Predicting knee osteoarthritis : development and application of segmentation and finite element modelling methods

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THE UNIVERSITY OF EASTERN FINLAND Dissertations in Forestry and Natural Sciences

ISBN 978-952-61-3042-2 ISSN 1798-5668

Dissertations in Forestry and Natural Sciences

DISSERTATIONS | MIMMI LIUKKONEN | PREDICTING KNEE OSTEOARTHRITIS | No 339

MIMMI LIUKKONEN

PREDICTING KNEE OSTEOARTHRITIS

Development and application of segmentation and finite element modelling methods

PUBLICATIONS OF

THE UNIVERSITY OF EASTERN FINLAND

Prevention of osteoarthritis (OA) is currently problematic. In order to enable prevention, one

should be able to predict the OA progression and suggest an intervention. In this thesis, the effect of obesity and weight loss on the progression of knee OA was studied using finite element modelling with a cartilage degeneration algorithm. In addition, a semi- automatic segmentation method to speed up

the modelling workflow was introduced.

These methods could be applied as a clinical tool to improve the diagnostics and treatment

of knee OA.

MIMMI LIUKKONEN

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PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND DISSERTATIONS IN FORESTRY AND NATURAL SCIENCES

N:o 339

Mimmi Liukkonen

PREDICTING KNEE OSTEOARTHRITIS

DEVELOPMENT AND APPLICATION OF SEGMENTATION AND FINITE ELEMENT MODELLING METHODS

ACADEMIC DISSERTATION

To be presented by the permission of the Faculty of Science and Forestry for public examination in the Auditorium CA102 in Canthia Building at the University of Eastern Finland, Kuopio, on April 5th, 2019, at 12 o’clock.

University of Eastern Finland Department of Applied Physics

Kuopio 2019

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Grano Oy Jyväskylä, 2019

Editors: Pertti Pasanen, Jukka Tuomela, Matti Tedre, and Raine Kortet

Distribution:

University of Eastern Finland Library / Sales of publications julkaisumyynti@uef.fi

http://www.uef.fi/kirjasto

ISBN: 978-952-61-3042-2 (print) ISSNL: 1798-5668

ISSN: 1798-5668 ISBN: 978-952-61-3043-9 (pdf)

ISSNL: 1798-5668 ISSN: 1798-5676

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Author’s address: University of Eastern Finland Department of Applied Physics P.O.Box 1627

70211 Kuopio, Finland

email: mimmi.liukkonen@gmail.com Supervisors: Professor Rami K. Korhonen

University of Eastern Finland Department of Applied Physics Kuopio, Finland

email: rami.korhonen@uef.fi Professor Jari P. Arokoski

Helsinki University Hospital / University of Helsinki Department of Physical and Rehabilitation Medicine Helsinki, Finland

email: jari.arokoski@hus.fi

Adjunct Professor, Mika E. Mononen University of Eastern Finland Department of Applied Physics Kuopio, Finland

email: mika.mononen@uef.fi Reviewers: Associate Professor Thor F. Besier

University of Auckland

Department of Engineering Science Auckland Bioengineering Institute Auckland, New Zealand

email: t.besier@auckland.ac.nz Adjunct Professor, Timo Liimatainen

University of Oulu / Oulu University Hospital Research Unit of Medical Imaging,

Physics and Technology Oulu, Finland

email: timo.liimatainen@oulu.fi

Opponent: Professor Donald D. Anderson

University of Iowa

Department of Orthopedics and Rehabilitation Orthopaedic Biomechanics Laboratory

Iowa City, United States

email: don-anderson@uiowa.edu

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Mimmi Liukkonen

Predicting knee osteoarthritis: Development and application of segmentation and finite element modelling methods

Kuopio: University of Eastern Finland,

Publications of the University of Eastern Finland

Dissertations in Forestry and Natural Sciences, 2019, 339.

ABSTRACT

Osteoarthritis (OA) is a joint disease primarily characterized by alterations in articular cartilage and subchondral bone. One of the main reasons for the development of OA is excessive loading. More than 250 million people throughout the world suffer from knee OA and the disease is a huge financial burden on both society and the patient him/herself. Currently, there is no cure for knee OA and even symptomatic treatment is very limited. The quality of life of OA patients is maintained by lifestyle choices, pain medication and rehabilitation. Ultimately, the only solution is knee replacement. Thus, the most cost-effective treatment would be prevention of the disease. To achieve this, clinically available tools for predicting the progression of OA are needed.

