Download Validation and application of computational knee joint models

Osteoarthritis or OA, especially in
the knee, is a common disease in
elderly people but also in athletes
that have suffered a trauma, e.g.
anterior cruciate ligament rupture.
Currently, OA cannot be cured,
but its risks can be estimated and
minimized. This thesis aims to
develop a novel, computational
model of the subject’s knee that
could, in future, be used by doctors
as a diagnostic tool to evaluate the
risk of post-traumatic OA before and
after surgical operations.
dissertations | 187 | Kimmo Halonen | Validation and application of computational knee joint models
Kimmo Halonen
Validation and application
of computational knee
joint models
Kimmo Halonen
Validation and application
of computational knee
joint models
Finite element modeling analysis
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences No 187
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
isbn: 978-952-61-1883-3 (printed)
issn: 1798-5668
isbn: 978-952-61-1884-0 (pdf)
issn: 1798-5676
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KIMMO HALONEN
Validation and application
of computational knee
joint models
Finite element modeling analysis
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
No 187
Academic Dissertation
To be presented by permission of the Faculty of Science and Forestry for public
examination in the SN201 in Snellmania Building at the University of Eastern
Finland, Kuopio, on 2nd October 2015,
at 12:00 o’clock.
Department of Applied Physics
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Grano Oy
Kuopio, 2015
Editors: Prof. Pertti Pasanen, Prof. Pekka Kilpeläinen
Prof. Kai Peiponen, Prof. Matti Vornanen
Distribution:
University of Eastern Finland Library / Sales of publications
P.O. Box 107, FI-80101 Joensuu, Finland
tel. +358-50-3058396
http://www.uef.fi/kirjasto
ISBN: 978-952-61-1883-3 (printed)
ISSNL: 1798-5668
ISSN: 1798-5668
ISBN: 978-952-61-1884-0 (pdf)
ISSN: 1798-5676
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Author’s address:
University of Eastern Finland
Dept. of Applied Physics
P.O.Box 1627
70211 Kuopio
FINLAND
email: [email protected] / [email protected]
Supervisors:
Associate Professor Rami K. Korhonen, Ph.D.
University of Eastern Finland
Dept. of Applied Physics
Kuopio, FINLAND
email: [email protected]
Dean Jukka S. Jurvelin, Ph.D.
University of Eastern Finland
Dept. of Applied Physics
Kuopio, FINLAND
email: [email protected]
Professor Juha Töyräs, Ph.D.1,2
1: University of Eastern Finland
Dept. of Applied Physics
2: Kuopio University Hospital
Diagnostic Imaging Center
Kuopio, FINLAND
email: [email protected]
Reviewers:
Director1 , Associate Prof.2 Guoan Li, Ph.D.
1: Massachusetts General Hospital
Dept. of Orthopaedic Surgery
55 Fruit Street, Boston, MA 02114
Massachusetts, United States
email: [email protected]
2: Harvard Medical School, 25 Shattuck St, Boston, MA 02115
Massachusetts, United States
Professor Jeffrey Weiss, Ph.D.
University of Utah
Dept. of Orthopedics and School of Computing
72 South Central Campus Dr., RM. 2646
Salt Lake City, UT 84112, Utah, United States
email: [email protected]
Opponent:
Assistant Prof. Ahmet Erdemir, Ph.D.
Cleveland Clinic Lerner Research Institute
Dept. of Biomedical Engineering (ND20)
9500 Euclid Avenue, Cleveland, Ohio, United States
email: ([email protected])
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ABSTRACT
Osteoarthritis (OA) is a joint disease in which the structure of articular cartilage slowly changes, which results in slow degeneration.
First the collagen fibril network starts to deorganize, the proteoglycan content decreases and the water content increases. Next, the
cartilage starts to crack and eventually wears away, at which point
the knee joint has to be replaced with a prosthesis. Since the treatment options for OA are currently very limited, prevention of OA
would be the most cost-efficient method to deal with it.
Even though the exact cause of OA is unknown, the disease is
believed to be a combination of inflammatory, biological and mechanical changes in the articular cartilage. Excessive stresses in the
articular cartilage have been shown to lead to the development of
OA as the mechanical structure of articular cartilage is damaged.
The cause of abnormal stresses in the cartilage might be a result of
the subject’s natural gait pattern, an injury (e.g. anterior cruciate
ligament (ACL) rupture) or a surgical operation (e.g. osteotomy,
ACL reconstruction).
The direct measurement of stresses in the knee joint is not possible in vivo. However, finite element (FE) modeling enables the
estimation of stresses and strains in a human knee joint during e.g.
walking or standing, which are the two most frequent daily activities for the joint. In FE modeling the geometry is discretized
into small elements and the loads and moments acting on the knee
joint are implemented through boundary conditions. With the use
of motion analysis the subject-specific gait pattern can be recorded
and implemented into the model. A validated, patient-specific FE
model would enable the evaluation of OA risk in the knee joint
before and after surgical operations.
In the present study, the knee joint was first imaged with a magnetic resonance (MR) scanner. Different tissues such as articular
cartilage, menisci, patellar cartilage, ligaments and muscles were
segmented from the MR images. The tissues were then transformed
into solid geometry, meshed (i.e. divided into finite elements) and
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given their material properties. In the first methodological study,
the gait was implemented as rotations and translations obtained
from literature. Five different material properties for the articular
cartilage were compared during dynamic and static loading. In the
second study, the strains in the articular cartilage were experimentally determined during static loading (standing) and compared to
the model. In the third study, the gait of the subject was determined
using skin markers and a camera system in a motion laboratory.
The gait was implemented into the model as moments and translational forces and the femoral rotations of the model were compared
to the measured rotations. Also the stresses, strains and pore pressures were evaluated in the patellar cartilage. In the fourth study,
the effect of ACL rupture, single bundle and double bundle ACL
reconstruction on knee joint motion was evaluated.
The results of the first study emphasized the importance of
arcade-like fibril network structure on dynamic tissue response and
the effect of proteoglycans on tissue response during static loading.
While fibril volume density was shown to have an effect on stresses
and strains in extreme scenarios, the depth-wise variation in real
cartilage is too small to have an effect on the simulations. In the
second study the cartilage was observed to deform most right after the introduction of load (half of body weight), but continued to
deform up to the 30 minute mark. The simulated strains matched
the observed strains surprisingly well considering the material parameters were not subject-specific. The third study highlighted the
importance of including the patella in moment and force driven
FE models. As expected, arcade-like collagen fibril network reduced fibril strains in superficial and deep zones compared to homogeneous model while the compressive strains were highest at all
depths in the model with the very early OA. In the fourth study,
the model with anterior cruciate ligament (ACL) deficiency showed
similar increased laxity to clinical findings. The results emphasized
that rather than the choice of technique, the stiffness and pre-strain
of the graft determine the success of the reconstruction.
In conclusion, the present study takes a step to create a new di-
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agnostic tool for the pre- and post-operational assessment of stresses
and strains in a human knee joint. This study is a part of the
progress in diagnostic imaging where the focus is shifting from
structural imaging of the knee joint to functional imaging and consequently, prevention of diseases. With over 100 million patients
in Europe alone, OA a substantial burden to economy in terms of
treatment costs and losses to productivity. With the public aging
the need for prevention is even more urgent. A validated, patientspecific FE model of the knee joint would help doctors assess the
risk sites for OA.
Medical Subject Headings: Biomechanical modeling; Finite element method;
Articular cartilage; Meniscus; Knee; Ligament, Collagen fiber; Proteoglycan; Anterior cruciate ligament; Reconstruction; Graft; Stress; Strain;
Pore pressure;
Yleinen suomalainen asiasanasto: Biomekaaninen mallintaminen; pienelementtimenetelmä; nivelrusto; nivelkierukka; polvi; nivelside; kollageenisäie;
proteoglykaani; eturistiside; korjaus; siirre; jännitys; venymä; nestepaine;
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Preface
This study was carried out during the years 2011-2015 in the Department of Applied Physics at the University of Eastern Finland.
First, I would like to thank my supervisors: Associate professor
Rami Korhonen, my main supervisor, has been the main driving
force behind my research, giving invaluable insight into the process of scientific thinking while making sure the research is always
grounded in reality. Rami has always represented the modeling aspect of my research support. Dean Jukka Jurvelin, for encouraging
and representing the empirical aspect of my research along with
Juha. Professor Juha Töyräs for guidance in the experimental parts
of my study, connections to the hospital and general encouragement. I thank all three supervisors for their contributions to this
thesis. Also for hiring me.
Special thanks go to my colleague, Dr. Mika Mononen, for extensive help in technical difficulties with Abaqus. Your magical
touch caused the ’reverse demo effect’, i.e. the problem ceased to
exist when you came to look at it. I doubt this thesis would have
been possible without your help.
I wish to also thank the referees who reviewed my thesis: Dr.
Guoan Li and Dr. Jeffrey Weiss.
I would like to thank my colleagues Lasse Räsänen, Mikko Venäläinen, Elvis Danso and Petri Tanska for inspiring conversations as
well as sharing technical knowledge on modeling. I thank James
Fick, Ari Ronkainen and before him, Lassi Rieppo, for a fun atmosphere in our shared room and our Friday tradition. Special thanks
go to the people in the laboratory corridor, namely Satu Turunen,
Juuso Honkanen, Markus Malo, Chibuzor Eneh, Jarkko Iivarinen,
Hans Linder, Mikko Pitkänen, Xiaowei Ojanen and Pia Puhakka
for putting up with me playing the Tico Tico song every Friday for
all these years. Thanks to all members of our research group for
making this a good place to work for.
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I wish to thank my parents Jorma and Pirjo Halonen, and my
little brother Tommi for your support during my studies.
For providing financial support, the International Doctoral Programme in Biomedical Engineering and Medical physics (iBioMEP),
Jenny & Antti Wihuri Foundation, Academy of Finland (grants
138574, 269315 and 218038), the strategic funding of University
of Eastern Finland and Kuopio University Hospital (EVO, grant
5041722), European Research Council under the European Union’s
Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement no. 281180 are acknowledged. CSC-IT Center for Science,
Finland, is acknowledged for computing resources.
Kimmo Halonen
Kuopio, 03.10.2015
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ABBREVIATIONS
2D
3D
A
AM
ACL
BW
C
C3D8
C3D8P
C3D20R
C3D20RP
CT
CTa
FE
FEM
FRPE
FRPVE
GRF
LCL
MCL
MR
MRI
PCL
PL
PML
PO
POR
TE
TR
T
Two-dimensional
Three-dimensional
Anterior bundle of PCL
Antero-medial bundle of ACL
Anterior cruciate ligament
Body weight
Central bundle of PCL
Continuum element type with 8 nodes
Continuum element type with 8 nodes and porosity
Continuum element type with 20 nodes and
8 integration points
Continuum element type with 20 nodes, 8 integration
points and porosity
Computed tomography
Computed tomography arthrography
Finite element
Finite element modeling
Fibril-reinforced poroelastic
Fibril-reinforced poroviscoelastic
Ground reaction force
Lateral collateral ligament
Medial collateral ligament
Magnetic resonance
Magnetic resonance imaging
Posterior cruciate ligament
Postero-lateral bundle (in ACL), Posterior-longitudinal
bundle (in PCL)
Posterior meniscofemoral ligament (in PCL)
Posterior-oblique bundle of PCL
Pore pressure
Time of echo
Time of repetition
Tesla (unit of magnetic flux density)
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SYMBOLS
B0
η
C
ε
ε̇
e
E0
Em
Eε
F
G
I
J
K
k0
k
ks
M
nf
p
S
σe
σf
σn f
σs
νm
z
External magnetic field in MRI
Viscous damping coefficient
Ratio of primary collagen fibrils to secondary fibrils
Strain
Time derivative of strain
Void ratio
Dynamic elastic modulus
Non-fibrillar matrix modulus
Fibril network modulus
Deformation tensor
Shear modulus
Unit tensor
Jacobian determinant
Bulk modulus
Initial permeability
Permeability
Spring constant
Material constant
Fluid fraction
Fluid pressure
Von Mises stress
Effective solid stress
Stress of fibrillar part
Stress of non-fibrillar part
Solid matrix stress
Poisson’s ratio
Normalized tissue depth
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LIST OF PUBLICATIONS
This thesis consists of a review of the author’s work in the field of
biomechanical modeling of the human knee joint and the following
selection of the author’s publications:
I Halonen K.S., Mononen, M.E., Jurvelin J.S., Töyräs, J., and Korhonen R.K., “Importance of depth-wise distribution of collagen and proteoglycans in articular cartilage - A 3D finite
element study of stresses and strains in human knee joint”.
Journal of Biomechanics. 46 (6), 1184–92 (2013).
II Halonen K.S., Mononen, M.E., Jurvelin J.S., Töyräs, J., Salo, J.,
and Korhonen R.K., “Deformation of articular cartilage during static loading of a knee joint - Experimental and finite
element analysis”. Journal of Biomechanics. 47 (10), 2467–74
(2014).
III Halonen K.S., Mononen, M.E., Jurvelin, J.S., Töyräs, J., Kłodowski,
A., Kulmala, J.-P., and Korhonen, R.K., “Importance of patella,
quadriceps forces and depth-wise cartilage structure on knee
joint motion and cartilage response during gait cycle”. (submitted) (2015).
IV Halonen K.S., Mononen, M.E., Töyräs, J., Kröger, H., Joukainen,
A. and Korhonen, R.K., “Optimal graft stiffness and pre-strain
restore normal joint laxity in ACL reconstructed knee”. (submitted) (2015).
Throughout the thesis, these papers will be referred to by Roman
numerals.
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AUTHOR’S CONTRIBUTION
The publications in this dissertation are original research papers on
simulation and experimental studies of tissues in the human knee
joint. The author has been the main contributor to each method presented in the publications and carried out all of the data analyses
and simulations. The author conducted all the simulations and experimental measurements and imaging measurements, apart from
the motion analysis and related inverse and forward dynamics analyses, which were carried out in University of Jyväskylä, Jyväskylä,
Finland and University of Technology, Lappeenranta, Finland. The
author has been the main writer of each paper.
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Contents
1
INTRODUCTION
2
ANATOMY AND FUNCTION OF THE KNEE JOINT
2.1 Bones . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Anatomy . . . . . . . . . . . . . . . . . . . . .
2.1.2 Biomechanics . . . . . . . . . . . . . . . . . .
2.2 Ligaments . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Anatomy . . . . . . . . . . . . . . . . . . . . .
2.2.2 Biomechanics . . . . . . . . . . . . . . . . . .
2.3 Menisci . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Anatomy . . . . . . . . . . . . . . . . . . . . .
2.3.2 Biomechanics . . . . . . . . . . . . . . . . . .
2.4 Muscles . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Anatomy . . . . . . . . . . . . . . . . . . . . .
2.4.2 Biomechanics . . . . . . . . . . . . . . . . . .
2.5 Articular cartilage . . . . . . . . . . . . . . . . . . . .
2.5.1 Tissue fluid . . . . . . . . . . . . . . . . . . .
2.5.2 Fibrillar part . . . . . . . . . . . . . . . . . . .
2.5.3 Non-fibrillar part . . . . . . . . . . . . . . . .
2.5.4 Biomechanics . . . . . . . . . . . . . . . . . .
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KNEE JOINT DISORDERS AND THEIR EVALUATION
3.1 Joint disorders and osteoarhritis . . . . . . . . . . . .
3.1.1 ACL rupture and reconstruction . . . . . . . .
3.1.2 Osteoarthritis . . . . . . . . . . . . . . . . . . .
3.2 Imaging of joint disorders and osteoarthritis . . . . .
3.2.1 Radiography . . . . . . . . . . . . . . . . . . .
3.2.2 Magnetic resonance imaging . . . . . . . . . .
3.3 Motion analysis . . . . . . . . . . . . . . . . . . . . . .
3.4 Limitations in current evaluation of joint disorders .
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4
COMPUTATIONAL MODELING OF THE HUMAN KNEE
JOINT
4.1 Knee joint models . . . . . . . . . . . . . . . . . . . . .
4.2 Material models of articular cartilage and meniscus .
4.2.1 Poroelastic biphasic theory . . . . . . . . . . .
4.2.2 Transversely isotropic material . . . . . . . . .
4.2.3 Fibril-reinforced poroviscoelastic material . .
4.3 Finite element method . . . . . . . . . . . . . . . . . .
4.4 Model validation and applicability . . . . . . . . . . .
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AIMS
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MATERIALS AND METHODS
6.1 Model geometry and parameters . . . . . . . . . . . .
6.1.1 Segmentation from MR images . . . . . . . . .
6.1.2 Material parameters . . . . . . . . . . . . . . .
6.1.3 Boundary and loading conditions . . . . . . .
6.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Effect of depth-wise tissue characteristics . . .
