cartilage.
These in-vivo cartilage contact data are necessary for validation of 3D computational
models which are used to predict the intrinsic biomechanical responses of the articular
joints and may be instrumental for the design of relevant ex-vivo experiments.
Even though the ACL is a passive component of the knee joint, due to its inherent
complex 3D structure, it plays an important role in the stability of the knee. The
biomechanical behavior of the ACL under physiological loading conditions is much more
complicated than previously thought. More research on the biomechanics of the ACL is
needed to fully understand the mechanisms contributing to ACL injuries as well as to
design an optimal graft and surgical techniques in order to improve the outcomes of ACL
reconstruction.
8.2 Future Directions
These studies provide a more detailed understanding of the function of the
anterior cruciate ligament than what has previously been reported in the literature.
However, much work remains to be done in order to improve the outcomes of ACL
reconstruction. In the future, the methodology used in this study should be extended to
investigate the ACL forces during dynamic activities such as gait, stair climbing, running,
etc. Also, by finding the force-elongation curves of different types of grafts, the in-vivo
forces in the graft should be studied and compared to those of the normal ACL. The
performance of different grafts during physiological activities will be assessed in this
manner.
The tension of the ligament under no weightbearing or when the knee is relaxed
(i.e., the start point on the force-elongation curve of the ligament) is still unknown. By
improving the technology, more research is needed to determine the ACL tension at the
beginning of loading. This initial tension is also very important, clinically. During the
fixation of the graft in ACL reconstruction, initial tension should be applied to the graft.
160
Finding an optimal initial tension for graft fixation is critical to avoid either overconstraint or unstable knee joint, post-operatively.
Recently, double-tunnel double-bundle technique is being used as one of the ACL
reconstruction techniques. However, the order of AM/PL graft fixation and the flexion
angles at which the AM and PL grafts should be fixed is controversial. Therefore, future
studies should focus on these issues to be able to replicate the behavior of normal ACL;
the goal of ACL reconstruction.
Another interesting area to work on is the tunnel placement. It has been discussed
that the outcome of ACL reconstruction is highly sensitive to the position of tunnels,
especially the femoral tunnel. Even though at the first glance it sound easy to simply use
the footprint of the native ACL on the femur and tibia, practical problems and technical
limitations during arthroscopic surgery and the impingement of the graft against the roof
of the femoral notch after surgery make tunnel placement a challenging decision. Thus,
introducing optimal femoral and tibial tunnel positions - which restores the knee stability
and is practically achievable, and also avoids reshaping the roof of the femoral notch would be a significant improvement in ACL reconstruction.
Finally, the estimation of in-vivo contact forces or contact pressure inside the
tibiofemoral joint should be considered in future studies. Using the same concept and
methodology discussed in this thesis, the data of the in-vivo tibiofemoral cartilage contact
deformation can be mapped to the in-vitro stress-strain data, and extract the in-vivo
contact pressure distribution. Therefore, it would be possible to determine whether the
medial and lateral compartments show significant differences in their contact forces. The
knowledge of in-vivo cartilage contact pressure and contact deformation in normal,
injured and osteoarthritic knee joints might provide useful insight into joint treatment and
joint design.
161