Magnetic resonance imaging (MRI) is widely used for evaluating soft tissues of the knee joint, but it is not suitable for investigating the effect of biomechanical factors on knee cartilage degeneration. Thus, computational modelling techniques, such as finite element (FE) modelling, are needed. In order to create subject-specific FE models, joint geometries should be extracted from medical images using segmentation. Time consuming and laborious manual segmentation is usually needed for knee cartilages, since there is a lack of accurate and fast automatic segmentation methods for biomechanical modelling purposes.

Globally, more than one third of adults are overweight and it is estimated that this number will increase in the future. Since obesity is one of the major risk factors for knee OA, it can be expected that the number of patients with overweight induced knee OA will also increase. The primary intervention for obese OA patients is weight loss, which has been shown to reduce knee joint loads and pain, and restore joint function i.e. improving the patient’s quality of life. On the other hand, the amount of satisfactory weight loss for an individual patient is not known. In order to encourage patients to undertake weight loss, a computational model, which could predict the progression of OA and the outcome of the intervention, would be beneficial.

The purpose of this thesis was to investigate the effect of obesity and weight loss on OA progression using a FE modelling with a cartilage degeneration algorithm. In addition, the purpose was to improve the workflow of FE model generation by introducing and validating new radial intensity based cartilage segmentation method. This degeneration algorithm together with the new segmentation method could be applied as a clinical tool to improve the diagnostics, as well as the prediction and treatment of knee OA in the future.

In this thesis, a total of 41 different subject-specific FE models were created

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between manually and semi-automatically segmented geometries were compared to verify the accuracy of the new radial intensity based segmentation method.

Second, 21 knee joint models of three different patient groups (one normal weight group with healthy knees (Kellgren-Lawrence (KL) grade 0) and two obese groups with knee OA (KL2 and KL3)) were generated and the ability of the previously developed cartilage degeneration algorithm to predict the overloading induced progression of OA during walking was evaluated and compared against experimental follow-up data. Third, knee joint models for four different subjects were created with subject-specific gait data before and after the bariatric surgery-induced weight loss, and cartilage degeneration levels at both time points were studied using the cartilage degeneration algorithm.

The results of this thesis indicated that volumes and thicknesses of cartilages were comparable between manual and semi-automatic segmentations. Differences in maximum stresses, strains and contact pressures between manually and semi-automatically segmented knee models were statistically insignificant (p >

0.05). The cartilage degeneration algorithm showed significantly higher (p < 0.05) maximum degenerations and degenerated volumes in the KL2 and KL3 groups compared to the KL0 group. Interestingly, the algorithm showed higher degeneration for more severe OA patients even though their body mass indexes were the same. Weight loss decreased the maximum degeneration and degenerated volumes of tibial cartilage but the decrease was not directly proportional to the amount of weight loss. Cartilage degeneration increased in one patient after weight loss due to altered gait kinematics and kinetics.

In conclusion, the radial intensity based segmentation method is a feasible quantification method for knee cartilage geometry and enables a sufficient accuracy for evaluating possible failure locations in clinical applications. Moreover, the finite element knee joint model combined with cartilage degeneration algorithm can predict the overload induced progression of knee OA and may be used for assessing the effect of weight loss on the disease progression. This thesis introduces advances of computational knee joint modelling that could improve the diagnostics, prediction and treatment of knee OA. The methods devised in this thesis may be applied as a clinical tool in the future.

National Library of Medicine Classification: QT 34.5, WE 300, WE 348, WE 870, WN 185

Medical Subject Headings: Cartilage, Articular; Collagen; Computer Simulation;

Diagnostic Imaging; Finite Element Analysis; Gait Analysis; Knee Injuries; Knee Joint;

Magnetic Resonance Imaging; Models, Theoretical; Obesity; Osteoarthritis; Overweight;

Stress, Mechanical; Weight Loss

Yleinen suomalainen asiasanasto: biomekaniikka; elementtimenetelmä; kollageenit;

kuormitus; kuvantaminen; lihavuus; liikarasitus; liikeanalyysi; magneettikuvaus;

mallintaminen; matemaattiset mallit; nivelrikko; nivelrusto; numeerinen analyysi; ylipaino

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ACKNOWLEDGEMENTS

This study was carried out during the years 2015-2019 in the Department of Applied Physics at the University of Eastern Finland.