6.2.2 ACL rupture and the effects of reconstruction
techniques . . . . . . . . . . . . . . . . . . . . .
6.3 Experiments - model validation and input . . . . . .
6.3.1 Computed tomography arthrography . . . . .
6.3.2 Motion analysis . . . . . . . . . . . . . . . . . .
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RESULTS
7.1 Model validation and parametric studies . . . . . . .
7.1.1 Cartilage deformation in vivo . . . . . . . . . .
7.1.2 Knee joint motion . . . . . . . . . . . . . . . .
7.1.3 Effect of depth-wise tissue properties and OA
7.2 ACL rupture and reconstruction . . . . . . . . . . . .
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DISCUSSION
8.1 Validity of the models . . . . . . . . . . . . . . . . . .
8.2 Importance of material properties . . . . . . . . . . .
8.2.1 Static loading . . . . . . . . . . . . . . . . . . .
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8.2.2
8.2.3
8.3
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Gait loading . . . . . . . . . . . . . . . . . . . . 73
Optimization of ACL reconstruction techniques
and graft properties . . . . . . . . . . . . . . . 75
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 76
SUMMARY AND CONCLUSIONS
9.1 Future . . . . . . . . . . . . . . . . . . . . . . . . . . .
REFERENCES
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1 Introduction
Articular cartilage is a lubricating, load bearing tissue found in diarthrodial joints. The structure of articular cartilage is complex,
consisting of chondrocytes and an extracellular matric (ECM) [1–3].
Depending on the depth, approximately 60-80% of the wet weight
of articular cartilage consists of interstitial water [2]. The second
largest constituents of cartilage are type II collagen fibers (70% of
dry weight) and proteoglycans (20-30%) [2]. Chondrocytes occupy
1-5% of the volume of articular cartilage [4]. The collagen fibers
form an organized network that resists dynamic deformation as
well as swelling [5, 6]. In early osteoarthritis (OA), the collagen fibril network starts to disorganize and the proteoglycan content decreases. The cartilage surface starts to fibrillate, after which cracks
start to form. Eventually the cartilage wears away, causing pain and
hindering joint movement [3]. OA, especially in the knee, causes a
major strain on health care, with approximately 34% of people over
the age of 60 suffering from the disease in the United States [7].
As the cartilage lacks blood vessels, its self-healing capabilities
are very limited. Currently OA can be treated to limited degree,
ranging from opioid pain treatment and glucosaminoglycan/chondroitin sulfate injections in the early stages of OA [8] to total knee
replacement in late stages [9]. In addition to the high cost of surgical operation, the knee prosthesis has an expected lifespan of 10-20
years [10, 11]. Because of these reasons the most cost-efficient treatment would be prevention of the disease.
The exact mechanisms of OA onset and development are unknown. However, abnormal stresses and strains in articular cartilage have been shown to greatly increase the risk of OA [3, 12, 13].
These stresses can be a result from the patient’s abnormal walking
pattern especially when paired with obesity [14] or a consequence
of an injury [15, 16]. Specifically a rupture in the anterior cruciate ligament (ACL) has been shown to greatly increase the risk of
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Kimmo Halonen: Validation and application of computational knee joint
models
OA [15–17]. While the patients with reconstructed ACL showed
nearly restored knee function [15], the outcome is dependent on
the success of the surgery.
In cadavers, the contact stresses can be measured [18–20]. Due
to ethical reasons, the direct assessment of stresses in the knee articular cartilage of a living human is not possible. Thus, an indirect
method is needed. Finite element (FE) method allows the simulation of stresses and strains in the knee joint during daily activities,
such as walking [21–23]. In this method, the knee joint geometry is
first obtained from magnetic resonance (MR) images, from which
the different tissues are segmented. The tissues are divided into
small (finite) elements and the solution is approximated iteratively.
Before the application of any computational model, validation is
needed. Examples of the types of knee joint model validation include material validation and motion validation. Material validation in the knee consists of the development of a theoretical material model and comparing it to actual response of the knee cartilage.
Motion validation requires determining the patient’s knee motion
in a motion laboratory and comparing it to simulated rotations and
translations. A validated model can then be used for applications,
such as simulating the effects of joint disorders on the knee cartilage
or the outcomes of surgical operations.
This study aims to develop a realistic model of a knee joint for
the simulation of stresses and possible failure sites in cartilage. In
study I, the effects of different types of theoretical cartilage tissue
models on the simulated depth-dependent stresses and strains during gait (walking) and at equilibrium (standing) were investigated.
In study II, the test subject’s knee was imaged during static loading and the deformation of tibial cartilage was compared with the
predictions based on the FE model. In study III, the subject’s gait
was analyzed in a motion laboratory. The gait was simulated using moments and forces in the FE model and the resulting rotations and translations were compared with those measured in the
motion analysis. Subject-specific quadriceps forces and a patellar
cartilage with depth-dependent characteristics were implemented
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Introduction
for the first time. Finally, in study IV, the effect of ACL rupture as
well as several ACL reconstruction techniques on the stresses and
strains in tibial cartilage surface were investigated.
This study contributes to the shift in diagnostic imaging, from
conventional structural imaging to imaging of the function of the
joints, evaluation of the effects of surgical operations and assessment of possible failure sites. This could provide medical doctors
with a novel diagnostic tool to assess, e.g., the outcome of surgical
knee operations pre- and post-operatively. If successful, the prevention of OA would greatly benefit the patients as well as reduce the
burden the disease causes to healthcare.
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Kimmo Halonen: Validation and application of computational knee joint
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2 Anatomy and function of
the knee joint
Human knee joint (Figure 2.1) is a complex structure consisting
of soft tissues and three bones: femur, tibia and patella. The soft
tissues include ligaments, tendons, menisci, muscles and articular
cartilages.
2.1
2.1.1
BONES
Anatomy
Femur is an asymmetrically shaped bone that attaches to the hip
at its proximal end [24]. There are two condyles in the distal end
of femur: lateral and medial, with medial being more prominent
than the lateral. Tibia has lateral and medial plateaus with which
the femur articulates. The medial tibial plateau is almost flat, while
the lateral has a convex shape. These two plateaus are covered with
articular cartilage and are in contact with the femoral condyles. The
plateaus are separated by a spine, which the anterior horn of lateral
and medial menisci as well as the anterior cruciate ligament are attached to [24]. In the anterior side of the tibia, there is a tubercle for
the insertion of patellar tendon. Patella is a sesamoid bone that articulates with the trochlea of the distal femur. Like femur and tibia,
the contacting surface of patella is covered with articular cartilage.
The articulating surface is divided into a medial and a lateral facet,
with the lateral side being wider in the lateral-medial direction but
smaller in the anterior-posterior direction. [24].
2.1.2
Biomechanics
The bones consist of two distinctive phases: cortical bone and trabecular bone. Cortical bone forms the outer layer of bones and is
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Kimmo Halonen: Validation and application of computational knee joint
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highly organized and very stiff. Trabecular bone forms the inside of
the bones and is porous in structure. Trabecular bone is also softer
than the cortical bone. The primary function of bones is to provide
a rigid base structure of the body, one the muscles attach to through
tendons. Bones also absorb some of the loads due to their elastic
nature [25]. The elastic modulus (representing bone stiffness) and
ultimate stress vary depending on the subject’s age. For example,
in human femur the elastic modulus varies between 17 GPa (ages
20-29) and 15.6 GPa (ages 80-89), and ultimate stress between 140
MPa and 120 MPa. The bone can withstand high loads, especially
in axial direction, but very low strains: the ultimate strain is only a
few percents, 3.4% in femur [26].
Figure 2.1: Anatomy of the human right knee joint, coronal view. Ligaments and muscles
have been omitted for clarity.
2.2
2.2.1
LIGAMENTS
Anatomy
The knee has four primary ligaments; anterior cruciate ligament
(ACL), posterior cruciate ligament (PCL), lateral collateral ligament
(LCL) and medial collateral ligament (MCL) (Figure 2.2), and one
secondary ligament, the anterolateral ligament (ALL) [24, 27]. The
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origin of ACL is in the medial femoral condyle at the posterior aspect of the intercondylar notch. The direction of the ACL is in the
anterior, distal and medial direction toward the tibia, where it is attached. The ACL is both vasculated and innervated. Upon close inspection, the ACL consists of two bundles, the antero-medial (AM)
and posterior-lateral (PL) bundles [24, 28].
Out of all the ligaments, PCL has the largest cross-section and
provides approximately 95% of the total restraint to posterior tibial
translation. The origin of PCL is in the medial femoral condyle at
the posterior aspect of the intercondylar notch. Its insertion site is
in the posterior intercondyloid fossa of the tibia, just posterior to the
lateral meniscus [24]. Although the PCL is characterized as a continuum of fibers [29, 30], its structure can be divided into five bundles: anterior (A), central (C), posterior-longitudinal (PL), posterioroblique (PO) and posterior meniscofemoral ligament (PML), which
attaches to the lateral meniscus [31].
LCL has its origin in the posterior part of lateral femoral epicondyle, just above the popliteus and insertion site in the proximal
tibia, on the lateral fibular head. The LCL is a strong, round, fibrous cord that functions as a major static support against varus
moments [24].
The origin of MCL is in the medial side of the knee, on the medial femoral epicondyle, near the instant center of rotation of the
knee. The surface of the MCL consists of parallel and oblique components [24, 32]. The parallel, thick fibers extend from the medial
femoral epicondyle to the medial surface of tibia. The oblique fibers
are more posterior and have their origin in the medial epicondyle
but blend with the posteromedial joint capsule. The MCL acts as a
primary support against valgus moments in the knee. It also resists
the external rotation of the tibia [24].
The existence of ALL was first reported in 1879, but mostly ignored until Claes et al. (2013) showed that the ligament is present in
approximately 97% of people [27]. The ALL has its origin in the lateral femoral condyle just anterior of the origin of LCL. Its insertion
site is in the proximal tibia, just posterior to Gerdy’s tubercle. Not
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much is known about ALL, but some preliminary results suggest
the ligament has only a minor role in resisting forces in a healthy
knee and ACL reconstructed knee, but the contribution is elevated
in an ACL deficient knee [33].
In addition to the primary ligaments, the knee also contains
smaller ligaments. Out of these the lateral and medial patellofemoral
ligaments (LPFL and MPFL, respectively) have been included in the
FE model used in studies I-IV (See Materials and methods, page 43).
As the names imply, the LPFL and MPFL are located in their respective sides in the lateral and medial sides of the knee. The LPFL
originates in the lateral side of the femur and attaches to the lateral
side of the patellofemoral ligament [34]. The MPFL has its origin in
the soft tissues of adductor magnus tendon and superficial MCL,
and attaches to the medial side of the patellofemoral ligament [32].
The patellofemoral ligaments contribute to the stabilization of the
patella [35].
2.2.2
Biomechanics
The function of ligaments is to stabilize the knee by resisting forces
and moments. The ligaments are very stiff in tension compared
with cartilage or meniscus (and soft in compression). This is due
to the fact that 90% of the ACL is composed of collagen fibers,
and 10% consisting of elastic fibers entangled in a mucopolysaccharide ground substance [36]. Ligaments are viscoelatic material.
However, their material properties in knee joint models are usually
described with linear stiffness and ultimate load of a ligament (approximately 242 N/mm and 2160 N for ACL, respectively) [37, 38]
due to the dynamic nature of knee loading. The cruciate ligaments
are the most important static stabilizer of the knee against anteroposterior translation of the femur with respect to tibia [24, 28]. The
ACL and PCL account for more than 80% of the resistance at flexion angles from 30◦ to 90◦ [39]. In ACL, the PL bundle experiences
highest loads at full extension, under an anterior tibial load. The
forces the AM bundle experiences increase as a function of flexion
angle up to 60◦ and decrease after that, but remain lower compared
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with the PL bundle forces [40]. Under rotatory loads, the PL loads
are higher at 15◦ and lower at 30◦ than the AM bundle [40]. The
PCL provides approximately 95% of the total restraint to posterior
tibial translation. The main function of LCL and MCL is to resist
varus and valgus moments, respectively [24].
Figure 2.2: Primary ligaments in the human knee joint. Left: coronal view. Dashed line
indicates the position of the sagittal plane. Right: sagittal view.
2.3
2.3.1
MENISCI
Anatomy
The lateral and medial menisci are crescent-shaped tissues situated
in their corresponding sides between the femoral condyle and tibial
plateau [41]. The meniscus is a structurally complex tissue comprised of cells, specialized ECM constituents and region-specific
innervation and vascularization. The primary constituent of meniscus is water (72% of wet weight), while the rest consists mostly of
the ECM and cells. Collagen fibers (mainly type I) take majority
of the dry weight (70-80% depending on the region), followed by
proteoglycans (17%), and other glycoproteins (1%) [42]. The me-
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dial meniscus is noticably larger than the lateral one. Though they
both are semi-lunar shaped with a wedge-like crossection, the lateral meniscus varies in size, shape, thickness and mobility compared with the medial meniscus [41]. The lateral meniscus also
covers a larger portion of the tibial plateau (75-93% of the lateral
plateau) compared with the medial meniscus (51-74% of the medial
plateau) [43].
The main stabilizing ligaments of the menisci are the medial
collateral ligament, transverse ligament, meniscofemoral ligaments
and the attachments to tibia at the anterior and posterior horns [41].
The meniscofemoral ligaments, also known as Humphrey and Wrisberg ligaments, connect the posterior horn of the lateral meniscus to
the location near the insertion site of the PCL. Only 46% of people
have both of these ligaments, but 91-100% of people have at least
one of them [31, 44].
At birth, the meniscus is fully vascularized. However, as the
tissue ages the vascularization begins to subside. At 10 years of
age, only 10-30% of vessels are present in the meniscus, and in
adults only the peripheral 10-20% of menisci have blood vessels
and nerves [43]. It is critical to note that only this vascularized,
innervated area at the outer edges of the meniscus has the capability
of healing [42].
The shape of the menisci are congruent with the femoral condyles, helping to distribute the loads exerted on the knee by increasing
the size of the contact area. In the case of total meniscectomy, the
contact pressure in the tibial articular cartilage is increased by 100235% [19, 45]. Due to this, in the case of meniscus injuries, the
prevalent trend in meniscus repair is to preserve as much of the
tissue as possible [46, 47].
2.3.2
Biomechanics
The main role of the menisci is load bearing and distribution in
the knee joint [48]. Furthermore, it has been demonstrated that the
menisci provide shock-absorbing capability to the knee, as meniscectomized knees show a reduction of 20% in shock-absorption [49].
