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ISBN 978-952-61-3252-5 ISSN 1798-5668
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DISSERTATIONS | KATARIINA MYLLER | QUANTITATIVE CONTRAST-ENHANCED COMPUTED TOMOGRAPHY... | No
KATARIINA MYLLER
QUANTITATIVE CONTRAST-ENHANCED COMPUTED TOMOGRAPHY OF THE KNEE JOINT
From Segmentation of Articular Cartilages to Computational Modelling of Injuries
PUBLICATIONS OF
THE UNIVERSITY OF EASTERN FINLAND
Early diagnosis of osteoarthritis is vital for the prevention of its progression. This thesis
presents novel techniques to investigate cartilage injuries and subchondral bone utilizing
contrast-enhanced computed tomography, automated segmentation, and computational
modeling. The developed methods show potential for the quantitative evaluation of the
knee joint condition, therefore, enabling more comprehensive diagnosis.
KATARIINA MYLLER
PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND DISSERTATIONS IN FORESTRY AND NATURAL SCIENCES
N:o 359
Katariina Myller
QUANTITATIVE CONTRAST-ENHANCED COMPUTED TOMOGRAPHY OF THE
KNEE JOINT
FROM SEGMENTATION OF ARTICULAR CARTILAGES TO COMPUTATIONAL MODELLING OF INJURIES
ACADEMIC DISSERTATION
To be presented by the permission of the Faculty of Science and Forestry for public examination in the Auditorium MS302 in Medistudia Building at the University of Eastern Finland, Kuopio, on December 13th, 2019, at 12 o’clock.
University of Eastern Finland Department of Applied Physics
Kuopio 2019
Grano Oy Jyväskylä, 2019
Editors: Pertti Pasanen, Matti Tedre, Jukka Tuomela, and Raine Kortet
Distribution:
University of Eastern Finland Library / Sales of publications julkaisumyynti@uef.fi
http://www.uef.fi/kirjasto
ISBN: 978-952-61-3252-5 (print) ISSNL: 1798-5668
ISSN: 1798-5668 ISBN: 978-952-61-3253-2 (pdf)
ISSNL: 1798-5668 ISSN: 1798-5668
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Author’s address: University of Eastern Finland Department of Applied Physics P.O. Box 1627
70211 Kuopio Finland
email: katariina.myller@uef.fi Supervisors: Professor Juha Töyräs
University of Eastern Finland Department of Applied Physics Kuopio, Finland
The University of Queensland School of Information Technology and Electrical Engineering Brisbane, Australia email: juha.toyras@uef.fi Dean Jukka Jurvelin
University of Eastern Finland
Faculty of Forestry and Natural Sciences Kuopio, Finland
email: jukka.jurvelin@uef.fi Sami Väänänen, Ph.D.
Kuopio University Hospital Diagnostic Imaging Center Kuopio, Finland
University of Eastern Finland Department of Applied Physics Kuopio, Finland
email: sami.vaananen@uef.fi
Reviewers: Professor Stephen Ferguson
ETH Zurich
Institute for Biomechanics Zurich, Switzerland email: sferguson@ethz.ch Professor Guoyan Zheng Shanghai Jiao Tong University Institute for Medical Robotics Shanghai, China
email: guoyan.zheng@sjtu.edu.cn Opponent: Associate Professor Andrew Anderson
University of Utah
Orthopaedic Research - Motion Capture Core Facility Salt Lake City, United States of America
email: andrew.anderson@hsc.utah.edu
Katariina Myller
Quantitative Contrast-enhanced Computed Tomography of the Knee Joint - From Segmentation of Articular Cartilages to Computational Modelling of Injuries Kuopio: University of Eastern Finland, 2019
Publications of the University of Eastern Finland Dissertations in Forestry and Natural Sciences, 359
ABSTRACT
Osteoarthritis (OA) is a joint disease that causes pain, joint malfunction, and even disability. Since there are limited curative possibilities to hinder the progression of moderately severe or severe OA, it would be advantageous to detect early changes in the joint. Furthermore, techniques that enable the prediction of the onset and progression of OA related changes would be beneficial. Thus, sensitive imaging techniques and quantitative methods for analysing the changes in the joint should be developed and validated.
The aim of this thesis was to develop and implement methods to quantitatively analyse clinical in vivo contrast-enhanced computed tomography (CT) images of the knee joint. In studyI, human knee joints were imaged with contrast-enhanced CT using an anionic contrast agent. Subsequently, the properties of chondral lesions, subchondral bone, and articular cartilage were investigated simultaneously from the images. In study II, a semiautomatic tool for segmenting contrast-enhanced CT images was developed and used to segment articular cartilages in the knee joint, with the semiautomatic segmentations being compared with manual segmentations. In studyIII, the semiautomatic segmentation method was applied to generate articular cartilage geometries to allow computational modelling. The biomechanical responses such as tissue strains in the models generated using both semiautomatic and manual segmentations were compared. In study IV, articular cartilage lesions were characterized with computational modelling to determine cartilage strains around the lesions. A fibril-reinforced poroviscoelastic model for cartilage was used in studiesIIIandIV.
The results of this thesis reveal that the severity of a chondral lesion correlates positively with the density of subchondral bone (p < 0.05). The normalized X-ray attenuation, i.e. contrast agent uptake in cartilage, may be associated with the severity of the lesion (p < 0.05); the more severe the lesion, the greater the contrast agent uptake in cartilage. Moreover, the uptake of contrast agent and bone mineral density varied between different anatomical regions. There was good correspondence between manual and semiautomatic segmentations; values of Dice similarity coefficient, specificity, and sensitivity were high (0.78 - 0.86).
Furthermore, when comparing the manual and semiautomatic segmentations, differences in cartilage thickness were low (0.25 - 0.31 mm). The biomechanical responses observed in models generated based on either manual or semiautomatic segmentations were not statistically significantly different (p > 0.5). Moreover, the differences in maximum principal strain (< 0.72%) and fibril strain (< 0.40%) were small. The depth and volume of the lesions correlated with the strains around the lesions (ρ = 0.717 - 0.767,p< 0.05). In all of the lesions, the strain distribution was clearly changed at the egdes of the lesion as compared with intact cartilage.
According to minimum principal and shear strains the lesions experienced under loading, the lesions could be divided into higher and lower OA risk groups.
To conclude, this thesis describes quantitative techniques which can analyse the characteristics of a knee joint from clinical CT images. Contrast-enhanced CT imaging displayed a potential to allow a quantitative analysis of subchondral bone, articular cartilage, and chondral defects. Computational modelling made it possible to categorize lesions based on the related risk of degeneration. The introduced segmentation method enabled an accurate determination of articular cartilage geometries and these geometries were used successfully for computational modelling of the knee joint function. Potentially, the introduced methods could enhance the diagnostics of early OA-related changes in knee joint function or aid in deciding the intervention or rehabilitation protocol.
Medical Subject Headings: Diagnostic Imaging; Knee Joint; Knee Injuries;
Osteoarthritis; Cartilage, Articular; Bone and Bones; Bone Density; Tomography, X-Ray Computed; Contrast Media; Image Processing, Computer-Assisted; Finite Element Analysis; Models, Theoretical; Computer Simulation
National Library of Medicine Classification: QT 34.5, WN 206, WE 300, WE 870, WE 872
Asiasanat: kuvantaminen; polvet; nivelrikko; nivelrusto; vammat; luu;
tietokonetomografia; kartiokeilatomografia; kontrasti; kuvankäsittely;
biomekaniikka; elementtimenetelmä; mallintaminen; simulaatio
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ACKNOWLEDGEMENTS
I thank Assoc. Prof. Andrew Anderson for agreeing to be opponent of this Ph.D.
thesis defence, and Prof. Guoyan Zheng and Prof. Stephen Ferguson for reviewing this Ph.D. thesis.
I want to thank my supervisors Prof. Juha Töyräs, Ph.D. Sami Väänänen, and Dean Jukka Jurvelin for their support and guidance throughout my Ph.D. process.
Thank you Jukka for hiring me and providing important comments and criticism on my studies. Sami, I appreciate your patience and helpful advice. Your experience of the research issues examined in this Ph.D. thesis has been highly valuable. Juha, I have never met a more dedicated, ambitious, and enthusiastic person than you. You have inspired me, and I really appreciate the time you have had for my research.
I thank the Science, Technology, and Computing Program (SCITECO, Faculty of Forestry and Nature Sciences, University of Eastern Finland), the Academy of Finland, and the Research Committee of the Kuopio University Hospital Catchment Area for the State Research Funding for financially supporting my work. Oulu University Hospital and Mehiläinen Hospital (Helsinki) are acknowledged for their collaboration related to data of the studies. I kindly thank Ewen MacDonald for proofreading this thesis.
I really appreciate all the help of my co-authors. Especially, I want to thank Mikko Venäläinen, Mika Mononen, Mikael Turunen, Petri Tanska, and Rami Korhonen for their effort. You are diamond-hard professionals, never doubt that.
I wish to send all my best wishes to all of the BBC members with whom I have worked. I am very thankful that I got so many memorable moments and great friends. The very best room (Me359) in the legendary lab corridor and working next to The Jukebox have saved so many of my days. Unfortunately (or fortunately), I will never forget the first rhythms of the piece of music number 112. Miitu, Mimmi, Ojasimo, Timo, Pete, Juuso, and Ari: thank you for sharing the journey all the way from my bachelor studies to our lives as colleagues.
My colleagues in Diagnostic Imaging Center and Cancer Center in Kuopio University Hospital, Mikkeli Central Hospital, and Vaasa Central Hospital: thank you for interesting work experiences and the pleasant time during this Ph.D.
project.
I want to thank all my friends for giving me so much understanding, support, and cheerful moments from the very beginning of my studies until the moments when I prepared the final drafts of the book. The famous Fantastic Four (aka FDB) and people related gave me the best start as a physics student and have given me so much joy and support ever since. The P.I. gang has provided me with so much understanding – and all had the guts to say when I have talked too much about work. KRock, Posse, Ghost Town/Tuikkalampimobi people, and others: I cannot say how much all the get-togethers have meant to me, I hope they will never stop.
Anni H., thank you for all the cheerful moments and the world-saving conversations which helped me through a lot. I thank Pole Center (former Ready Set Pole) for giving me some other thoughts after working hours. When you are three meters above the ground upside down trying to make a flip or a dropping, it is better not to think about MATLAB algorithms. Special thanks to my +70 years lady friends from Tuesday sauna shift at Saarijärvi, you rock!
Finally, my thanks go to my family members Aija, Pekka, Kristiina, and Annika.
Thank you for being there for me during these years. My dearest thanks go to my
beloved Simo. Without you, this thesis would never have happened. You made me believe in my dreams.
Kuopio, October 5th, 2019
Katariina Myller
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LIST OF PUBLICATIONS
This thesis consists of the present review of the author’s work in the field of medical imaging and the following selection of the author’s publications:
I Myller KAH, Turunen MJ, Honkanen JTJ, Väänänen SP, Salo J, Jurvelin JS, Töyräs J. "In Vivo Contrast-Enhanced Cone Beam CT Provides Quantitative Information on Articular Cartilage and Subchondral Bone." Annals of Biomedical Engineering, 2017. 45(3):811-818. doi: 10.1007/s10439-016-1730-3.
II Myller KAH, Honkanen JTJ, Jurvelin JS, Saarakkala S, Töyräs J, Väänänen SP.
"Method for Segmentation of Knee Articular Cartilages Based on Contrast- Enhanced CT Images."Annals of Biomedical Engineering, 2018. 46(11):1756-1767 doi: 10.1007/s10439-018-2081-z.
III Myller KAH, Korhonen RK, Töyräs J, Tanska P, Väänänen SP, Jurvelin JS, Saarakkala S, Mononen ME. "Clinical Contrast-Enhanced Computed Tomography with Novel Semiautomatic Segmentation Provides Feasible Input for Computational Models of the Knee Joint." Journal of Biomechanical Engineering. Accepted manuscript (electronic publication ahead of print). doi:
10.1115/1.4045279.
IV Myller KAH, Korhonen RK, Töyräs J, Salo J, Jurvelin JS, Venäläinen MS.
"Computational Evaluation of Altered Biomechanics Related to Articular Cartilage Lesions Observed In Vivo." Journal of Orthopaedic Research, 2019.
37(5):1042-1051. doi: 10.1002/jor.24273.
Throughout the thesis, these papers will be referred by Roman numerals.
AUTHOR’S CONTRIBUTION
The publications selected in this dissertation are original research papers investigating contrast-enhanced CT imaging of the knee joint. In all of the papers, the author participated in the study design and was the principal author. In vivo image acquisitions were conducted in collaboration with Mehiläinen Hospital in Helsinki (studies I and IV) and Oulu University Hospital (studies II and III). In study I, the author conducted manual segmentations, image analyses, and performed the statistical analyses of the results. In study II, the author developed an algorithm to segment articular cartilages from contrast-enhanced CT images, validated it by comparing the segmentations to manual segmentations conducted by the author and a co-author, and analysed the results. In study III, the author conducted half of the computational models in the study, performed all of the manual and semiautomatic segmentations, and analysed the results of the models.
In study IV, the author conducted the segmentation of the injuries and analysed the results. In all of the papers, the author was the main writer of the manuscripts.