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The uppermost layer of the menisci has been shown to behave
isotropically, with radially and circumferentially oriented samples
having tensile moduli of 48 and 71 MPa, respectively [50]. This
direction-dependency in modulus is primarily due to colalgen fiber
orientation. The middle meniscal portion, which covers the vast
majority of the axial thickness of the meniscus, has a tensile modulus of over two magnitudes greater (198 MPa) than the radially
oriented samples (2.8 MPa) [48]. The tensile stiffness of meniscus
also varies spatially: the tensile modulus in posterior two-thirds
of the medial meniscus is significantly smaller than in the anterior one-third of the medial meniscus or the whole lateral meniscus [51]. Compared to i.e. articular cartilage, the stress-strain curve
of the meniscus is more linear, with small toe and yield regions [52].
The human meniscus is much less stiff in compression than tension, with aggregate modulus and permeability in the range of
0.11 − 0.41 MPa and 1.8 − 2.0 × 10−15 m4 N−1 s−1 , respectively [48].
2.4
2.4.1
MUSCLES
Anatomy
In the anterior side of the knee, the quadriceps muscle group controls the extension of the knee [24]. The four constituents of the
quadriceps are as follows: rectus femoris, vastus lateralis, vastus
intermedius and vastus medialis. The origin of rectus femoris is in
the anterior inferior iliac spine. It narrows down to a tendon 5-8 cm
above the patella [24]. The true insertion site of the rectus femoris
is into the tibial tubercle, but conventionally its insertion site is considered to be in the patella [53]. Being the largest muscle in the
quadriceps muscle, the vastus lateralis has its origin at the proximal part of the intertrochanteric line and extends to halfway down
the linea aspera on the femur. The vastus medialis can be divided
into two parts: the vastus medialis obliquus and the vastus medialis
longus. Its origin is in the medial side of the femur and insertion
in the quadriceps tendon. Vastus intermedius has its origin in the
anterior and lateral shaft of the femur. The insertion site of the vas-
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tus intermedius forms the deepest layer of the trilaminar superior
border of the patella. Vastus medialis and lateralis contribute to the
middle layer, and the rectus femoris contributes to the superficial
layer of the trilaminar patellar border [24].
The flexion and internal rotations of the knee are strongly controlled by the pes anserinus muscles, which are the sartorius, gracilis and semimembranosus muscles. These muscles are located in
the medial side of the knee. Also in the medial side is the medial head of the gastrocnemius. The lateral side contains the biceps
femoris, iliotibial band and lateral gastrocnemius muscles [24, 54].
2.4.2
Biomechanics
The primary function of muscles is to move the body by contracting.
They also provide stability and shield vital organs from damage.
Muscles attach to bones via tendons. Muscle functions can be tested
by measuring the force they can produce by using resistance-based
measurements. The electrical activity of muscles can be examined
using electromyography (EMG) [55, 56], although the relationship
between EMG activity and muscle output is not clear due to redundancy in muscle recruitment [56]. In EMG the electric potential in
muscles is measured using electrodes attached to the skin. Muscle coordination during activities such as walking is captured using
motion analysis [56].
2.5
ARTICULAR CARTILAGE
Human articular cartilage (Figure 2.3) is an avascular [57] tissue
that behaves like a sponge; exuding water when compressed and
draining water in after the pressures is released. Articular cartilage
consists of chondroctes and the extracellular matrix (ECM) [2, 6].
The ECM can be further divided into tissue fluid, fibrillar and nonfibrillar parts [6].
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Figure 2.3: Structure of human articular cartilage.
2.5.1
Tissue fluid
The fluid phase consists of interstitial water and mobile ions. The
water is distributed unevenly throughout the depth of the cartilage,
with 8̃0% of the cartilage wet weight in the superficial zone and
65% in the cartilage-bone interface [2, 58]. This fluid contains small
proteins, metabolites, gases and a high concentration of cations to
balance the negatively charged proteoglycans [58]. The large concentration of negative charges causes an electrical inbalance, which
in turn causes osmotic pressure in the tissue (the Donnan effect [6]).
The collagen network acts as a counterbalancer to the influx of tissue fluid, resisting the Donnan osmotic pressure associated with
the proteoglycans [59]. The incompressible fluid helps the cartilage
absorb impact loads.
2.5.2
Fibrillar part
Collagen fiber network
In healthy articular cartilage, the fibrillar part consists of an organized, mainly type II collagen (90-95%) fiber network, with each
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fiber consisting of primary and secondary fibrils [6]. Other collagen types in articular cartilage include type VI, IX, X and XI [6, 58].
Collagen fibers take approximately 60% of the dry weight of articular cartilage [6]. Collagen fibers are long, rope-like structures that
have a high tensile strenght but almost no compressive stiffness [6].
They also behave in a viscoelastic manner. The main function of
the collagen network is to resist tensile forces [6] and instantaneous
deformation [5]. The collagen network also contributes to the cohesiveness of the articular cartilage by trapping the large proteoglycan
molecules in its meshwork [6].
Near the cartilage surface (superficial zone), the collagen fibers
are oriented parallel to the surface. In humans, collagen concentration is lowest close to the surface, which itself has a higher density
of collagen [60]. This dense and organized layer of collagen fibrils gives the superficial zone a greater tensile stiffness and strenght
than the deeper zones [6]. It also affects the movement of molecules
through the surface of cartilage [6]. In vitro studies have shown this
zone to also have an important contribution to the compressive behavior of articular cartilage [61].
Below the surface, in the middle zone, the fibers start to arc towards the bone and are larger in diameter than in the superficial zone. This zone can be 2-3 times thicker than the superficial
zone [6, 62]. Recent evidence suggests that the middle zone has a
major contribution to resisting shear forces caused by joint movement [63].
In the deep zone, the fibers are perpendicular to the cartilagebone interface [1] and are largest in diameter [6]. Their concentration is also highest in the deep zone in humans [60]. The collagen
fibers pass into the tidemark, which is a thin basophilic line that
can be seen on light microscopic sections of decalcified articular
cartilage [6].
Split-line patterns are another characteristic of the collagen fiber
network. If pierced with an ink stained needle, the cartilage stretches
the resulting hole in a certain direction, shaping a line. In macroscopic scale, these lines show a pattern resembling the directions in
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which the collagen fibers are aligned along the surface [64].
2.5.3
Non-fibrillar part
Proteoglycans
The proteoglycans can be divided into two major classes: large aggregating molecules (aggrecans) and smaller proteoglycans including dEcoRIn, biglycan and fibromodulin [6]. Cartilage also contains large non-aggregating proteoglycans. They may represent degraded aggrecans as they resemble aggrecans in structure and composition [6]. Aggrecan molecules take up most of the interfibrillar
space in the cartilage matrix [6]. Large aggregating proteoglycans
take approximately 90% of the proteoglycan mass, with large nonaggregating proteoglycans taking 10% and small nonaggregating
proteoglycans approximately 3%. In articular cartilage, majority of
the aggrecans associate noncovalently with hyaluronic acid and link
proteins to form proteoglycan aggregates [6, 58].
Proteoglycans are large macromolecules with a protein core and
one or more glycosaminoglycan chains. These chains are long, unbranched polysaccharide chains consisting of repeating disaccharides that contain an amino sugar [6, 58]. Each disaccharide unit
has at least one negatively charded carboxylate or sulfate group so
the glycosaminoglycans form long strings of negative charges. Proteoglycans and noncollagenous proteins are either bound or mechanically entrapped within the collagen network [6]. Proteoglycan
content is lowest in the superficial zone and increases as a function
of cartilage depth, the highest concentration being in the deep zone
near the calcified cartilage [6]. The concentration of proteoglycans
varies also with patient’s age and health [6].
The negative charges attract cations in the tissue fluid while repelling other negative charges and negatively charged molecules
[6]. The ionic inbalance in the tissue fluid causes swelling in cartilage, counterbalanced by the tensile resistance of the collagen network. Proteoglycans mainly contribute to fluid flow in cartilage [5]
(although the collagen network also contributes [65–67]) and stiff-
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ness in mechanical equilibrium [68].
Chondrocytes
Chondrocytes are the only cell type that exists in articular cartilage [6]. Occupying only approximately 1% of the volume of adult
human articular cartilage, chondrocytes are highly specialized cells
that regulate the macromolecular content of articular cartilage [6].
Having all the organelles necessary for matrix synthesis, chondrocytes synthesize various macromolecules, including proteoglycans.
Chondrocytes organize the collagens, proteoglycans and noncollagenous proteins and glycoproteins into a complex, organized cartilage structure [6]. The cells respond to changes in the matrix
composition [6] as well as external stresses. Chondrocytes are surroundend by a pericellular matrix and do not form direct cell-to-cell
contact with other chondrocytes [6]. The pericellular matrix has a
high concentration of proteoglycans and also contains noncollagenous matrix proteins and collagens (mainly type VI collagen [69]).
The uppermost layer of superficial zone is void of chondrocytes.
Just below the uppermost layer, chondrocytes have a flattened ellipsoid shape and orient themselves parallel to the surface just like
collagen fibers. In this layer, the chondrocytes synthesize matrix
that has a high concentration of collagen and a low concentration
of proteoglycans relative to the other cartilage zones [6, 58]. In the
middle zone, the chondrocytes take a spheroidal shape and synthesize a matrix that has larger diameter collagen fibrils and higher
concentration of proteoglycans. However, the water and collagen
concentrations are lower than in the superficial zone [6]. In the deep
zone, the chodrocytes are aligned in columns that run perpendicular to the surface [58]. The rate at which chondrocytes synthesize
appears to be in response to the structural needs of the cartilage
matrix, possibly including the loading of the cartilage detected by
the cells [6,58]. In adults, the repairing capability of chondrocytes is
very limited. Therefore they are unable to repair damage induced
to the cartilage due to overweight or abnormal loading. Therefore
it would be crucial to prevent any damage to the cartilage.
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2.5.4
Biomechanics
An essential part of the mechanical response of the articular cartilage is the dynamic between swelling of proteoglycans and the
constraints the collagen fiber network exerts on the swelling [70].
The response to long-term loading is also tied to the fluid flow
through cartilage. Under impact loading, cartilage is very stiff (but
softer than meniscus) and behaves as an incompressible, elastic material because the fluid has no time to flow and collagen fibers are
stretched [70]. At equilibrium, the aggregate modulus of articular cartilage is typically in the range of 0.5 − 0.9 MPa and Young’s
modulus in the range of 0.45 − 1 MPa [6, 71]. These equilibrium
properties are primarily controlled by proteoglycans. Permeability
ranges between 10−15 and 10−16 m4 /Ns [70].
Cartilage can withstand mechanical contact stresses of 15 to 20
MPa during daily activities such as walking or climbing stairs.
These stresses, experienced over short time periods of less than
a second, can lead to small cartilage compressive strains of about
1 − 3 %. During long term loading, the stresses can be as high as
3.5 MPa and strains as high as 35 − 45% [6]. Cartilage loading is
necessary: immobilization or reduced loading can cause substantial
decreases in matrix synthesis and content, and result in softening
of the tissue. On the other hand, high impact loads or strenuous
exercise loading can cause cartilage degeneration [6, 72].
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3 Knee joint disorders and
their evaluation
3.1
JOINT DISORDERS AND OSTEOARHRITIS
Knee joint disorders are a collection of trauma-induced disabilities, defects acquired at birth as well as diseases. Common traumainduced disorders include ACL rupture and meniscus damage, both
of which are often present in the damaged knee [73, 74]. Meniscal
lesions are very common, with annual incidence of 66 reported per
100,000 inhabitants in the United States [75] and 9 or 4 (male, female respectively) per 10,000 in Denmark [76]. Sports are involved
in more than a third of all cases. These injuries usually involve
cutting or twisting movements, hyperextension or actions of large
forces [41]. Meniscal tears are accompanied by ACL tearing in over
80% of cases [73, 74]. Natural defects include knee malalignment, a
condition where a substantial portion of body weight is loaded on
either lateral or medial side of the knee. Malalignment is associated
with osteoarthritis (OA), both with the development and progression [77]. The most common knee joint disease is osteoarthritis,
which can either develop in its own or post-traumatically, e.g. as a
result of the aforementioned disorders. Out of these knee joint disorders, the focus of this thesis is on ACL rupture and osteoarthritis.
3.1.1
ACL rupture and reconstruction
With over 250,000 incidents in the US every year, the ACL rupture
is one of the most common injury types [78]. The vast majority of
these injuries are sports related and concern active 15 to 44 year-old
people [79]. A knee with ACL rupture becomes less stable with increased tibial translation in the anterior direction and increased tibial rotation in the interior direction [80,81]. Furthermore, this instability may cause clinical symptoms such as meniscal tears [82] and
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damage to articular cartilage [83]. In fact, ACL deficiency greatly
increases the risk of OA in the knee [15–17, 84–86], especially if
meniscal injury is also present [16, 82, 85].
ACL reconstruction is a surgical technique in which a graft tissue is harvested either from the patient (autograft) or a donor (allograft) and used to replace the severed ligament [87]. The graft is
harvested either from central patellar tendon or from gracilis and
semitendinosus tendons [86–89]. A meta-analysis showed that the
choice of graft has no significant effect on the outcome [89]. Two
common techniques are used: the single bundle and double bundle
reconstruction method. In single bundle reconstruction a tunnel is
drilled through both femur and tibia. The graft is inserted through
the tunnel, tightened and fixed with special screws. Double bundle
reconstruction mimics the AM and PL bundles of a healthy ACL
by using two bundles made from the harvested graft [87]. It has
been hypothesized that the anatomical resemblance would result
in reduction of graft failures [90]. Single bundle reconstruction is
still the default technique [91], but the double bundle technique
is becoming more common. Despite its increasing popularity, in
a meta-analysis double bundle was shown to yield no clinically
significant differences in joint laxity compared with single bundle
technique [87]. Unfortunately, the risk of OA is still increased in the
ACL reconstructed knees compared with healthy knees [86, 92–95].
3.1.2
Osteoarthritis
Osteoarthritis (OA) is a degenerative joint disease in which articular cartilage starts to degenerate and eventually wears away, causing pain and limiting joint mobility [6]. Although the exact cause
of OA is not known, overloading of the cartilage has been shown to
substantially increase the risk of OA [96,97]. The disease progresses
in three overlapping stages: cartilage matrix damage or alteration,
chondrocyte response to tissue damage, and the decline of the chondrocyte synthetic response and progressive loss of tissue [98–100].
In the first stage, the collagen architecture starts to disorganize,
along which the macromolecular framework of the cartilage matrix
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is disturbed or altered at the molecular level, and the water content
rises. Usually the proteoglycan concentration decreases in the superficial layer [98–101]. These factors increase the permeability of
cartilage and decrease its stiffness [3, 6].
In the second stage, the chondrocytes detect the tissue damage
and react to it by changing their anabolic and catabolic activity. The
repair response, or increased synthesis of matrix macromolecules,
may last for several years and in a very few instances, restore the
tissue. Although rare, some studies have reported that altering the
joint’s mechanical enviroment, e.g., by osteotomy can stimulate the
restoration of an articular surface [102–104]. However, a failure
to do so results in the third stage, in which the loss of articular
cartilage progresses and a decline in chondrocytic activity is observed [6]. The cartilage starts to crack and eventually wears away.
As the cracks grow deeper, the superficial tips of the fibrillated cartilage tear and fragments of the cartilage are released into the joint
space [6]. Simultaneously, enzymatic degradation of the cartilage
matrix further reduces the cartilage volume further [105, 106]. Also,
extensive bone remodeling and sclerosis takes place in the subchondral bone [3], as well as the formation of fibrous, cartilaginous and
bony prominences called osteophytes [6].
Symptoms of OA include joint pain, restriction of joint motion, crepitus with motion, joint effusions and deformity [6]. Most
common occurrences of OA are in the foot, knee, hip, spine and
hand joints [107]. Even though OA concerns all tissues of the
synovial joint, including articular cartilage, synovium, subchondral
and metaphyseal bone, joint capsules, ligaments and muscles, the
primary changes occur in articular cartilage [101, 108].