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TABLE OF CONTENTS
1 Introduction
12 Knee joint
32.1 Articular cartilage
... 42.1.1 Structure and composition
... 42.1.2 Biomechanical characteristics
... 52.2 Subchondral bone
... 52.2.1 Structure and composition
... 52.2.2 Biomechanical characteristics
... 62.3 Meniscus
... 73 Knee osteoarthritis
93.1 Degeneration in osteoarthritis
... 93.2 Post-traumatic osteoarthritis
... 103.3 Diagnostics of knee osteoarthritis
... 104 Contrast-enhanced computed tomography of the knee joint
134.1 Computed tomography
... 134.2 Quantitative computed tomography of bone
... 144.3 Contrast enhancement in knee joint arthrography
... 144.3.1 Contrast agents
... 144.3.2 Diffusion kinematics in articular cartilage
... 155 Segmentation of bone and cartilage
175.1 Segmentation of cortical bone from CT images
... 185.2 Generation of 3D shapes from sparse contours
... 206 Finite element modelling of the knee joint
236.1 Material properties in knee joint models
... 246.1.1 Modelling of elastic properties of bone
... 246.1.2 Poroelastic and biphasic cartilage models
... 246.1.3 Fibril-reinforced poro-visco-elastic cartilage models
... 257 Aims and hypothesis
278 Materials and methods
298.1 Contrast-enhanced computed tomography of the knee
... 298.2 Segmentation of contrast-enhanced computed tomography images
.... 308.2.1 Manual segmentation
... 308.2.2 Semiautomatic segmentation
... 318.3 Finite element modelling of the knee
... 338.3.1 Meshing
... 338.3.2 Material properties
... 338.3.3 Simulations
... 358.3.4 Submodelling of lesions
... 368.4 Quantitative analysis of articular cartilage, subchondral bone, and defects
... 368.5 Quantitative comparison of segmentation methods
... 378.6 Statistical analysis
... 379 Results
399.1 Comparison of segmentation methods
... 399.1.1 Cartilage volume and thickness
... 399.1.2 Dice similarity coefficient, sensitivity, and specificity
... 419.1.3 Biomechanical responses
... 419.2 Effect of chondral lesions to cartilage and bone properties
... 4410 Discussion
4910.1 Contrast-enhanced computed tomography of chondral injuries
... 4910.2 Computational modelling of chondral lesions
... 5110.3 The semiautomatic segmentation method
... 5210.4 Computational modelling of semiautomatically segmented articular cartilages
... 5411 Summary and conclusions
57BIBLIOGRAPHY
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ABBREVIATIONS
1D One-dimensional
2D Two-dimensional
3D Three-dimensional
AB Acetabular bone
AC Articular cartilage BMD Bone mineral density
BLOKS Boston Leeds Osteoarthritis Knee Score
BW Body weight
CBCT Cone beam computed tomography
CT Computed tomography
DF Distal femur
dGEMRIC Delayed Gadolinium-Enhanced MRI of Cartilage DSC Dice similarity coefficient
ECM Extra cellular matrix FCD Fixed charged density FEM Finite element modelling
FG Femoral groove
FLC Femoral lateral condyle FMC Femoral medial condyle
FRPVE Fibril-reinforced poroviscoelastic FWHM Full width at half maximum GAG Glycosaminoglycan
HU Hounsfield unit ICC Intraclass coefficient
ICRS International Cartilage Repair Society
MOAKS Magnetic Resonance Imaging Osteoarthritis Knee Score MRI Magnetic resonance imaging
OA Osteoarthritis
PAT Patella
PDE Partial differential equations PET Positron emission tomography
PF Proximal femur
PT Proximal tibia
RPC Reproducibility coefficient
SB Subchondral bone
SBP Subchondral bone plate
TB Trabecular bone
Tb.N The average number of trabeculae Tb.Sp The average trabecular spacing Tb.Th The average trabecular thickness TLC Tibial lateral condyle
TMC Tibial medial condyle VOI Volume of interest
vBMD Volumetric bone mineral density
WORMS Whole Organ Magnetic Resonance Imaging Score
SYMBOLS
α Angle between the imaging plane and the normal of cortical surface
β Constant
Cstif Stiffness tensor C Concentration
D The diffusion coefficient E0 Initial elastic modulus Ee Strain-dependent modulus Em Elastic modulus
En Elastic modulus of over an element e Void ratio
e0 Original void ratio
η Viscous damping coefficient eelastic Elastic strain
ef Fibril strain e0 Fibril limit strain erf Error function e Elastic strain tensor F Faraday’s constant
F Deformation gradient tensor gin In-plane blur
gout Out-of-plane blur Gm Bulk modulus
γ Constant
H Rectangular function
h Thickness
hz Normalised depth I Unit matrix
I Intensity of the radiation I0 Initial intensity of the radiation
J Determinant of the deformation gradient tensor Jdiff Diffusion flux
Jind Jaccard index k Permeability k0 Initial permeability Km Shear modulus M Positive constant
µ Linear attenuation coefficient nfluid Partition of fluid phase nsolid Partition of solid phase νm Poisson’s ratio
p Fluid pressure
∇Ψ Potential difference q Fluid flux
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ρ Spearman correlation coefficient
ρd Density
R Gas constant
r Extent of blur in CT images s Slice thickness in CT images σ Point spread function defined blur σeffect Effective solid stress
σfluid Fluid stress σf Stress of fibril
σnf Stress of nonfibrillar matrix σsolid Stress of solid part
σstress Stress σtotal Total stress
t Time
T Temperature
V Volume
Vintersection Volume of intersection
Vunion Volume of union
x0 Location of periosteal surface x1 Location of endocortical surface
y0 Hounsfield unit value of surrounding tissue y1 Housfield unit value of cortical bone y2 Housfield unit value of trabecular bone
z Atomic number
zv Valence of the particle
1 Introduction
Osteoarthritis (OA) is a common, degenerative musculoskeletal joint disorder causing pain and disability. It has been predicted that its prevalence will increase in the future [1]. Approximately 3.8% of the world’s population is suffering from knee OA [2]. OA can be categorized as either primary or secondary. The former type has no explicit cause or starting point, whereas the latter is often caused by trauma or injury. Since high intensity impacts predispose to joint injuries [3], post-traumatic OA is rather common among athletes and younger people. Despite the extensive research conducted on OA, the curative possibilities to repair advanced tissue degeneration have remained unimpressive. In advanced OA, radical surgeries, such as arthroplasties, are often the only therapeutic option.
Novel theraphies have been introduced in attempt to hinder degeneration [4, 5], or even stop it, provided that the changes can be detected at an early stage,i.e. before the development of post-traumatic OA. Thus, it is crucial to develop novel techniques capable of detecting the delicate, early changes occurring in the joint.
Moreover, a focus should be placed on techniques that enable the prediction of the onset of the disease as well as its progression.
The knee joint carries heavy loads and in combination with other joints, muscles and bones, enables our everyday movements. The composition and structure of each knee joint tissue are optimally adapted for its functional purpose. In OA, tissues in the joint undergo several pathological changes, causing pain that limits the use of the joint. There is a reduction in the thickness of articular cartilage as the disease advances. At the same time, changes in its composition makes it more prone to be subjected for further degeneration. In addition, the bone underneath the cartilage layer undergoes structural and compositional alterations. In the late stage of the disease, more easily distinguishable changes appear such as sclerosis and osteophytes.
OA is most commonly diagnosed with conventional X-ray imaging. Magnetic resonance (MR) imaging is also widely used. X-ray imaging is capable of assessing the decrease in the joint space and bone alterations but it cannot detect direct changes in articular cartilage due to the low X-ray attenuation of soft tissues. MR images visualize soft tissues accurately, but its ability to reveal changes in bone composition and structure is not comparable with X-rays. Previous studies have shown that contrast-enhanced computed tomography (CT) is as a potential imaging modality to observe the changes related to osteoarthritis and injuries [6, 7].
When a contrast agent,i.e. a substance visible in X-ray images, is administered in the joint space, articular surfaces can be visualized. Since the modality is based on X-ray imaging, the CT images reveal also bone structures sensitively. Furthermore, the diffusion of the contrast agent into cartilage provides information on the composition of the cartilage, and hence, the extent of the degeneration [7–9].
Instead of visual inspection of the joint pathologies, it has been claimed that the changes in the joint could also be evaluated quantitatively by using contrast- enhanced CT [10, 11]. For instance, an abnormal cartilage thickness and sclerosis of subchondral bone may be used as indicators for the stage of OA. If one wishes
to analyze the overall morphology of the cartilage surface, the articular cartilage layers need to be segmented in the clinical images. Conventionally, segmentations have been conducted manually which is both very time-consuming and impractical.