3.2
IMAGING OF JOINT DISORDERS AND OSTEOARTHRITIS
The knee joint condition and health of cartilage and other tissues
can be determined invasively or non-invasively. Arthroscopy is an
invasive method in which the joint is examined from the inside.
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The health of the cartilage can be assessed by palpation, indentation or by inserting a probe with a catheter inside into the knee
cavity of the patient. The probe can be a camera to image the surface of cartilage or, possibly in the future, an ultrasonic tranducer,
allowing the surgeon to image the inner structure of the cartilage.
However, arthroscopy carries the usual downsides of invasive techniques, such as a high cost and risk of infections. Therefore, noninvasive techniques such as radiography (X-rays) and MRI are preferred. It should also be noted that due to the invasive nature of
arthroscopy, it is never conducted as the first means to assess the
state of cartilage. On the other hand, the knee is thoroughly inspected arthroscopically before an ACL reconstruction [88, 109, 110]
or in case of chondral or meniscal injury [109].
3.2.1
Radiography
Radiography is still the predominant imaging technique for the
structural assessment of OA [111–113]. Traditional x-rays are unable to image the cartilage due to its similar attenuation coefficient
with the synovial fluid (Figure 3.1). However, OA can be detected
indirectly by the assessment of osteophytes, subchondral sclerosis,
subchondral cysts, and joint space narrowing [112]. In the standard
procedure, the patient stands on both feet in front of a vertically
tilted x-ray tube and the knee is imaged in coronal plane [114]. The
image is scored based on predetermined criteria such as joint space
narrowing, osteophyte size and level of bone attrition [115]. Different features need to be studied with equal importance, which is
best done by directly measuring the distribution and size of each
feature [116]. The advantages of radiography include low cost and
availability [112, 115, 117, 118].
3.2.2
Magnetic resonance imaging
In evaluation of articular cartilage defects, magnetic resonance imaging (Figure 3.1) is superior to radiography as it is able to assess the
health and thickness of the cartilage directly [119–121]. In addition
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Figure 3.1: Imaging of the knee joint using X-ray or fluoroscopy, contrast enhanced CT,
and MRI.
to cartilage lesions, MRI is also used for the assessment of meniscal
tears [122] and ACL ruptures [123, 124]. Generally, the MR signal
can be weighted by proton density (which relates to water in the
tissue), T1 or T2 by choosing TR and TE conveniently [125]. While
there are dozens of pulse sequences, the most commonly used for
clinical cartilage imaging are based on T2-weighed fast spin-echo
(FSE) [126] and gradient-recalled echo (GRE) sequences [127] or
proton density weighting [128], with or without fat suppression.
Fast-spin echo sequences use refocusing 90◦ pulses that allow highresolution images to be acquired in a very short time period. The
multiple refocusing pulses produce a magnetization transfer effect
in the articular cartilage, which decreases its signal intensity. This
phenomenon does not occur in the synovial fluid, which enables
a sharp contrast between cartilage and synovial fluid as well as
improves the conspicuity of chondral effects [129]. However, the
refocusing pulse cancels the effect of field inhomogeneities, which
are desired in T20 images.
In GRE sequence the signal is refocused without cancelling the
effects by applying two gradient pulses: first dephases the magnetization proportionally to its time integral, and the second rephases
it [130]. In proton density weighting, the signal is proportional
to the water content, which decreases from surface to the deeper
layer [131]. Fat suppression is a method that allows the cartilage
to show up bright against dark bone. Fat suppression is based on
T20
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the inherently different resonance frequencies of protons in water
and fat [131, 132]. When a presaturation pulse is applied to this
frequency, protons are saturated, which results in a lower signal
compared with the other tissues [133]. While the images without
fat suppression are accurate, the fat suppression allows the detection of changes in the subchondral bone marrow signal [129]. Novel
MRI methods allow the structural assessment of articular cartilage,
e.g. collagen architecture with T2 weighted MR imaging [134, 135]
or fixed charge density distribution with 23 Na MR imaging [136].
3.3
MOTION ANALYSIS
Although a myriad of activities involving the knee joint are performed daily, the two most common ones are standing and walking (gait). Simulation of standing is fairly straight-forward as only
the patient-specific stance has to be accounted for. Gait is far more
complex to simulate. Walking pattern varies from patient to patient [137] and is affected by knee joint disorders such as ACL rupture [138, 139] and OA [137, 140].
There are two approaches to motion analysis in terms of finding
individual muscle forces: forward and inverse dynamics. Forward
dynamics calculates the motion based on a predicted muscular activation. While being attractive in terms of modeling a myriad of
activities, the forward dynamics approach is a very computationally costly optimal control problem that requires a demanding optimization to make the model work [55, 141]. Inverse dynamics, on
the other hand, computes muscle activation based on known motion. This causes restrictions on the model, but makes it computationally more efficient. The computation is done by minimizing an
objective function, which is effectively the assumed criterion of the
recruitment strategy of the central nervous system, and is a function
of muscle forces. The minimization is done with respect to all unknown forces, i.e. muscle forces and joint reaction forces [141]. The
inverse dynamics method has some limitations, as it is sensitive to
inaccuracies in the various input parameters. The errors arise from
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estimating body segment parameters, joint parameters, skin movement artifacts, noise on skin-mounted marker data or force plate
calibration [142].
The most common method to capture the gait motion is by using
multiple cameras to capture the movement of retroreflective markers placed on anatomic landmarks. The markers are assigned an
arbitrary mass and the center of mass and the inertia tensor of this
cluster of points are calculated [143]. Using the inverse dynamics
method, the joint forces and moments are then calculated [144,145].
By using dozens of markers, the effect of skin movement under
one marker on the center of mass of the whole system is minimized.
The marker-based system allows a substantial reduction to the error
caused by the non-rigid body movement [143].
An alternative to the marker-based method is the dual fluoroscopy method, where two X-ray fluoroscopes are positioned nearly
perpendicularly to each other, so that the beams intersect at the location of the knee. The subject walks on a treadmill at a constant
pace while the knee is imaged. The projected images are matched
with a 3D geometry of the bones and the rotations and translations
are determined from a set point, usually the rotation center of the
femur, i.e. midpoint between the epicondyles [146,147]. The method
eliminates the error caused by skin movement, which makes it superior to the marker-based method.
3.4
LIMITATIONS IN CURRENT EVALUATION OF JOINT DISORDERS
Despite the advances in the diagnostics of joint disorders, some
limitations exist. Radiography has good specificity [112] and reproducibility [118] but low sensitivity for cartilage loss [112], especially
in the early stages of OA [117]. In order to acquire reproducible results, the positioning of the leg needs to be highly standardized and
ideally fluoroscopically verified [148, 149]. In addition, it has been
shown that radiobraphy is only able to produce relatively accurate
results in the medial compartment of the knee in the detection of
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OA [150], and it cannot differentiate between femoral and tibial cartilage loss. Although traditional radiography is unable to directly
detect changes in cartilage, contrast-enhanced computed tomography (CECT) and its clinical application, delayed CT arthrography,
have been shown to be able to diagnose cartilage injuries and degeneration [151, 152]. In addition, novel cone beam CT (CBCT)
scanners (Figure 3.1), dedicated to musculoskeletal imaging, are
able to image joints during weight-bearing and non-weight-bearing
modes [153, 154].
Even though MRI has exceptional specificity and sensitivity in
cartilage imaging when compared with radiography, the method is
not without several downsides. The biggest downside is its high
cost: novel MR scanners run at prices of 1-2 Me. Due to the relatively long TR times of some tissues, the image acquisition times
are long compared with radiography [120].
In motion analysis, the skin marker based method is prone to errors in the measurement of very small motions, such as the internalexternal rotation, abduction-adduction or mediolateral translation.
Even though the center-of-mass method reduces the error caused by
the movement of skin and soft tissues, it affects the measurement of
the small movements [143, 155, 156]. Dual fluoroscopy, on the other
hand, is a very expensive method as it requires two fluoroscopes
as well as proper facilities that meet the requirements for the use
of radiation. Due to the limited space, the activities the system is
able to measure are limited to treadmill gait, stair ascent/descent
and lunge. In addition, as the walking speed increases the error of
the measured motions also increases [146]. Dual fluoroscopy also
causes a high radiation dose on the subject.
These methods enable the assessments of OA symptoms and in
some cases, possible risks of OA, but are unable to estimate the
stresses the cartilage goes through during various types of loading.
For that purpose, simulation is needed.
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4 Computational modeling of
the human knee joint
4.1
KNEE JOINT MODELS
Computational modeling of the knee is a new branch of diagnostics that aims to assess the knee’s possible failure sites that could
be susceptible to damage, and consequently, OA. Musculoskeletal
modeling considers the human body as a framework of rigid bodies controlled by muscle activation. Using either forward dynamics
(muscle forces causing knee motion) or inverse dynamics (observed
knee motion is caused by muscle forces) the dynamics of a joint can
be determined [145]. These models, however, do not investigate the
stresses and strains in the tissue level. Finite element models (FE or
FEM for FE method) are used for that purpose. Knee joint models, specifically those utilizing the FE method, have been shown to
be able to simulate stresses in the human knee [157–159]. Earliest FEM studies date back to 1970s, when the method was used to
estimate stresses and strains in the femur [160, 161]. Bendjaballah
et al. (1995) [157] published one of the earliest articles featuring a
fully three-dimensional FE model of the knee joint, that featured
cartilages modeled as linearly elastic solids as well as menisci with
circumferential fibers. Guoan Li et al. (1999) [162] introduced their
model, that had a substantially more refined mesh and non-linear
springs representing ligaments. Articular cartilage was modeled
as linear elastic solid. Donahue et al. (2002) [158] developed a
knee joint model to assess the effect of bony deformations and constrained rotations on the contact behavior of articulating surfaces.
Again, the cartilage was modeled as linearly elastic. However, the
menisci were defined as transversely isotropic elastic to simulate
the anisotropy in menisci caused by the circumferential collagen
fibers.
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Peña et al. (2006) [163] included hyperelastic and transversely
isotropic ligaments with prestrain in their model. The model also
included patellar cartilage and patellar tendon. Cartilages were
once again modeled as homogeneous, linearly elastic and isotropic.
In addition to hyperelastic material, the ligaments are commonly
modeled as linear or non-linear springs [157, 164–166]. The first
model to use fibril-reinforced material for cartilage in a knee joint
geometry was Shirazi et al. (2008) [164], which was followed by
studies like Gu et al. (2011) [167]. Mononen et al. (2012) [168] even
included split-line patterns in their 3D knee joint model.
4.2
MATERIAL MODELS OF ARTICULAR CARTILAGE AND
MENISCUS
For articular cartilage and meniscus, multiple different material
models have been designed in the past, including linear elastic,
biphasic, transversely isotropic (poro)elastic to fibril-reinforced biphasic models. The linear elastic model can simulate contact pressures fairly well, but not much else. Linear elastic material is usually implemented into the knee model when the main focus is not
on cartilage or the main parameters being investigated are contact
pressures and small deformations. Considering those parameters,
the linear elastic model behaves similarly to the biphasic model
[169], which consists of a solid phase and a fluid phase [170]. The
biphasic linear elastic models of cartilage are able to simulate experimentally measured data from confined compression [170, 171].
However, in unconfined compression, the model cannot account for
the time-dependent stress-relaxation response of cartilage [172] and
has difficulty explaining creep indentation results for short time
periods [173]. Cohen et al. (1998) [174] presented a transversely
isotropic model that could fit the data from creep indentation and
unconfined compression experiments.
Two poroviscoelastic models have been introduced in literature:
first of which defines the solid matrix as viscoelastic in shear deformation [175], and the second both in shear and bulk deforma-
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tion [176]. The material was able to model lateral displacements
and reaction forces simultaneously. Also the modeling unconfined
compression and either indentation or confined compression was
possible at the same time. However, the model lacks the anisotropy
and compression-tension non-linearity of the cartilage, which likely
explains why the experiments could not be conducted simultaneously.
Transversely isotropic poroelastic model is able to simulate lateral displacements and realistic reaction forces, but not both at the
same time. The model is also not ideal for confined compression [177]. Conewise elastic model [178] has the same properties in in-plane compression and tension, but takes into account
the compression-tension non-linearity of the tissue into account,
while still being linear. However, like the transversely isotropic
poroelastic model, the conewise linear elastic model cannot account
for the lateral displacements and reaction forces at the same time
[177]. These models do not account for the non-linear compressiontension behavior of collagen fibers, which was later taken into account in fibril-reinforced models.
Fibril-reinforced biphasic models, namely Le Ping Li et al. in
1999 [179], Korhonen et al. in 2003 [68] (fibri-reinforced poroelastic,
FRPE), and Wilson et al. in 2004 [180, 181] (fibril-reinforced poroviscoelastic, FRPVE) and Li et al. (2004) again [182] (FRPVE), consider a fluid phase and a solid phase, which consists of a fibrillar
and non-fibrillar part. The fibril-reinforced biphasic model allows
the simulation of cartilage deformation simultaneously in multiple
loading conditions. Many reseachers have started to incorporate
the material in their 3D knee models [154, 164–168, 183–185].
4.2.1
Poroelastic biphasic theory
The poroelastic biphasic theory for porous materials was first published by Biot in 1941 [186] and later introduced for cartilage by
Mow et al. in 1980 [170]. It assumes an intrinsically incompressible, linearly elastic solid matrix and a separate, also incompressible
fluid phase. The only time-dependent feature in the theory is the
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fluid flow. The total stress σtot is given by the sum of solid matrix
stress σs and fluid stress σ f [170, 187, 188]:
σtot = σs + σ f ,
(4.1)
where σs and σ f are defined as
σs = −φs pI + σe ,
f
(4.2)
f
σ = −φ pI ,
(4.3)
σtot = σe + − pI ,
(4.4)
and therefore
where φs is solid volume fraction, φ f fluid volume fraction, p fluid
pressure, I identity tensor and σe effective elastic stress. The fluid
flow through a surface J is considered to follow Darcy’s law [187]:
∆p
,
(4.5)
h
where A is the surface area through which the fluid flows, k permeability of the solid, ∆p the hydrostatic pressure difference between
the sides and h the thickness of the perfused tissue. As the tissue deforms, the fluid flows out, which changes the porosity of
the solid phase. The permeability k is therefore considered to be
porosity-dependent [189]:
J = Ak
k = k0
1+e
1 + e0
M
,
(4.6)
where k0 is the initial permeability, e void ratio, e0 initial void ratio
and M material constant. Void ratio is the ratio of fluid to solid
material:
e=
nf
,
ns
(4.7)
where n f is the fluid fraction and ns the solid fraction.
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4.2.2
Transversely isotropic material
Given the highly anisotropic structure of articular cartilage and
meniscus, simple isotropic elastic or poroelastic material is unable
to capture most of the characteristics of the tissue. Transversely
isotropic model mimics the compression-tension nonlinearity by
assigning direction-dependent elastic moduli. In a transversely isotropic material, the effective stress in the solid is given by [190,191]:
  1
σ11
ET
νTT
σ22  
−

   ET
σ   − νTL
 33 
ET
σe =   = 
σ12  
0

  
σ13   0
σ23
0

− νETTT
1
ET
− νETLT
0
0
0
− νETTL
− νELTL
0
0
0
0
0
0
1
GL
1
EL
0
0
0
0
0
0
1
GL
0
0
0
0
0
0
1
GT


ε 11
 
 ε 22 
 
 ε 33 
 ,
 ε 
  12 
 
 ε 13
ε 23
(4.8)
where EL and ET are the longitudinal and transverse Young’s moduli, respectively, GL the longitudinal shear modulus, and νLT , νTT
and νTL are the Poisson’s ratios that give the strain in the longitudinal direction for a transverse stretch and transverse direction for
a longitudinal stretch, respectively. The transverse shear modulus
GT is defined as
GT =
ET
.
2 (1 + νTT )
(4.9)
Due to symmetry the following holds true:
νLT
ν
= TL .