Several automatic segmentation methods have been introduced for handling MR images of the knee joint [12–14]. However, no methods to segment articular cartilage geometries from contrast-enhanced CT images of the knee joint have been presented.
Segmented articular cartilage geometries are also needed for computational modelling of the function of the knee joint. Finite element (FE) modelling is a useful method with which to obtain information on the biomechanics of the joint.
By simulating the knee joint motion, biomechanical responses, such as tensile and compressive tissue strains in cartilage, can be determined in cartilage under physiologically relevant loading conditions [15, 16]. Biomechanical models can help to reveal the onset of cartilage degeneration or risk for cartilage failure [17, 18].
Moreover, the results emerging from the models could be utilized in planning interventions or deciding on the optimal rehabilitation procedures. This kind of diagnostically valuable information cannot be obtained from in vivo data without simulations.
In this thesis, the applicability of contrast-enhanced CT images to improve knee joint diagnostics was studied. A method for segmenting articular cartilages was developed and validated. Furthermore, quantitative analysis and computational modelling were applied to investigate chondral injuries and a method was developed and validated for segmenting articular cartilages. This thesis comprises four independent studies. In study I, we investigated whether contrast-enhanced CT would be capable of allowing sensitive evaluation of chondral lesion related changes in subchondral bone and articular cartilage. Study II focused on developing an automatic method to segment articular cartilages of knee joint from contrast-enhanced CT images. The segmentation method was used to generate cartilage geometries for computational modelling in study III. In study IV, a general walking gait was used in the knees to simulate the biomechanical responses aroundin vivochondral lesions.
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2 Knee joint
A human knee joint comprises distal femur, proximal tibia, and patella whose ends are covered by articular cartilage (Figure 2.1). The menisci, which are located between the tibial and femoral articular cartilages, are connected to tibia. The bones are connected to each other by tendons and ligaments. The most significant tendon for the knee joint is the patellar tendon. The medial collateral ligament connects the tibia with the femur and the lateral collateral ligament links the fibula with the femur. The anterior and posterior cruciate ligaments connect the tibia and the femur.
The knee joint is the largest joint in the human body; it carries loads up to several times the individual’s bodyweight, depending on the activity [19]. The muscles around the knee, together with the ligaments, enable the motion of the joint as well as the stable flexion and the extension movements of a leg. Articular cartilage operates as a load-bearing layer at the end of the bones while the menisci contribute to shock absorption and help to stabilize the joint. Synovial fluid provides almost frictionless sliding between the articular surfaces [20].
Figure 2.1:Major structures of knee joint (anterior point of view).
2.1 ARTICULAR CARTILAGE 2.1.1 Structure and composition
About 60-85% of wet weight of articular cartilage is interstitial fluid [20, 21].
Cartilage cells, i.e. chondrocytes, account for 1-10% of the total wet weight of cartilage [21]. Collagen comprises around 10-20% and proteoglycans for 5-10% of the cartilage wet weigth [20, 21]. The extracellular matrix (ECM) of articular cartilage consists of collagen network, proteoglycans, and interstitial water.
Proteoglycans (PGs) are macromolecules consisting of proteins, most commonly aggregans, with glycosaminoglycans (GAGs) connected to them [22]. Most PGs form PG aggregates by non-covalent bonding to hyaluronic acid chains. The main function of proteoglycans is to maintain the colloidal pressure of the cartilage. The collagen in articular cartilage is mostly structured from arrays of collagen fibrils arranged in triple helical shape [20]. Collagen network sustains the shape of the cartilage. In hyaline cartilage, including articular cartilage, the collagen is mainly of type II [22].
Chondrocytes are sparsely distributed in cartilage; these cells are responsible for the synthesis and organization of ECM macromolecules. The processes are controlled by enzymatic reactions in the cell as well as by the mechanical stimuli to which the cell is exposed. Since cartilage tissue is avascular, chondrocytes obtain their nutrients from synovial fluid by means of diffusion [22].
Articular cartilage can be divided into deep, middle, and superficial zones according to its structure and composition (Figure 2.2) [20]. The articular surface is made up of a collagen network that is oriented in parallel to the surface.
Furthermore, in the superficial zone, chondrocytes are flattened to lay parallel to the surface. In the middle zone, collagen fibers are randomly oriented and in this region, the chondrocytes are round. Closer to the bone,i.e. in deep cartilage, the collagen fibers become oriented perpendicularly to the bone surface. In deep cartilage, the chondrocytes are oriented in colums.
Figure 2.2: Structure of articular cartilage.
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2.1.2 Biomechanical characteristics
The multiphasic structure and composition of tissue are the basis for the unique functional biomechanical properties of articular cartilage. Articular cartilage has to be able not only to resist wear and high loads but also have the capability to slide almost frictionlessly during movement. As compositional and structural properties differ between the different cartilage zones, their mechanical properties also differ [21, 23, 24]. Furthermore, the biomechanical properties of articular cartilage are anisotrophic due to its structure [21, 24].
Articular cartilage is poroviscoelastic; it has low permeability, i.e. cartilage matrix effectively restricts fluid flow [24]. Thus, the mechanical behavior of articular cartilage is time-dependent during loading. During instantaneous loading, articular cartilage behaves as an almost incompressible elastic material whereas at the equilibrium,i.e. when there is no longer fluid flow, it is almost fully compressible. At equilibrium, proteoglycans are responsible of the stiffness of articular cartilage [21, 22]. The presence of proteoglycans provides the fixed charged density (FCD) of the tissue; negatively charged GAGs create the osmotic pressure in the matrix [25]. The collagen network contributes to the tissue’s high dynamic stiffness [21]. Furthermore, collagen fibers contribute to the strength and shear modulus of the tissue [20].
2.2 SUBCHONDRAL BONE 2.2.1 Structure and composition
Bone consists of bone cells and bone matrix. The matrix forms the bone structure and it has both organic and mineralized components. It consists of type I collagen, hydroxyapatite [Ca10(PO4)6(OH)2], proteoglycans, and glycoproteins [26]. The bone matrix accounts for the mechanical properties and mineral density of the bone. Bone cells, i.e. osteoclasts, osteoblasts, and osteocytes, participate in the synthesis and maintenance of the bone matrix. About 75% of the wet weight of bone is inorganic material [26], the rest being made up of organic material and cells.
On the microscale, bone can be subdivided into cortical or trabecular bone according to its structure (Figure 2.3). The relative density of cortical bone varies between 0.7-0.9 whereas in trabecular bone, it is more variable, between 0.05-0.7 [26]. In cortical bone, the lamellae are organized in osteons [26]. Blood vessels and neurons are located inside osteons, in Haversian canals [23, 27].
Volkman’s canals connect osteons, enabling the cells undergo interactions [23, 27].
Trabecular bone has a sparser matrix structure, constructed from trabeculae which can be differentiated into rod-like or plate-like forms. The pores in trabecular bone are filled by bone marrow tissue which maintains the nutritional supply of the bone tissue [27].
Mechanical and metabolic changes affect the formation and resorption of the bone. The adaptation of bone tissue to mechanical loading is represented by Wolff’s law [28]. Osteoblasts are responsible for the reconstruction of bone whereas osteoclasts resorp the bone. These cells work in harmony to form a multicellular unit. In this ongoing procedure, osteoblasts, trapped in the matrix, differentiate into osteocytes that maintain the matrix [26]. Bone formation and the resorption
process continues throughout the individual’s lifetime; however, bone mass starts slowly to decrease after the age of thirty years [26].
The subchondral bone lies underneath the calcified cartilage. The cortical bone under the cartilage is called the subchondral bone plate and bone located underneath that is called subchondral trabecular bone. The cement wall separates subchondral bone from the calcified cartilage [26]. At the bone and cartilage interface, blood vessels may come into contact with the calcified cartilage.
Cortical bone
Trabecular bone
Osteon Harvesian canal Lamellae
Figure 2.3: Structure of bone.
2.2.2 Biomechanical characteristics
The structure and composition of bone are responsible for its high stiffness and strength. At the same time, it is relatively light and flexible. These properties are highly beneficial since bone has to enable everyday movement but also to resist fractures. Furthermore, trabecular bone plays an important role as a shock absorber.
As a result, trabecular bone has different mechanical properties than cortical bone. Similar to articular cartilage, the properties of bone depend on the direction:
the anisotrophic structure reveals differences in mechanical characteristics depending the observed direction. Also reminiscent of articular cartilage, bone has viscoelastic properties. The Young’s modulus values are multiplied when increasing the strain rate from extremely slow to high impact [26].
The elastic modulus values for femoral cortical bone are dependent on the direction of the loading (Table 2.1) [29, 30]. Similarly, the ultimate strength values in the longitudinal direction [compressive (193 MPa) and tensile (133 MPa)] and transverse direction [compressive (133 MPa) and tensile (51 MPa)] differ from each other [29, 30].
Table 2.1:Elastic modulus (E) values for femoral cortical bone [29, 30].
E(GPa) Longitudinal 17.5 Transverse 11.5
Shear 3.3
Values of elastic modulus are clearly lower in trabecular than in cortical bone [26]. Due to greater variability in the density of trabecular bone, its elastic modulus
6
and strength values vary extensively. Experimental studies have revealed that the characteristic stress of bone is linked to the bone density in the following manner
σstress=γρβd, (2.1)
where σstress is the stress, γis a constant, ρd is the density of the bone, and βis a constant [31, 32].
2.3 MENISCUS
Menisci are C-shaped, cartilaginous tissue located between the femur and the tibia;
they can be found on both the lateral and medial sides of the joint. They are attached to the tibia via liganous horns. The outer ring of the meniscus is thicker which makes the cross-sectional shape of the meniscus resemble a wedge. Meniscus tissue consists mainly of water (>75% ), collagen (22%, mainly type I), proteoglycans (1%), glycoproteins, and other proteins [21, 33].
The ECM of meniscus, similar to articular cartilage, contains a collagen network and proteoglycans. However, the structure of meniscal ECM differs from that in articular cartilage. The meniscus has three different layers, central, lamellar and superficial, which have different collagen orientations [21]. The unique composition makes meniscus an excellent damper for loading of the knee: it provides stabilization and shock absorption for the joint. Since it has a similar composition to articular cartilage, their biomechanical properties also display similarities. The elastic stiffness of meniscus is however higher than that of articular cartilage whereas cartilage tolerates higher strains before failure [34].
3 Knee osteoarthritis
Osteoarthritis (OA) is one of the most prevalent musculosceletal diseases, affecting at least 19% of American adults older than 45 years [35]. In 2009, the annual costs related to OA only in USA have been estimated to be around 185 billion dollars [36].
Based on data from 2010, 3.8% of global population was estimated to suffer from knee OA [2]. It has also been estimated that the prevalence of knee OA has been doubled from 1950s, and it has been suggested that the numbers of sufferers will continue to increase [1].
OA is a degenerative disease that changes the composition and structure of articular tissues. As a consequence, the functionality of the joint becomes impaired.
For instance, the disease causes pain and immobility of the joint and ultimately leads to disability [2]. Based on the characteristics and initiation of the disease, OA can be divided into different phenotypes, such as post-traumatic and idiopathic osteoarthritis. However, the wearing of articular cartilage and ongoing inflammation processes are characteristics of all phenotypes [20, 37, 38]. In OA, joint tissues fail to maintain their structure and composition and they start to become deformed or degenerated.
Several factors affect the development of OA. Old age predisposes for the disease. Statistically, female gender increases the risk for the disease [2]. Obesity is another risk factor, for instance due to higher chronic excessive loading [39]. On the other hand, OA is prevalent among athletes, for instance, a joint injury due to a high impact experienced during exercise, may initiate the disease [3, 40].
3.1 DEGENERATION IN OSTEOARTHRITIS
Early changes in OA comprise the decrease of proteoglycans, the increase in the water content, and fibrillation of the collagen network in the cartilage surface [22].
The changes affect the biomechanical properties of cartilage by reducing its stiffness and increasing its permeability. In addition to these changes in cartilage, the subchondral bone plate becomes thinner [41].
In the next stage of the disease, the increased formation of bone causes thickening of the subchondral bone plate [41]. Furthermore, bone cysts and osteophytes may be formed. In the cartilage, the fissures in the ECM penetrate deeper into the cartilage, inducing a further disorganization of the collagen network [22, 38]. The cellular processes aim to maintain the amount of macromolecules in the tissue: chondrocytes react and detect the degenerative changes in cartilage [38].
In the late stage of the disease, the rate of degeneration accelerates, there is a failure to synthesize new macromolecules and the articular cartilage experiences a loss of tissue. The subchondral bone plate continues to thicken whereas the subchondral trabecular bone mass decreases [41]. Due to changes in the later stage of the disease, the joint space narrows. Furthermore, the vascular system invades the tidemark and calcified cartilage thickens [41]. In the final stage, the bone surfaces might become exposed due to the total loss of articular cartilage.
3.2 POST-TRAUMATIC OSTEOARTHRITIS
Post-traumatic OA is a type of OA that has been initiated by trauma or injury.
Around every tenth (9.8%) of all the knee OA cases are post-traumatic [40].
Furthermore, it has been claimed that incidence of post-traumatic OA is on the increase [42].
Post-traumatic OA has an anatomically and temporally well-defined starting point. The trauma may include changes in cartilage or bone as well as in menisci or ligaments. Anterior-cruciate ligament and meniscal injuries are common and they expose cartilage to post-traumatic OA [40]. As an early symptom, anterior cruciate injuries have been shown to reduce the amount of proteoglycans in articular cartilage [43], which further predisposes to disease progression. The increased stresses in the cartilage after menisectomy have been evaluated also biomechanically using computational modelling [44].
Injuries in articular cartilage may be differentiated into either soft tissue damage or osteochondral damage, depending on whether they reach the subchondral bone.
Even though articular cartilage might undergo significant changes, not all of the injuries inevidably lead to the development of OA [40]. No clear consensus exists about the stability of articular cartilage lesions. Additionally, it is hard to estimate the time required for development of OA after the initiation event [40].
New pharmaceutical compounds have been developed to modify the disease [4, 5]. Furthermore, articular cartilage injuries may be modified surgically with multiple ways [11]. However, currently there is little convincing evidence to support the success of these modifications. As OA advances, analgesic drugs are commonly prescribed. Ultimately, a total knee replacement might be the only reasonable option. However, advances in imaging modalities, biochemistry, and novel joint-preserving interventions have shown potential for early diagnostics and delaying disease progression [4, 5].
3.3 DIAGNOSTICS OF KNEE OSTEOARTHRITIS
The signs of OA include pain and a resctriction of joint movement. When a knee joint disorder is suspected, the common procedure for diagnostics is clinical examination followed by diagnostic imaging. When necessary, an arthroscopic examination of the knee can be conducted. OA can be defined as symptomatic, radiographic, or clinical based on the evaluation method.