EL
ET
(4.10)
Therefore in a transversely isotropic material, only five parameters
are independent: EL , ET , νLT , νTT and GL . If the material is biphasic, permeability k (equation 4.6) is also independent from other
parameters [191].
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4.2.3
Fibril-reinforced poroviscoelastic material
In fibril-reinforced poroelastic (FRPE) and poroviscoelastic (FRPVE)
materials, in addition to the fluid phase and solid phase, the solid
phase consists of a fibrillar part and a non-fibrillar part [191]. The
stress of the tissue (σtot ) is therefore a sum of the fibrillar stress (σ f ),
non-fibrillar stress (σn f ) and fluid pressure (p) [180, 181, 192]:
σtot = σn f + σ f − pI
N
= σn f + ∑ σi − pI ,
f
(4.11)
(4.12)
i
f
where (σi ) is the stress of a single fibril (σ f in the derivation below).
Fibrillar matrix
In the FRPE material, the stress of the fibrillar network (σ f ) is usually defined as [179]
σf =
1 ε 2
E ε + E0f ε,
2 f f
(4.13)
where ε f is the tensile strain of the fibrils, and Eεf and E0f are constants. Collagen fibrils are considered to have no resistance to compression, i.e. for ε < 0, E f = 0.
In the FRPVE material, the viscoelastic fibrils are modeled as
a system consisting of an elastic spring (with spring constant E0 )
parallel with a series of a non-linear spring (with constant Eε ) and
a dashpot (damping coefficient η) (Figure 4.1) [180, 181, 192].
The stress of one fibril is derived as follows:
σ f = E0 ε f + η ε̇ ν ,
= E0 ε f + η (ε̇ f − ε̇ e ) ,
(4.14)
(4.15)
where ε̇ denotes the time derivative of strain. In addition,
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Figure 4.1: Schematic depiction of the linear spring (with spring constant E0 ) parallel
to a series consisting of a non-linear spring (with constant Eε ) and a dashpot (damping
coefficient η). ε f denotes fibril strain, ε e and ε ν denote the strain experienced by the
non-linear spring and the dashpot, respectively.
r
σe
,
Eε
1
ε̇ e = √
σ̇e
2 σe Eε
εe =
(4.16)
, and
σe = σ f − E0 ε f .
(4.17)
(4.18)
Inserting equations 4.16, 4.17 and 4.18 into equation 4.15 yields the
final form for the fibril stress:


ηE0
η
 ε̇ f
σ̇ f + E0 ε f + η + q
σf = − q
2 (σ f − E0 ε f ) Eε
2 (σ f − E0 ε f ) Eε
(4.19)
Similarly as for the elastic fibrils, equation 4.19 is only true for
ε f > 0 (and σ f = 0 if ε f ≤ 0). The model used in this thesis
takes into account the primary (organized, arcade-like) and secondary (randomly organized) collagen fibrils [193, 194] by defining
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σ f ,p (stress of primary fibrils) and σ f s (stress of secondary fibrils) as
well as the depth-dependent fibril volume fraction ρz :
σ f ,p = ρz Cσ f
(4.20)
σ f ,s = ρz σ f ,
(4.21)
(4.22)
where C denotes the relative density of primary fibrils with respect
to the secondary fibrils.
Non-fibrillar matrix
The non-fibrillar matrix is considered as either elastic according to
Hooke’s law or Neo-Hookean hyperelastic material [192]. For an
elastic material, the stress is given by Hooke’s law:
σn f = Kεn f ,
(4.23)
where K is the stiffness matrix. For the Neo-hookean non-fibrillar
matrix, the stress of the nonfibrillar part σn f is given as:
σn f = K
2
ln( J )
G
I + (F · F T − J 3 I) ,
J
J
(4.24)
where J is the determinant of the deformation tensor F, K the bulk
modulus and G the shear modulus. K and G are defined as
Em
,
3(1 − 2νm )
Em
,
G=
2(1 + νm )
K=
(4.25)
(4.26)
where Em is the Young’s modulus and νm the Poisson’s ratio. Permeability k of the non-fibrillar matrix can be considered to be either
constant or porosity-dependent similarly as in equation 4.6.
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4.3
FINITE ELEMENT METHOD
Complex behavior of soft and hard tissues in the joint cannot be
solved analytically. Finite element method offers an iterative way
to approximate how a material behaves. In FEM, the object geometry is divided into small (finite) elements, which are given material
properties (see Materials and methods, page 43). The corners of these
elements are called nodes, which are typically given displacements
or forces (either fixed or several degrees of freedom). The solution is then interpolated between the nodes using polynomial base
functions, which may be linear, quadratic or higher order [195]. The
investigated material (see above) dictates the differential equations
needed to be solved.
Consider a simple, second order differential equation [196, 197]:
−u00 ( x ) + q( x )u( x ) = f ( x ) ,
0<x<0
(4.27)
u (0) = 0
(4.28)
u (1) = 0
(4.29)
The aim is to find an approximate solution in the form of
N
u( x ) ≈ uh ( x ) =
∑ αl φl (x) ,
(4.30)
l =1
where αl are unknown constants and φl are known base functions.
In the FEM, this is done by considering a residual function in the
form of
r = −u00 + qu − f ,
(4.31)
and requiring that r = 0 in a weak sense [196–198], e.g. we get
Z 1
0
r ( x )v( x )dx = 0 ,
(4.32)
where v is a test function. Equation 4.32 can be written in the form
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Kimmo Halonen: Validation and application of computational knee joint
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Z 1
0
(−u00 + qu − f )v( x )dx = 0 ,
(4.33)
and by using partial integration [196, 197]
Z 1
0
0 0
(u v + quv)dx −
.1
0
uv=
0
Z 1
f vdx .
0
(4.34)
Because v(0) = v(1) = 0, the middle term vanishes and we are
left with a variational problem (i.e. Galerkin method [196, 197, 199,
200]): how to find u so that
a(u, v) = F (v)
(4.35)
and
a(u, v) =
Z 1
0
F (v) =
Z 1
0
(u0 v0 + quv)dx ,
(4.36)
f vdx .
(4.37)
This variational problem is equivalent with equation 4.27, which
means that function u is the solution to the equation 4.27 only if u
is the solution to the variational equation (equation 4.35) and vice
versa. The solution to the variational equation is approximated
by inserting the approximation uh = ∑lN=1 αl φl (equation 4.30) and
choosing the test functions φj so that
a(uh , v j ) = F (φj )
⇔
Z 1
0
for all j = 1, 2, . . . , N
!
Z 1
1
1
0 0
α
φ
φ
+
q
α
φ
φ
dx
=
f φj dx.
∑ l l j ∑ l l j
l =1
l =1
0
(4.38)
(4.39)
Equation 4.39 can be rearranged as
1
⇔
∑
Z 1
l =1 0
36
Z
φl0 φ0j + qφl φj dxαl =
1
0
f φj dx
(4.40)
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Figure 4.2: One-dimensional example of the finite element method. The analytical solution (y = −3x2 + 3x, blue) of a differential equation and FEM approximation (green).
Elements (black, red) consist of linear base functions.
and written as
∑ k jl αl = bj
for all J = 1, 2, . . . , N
(4.41)
l
or
Kα = b ,
(4.42)
where
Z 1
(φl0 φ0j + qφl φj )dx ,
(4.43)
f φj dx ,
(4.44)
α = ( α1 , α2 , . . . , α N ) T .
(4.45)
K = k jl =
b = bj =
0
Z 1
0
By solving α = K −1 b, the final solution for the initial equation
4.27 in the investigated is the element approximation
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N
uh =
∑ αl φl .
(4.46)
l =1
The matrix K is called stiffness matrix and b the load vector [196,
199]. The equation 4.42 is solved numerically. The investigated area
is divided into small elements, defined by nodes. Each node has
a base function φl that is chosen so that it has the value 1 at the
node and 0 in other nodes. Because the base function has the value
1 at the nodes, equation 4.46 is reduced to just uh = ∑lN=1 αl at the
nodes. Base functions φl are usually chosen to be linear functions
(Figure 4.2) in order to make the matrix K sparse and therefore
minimize the number of integrals needed to be solved. In higher
dimensions, the investigated area is divided into triangles or quadrangles (in two dimensions) and tetrahedrons or hexahedrons (in
three dimensions) [196, 198].
A base element is transformed into the investigated element by
making a variable substitution. During this substitution, the base
function of the investigated element is transformed into the base
function of the base element, e.g. [0, 1]. Using a numerical integration
method, e.g. Gauss quadrature, the solutions can be calculated for
the base element, to which the abritrary element was transformed
into [196]. The precision of the solution is controlled using convergence criteria for different parameters [200].
4.4
MODEL VALIDATION AND APPLICABILITY
Before application of any biomechanical model, there has to be
model validation or verification [201]. The biomechanical behavior
of tissue level model is typically validated using in vitro or in situ
tests. Generally, the model is first applied to cartilage plugs harvested from human cadavers or animals (such as bovine, porcine,
rabbit) [202]. Typical in vitro experimental protocols include unconfined compression [172, 175, 203–205] and confined compression
[175, 188, 202, 204, 206, 207]. In unconfined compression, the surface and bottom of the plug is fixed and the plug is compressed,
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allowing the cartilage to expand at the sides [172, 203–205]. In confined compression, the cartilage is not allowed to expand but has
to deform in a confined space [202, 206]. Typical test protocols include creep and relaxation tests [188, 202–207]. Other in vitro tests
include optical measurement of deformation either by observing
fluoroscopically stained chondrocytes [207] or the expansion of the
cartilage plug [208].
In situ tests are conducted without disturbing the cartilage structure and without removing cartilage from bone. Indentation is an
example of an in situ test [175, 204, 209–211]. In indentation testing
the tip of a probe is pressed againt the cartilage, while the probe
measures the force at which the cartilage resists compression. The
FRPVE material used in this study has been validated in several
studies using unconfined and confined compression data as well as
indentation testing [175, 180, 181, 192].
Relevant to this thesis, in vivo tests can be conducted with a
patient or a healthy test subject. Non-invasive in vivo tests include
MRI, CT, motion analysis and fluoroscopy. Tissues and bones in the
subject’s can be segmented from MR and CT images and the simulated deformation of articular cartilage can be compared with those
observed in CT/MR images. The gait motion of the test subject
as well as forces and moments can determined in a motion laboratory. The subject’s gait can then be simulated using the forces and
moments as input, and compare the resulting rotations and translations to those observed during the motion analysis. A validated,
patient-specific model could help assess the possible risk sites in
cartilage associated with alterations to the knee by surgical operations such as ACL reconstruction. This new diagnostic tool could
provide surgeons with a means to assess the outcome of surgical
operations before and after the procedure.
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5 Aims
In this thesis, the FRPVE material is implemented into 3D models of
knee joints. Depth-dependent characteristics of articular cartilage,
including PG and collagen distribution along with collagen fiber architecture, are incorporated into the model. The process towards a
realistic model starts from a methodological study with motion data
obtained from literature, and evolves into a more patient-specific
model with complex knee joint geometry and force and moment
driven input data. The model is validated against experimental
imaging and motion analysis data, and applied to assess the outcomes of various ACL reconstruction techniques.
The specific aims of this thesis are:
1. To investigate depth-dependent stresses and strains in articular cartilage during simulated gait and under static loading
of the knee joint. Five models, ranging from homogeneous to
highly depth-dependent characteristics are compared.
2. To measure in vivo deformation of articular cartilage using
cone beam CT and compare them to the simulated strains in
the model.
3. To implement the patient-specific forces and moments acting
on the knee and patella. The depth-dependent stresses and
strains in the patellar articular cartilage during gait are studied.
4. To study the effect of ACL rupture and various ACL reconstruction techniques on the stresses and strains in the tibial
articular cartilage during patient-specific gait.
This study will take a step towards a new diagnostic tool for the
assessment of possible risks sites in the knee cartilage as well as to
assess the outcomes of surgical operations.
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6 Materials and methods
6.1
6.1.1
MODEL GEOMETRY AND PARAMETERS
Segmentation from MR images
In study I the left knee of a healthy 61-year-old male (weight = 100
kg) was imaged with a MR scanner (GE Signa Twin-Speed 1.5 T
clinical scanner, GE Healthcare, Milwaukee, WI, USA) using a fast
spoiled gradient echo sequence (TR = 26.7 ms, TE = 6.7 ms, flip
angle = 20◦ , slice thickness = 1.5 mm, matrix size = 512 × 512, inplane resolution = 0.27 mm). In studies II-IV, the imaged subject
was a healthy 28 year-old male (weight = 82 kg), whose left knee
was imaged using a clinical 3.0 T MR scanner (Philips, Best, The
Netherlands) (Figure 6.1). The pulse sequence was 3D fast spinecho (VISTA) with in-plane resolution = 0.5 mm, slice thickness =
0.5 mm, TR = 1300 ms, TE = 32.3 ms. The workflow from MR
images to the FE model is presented in Figure 6.1.
In all studies the femoral and tibial articular cartilages as well as
menisci and the insertion points for ACL, PCL, LCL and MCL were
segmented from the MR images using Mimics software (v.12.3 in
study I, v. 15.01. in studies II-IV, Materialise, Leuven, Belgium). In
studies III and IV, patellar cartilage and insertion points for quadriceps tendon and patellar tendon were also segmented. In study IV,
the full insertion sites of ACL and PCl were segmented from the
images with the help of two experienced orthopedists. In study I,
the segmented tissues were first imported into SolidWorks v. 2008
SP2.1 (SolidWorks Corp., Concord, MA, USA) and transformed into
a solid geometry before importing into Abaqus v.6.10-EF1 (Simulia,
Providence, RI, USA). In studies II-IV the segmented sections were
imported straight into Abaqus v.6.12-3 (Dassault Systèmes Simulia
Corp., Providence, RI, USA).
In study I the femoral and tibial cartilages (Figure 6.2) were
meshed with the element type C3D20RP for dynamic loading (i.e.
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Kimmo Halonen: Validation and application of computational knee joint
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gait) and C3D8 for mechanical equilibrium analysis (i.e. standing).
C3D20RP is a three-dimensional (3D) hexahedral continuum element with 20 nodes and reduced number of integration points (8
instead of the 20 in C3D20P) and porosity. C3D8 is a 3D hexahedral continuum element with 8 nodes and 8 integration points. The
menisci were meshed with the element type C3D20R, a 3D hexahedral continuum element with 20 nodes and 8 integration points
but no porosity. In study II C3D20RP was used for all tissues and
in studies III and IV the element type C3D8P (like C3D8 but with
porosity) was used for all tissues.
6.1.2
Material parameters
In all studies, femoral and tibial articular cartilages were defined as
FRPVE (Tables 6.1 and 6.2). In addition, patellar cartilage was implemented into the model as FRPVE in studies III and IV. Arcadelike collagen fiber architecture with split-lines was implemented
into the cartilages in all studies.
In study I, the depth-wise distribution of PGs was simulated
with the non-fibrillar matrix modulus Em , calculated from the data
of Schinagl et al. [207]. The depth-wise fibril volume density ρz was
obtained from the data of Saarakkala et al. [60]. Fluid fraction was
also considered depth-dependent [2]:
n f = 0.8 − 0.15z ,
(6.1)
where z is the normalized depth of the articular cartilage (0 being
the surface and 1 the cartilage-bone interface). The complete list of
parameters used in study I is presented in Table 6.1.
In study I, the menisci were defined as transversely isotropic
elastic during the gait: the Young’s modulus was set as 20 MPa in
the axial and radial directions and as 140 MPa in the circumferential
direction [158, 212]. The in-plane and out-of-plane Poisson’s ratios
were set to 0.2 and 0.3, respectively, and in-plane shear modulus
was 57.7 MPa.
In study II-IV, the menisci were defined as FRPE (Table 6.2).
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Figure 6.1: Summary of the methods used in studies I-IV.