Native X-ray imaging is suitable for detecting a malalignment of the knee and for defining the joint space width. Although osteophytes and sclerosis are also visible in the X-ray images, the soft tissues are poorly visible. Magnetic resonance imaging (MRI) can be performed to evaluate possible soft tissue defects and thinning of articular cartilage [11]. MRI provides 3D images with high contrast which makes it possible to visualize the various soft tissues. During arthroscopy, articular surfaces are visually evaluated using invasive scoping of the knee.
In order to classify the stage of OA in more detail, several semi-quantitative methods, based on clinical imaging modalities, can be applied. Some of these methods are presented in Table 3.1. The methods differ with respect to the imaging method and tissue(s) used for evaluation. The fundamental aim of the scoring is to define the stage of the disease in an objective manner.
10
Table 3.1: Semi-quantitative criteria for knee OA and injuries based on clinical imaging and arthroscopy.
Method Modality Grading Evaluated tissues
Kellgren-Lawrence [45] Radiography 1 - 4 Bone structures, Joint space width ICRS [46] Arthroscopy 0 - 4 Articular cartilage surfaces
WORMS [47], MRI Each feature Bone marrow lesions, Articular cartilage, BLOKS [48], (e.g. 0 - 3) Osteophytes, Synovitis, Meniscus, Ligaments MOAKS [49]
All these scoring techniques have their disadvantages and benefits. A radiographic evaluation is unable to visualize articular cartilage, preventing any detection of its early changes. Even though artroscopic scoring enables visualisation of true lesions, it has been reported to have questionable intra- and inter-observer repeatability [50]. MR methods make possible a comprehensive evaluation of the joint. However, these classification methods may be relatively laborious and require expertise.
4 Contrast-enhanced computed tomography of the knee joint
4.1 COMPUTED TOMOGRAPHY
Radiography is based on electromagnetic X-rays. X-rays can be utilized in medical imaging since they attenuate exponentially in a medium according to the equation
I =I0e−µx, (4.1)
where the I0 is the original intensity of the radiation, I is the intensity of the attenuated radiation,µis the linear attenuation coefficient of the medium, and xis the distance in the medium. Thus, in addition to distance, the attenuation is based on the medium: the higher the atomic number (Z) and density of the medium, the greater the attenuation [51]. Furthermore, the linear attenuation coefficient is dependent on the energy of the radiation [52]. With the photon energies of clinical X-ray devices, X-ray attenuation in tissues is related to the reduction occurring in the intensity of radiation in physical interactions, such as photoelectric effect, Compton scattering, and elastic scattering.
Computed tomography (CT) is a 3D imaging method in which X-ray projections are acquired from several angles around the object. Based on a system of equations (4.1), 3D reconstruction is created either using filtered back projection or iterative reconstruction methods [51]. The grey values of reconstructed CT images are scaled to be comparable between images and presented as Hounsfield units (HU). In clinical CT scanners, the radiation source rotates around the patient while multirow detectors are located on the outside ring. The radiation beam is shaped as a fan and spiral scanning around the subject can be applied.
Nowadays, imaging a knee with a CT device may take less than a couple of seconds and novel CT devices have multi-energy imaging possibilities.
Furthermore, reconstruction algorithms have evolved greatly during recent years, enabling more effective reconstructions or reconstructions with a lower number of projections. Cone beam computed tomography (CBCT) is based on a cone shaped beam, commonly used in dental imaging [53]. Due to the shape of the beam, CBCT imaging of knee can be conducted with one rotation around the joint, meaning that the imaging procedure is efficient. Nevertheless, the CBCT images may have a lower signal-to-noise ratio. Therefore, methods to enhance the quality of CBCT images have been devised [54].
Diagnostic imaging requires good contrast in order to visualize tissues. The contrast between soft tissues is generally poor in CT images due to their similar X- ray attenuation properties. This issue may be remedied by exploitation of contrast agents, described in detail in section 4.3. Articular cartilage is relatively thin and, hence, its visualization requires high resolution. Clinical CT is able to achieve a higher signal-to-noise ratio and has often better spatial resolution compared with MR, and these properties are beneficial in imaging thin structures [55].
4.2 QUANTITATIVE COMPUTED TOMOGRAPHY OF BONE
The presence of relatively highly attenuating of phosphorus and calcium (atomic numbers of Z = 15 and Z = 20, respectively), makes the CT imaging of bone structures feasible. In contrast to plain radiographs, CT imaging allows a quantitation of the bone volume fraction in 3D. When one has a high enough image resolution, a characterictic to microCT imaging, the average trabecular thickness (Tb.Th), average trabecular spacing (Tb.Sp), and the average number of trabeculae (Tb.N) can be determined. By segmenting different parts of the bone, such as subchondral bone plate or trabecular bone, the values of the above mentioned parameters can be determined separately for different regions of interest. In order to determine the mineral density of the calcified matrix accurately, hydroxyapatite (HA) phantoms must be imaged together with the patient [56].
4.3 CONTRAST ENHANCEMENT IN KNEE JOINT ARTHROGRAPHY 4.3.1 Contrast agents
Contrast agents have been used to visualize soft tissues with CT. In knee joint imaging, contrast agents are usually administered intra-articularly into the joint space. Generally, an important characteristic of a contrast agents is that it should possess a high X-ray attenuation. Iodine is the element commonly used for contrast enhancement with a relatively high atomic number (Z= 53). Moreover, its K-edge at the energy of 33.2 keV induces a further attenuation at the clinical CT energy levels. Other potential materials for contrast enhancement include e.g. gold (Z = 79) and tantalum (Z= 73).
Generally, the presence of a constrast agent solution in a joint space assists visualizing the articular cartilage surface when imaged immediately after its administration. Based on the diffusion kinematics, described in more detail in section 4.3.2, the administered constrast agent starts to diffuse into the cartilage.
The diffusion of contrast agent provides information on the composition of the articular cartilage and, hence, the concentration of the contrast agent has been found to be related to the biomechanical properties of cartilage [57].
If the contrast agent is electrically neutral,i.e. it has no electrochemical charge, its concentration in articular cartilage is determined by permeability, water content, and the integrity of collagen in the cartilage [8]. GAGs in the cartilage are positively charged causing repulsive electrochemical forces on negatively charged particles,i.e.
anions. The diffusion of anionic contrast agents is inversely proportional to the GAG content of cartilage [58]. The diffusion of an anionic contrast agent is also affected by the integrity of the collagen network, but the effect is not as evident as the repulsion due to the presence of the negatively charged GAGs [9]. Previously, anin vivostudy described a technique to image both cartilage injuries and degeneration in cartilage [6]. The CT image taken immediately after anionic contrast agent administration revealed the articular cartilage injuries, whereas the CT image taken after 45 min provided information on the the extent of the degeneration in the cartilage. Another in vivostudy revealed the correlation the uptake of an anionic contrast agent and the GAG content in cartilage [7]. In contrast to the situation with anionic contrast agents, cationic ones are attracted by the GAGs in the tissue. However, the rate of the diffusion is also proportional to water content, making it hard to determine whether a diffusion is due to high water content or high GAG content. Nevertheless, since 14
cationic contrast agents display good correlations with the GAG content and higher X-ray attenuations in cartilage due to diffusion [59, 60], they have been proposed to have potential for diagnostics.