The direction of the collagen fibers were defined as circumferential
at all depths of the menisci due to the number of depth-wise element layers: assigning radial or randomly oriented fibers would
have exaggerated the thickness of the radial layer, which is only
150 − 200 µm thick [213]. The list of material parameters used in
studies II-IV are listed in table 6.2.
No ligaments were included in the model of study I. Instead,
the effect of muscles and ligaments was included in the gait input,
which used rotation, translation and axial force data taken from
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Figure 6.2: Development of finite element models and meshes from study I to study IV.
literature [147, 214], as well as during long term standing (mechanical equilibrium). In studies II and III the ligaments were modeled as linear springs with the following stiffness k s : 201 Nmm−1 ,
258 Nmm−1 , 114 Nmm−1 and 134 Nmm−1 for ACL, PCL, LCL and
MCL, respectively [37]. In study IV, non-linear spring elements
were used for the ligaments in order to cause a prestrain of 5%
for ACL and PCL and 4% for LCL and PCL [215], respectively, at
0 mm displacement. In studies III and IV, the quadriceps tendon
and patellar tendon were also defined as a set of linear springs
with a combined stiffness of 545 Nmm−1 and 475 Nmm−1 , respectively [216]. In those studies, the LPFL and MPFL were modeled using truss elements without compressive stiffness. The elastic mod-
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ulus was defined as 17 MPa for LPFL and 19 MPa for MPFL [217].
Poisson’s ratio was set as 0.499 for both.
The bones were considered rigid in all studies. Four anchor
points (simulating the meniscal attachments) were defined, one for
each meniscal horn, and a set of linear springs with a total stiffness
of 2000 Nmm−1 [158, 212]. In study II, because the lateral anterior
horn was observed to nudge anteriorly when the load was applied,
a non-linear spring in the lateral anterior horn was used to replicate
this translation.
6.1.3
Boundary and loading conditions
All models consisted of three fundamental modeling phases or steps
(not to be confused with the physical step of gait): in the first step
(duration = 0.1 s), the articulating surfaces were brought into light
contact. In Abaqus, in order to achieve convergence a direct contact between two surfaces has to be first introduced using displacement instead of forces. Then, in step two (duration = 0.1 s) the
femur is rotated into the position the knee is at the beginning of
gait (as opposed to the initial position the knee was during MR
imaging). Simultaneously, the joint forces acting on the joint are
implemented. Finally, in step 3 (duration varies depending on the
type of simulation), the time-dependent forces, moments, rotations
and/or translations are applied. Depending on the type of simulation, either ’soils’ option or ’static’ option was used for the step for
time-dependent or equilibrium analysis, respectively.
The forces, moments, rotations and translations of the knee were
applied through a reference point determined in the midpoint between the epicondyles of femur (also known as the rotation center,
Figure 6.2) [219]. This was done by coupling the cartilage-bone interface to the reference point.
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Model 1
0.46
0.47
673
0.42
947
1
1.74
7.1
0.8 − 0.15z
12.16
Parallel
to surface
Arcing
Perpendicular
to surface
Parallel
to surface
Arcing
Model 5
0.11 − 0.84
0.46
673
0.42
947
0.89 − 1.16
1.74
7.1
0.8 − 0.15z
12.16
Parallel
to surface
Arcing
Perpendicular
to surface
Model 4
0.46
0.46
673
0.42
947
0.89 − 1.16
1.74
7.1
0.8 − 0.15z
12.16
Parallel
to surface
Arcing
Perpendicular
to surface
Model 3
0.11 − 0.84
0.46
673
0.42
947
1
1.74
7.1
0.8 − 0.15z
12.16
Perpendicular
to surface
Model 2
0.46
0.46
673
0.42
947
1
1.74
7.1
0.8 − 0.15z
12.16
Table 6.1: Material parameters for the FRPVE material used in different models in study I [2, 60, 67, 180, 181, 207, 218]. Em =
non-fibrillar matrix modulus, E0 = initial fibril network modulus, Eε = strain-dependent fibril network modulus, νm = Poisson’s
ratio of the non-fibrillar matrix, η = damping coefficient, k0 = initial permeability, M = material constant for void ratio dependent
permeability, n f = fluid fraction, z = normalized depth, C = density ratio of primary fibrils to secondary fibrils.
Parameter
Em (MPa)
E0 (MPa)
Eε (MPa)
νm
η (MPas)
ρz
k0 ( × 10−15 m)4 /Ns
M
nf
C
Fibril orientation
- superficial zone
- middle zone
Parallel
to surface
Parallel
to surface
Parallel
to surface
Homogeneous, with collagen fibers parallel to surface at all depths
Arcade-like collagen fibers
Arcade-like collagen fibers, depth-dependent PG distribution
Arcade-like collagen fibers, depth-dependent fibril volume density distribution
Arcade-like collagen fibers, depth-dependent PG and fibril volume density distribution
- deep zone
Model 1:
Model 2:
Model 3:
Model 4:
Model 5:
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6.2
6.2.1
SIMULATIONS
Effect of depth-wise tissue characteristics
In study I, the effects of depth-wise characteristics of the FRPVE
cartilage material were studied during dynamic loading (gait) and
at mechanical equilibrium (long-term standing). Five models with
different depth-wise properties were created:
1. Homogeneous model with collagen fibers parallel to surface
at all depths
2. Inhomogeneous model with arcade-like collagen fiber architecture
3. Inhomogeneous model with arcade-like fibers and depth-wise
PG distribution
4. Inhomogeneous model with arcade-like fibers and depth-wise
fibril volume density distribution
5. Inhomogeneous model with arcade-like fibers and depth-wise
PG and fibril volume density distributions
Femoral and tibial cartilages were meshed to have four element
layers (layer 1 representing the superficial zone, layer 4 the deep
zone near cartilage-bone interface), and the PG [207] and fibril volume density [60] distributions were averaged at their respective
bulk depths and implemented into the corresponding element layer
(see Table 6.1 for the exact values). The fibril volume density distribution was normalized so that the average of the values in all
four element layers was 1 (same as the homogeneous fibril volume
density in models 1-3). Maximum principal stresses, strains, pore
pressures and contact pressures were evaluated during gait. Von
Mises stresses, axial strains and pore pressures were determined in
the contact area at different depths during the first peak force of
gait, while Von Mises stresses and axial strains were determined at
equilibrium.
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Finally, a parametric study was done on the PG and fibril volume density distributions (Table 7.1) to emphasize the effect of
these distributions in extreme cases. The gradient of fibril volume
density distribution was allowed to vary from 0.89 in the surface
all the way to 10 in the deep zone, while Em was allowed to vary
from 0.11 MPa in the surface to 10 MPa in the deep zone. Again,
the depth-wise Von Mises stresses, axial strains and pore pressures
(only during gait) were determined at the contact area.
In study III, the effects of collagen fiber architecture was investigated by creating three models (Figure 6.3):
1. Homogeneous
2. Arcade-like
3. Early OA
The homogeneous and arcade-like models were similar to models 1 and 2 in study I: in the homogeneous model, the fibers were
parallel to surface at all depths, while the arcade-like model had
superficial fibers parallel to surface, arcing fibers in the middle and
perpendicular fibers in the deep zone. The early OA model had
randomly oriented fibers in the superficial zone to mimic the deterioration of the collagen architecture observed in the earliest stages
of OA [6]. The split-line patterns were defined in the superioranterior direction according to Bae et al. (2007) [220]. Fibril strains,
compressive strains and maximum principal stresses in the patellar
cartilage were determined during the stance phase of gait.
6.2.2
ACL rupture and the effects of reconstruction techniques
The objective of study IV was to assess the outcome of ACL reconstruction in terms of knee joint motion and deformation patterns of
the tibial articular cartilage. The same mesh for femoral and tibial
cartilages as well as menisci was used as in study III, but patellar
cartilage was meshed more sparsely in order to improve convergence. For the healthy ACL, the AM and PL bundles were defined
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Figure 6.3: Finite element model used in study III. (a) Sagittal and coronal views of the
model. In order to account for the quadriceps force acting on the knee joint, a force of equal
magnitude was applied to a point coupled to the reference point (midpoint between the
epicondyles of femur). (b) Left: Different depth-wise fibril architectures used in the model.
Right: Split-line pattern in the patellar cartilage surface. Coronal view from the posterior
direction.
separately using the non-linear spring element SPRINGA. For the
PCL, five bundles were defined using the same spring elements: A,
C, PL, PO and PML. Six models were created:
1. Healthy ACL
2. ACL rupture
3. Single bundle reconstruction
4. Double bundle reconstruction
5. Single bundle, weakened graft
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6. Single bundle, less graft prestrain
The model with healthy ACL consisted of the normal knee joint
geometry (Figure 6.4), including the normal AM and PL bundles
of the ACL and their anatomical insertion sites. As the name implies, the model with ACL rupture had ACL completely removed.
Two ACL reconstruction techniques were simulated: single bundle
and double bundle techniques. In both models insertion sites of
the graft were positioned with the help of two orthopedists. The
diameter of the graft (and in double bundle technique, diameter of
a bundle) was approximately 6-8 mm. The grafts were modeled as
gracilis/semitendinosus grafts with a stiffness of 715 Nmm−1 [221].
Several studies [89, 222] have reported no significant differences between the outcomes of patellar tendon grafts and gracilis/semitendinosus grafts, therefore only gracilis/semitendinosus graft stiffness was used in the simulations. In order to study the effect of
graft stiffness and pretension, in the model with weakened graft the
graft stiffness was defined the same as the healthy ACL (201 Nmm−1
[37]). To study the effect of prestrain (and consequently, pretension), in the model with less graft prestrain the effect of post-operational graft loosening, as reported by [223], was simulated by reducing the prestrain of ACL graft from 5% [215] to 2%.
Reaction forces in the tibial cartilage-bone interface and maximum principal strains in the tibial surface were determined during
gait. In order to highlight differences between models, subtraction
images of maximum principal strains, fibril strains, pore pressures
and maximum principal stresses were created by subtracting the
values of the healthy joint model from those in other models. Finally, the mean values of these parameters in the contact area were
plotted as a function of time during the gait.
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- middle zone
- deep zone
Parameter
Em (MPa)
E0 (MPa)
Eε (MPa)
νm
η (MPas)
ρz
k0 ( × 10−15 m)4 /Ns
M
nf
C
Fibril orientation
- superficial zone
Tibial cartilage
0.106
0.18
23.6
0.15
1062
1
18
15.64
0.8 − 0.15z
12.16
Parallel
to surface
Arcing
Perpendicular
to surface
Studies II-IV
Femoral cartilage
0.215
0.92
150
0.15
1062
1
6
5.09
0.8 − 0.15z
12.16
Parallel
to surface
Arcing
Perpendicular
to surface
Circumferential
Circumferential
Circumferential
Menisci
0.5
28
0.36
1
1.25
5.09
0.72
12.16
Parallel
to surface
Arcing
Perpendicular
to surface
Studies III & IV
Patellar cartilage
0.505
1.88
597
0.15
1062
1
1.9
15.93
0.8 − 0.15z
12.16
Table 6.2: Material parameters for the FRPVE material used in different models in studies II-IV [2, 41, 67, 218, 224, 225]. The patellar fibril
orientation presented here is the healthy patellar cartilage model in study III. Em = non-fibrillar matrix modulus, E0 = initial fibril network
modulus, Eε = strain-dependent fibril network modulus, νm = Poisson’s ratio of the non-fibrillar matrix, η = damping coefficient, k0 = initial
permeability, M = material constant for void ration dependent permeability, n f = fluid fraction, z = normalized depth, C = density ratio of
primary fibrils to secondary fibrils.
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Figure 6.4: (a) Finite element model used in study IV. As with previous studies, the
bones are modeled as rigid. (b) Tibial insertion sites of healthy ACL (red) and healthy
PCL (blue). The attachments of double bundle reconstruction bundles are circulated and
labeled as AM (A) and PL (P). The attachment of single bundle reconstruction is in cyan.
Axial view from the superior direction. (c) Femoral insertion site of healthy ACL (red) and
attachments of double bundle reconstruction (A and P) as well as the single bundle (cyan).
Sagittal view from the medial direction. (d) Femoral insertion site of healthy PCL (blue).
Sagittal view from the lateral direction.
6.3
6.3.1
EXPERIMENTS - MODEL VALIDATION AND INPUT
Computed tomography arthrography
The aim of study II was to determine the in vivo deformation of articular cartilage in a knee joint using contrast enhanced CT arthrography (CTa) during long term loading and compare the strains to
the simulated strains in the FE model. An isotonic contrast agent
solution of ioxaglate-based Hexabrix® (53% of the total volume) and
distilled water (47% of the total volume) was prepared to match the
osmolarity of synovial fluid (300 mOsm/L) in the knee joint [226].
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A commercial cone-beam CT (Verity® , Planmed, Finland) with a
voxel size of 0.2 × 0.2 × 0.2 mm was used to image the left knee of
the subject. First, the knee was imaged with light contact (12.8 ± 2.8
of the body weight, BW) between the cartilages (referred to from
now on as reference stack), then immediately after introducing a load
of approximately half of body weight (47.1 ± 2.3% of BW). After
that the weight was held constant and the knee was imaged at 1,
5 and 30 min after the initial contact. Preliminary tests showed 30
min was the last time point in which the surfaces of the articular
cartilages were distinguishable. During the imaging, half of the
subject’s BW was suspended by harnesses attached to the surface
(Figure 6.5). The subject held a quick-release lever that allowed the
instantaneous increase of load from light contact to half of BW. The
force under volunteer’s foot was monitored in real time using a
custom-made Python program and Nintendo Wii Balance Board® .
The femoral and tibial cartilages as well as menisci were segmented from the CTa images (Figure 6.5) in Mimics v.15.01. The
cartilage-cartilage interface was determined to be in the halfway
point of the contrast agent film between articulating surfaces in
the tibio-femoral contact. The image stacks were manually coregistered in Analyze v.10.0 (Biomedical Imaging Sources, MN) by
rotating the stacks so that the edges of the tibia bone in the reference stack matched in all of the stacks at other time points of
creep. The local cartilage thicknesses were determined in Matlab v.
R2012a by calculating the closest euclidian distance between nodes
in the surface and cartilage-bone interface [119]. The mean strains
were calculated at each time point and compared to the model. In
addition, the displacement of the menisci during the creep was determined.
Similarly to study I, in study II the effect of material parameters on the creep response was investigated by varying the stiffness
of the collagen fiber network, non-fibrillar matrix modulus, permeability and fluid flow boundary conditions (Table 7.1). In the case
of fluid flow boundary conditions, the fluid was allowed to flow
through non-contacting surfaces in the reference model by defining
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pore pressure P = 0 at non-contacting nodes, and was inhibited in
the parametric study.
6.3.2
Motion analysis
Study III focused on validating the joint movement as well as investigating the importance of patella and quadriceps forces in the
simulation of knee joints. The aim was to first determine the subject’s gait pattern, then determine the forces and moments acting
on the knee and use them as input for the model. Analysis of the
subject’s gait was conducted in Department of Biology of Physical
Activity, University of Jyväskylä, Jyväskylä, Finland, and the multibody analysis in Laboratory of Machine Design, Lappeenranta University of Technology, Lappeenranta, Finland. The subject’s height,
weight, length of the leg and diameter of the knee and ankle were
measured. 34 retro-reflective skin markers were placed on anatomical landmarks according to the instruction of Plug-in Gait full body
model (Vicon, Oxford, UK). Four additional markers were placed
on the anterior side of the thigh, two markers on the anterior side
of the tibia, one marker to the medial knee joint line and one marker
to the patella. The subject walked along a 10 m track at self-selected
speed (1.7 m/s). A ten-camera system (Vicon T40, Vicon) and a
force platfrom (AMTI OR6-6, Advanced Mechanical Technology,
Watertown, MA, USA) were used to record marker positions and
ground force (GRF) data synchronously at 500 and 1500 Hz, respectively.
A multibody musculoskeletal modeling was conducted in Lappeenranta University of Technology using LifeMOD (LifeModeler,
San Clemente CA, US) virtual human modeling plug-in and general purpose MD Adams simulation software (MSC Software, Newport Beach, CA, US) [227–229]. From this data and analysis, knee
joint moments, translational forces, and corresponding rotations
and translations were acquired (Figure 6.1). In addition, quadriceps forces during the stance phase of gait were determined using
an inverse dynamics driven biomechanical modeling according to
Brechter et al. (2002) [230]. For this analysis, the moment arms of
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Em (MPa)
E0 (MPa)
Eε (MPa)
η (MPas)
ρz
k0 ( × 10−15 m)4 /Ns
Fluid flow
(non-contact surfaces)
Study I
Reference value
0.11-0.84
0.47
673
947
0.89-1.16
1.74
No
Max
0.11-10
0.89-10
-
Study II
Reference value
0.106
0.18
23.6
1062
1
18
Yes (P = 0)
Min
0.106
0.1
13.6
700
1e−6
No
Max
1
1
50
2000
1e6
-
Table 6.3: Parametric investigations of studies I and II. Em = non-fibrillar matrix modulus, E0 = initial fibril network modulus, Eε = straindependent fibril network modulus, νm = Poisson’s ratio of the non-fibrillar matrix, η = damping coefficient, k0 = initial permeability, and
ρz =fibril volume density.
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the patella and femur were determined from the MR images around
the epicondylar axis of femur, which is also the axis of knee rotation [231].
The final input for the FE analysis consisted of the extensionflexion rotation, varus-valgus and internal-external moments as well
as translational forces in axial, anterior-posterior and lateral-medial
directions. The rotations, moments and tranlational forces were implemented into the model as boundary conditions. The rotations
resulting from the moment and force input were compared to the
rotations measured in the motion analysis as well as the dual fluoroscopy data by Kozanek et al. (2009) [147]. In addition, the reaction
forces in lateral and medial tibial cartilages as well as at the surface
of the patellar cartilage were investigated.
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Figure 6.5: (a) Experiment setup in study II. The subject wore harnesses that suspended
50% of the body weight while standing on one leg. The force under the leg was monitored
in real time using Nintendo Wii Balance Board® and displayed on the laptop screen using
a custom made Python program. (b) Deformation in lateral tibial cartilage before the load
(’No contact’), immediately after application of the load (’Contact 0 min’) and after 30
minutes (’Contact 30 min’).
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7 Results
The most important results of studies I-IV are summarized in this
chapter. For details and rest of the results, see ’Original publications’.
7.1
7.1.1
MODEL VALIDATION AND PARAMETRIC STUDIES
Cartilage deformation in vivo
In the CTa measurements of study II, the medial meniscus stayed
nearly stationary during the experiment (Figure 7.1a). On the other
hand, the anterior horn of the lateral meniscus shifted in the anterolateral direction when the load was introduced. 80% of the in vivo
strains in the tibial cartilage were observed immediately after the
introduction of the load. However, cartilage continued to deform
up to the 30 minute time point (Figure 7.1b). Immediately after
loading the peak strains were 24% and 29% in lateral and medial
tibial compartments, respectively. At 30 minutes, the peak strains
were 30% and 39% in the lateral and medial compartments, respectively.
The first minute of the creep was simulated and the measured
mean strains in the contact area were compared with the simulated
ones (Figure 7.1c). The reference model slightly underestimated
the observed mean strains, while the other model with the reduced
fibril stiffness gave the best match. The parametric study showed
that the fibril stiffness shifted the creep curve the most (Figure 7.2),
while change in the non-fibrillar matrix modulus changed the slope
of the curve the most. In the 30 minute simulation with a load of
50 N, changes to fibril stiffness values still substantially affected the
creep curve: high fibril network stiffness reduced mean strains by
27% while low fibril network stiffness increased them by 11% at 30
min of creep. At 30 minutes, the increase in non-fibrillar modulus caused a reduction of 31% in the mean strains. Change in the
initial permeability and fluid flow boundary conditions (fluid ei-
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ther allowed or prohibited to flow through cartilage surfaces) had
minimal effect on the both short term and long-term strains.
Figure 7.1: (a) Position of the menisci during the experiment in study II. (b) Strains in
the tibial cartilage immediately after the introduction of a load of 50% BW, then 1, 5 and
30 minutes after that. The position of the menisci are marked with the colored lines. (c)
Average strains in the medial and lateral tibial cartilage surfaces.
7.1.2
Knee joint motion
In study III, the inclusion of patella and quadriceps forces caused a
substantial decrease in the range of internal-external tibial rotation.
The level of the internal-external rotation matched the measured
rotation well, and the shape of the internal-external rotation was
congruent with the literature data as well (Figure 7.3a-c). In the
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Figure 7.2: Parametric investigation in study II. Effect of collagen fiber network stiffness
(a), non-fibrillar matrix modulus (b), permeability (c), and fluid flow boundary conditions
(d) on the mean strains of tibial articular cartilage.
varus-valgus rotation, the patella and quadriceps forces showed a
minimal effect.
Quadriceps forces caused an increase of up to 160% in the total
tibial cartilage reaction forces during the first 20% of the stance
phase of gait (Figure 7.3d-e). Peak reaction forces in the lateral
and medial tibial plateaus were 860 N and 1700 N, respectively.
Between 50% and 100% of the stance, differences in the reaction
forces between the models were reduced. The combined peak tibial
reaction force at medial and lateral compartments was 2560 N (3.2 ×
BW), while the peak patellar reaction force was 688 N (at 20% of the
stance) (Figure 7.3f).
Figure 7.4 shows the tibial translations and rotations relative to
femur compared with data obtained from literature [147, 232, 233].
The data has been shifted to start from 0 for easier comparison.
The simulated translations are in accordance with the literature
apart from medial-lateral translation in the study by Kozanek et al.
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(2009), where the literature values are substantially lower during
the first 50% of stance and elevated during the last 50% of stance,
compared with the model. In the rotations, the curves from the
model follow the same trends as the literature data.
7.1.3
Effect of depth-wise tissue properties and OA
In study I, the arcade-like collagen fiber orientation in the knee joint
cartilage reduced maximum principal strains and contact pressures
in the cartilage surface during the whole stance phase of gait, with
the peak differences seen during the second peak force (80% of the
stance phase of gait), compared with the homogeneous model. The
Figure 7.3: Simulated, measured and literature values for the tibial rotations (a)-(c) in
study III. (a) Extension-flexion rotation. (b) Internal-external rotation. (c) Varus-valgus
rotation. Reaction forces in the (d) lateral tibial plateau, (e) medial tibial plateau and (f)
patellar cartilage surface.
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Figure 7.4: Simulated tibial traslations (a)-(c) and rotations (d)-(f) during the stance
phase of gait, compared with literature [147, 232, 233]. All literature values are averages
over many test subjects (Kozanek: n = 8; Li: n = 3; Barre: n = 19). The data has been
shifted to start from 0 for better comparison.
effect of both fibril volume density distribution and PG distribution
on strains and contact pressures was minimal during the dynamic
loading (gait). However, in mechanical equilibrium the depth-wise
distribution of PGs caused a substantial increase in axial strains at
the superficial zone and a decrease at the deep zone (Table 7.1). As
with gait, in equilibrium the effect of fibril volume density distribution on the axial strains was minimal.
The parametric study showed that an extreme, nonphysiological gradient in fibril volume density affected the tissue response
during dynamic loading, as the Von Mises stresses and Pore pressures were increased at all depths by up to +50%. The depth-wise
strains decreased substantially, especially in the deep zone near
cartilage-bone interface, where they decreased by up to −52%. In
equilibrium, the most extreme, non-physiological distribution increased the Von mises stresses in the deep zone. However, even
then the effect on axial strains in equilibrium was minimal. The
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depth-wise PG distribution showed the opposite effect: during dynamic loading, its effect on the stresses, strains and pore pressures
was again negligible, but in equilibrium, a more steep gradient increased depth-wise strains in the superficial zone by up to +16%
and reduced them in the deep zone by up to −86%.
In study III, the arcade-like collagen architecture substantially
increased maximum principal stresses (Figure 7.5), particularly in
the middle zone of the patellar cartilage, compared with the homogeneous model with collagen fibers parallel to surface at all depths.
The model with early OA changes (superficial fibrillation) showed
increased compressive strains in the superficial and middle zones
and decreased stresses and fibril strains especially in the middle
zone.
Figure 7.5: Maximum principal stresses at different depths of the patellar cartilage in
homogeneous (collagen fibers parallel to surface at all depths), inhomogeneous (arcade-like
fibers) and osteoarthritic models (randomly oriented fibers in the superficial zone). Study
III.
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Model 1:
Model 2:
Model 3:
Model 4:
Model 5:
Model 2
Gait Equilibrium
9.4
0.35
4.7
0.30
3.6
0.19
2.3
0.12
4.0
18.3
6.1
18.0
4.1
17.6
2.1
17.5
11.8
8.8
8.2
8.1
-
Homogeneous, with collagen fibers parallel to surface at all depths
Arcade-like collagen fibers
Arcade-like collagen fibers, depth-dependent PG distribution
Arcade-like collagen fibers, depth-dependent fibril volume density distribution
Arcade-like collagen fibers, depth-dependent PG and fibril volume density distribution
Mises stress (MPa) Layer 1
Mises stress (MPa) Layer 2
Mises stress (MPa) Layer 3
Mises stress (MPa) Layer 4
Axial strain (%) Layer 1
Axial strain (%) Layer 2
Axial strain (%) Layer 3
Axial strain (%) Layer 4
Pore press. (MPa) Layer 1
Pore press. (MPa) Layer 2
Pore press. (MPa) Layer 3
Pore press. (MPa) Layer 4
Model 1
Gait Equilibrium
11.0
0.28
9.2
0.56
8.1
0.39
5.5
0.26
2.3
18.8
5.5
16.6
3.1
15.9
1.5
15.5
13.4
10.7
10.2
9.8
-
Model 3
Gait Equilibrium
9.6
0.55
4.7
0.26
3.6
0.15
2.3
0.09
4.2
57.1
6.0
20.6
4.1
15.4
2.1
9.5
12.1
9.0
8.4
8.2
-
Model 4
Gait Equilibrium
9.5
0.34
4.5
0.30
3.5
0.19
2.4
0.13
4.4
18.4
6.1
18.1
4.1
17.6
2.0
17.4
12.0
8.9
8.4
8.2
-
Model 5
Gait Equilibrium
9.5
0.53
4.5
0.26
3.5
0.15
2.4
0.10
4.4
57.4
6.1
20.6
4.0
15.4
2.0
9.5
11.9
8.9
8.3
8.2
-
Table 7.1: Depth-wise comparison of Von Mises stresses, axial strains and pore pressures during the second peak force (80%) of gait cycle and at
equilibrium (load = 150 N) in study I. Values are averaged from the integration points of 5 elements located at the area with peak contact pressure. Layer
1 corresponds to the superficial zone, Layer 4 the deep zone near the cartilage-bone interface.
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7.2
ACL RUPTURE AND RECONSTRUCTION
In study IV, the ACL rupture caused an increase of up to 542% in
tibial anterior translation during the first 50% of the stance phase of
gait (Figure 7.6). The peak translation occurred during the heel
strike, while the lowest increase in translation was between the
ipsilateral heelrise and contralateral heelstrike. ACL rupture also
caused an increase in the lateral tibial translation as well as elevated internal tibial rotation. No difference in the translations and
rotations of the knee between the single and double bundle models
were seen. The model with the reduced ACL graft stiffness provided the best match with the healthy joint model, followed closely
by the model with the reduced pre-strain of the graft.
Figure 7.6: Simulated tibial translations (a)-(c) and rotations (d)-(f) with respect to femur
during the stance phase of gait (study IV). Subject-specific moment and force driven gait
was implemented into six models: healthy knee joint with ACL intact, with ACL rupture,
with single bundle ACL reconstruction, with double bundle ACL reconstruction, single
bundle ACL reconstruction with softer graft, and single bundle ACL reconstruction with
reduced graft pre-strain. Due to the input, the flexion-extension rotations are identical
accross all models.
During the first peak force of gait (20% of stance), the ACL rup-
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ture caused a shift in the contact area in the posterior direction
and consequently, increased strains in some areas and decreased
strains in others. The peak maximum principal strain was actually increased compared with the healthy knee joint model (17.8%
vs. 13.8%). However, the reaction forces as well as average contact
pressures, maximum principal strains, fibril strains, pore pressures
and maximum principal stresses calculated over the contact area
were all reduced compared with the healthy knee joint model (Figure 7.7). The maximum difference between the healthy joint model
and the model with ACL rupture was in average pore pressures,
which were decreased by up to 80%.
Both the single bundle and double bundle ACL reconstruction
techniques produced similarly elevated strains and stresses in the
tibial cartilage surface compared with the healthy knee joint model.
The maximum difference compared with the healthy joint model
was in the single bundle model, in fibril strains, which were increased by up to 79%. Maximum difference between the single
bundle and double bundle models was in 12% in the maximum
principal stresses. The models with the reduced ACL graft stiffness
and pre-strain produced stress and strain patterns most similar to
those in the healthy knee. A closer look at the mean contact pressures, strains and stresses showed that the model with the reduced
graft stiffness provided the best fit with the healthy ACL model:
the maximum difference between the healthy joint model and the
model with the reduced pre-strain was 37% in the average contact
pressures, and for the model with the weakened graft, the maximum difference was 10%, in average maximum principal stress.
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Figure 7.7: Average values at the contact area of the medial tibial compartment of a healthy
joint model, ACL rupture model and ACL reconstruction models in study IV. (a) contact
pressures, (b) maximum principal strains, (c) fibril strains, (e) pore pressures and (f)
maximum principal stresses in the medial tibial cartilage surface during the stance phase
of gait. The values are averaged at the contact area nodes of the healthy joint model as a
function of time.
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8 Discussion
Previous chapters described the fundamental theory and anatomy
behind the FE knee model and how the experiments (used to validate the models) and simulations were conducted, as well as the
results of these investigations. In the following sections, the meaning and significance of these results are discussed.
8.1
VALIDITY OF THE MODELS
In the CTa measurements of study II, the majority of cartilage deformation occurred during the first few seconds, but the cartilage
continued to slowly deform up to the 30 minute mark. This is consistent with the results of Hosseini et al. (2010) [234], who reported
similar in vivo creep response for cartilage. However, unlike Hosseini et al., who measured the cartilage thickness indirectly by determining the distance between bones, in this study the local tibial
cartilage thickness was assessed directly from tibial cartilage surface to cartilage-bone interface. The results suggest that, in a real
knee joint, the cartilage may never reach mechanical equilibrium.
During the experiment, only the anterior horn of the lateral meniscus moved from under the load when the 50% of BW was applied,
while the medial meniscus stayed nearly stationary. This is in accordance with earlier findings suggesting that the anterior horn of
the lateral meniscus is less susceptible to mechanical damage compared with the posterior horn of the medial meniscus [235].
The model was able to match the observed average strains surprisingly well, especially since the material parameters for the articular cartilage were obtained from bovine studies [2, 67, 224] and
thus were not subject-specific. Rather than pursuing the best fit, the
focus was on the mechanisms controlling the creep. The model was
also able to capture the translation of the lateral meniscus in the
anterior direction that was observed in the experiment.