During recent years, nanoparticles have become increasingly popular as CT contrast agents in in vitro studies [61]. There are different kinds of nanoparticle contrast agents e.g. organic components such as liposomes, micelles, and polymers that can be doped with highly attenuating materials. Inorganic materials, such as gold, can be manufactured as nanoparticles with a specific particle size.
Nanoparticle contrast agents can be used to determine cartilage surface. The cartilage surface can be visualized with nanoparticles that are so large that they cannot diffuse inside of the cartilage [62]. Degenerated cartilage lets through larger particles than intact one. Therefore, the level of degeneration can be determined, provided that the size of the particle that is diffusing into cartilage is known [63]. A summary of the different contrast agents for CT imaging of articular cartilage are presented in Table 4.1.
Table 4.1:Summary of contrast agents used for CT imaging of articular cartilage.
Type Element References
neutral gadolinium [8]
anionic ioxaglate, iodine [64, 65]
cationic iodine [59, 66]
nanoparticles tantalum, bismuth [62, 63]
4.3.2 Diffusion kinematics in articular cartilage
Delayed CT arthrography relies on the diffusion of the contrast agent into articular cartilage. Diffusion refers to the gradient driven random movement of particles,i.e.
the flux occurs from a higher concentration to a lower one. Fick’s first law describes this movement as
Jdiff=−D∂C
∂x, (4.2)
whereJdiffis the diffusion flux,Dis the diffusion coefficient,Csolute concentration, and x is the location. The diffusion coefficient, C, is dependent on the size of the molecule, Bolzman’s constant, temperature, pressure, and the viscosity of the fluid.
Fick’s first law assumes that diffusion is not time dependent. When including the time dependence, the Fick’s second law
∂C
∂t =D∂2C
∂x2, (4.3)
wheretis time, describes the diffusion.
The Nernst equation defines the potential difference (∆Ψ) between the sides of a semi-permeable membrane as
∆Ψ=−RT zvFlnC1
C2, (4.4)
where Ris the gas constant,Tis temperature,zv is the valence of the particle, Fis Faraday’s constant, andC1andC2are the concentrations of the particle. In addition to the free ions in the tissue, articular cartilage possesses a fixed charge that is related to the presence of the GAGs in the tissue. Therefore, diffusion of a contrast agent is affected by the electrochemical charge of the tissue. Based on the Donnan ratio at the electrochemical equilibrium [25, 67],i.e. the stage of diffusion when diffusion is no longer happening, the following equation applies
z[cation]tissue=z[anion]tissue+FCD, (4.5) where FCD is the fixed charge density of the tissue. Based on this equation, the concentration of the contrast agent inside tissue is dependent on FCD that is mainly created by the GAG content. The concentration of charged contrast agent in the articular cartilage is, hence, dependent on the GAG content of the cartilage at equilibrium.
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5 Segmentation of bone and cartilage
Image segmentation is needed to measure volumes and perform various analyses of the different body parts or organs visible in the images. Conventionally, segmentation is conducted manually, slice by slice from 3D images, which is very time-consuming and often impractical for clinical use. To resolve this issue, several semiautomatic or automatic segmentation techniques have been developed for medical purposes [68–70]. Due to the many years of active development and the considerable scientific interest in the subject, the methods are nowadays sophisticated, often focusing on the segmentation of a specific tissue.
As mentioned in chapter 3, OA causes structural and compositional changes in knee joint tissues and subchondral bone plate thickness and, moreover, as the disease progress, there are alterations in the volume of articular cartilage. Instead of having only a visual observation on these changes, determination of tissue geometries may lead to a better screening of the underlying pathologies [10, 47].
This kind of quantitative analysis of knee joint structures requires, however, a highly accurate 3D segmentation of the tissues. One challenge to the accurate segmentation is that articular cartilage and subchondral bone plate may be rather thin, at least when compared to the image resolution. Additionally, cartilage surfaces can be defected and the geometries of various individuals could be very different, which makes segmentation challenging. In clinical practice, the articular cartilage is conventionally imaged with MR. Therefore, the segmentation of articular cartilage has been based on MR images, while the segmentation of bone structures has usually been based on CT images. However, some studies have described the segmentation of bone structures from MR images and segmentation of acetabular articular cartilages from contrast-enhanced CT images has also been introduced [14, 71, 72].
Classical segmentation techniques include thresholding, region growing, and edge detection [68]. These techniques are straightforward and useful in several cases. However, they are susceptible to flaws and not very applicable for the segmentation of thin musculoskeletal structures in the CT images. More sophisticated segmentation techniques can be based on, for instance, statistical models, atlases, and neural networks [68]. These techniques have been applied to segment bone and cartilage structures from clinical MR and CT images [73–75].
Tables 5.1 and 5.2 summarize the segmentation techniques for knee and hip CT and MR images that have been published during the past years. Methodological accuracies are reported with Dice similarity coefficient (DSC) values where available. DSC is a commonly used parameter that measures the correspondence between two geometries [76]. It is defined as
DSC= 2Jind
Jind+1, (5.1)
where,Jindis Jaccard index, defined as
Jind= Vintersection
V , (5.2)
where Vunionis the union of segmented volumes and Vintersectionis the intersection of segmented volumes. There are other common measures which can be applied for segmentation correspondence e.g. differences in thickness of volume.
Table 5.1: Semiautomatic and automatic methods to segment hip joint CT images published during past years (2016 - March 2019).
Tissue(s) Technique DSC Year Reference
PF Adaptive thresholding - 2018 [77]
PF, AB Refined contouring - 2016 [78]
PF Interactive graph cut - 2016 [79]
PF, AB Statistical shape model - 2019 [80]
F Active and statistical shape model 0.94 2016 [81]
PF = proximal femur, F = femur, AB = acetabular bone
Table 5.2:Semiautomatic and automatic methods to segment knee joint MR images published during past years (2016 - March 2019).
Tissue(s) Technique DSC Year Reference
AC Atlas based 0.82 - 0.87 2016 [12]
DF,PT Graph based 0.95 2016 [72]
AC Neural networks - 2018 [13]
AC, DF Neural networks 0.90 2018 [14]
/ Statistical shape model
AC Intensity thresholding 0.76 2017 [82]
AC Neural networks - 2018 [83]
AC Atlas, voxel-based relaxometry - 2016 [84]
AC = articular cartilage, DF = distal femur, PT = proximal tibia
5.1 SEGMENTATION OF CORTICAL BONE FROM CT IMAGES
Osteoarthritis affects the both thickness and structure of subchondral bone plate [41, 85]. These changes are challenging to define from clinical CT images using conventional segmentation methods due to the thin structure of cortical bone. The first attempts to resolve this issue were based on e.g. thresholding, however, this approach encoutered to difficulties, for instance, due to biological variation of BMD which leads to variation in the HU values in CT images [86]. Full width half maximum (FWHM) can be used for the detection of thin structures in CT images. In this technique, interfaces with strong intensity changes are determined by searching for minimum and maximum values around the change in an intensity profile. The interface is determined to be in the middle of these two 18extremes. When the intensity line is set as being perpendicular to and through the cortical surface, the FWHM defines cortical thickness based on the profile maximum and its width. This approach is demonstrated in figure 5.1. However, FWHM width depends also on image spatial resolution which is characterized by the point spread function (PSF), which introduces a bias with respect to the cortical thickness as determined from clinical CT images.