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The simulated femoral rotations matched well with those observed in the motion analysis of study III. The simulated internalexternal rotations highlight the importance of including the patella
and quadriceps forces in moment and force driven models, as the
model with the patella produced a substantially better match with
the observed rotations. In knee joint models, if no quadriceps force
data during gait is available however, the results suggest a rotation
and translation based input should be used instead of forces and
moments. The inclusion of quadriceps forces caused a total peak
reaction force of 3.2 × BW through the tibiofemoral contact (at 20%
of the stance phase of gait), which is in accordance with the results
of Bergman et al. (2014) [236], who reported a force of 3.2 × BW at
20% of the stance phase of gait. The reaction forces in the patellar
cartilage surface were also consistent with those reported by Huberti and Hayes (1984) [237].
It is well known that ACL rupture causes a substantial increase
in anterior tibial laxity and internal tibial rotation at the beginning
of the stance phase of gait [80, 81]. This exact phenomenon was
seen in the model with the ACL rupture in study IV. In addition to
these increased motions, an increase in lateral tibial translation was
observed, which could possibly contribute to the increased peak
stresses and strains observed in the medial tibial plateau. Concerning the ACL reconstruction’s ability to restore knee motion close
to healthy levels, minimal differences between the single bundle
and double bundle ACL reconstruction techniques were observed,
which is in accordance with experimental results [87].
8.2
8.2.1
IMPORTANCE OF MATERIAL PROPERTIES
Static loading
Under physiological load, changes in the collagen fiber network
caused the most drastic change in the initial creep of study II. However, as the creep advanced, the effect began to diminish, which is
in accordance with studies suggesting that the collagen network
primarily controls the dynamic response of cartilage [5,68,209,238],
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shown here in the knee, to our knowledge, for the first time. Change
in the non-fibrillar matrix (simulating mainly the effect of PGs)
modulus altered the creep rate the most, although the effect was
substantially lower than the effect of the collagen fiber network, especially considering a 10-fold increase in the modulus in the parametric study. Due to excessive strains in the superficial zone, the
load was reduced to 50 N for the 30 minute simulation. The simulation showed that in the knee joint, the increased non-fibrillar
matrix modulus caused a substantial decrease in mean strains at
30 minutes. As the PGs have been shown to mainly contribute to
the equilibrium response of articular cartilage, the results were in
accordance with experimental laboratory studies [68, 209, 239].
Neither a change of 12 orders of magnitude to permeability nor
the prohibition of fluid flow out of the cartilage had an effect on the
creep during the first minute of creep, but both had a substantial
effect during the 30 minute simulation. In the knee, the vast majority of tibial cartilage surface is compressed by femoral cartilage
and menisci [240]. Due to this the pore pressure distribution was
uniform throughout the depth and width of the cartilage under the
contacting areas, causing the creep behavior to initially arise primarily from a redistribution of fluid within cartilage and collagen
viscoelasticity. A closer inspection revealed that only after 20 minutes of creep the fluid velocity increased substantially through the
free surfaces. The results suggest that fluid flow boundary conditions are not an important factor when considering models of short
term loading, which was also suggested by Gu and Li (2011) [167].
8.2.2
Gait loading
In study I, the gait cycle simulation emphasized the importance
of the arcade-like collagen architecture on the stresses and strains
in articular cartilage during dynamic loading. This is in accordance
with experimental studies reporting that the collagen network modulates the dynamic response of cartilage [5, 68, 209, 238, 239]. Based
on the results, the collagen architecture seems to be more important than the fibril volume density, which was shown to have a
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negligible effect during both dynamic and static loading. This is
most likely due to the low depth-wise variation [60], a point that
was highlighted by the parametric study: the fibril volume density
has a substantial effect on the stresses and strains during dynamic
loading, but only if implemented unrealistically into the model.
In the knee cartilage, the effect of PGs was shown to be almost non-existent during dynamic loading but substantial in static
loading, which is in accordance with the experimental laboratory
studies [68, 209, 239], suggesting that the PGs mainly contribute to
the equilibrium response of the cartilage. Varying the PG gradient
caused an increase in the superficial axial strains during static loading, which is a result from the increased stiffness of the deep zone.
The results suggest that when simulating the dynamic loading of
a knee joint, the arcade-like collagen architecture should be taken
into consideration. However, the depth-wise fibril volume density
and PG distributions may be omitted.
During gait, patellar cartilage undergoes substantial shear forces.
Results of study III suggest that the middle zone plays an important role in resisting shear forces in the patellar cartilage. This is
in agreement with experimental results suggesting that the depthwise collagen fiber orientation causes the depth-dependent shear
modulus and energy dissipation of cartilage, and that the middle
layer controls cartilage response to shear forces [63]. Compared
with the arcade-like model, the model mimicking fibrillation of collagen network in very early OA showed reduced fibril strains and
maximum principal stresses in the superficial and middle zones.
Consequently, compressive strains were substantially elevated in
those zones of the OA model. Results suggest that, during the
very early stages of OA, substantial changes in the patellar tissue
response occur during walking, and the changes are concentrated
on the middle zone. This is also consistent with experimental results [63], suggesting that altered energy absorption of shear forces
in the middle zone of the patellar cartilage may expose cartilage to
further damage and progression of OA.
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8.2.3
Optimization of ACL reconstruction techniques and graft
properties
In study IV, the ACL rupture model showed the same altered joint
motion that has been reported in clinical studies [80, 81]. ACL rupture model also showed a consistent trend of decreased mean reaction forces, stresses and strains in the medial tibial cartilage compared with the healthy joint model. However, the local stresses
could be increased or decreased. The elevated peak values in the
posterior medial tibial cartilage could expose the site to an elevated
risk of OA [241]. All ACL reconstruction models showed a movement pattern similar to the healthy joint model, with the single bundle model with weakened (softer) graft stiffness providing the best
match. Even though the single bundle ACL reconstruction model
produced marginally higher values than the double bundle ACL
reconstruction model, both the distributions and quantitative mean
values in reaction forces, stresses and strains were consistently and
similarly elevated in both models, compared with the healthy joint
model. This is again in agreement with the literature data [87],
suggesting that the choice of reconstruction technique may not determine the outcome of the reconstruction.
It is well known that patients with ACL deficiency have a high
risk of post-traumatic OA [15, 242]. Many mechanisms are thought
to contribute to the development of post-traumatic OA, including
the damage to articular cartilage and subchondral bone occurring at
the time of the ACL injury [243]. However, the results of this thesis
suggest that the change in contact area could also contribute to the
disease. Experimental studies show that in the knee, the stiffness of
tibial articular cartilage varies depending on the site. Specifically,
the cartilage is softest at areas that experience high loads, and stiffer
elsewhere, e.g. under the menisci [19, 244, 245]. The results indicate
that in cases where the ACL is not reconstructed, the forces the
cartilage goes through are lowered due to the lack of ACL, but the
contact area changes. This shift causes the stiffer areas of cartilage that are normally less loaded - to experience abnormal stresses due
to their differing mechanical properties, which in turn increases the
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risk of OA. On the other hand, in the case of ACL reconstruction,
the results show that due to the high stiffness of the ACL graft
(compared with the healthy ACL), the cartilage is still exposed to
elevated stresses. This, again, could increase the risk of OA, even
though the motion of the knee would be restored back to healthy
levels.
The best match with the healthy joint model, in terms of joint
motion, distribution and values of stresses, was provided by the
single bundle model with weakened graft stiffness. Though not as
good, the second best fit was with the single bundle reconstruction
with reduced pre-strain of the graft. To see if the double bundle
reconstruction technique would yield better results than the weakened single bundle with the modulated graft properties, an additional simulation was conducted with a weakened double bundle
graft. The model showed a good match with the healthy knee joint,
similarly as the weakened single bundle model. The results indicate that rather than the choice of technique, the graft stiffness and
pre-strain play a major role in restoring the function of the knee.
It is known that the graft loses some of its tension immediately
after the surgery, which results in increased laxity in the anteriorposterior direction [80]. According to a cadaveric study by Arnold
et al. (2005) [223] the graft loses 46% of its tension after 1500
extension-flexion cycles. The results of this study emphasize the
importance of the final tension the graft ends up with - therefore
it is beneficial for the function of the knee that the graft is initially
over-tensioned as it relaxes after the operation.
8.3
LIMITATIONS
Some limitations have to be noted. In studies I and II, the physiological forces exerted onto the joint caused excessive strains in the
superficial zone, which prevented the simulation of the full equilibrium (or 30 minutes static loading in study II). In study I the
’static’ option was used to simulate the equilibrium response. In
study II, because of this and the fact that 80% of the observed max-
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imum strains occurred during the first few seconds after the application of the load, only the first minute of creep was simulated
with physiological loads. To study the long-term effects of different
parameters on the creep, the 30 minute simulation was done with a
force of 50 N. The conclusions from the 50 N simulation were consistent with the conclusions drawn from the 1 minute simulation of
physiological loading - only the absolute values would differ.
In study III, while the level of the internal-external rotation (in
the model with the patella and quadriceps forces) matched the
measured ones, there were some differences in the shape of the
internal-external rotation. This is likely due to the limitation of
the camera-based motion capture method, which is prone to errors
arising from the skin and soft tissue movement [155, 156]. This effect is most prominent in the internal-external rotations that are, by
nature, very small. Therefore a fluoroscopy study by Kozanek et al.
(2009) [147] was included as a reference. The shape of the rotations
in the model with the patella matched the literature data well, differences arising likely from subject-specific factors. Furthermore, a
similar implementation of the gait data into the FE model as presented here was done recently [246].
It is well known that patients with a ruptured ACL adapt their
gait, specifically many develop a pattern called quadriceps avoidance [138,247,248]. Because the only a healthy subject was used, the
model does not take into account the altered forces and moments
after the incidence of ACL rupture. The reason is that it would be
difficult to conduct an experiment in which the subject is modeled
before and after undergoing a rupture and reconstructive surgery.
In study I, the effect of ligaments was implemented using rotation and translation based input obtained from literature [147]. Due
to this the knee motion was not subject-specific. However, because
the objective was to conduct a methodological study that focuses
on the depth-wise characteristics of articular cartilage and not a realistic simulation of gait, one can argue the input is sufficient. In
studies II-IV, the ligaments were modeled as linear springs instead
of solids, using ligament stiffnesses obtained from literature [37].
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In the static loading used in study II the use of linear springs is
justified due to the stationary nature of the simulation. However, in
gait studies (III and IV), the model may not represent the nonlinear,
viscoelastic properties of ligaments accurately [249]. However, the
joint motion observed during the motion analysis showed a good
agreement with the simulated joint motion. Further, as the focus
of studies III and IV was on the stresses the cartilages experience,
and not the ligaments, the decision to use linear springs to model
ligaments can be considered justifiable.
In all of the studies, only one subject was investigated. However, given the methodological nature of this thesis, the focus is on
validating the model and investigating the effects of different parameters (such as cartilage properties, quadriceps forces, patella)
on the model response before applying it for further clinical studies
with more subjects. Furthermore, the mechanisms investigated in
this thesis, which can only be studied through modeling, should
not depend on joint geometry or other variables. The exact values
of stresses and strains would vary from subject to subject, but the
conclusions would not change [250].
Finally, despite all the advantages FE modeling of the knee joint
brings, there are currently several issues that prevent its use in clinical practice. The crux of the problem is time, as all stages of modeling are time-consuming, limiting their use in clinical applications.
All modeling begins from acquiring the geometry, which is typically done by manually segmenting the tissues from MR image
stacks. For clinical practices, the segmentation needs to be automated. The next step, meshing, is also very time consuming and
difficult to automate if using hexahedral elements (such as in this
thesis). It is common to have to manually cut the edges of the tissues to achieve a functioning mesh, a process that is difficult for
the computer. The gait input is currently semi-automated, usually
needing manual processing in noise-reduction. Even after obtaining the geometry, mesh and motion input, it takes time to make
the model work and get the simulation results. The model calculation is very demanding in terms of computing resources: on a fairly
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Discussion
powerful computer a full gait cycle can take over 16 hours, although
the process could be optimized by altering the material code. To be
feasible in clinical practice, the segmentation, meshing, model creation and analysis should all be automatic or semiautomatic and
instantaneous.
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9 Summary and conclusions
In this thesis, fibril-reinforced poro(visco)elastic materials were implemented into articular cartilages as well as menisci in three-dimensional, subject-specific FE models of knee joints. The in vivo deformation of articular cartilage was determined during static loading using CTa imaging, and the strains were compared to the subjectspecific model. Motion analysis was used to determine the rotations, translations, forces and moments in the subject’s knee, and
were then compared to the model. The effect of the architecture
of collagen fibers and depth-wise distributions of collagen and PG
contents of tibial and patellar cartilage were investigated during
gait and static loading. Finally, the moment-driven gait model was
used to assess the outcomes of different ACL reconstruction techniques. The main conclusions of these studies can be summarized
as follows:
1. Collagen fiber architecture controls the dynamic response of
articular cartilage in vivo. During dynamic loading, the effect
of both the depth-wise fibril volume density distribution and
PG distribution on the stresses and strains in the cartilage is
negligible. However, during static loading the PG distribution
plays a major role and should be considered in simulations of
static loading.
2. In an intact knee, the vast majority of cartilage deformation
occurs within the first few seconds after the application of the
load, but the cartilage continues to deform slowly and may
never reach mechanical equilibrium in vivo. Collagen fibril
stiffness modulates the initial creep response, but the effect of
PGs increases as the creep advances. Permeability and fluid
flow boundary conditions have a negligible effect on the initial
response, but more substantial effect in later stages of creep
(post-20 min).
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3. The moment and force driven model is able to replicate the
observed rotations of the subject’s knee during gait. As the
patella and quadriceps forces play a major role in resisting
the rotations, especially the internal-external rotation, they
should be included in force and moment driven models of
knee joints. In the patellar cartilage, the middle zone plays a
major role in resisting shear forces during gait.
4. When the ACL rupture is introduced, the moment and force
driven model shows a substantial increase in anterior tibial
translation and internal rotation, similarly to clinical findings.
The ACL rupture reduces reaction forces, strains and stresses
in the tibial cartilage, but increases peak local stresses compared with the healthy joint model. All investigated ACL reconstruction techniques show similar capability to restore the
movement of the joint close to the healthy knee joint model.
Between the single bundle and double bundle reconstruction
techniques, only minor differences in joint function or stresses
and strains was seen. Rather than the choice of technique, the
graft stiffness and pre-strain seem to modulate the outcome
of the ACL reconstruction.
In conclusion, the work presented in here takes a step towards
a novel diagnostic tool for the assessment of possible failure sites
in the human knee. Ultimately, a validated model could provide
a means to assess the outcome of treatments (e.g. weight loss) or
surgical procedures (e.g. ACL reconstruction), and it could be then
used in clinical decision making.
9.1
FUTURE
The modeling process has several issues that future studies will
need to solve. Those are for instance: a reliable automatic segmentation of tissues from MR images, ligament tissue properties,
patient-specific physiological loading conditions as well a selection
of different functional activities. Time-wise, the need for manual
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Summary and conclusions
segmentation is currently the most demanding process if the material model is simple. While patient-specific tissue properties may
never be acquired, in future studies the ligaments should be modeled as solids rather than linear springs, with more accurate viscoelastic material models. Ideally, the patient’s gait should be captured using dual fluoroscopy to minimize motion artifact resulting
from skin movement. Although gait is the default physical activity to be simulated, the research will eventually expand to other
activities such as stair-climbing or lunge.
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Osteoarthritis or OA, especially in
the knee, is a common disease in
elderly people but also in athletes
that have suffered a trauma, e.g.
anterior cruciate ligament rupture.
Currently, OA cannot be cured,
but its risks can be estimated and
minimized. This thesis aims to
develop a novel, computational
model of the subject’s knee that
could, in future, be used by doctors
as a diagnostic tool to evaluate the
risk of post-traumatic OA before and
after surgical operations.
dissertations | 187 | Kimmo Halonen | Validation and application of computational knee joint models
Kimmo Halonen
Validation and application
of computational knee
joint models
Kimmo Halonen
Validation and application
of computational knee
joint models
Finite element modeling analysis
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