Figure 5.1: Application of full width half maximum (FWHM) to determine the thickness of cortical bone. a) An axial CT slice of a distal human femur. The red arrow from trabecular bone through cortical bone to soft tissue represents the location of the profile in subfigure b).b)Intensity profile of HU values in a CT slice.
FWHM is used to determine the thickness of cortical bone even though HU values of soft tissue and trabecular bone differ from each other.
In earlier studies, techniques, such as deconvolution algorithms [87], have been introduced to improve the accuracy of measurements of cortical thickness. For instance, intensity profile on a CT image can be presented as the convolution of true intensity with in-plane and out-of-plane PSF [88]. In-plane PSF, i.e. PSF in a single CT slice, can be modeled as normalized Gaussian function
gin(x) = 1 σ
√2πe−x
2
2σ2, (5.3)
whereσis a quantitative constant for the blurring [89]. The thickness of the cortical
bone in the CT slice depends on the direction of the cortical bone surface in relation to slice orientation. This affects the out-of-plane PSF which can be calculated with a rectangular function
gout(x) = 1
2r[H(x+r)−H(x−r)], (5.4) where 2r, the extent of blur, is calculated as
r= s
2tan(α), (5.5)
wheresis the slice thickness andαis the angle between the imaging plane and the normal of the cortical bone surface [88]. When the slice thickness and the cortical surface direction are known and used as prior information, the variation in CT data across the cortex can be presented as combination of the equations (5.3) and (5.4)
y=y0+y1−y0 2
1+erf
x−x0 σ
√2
+y2−y1 2
1+erf
x−x1 σ
√2
, (5.6) where y0, y1 and y2 are the HU values in the surrounding tissue, cortical and trabecular bone, respectively, x0 and x1 are the locations of the periosteal and endocortical surfaces respectively [90]. The error function erf is defined as
erf(x) = 2 π
Z x
0 e−t2dt. (5.7)
Equation 5.6 can be utilized to determine x0 and x1,i.e., the location of the cortex, by fitting the function iteratively to the actual data across cortex in the CT image. A similar approach has been used to model the thickness of articular cartilage at the sub millimeter range [91]. In addition, the cortical bone density has been estimated using this method by adding a variable for density to the optimization model [90].
5.2 GENERATION OF 3D SHAPES FROM SPARSE CONTOURS
A common way to generate 3D surfaces is to use information from 2D contours drawn on image slices. For instance, these contours can be combined with rendering techniques that utilize for instance linear interpolation. Sparsely drawn or sparse contours are contours drawn on every third or fewer slices. If contours are determined manually, reducing the amount of drawn contours decreases the manual work. However, when working with sparse contours, linear interpolation can produce unrealistic and irregular 3D representation of the target.There are numerous sophisticated 3D surface rendering techniques [92–95].
Typically they can be categorized into either direct triangulation techniques or techniques that use image data between the contoured slices in order to create a 3D surface. Direct triangulation uses only drawn contours in 3D surface generation.
Non-direct triangulation is a more advanced approach: a surface is estimated with a specific function which is based on both contours and image data between drawn contours. For instance, triangulation can then be done using the marching cubes technique [96].
Region correspondence based surface interpolation has been proposed to provide a suitable method for handling the data in clinical images [97]. The 20
method utilizes disc templates, i.e. circles or ellipses, that are created to loosely represent the shape of drawn cross-section contours on each image slice. The correspondence between these disc templates is calculated using distance transforms. In this context, distance transforms are vectors that give each disc point a weight and direction. These values are based on the correspondence of the discs in adjacent slices. The determined distance transforms are used to determine the direction of a non-linear interpolation between the drawn contours.
Furthermore, the direction of interpolation is allowed to vary at each slice between the drawn contours. Due to these weighted and varying distance transforms, only a few contours are needed for 3D rendering, and the method can still be successfully applied for contours that differ significantly from each other.
6 Finite element modelling of the knee joint
Finite element modelling (FEM) is a computational method for analyzing physical events, such as mechanical responses and fluid flow. In the method, the physical entity of interest is described with partial differential equations (PDE). Generally, PDE can be solved analytically only in restricted simple regions, such as for a cylindrical shape. If the target is divided into small elements, PDE can be used to solve in more complex shapes using numerical solutions. Furthermore, the non-linearity of the material properties can be implemented in the numerical evaluation. One of the strengths of FEM is that it makes possible to analyze phenomena that are inaccessible with fully experimental methods. It is laborious, often challenging or even impossible to measure directly the biomechanical responses of the knee joint. For these reasons, FEM has been found to be useful for analyzing the function of a knee joint.
Generating a FE model of the knee joint requires several steps, each of which will affect the results of the FE analysis. First, the anatomy of the knee joint is acquired via clinical imaging. In knee joint modelling, MR images are most commonly used. Secondly, the tissues need to be segmented in the images. The conventional way is to use manual segmentations with simplistic tools, such as thresholding, morphological, and Boolean operations, obtainable from some segmentation software. After segmentation, the 3D voxel volumes are constructed as a volume of elements. A typical mesh consists of tetrahedral or hexahedral elements, completed with the specific material properties. By adding a sufficient contact between the cartilages and further changing the knee angle with time, the model can simulate physiologically relevant movement and loading of the joint.
With these simulations, biomechanical parameters, such as stresses or strains, can be evaluated in the tissues. In figure 1.1, the general work flow of the generating FE model is presented.
Material models of articular cartilage have evolved over time from the first somewhat over-simplified models to the current very complex tecnhniques. The earliest models considered articular cartilage as a linearly elastic material. In the biphasic theory the cartilage is assessed in a more realistic manner: the theory models articular cartilage as a material with distinct solid and liquid phases [98].
Nowadays, FE models of the knee joint take into account the multiform structure of cartilage or cartilage properties such as collagen orientation or swelling [15, 99, 100]. The implementation of the models may take into account ligament strains or muscle forces [16, 101]. For instance, the imaging techniques makes it possible to utilize knowledge of the inhomogeneous proteoglycan content in the cartilage [102]. Moreover, the addition of inhomogeneous elastic properties of the bone in the knee joint models has shown to affect the stresses experienced by articular cartilage [103].
Imaging
Segmentation
Meshing
Adding material properties
Applying boundary conditions and movement
Evaluation of stresses and strains
Figure 6.1: Construction of FEM.
6.1 MATERIAL PROPERTIES IN KNEE JOINT MODELS 6.1.1 Modelling of elastic properties of bone
The connection between bone mineral density and values of Young’s modulus was presented in chapter 2.1. This relationship can be used to derive a voxel-specific map of the values of Young’s modulus. The conversion could further be utilized in finite element modelling by calculating the HU values over each element: the Young’s modulus field over the element can be calculated as
En = R
VnE(x,y,z)dV R
VndV , (6.1)
wherex,y, andzrefer to the image coordinates (CT) andE(x,y,z)is the interpolated Young’s modulus value between the adjacent grid points in a generic point in the CT domain [103, 104].
6.1.2 Poroelastic and biphasic cartilage models
Hooke’s law links the strains and stresses in the linearly elastic material as
σeffect=Ceelastic, (6.2)
whereσeffectis a effective stress tensor, Cis a stiffness matrix, andeelastic is a strain tensor. The stiffness matrix defines the material properties; it can be specified to be an isotropic, transversely isotropic, or anisotropic material.
In the biphasic theory, articular cartilage may be divided into two phases [98], fluid and solid, and their stresses are defined as
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