The study was financially supported by the Doctoral Programme in Science, Technology and Computing (SCITECO), the Department of Applied Physics, Kuopio University Hospital and the strategic funding of the University of Eastern Finland and Kuopio University Hospital. CSC – IT Center for Science Ltd, Finland is acknowledged for providing the finite-element modeling software.

First and foremost, I would like to thank my supervisors professor Rami Korhonen, professor Jari Arokoski and adjunct professor Mika Mononen for their encouragement and guidance during this project. Especially, I would like to thank Rami for creating a great working environment where scientific (and not so scientific) discussions have pushed me towards finish line. I’m also very grateful for your support during my maternity leave and working periods in the hospitals.

I would like to thank Jari for all help you have given me during these years. It was pleasure to follow your enthusiasm. I would also like to thank Mika for all help and technical guidance; you showed me the secrets of Finite Element modelling.

I wish to thank the official reviewers associate professor Thor Besier and adjunct professor Timo Liimatainen for giving me professional and constructive feedback on my thesis. I’d also like to thank Dr Ewen MacDonald for linguistic review of my thesis. I also want to thank all co-authors of my publications. It was pleasure to work with you.

I warmly thank my roommates Petri Tanska, Lasse Räsänen, Mikko Venäläinen, Simo Ojanen, Lauri Stenroth, Nina Hänninen, Aapo Ristaniemi and Mohammad Ebrahimi. All of you have helped me a lot during this journey. Special thank you goes to Simo; it has been privilege to get to know you. I also want to thank all former and current members of the BBC research group; all of you have created outstanding working environment. Especially, I would like to thank Kata, Miitu and Simo for all leisure time you have spent with me. In addition, I wish to thank all my co-workers in KYS and ESSOTE. I also warmly thank my fellow physicist Timo Leppänen; without you, studies in the university would have been much more boring. A very warm thank you goes to my childhood friend Anni Himanen;

one of the most beautiful qualities of true friendship is to understand and to be understood.

My warmest gratitude goes to my parents Esa and Tuula, siblings Henri and Eija (and her family) and in-laws Jari, Merja and Aleksi for all your support during these years. Especially, I want to thank my parents for their physical, mental and financial support. Without you, this journey would have been much more difficult.

Last but not least, I want to express my deepest gratitude to my beloved husband Jani for his love, patience and understanding during this long journey. It is privilege to have you on my side. Finally, our little daughter Juulia, you make me always smile, even the day would be worst ever. I love you both.

Mimmi Liukkonen

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LIST OF PUBLICATIONS

This thesis consists of the present review of the author’s work in the field of biomechanical modelling of the human knee joint and the following selection of the author’s publications:

I Liukkonen MK, Mononen ME, Tanska P, Saarakkala S, Nieminen MT, Korhonen RK. "Application of a semi-automatic cartilage segmentation method for biomechanical modeling of the knee joint." Comput. Methods Biomech. Biomed. Engin., 2017, 20(13):1453-1463.

II Liukkonen MK, Mononen ME, Klets O, Arokoski JP, Saarakkala S, Korhonen RK. "Simulation of Subject-Specific Progression of Knee Osteoarthritis and Comparison to Experimental Follow-up Data: Data from the Osteoarthritis Initiative."Sci. Rep., 2017, 7(1):9177.

III Liukkonen MK, Mononen ME, Vartiainen P, Kaukiainen P, Bragge T, Suomalainen JS, Karjalainen PA, Arokoski JP and Korhonen RK. "Evaluation of the effect of bariatric surgery-induced weight loss on knee gait and cartilage degeneration."J. Biomech. Eng., 2018, 140(4):041008.

Throughout the overview, these papers will be referred to by Roman numerals.

AUTHOR’S CONTRIBUTION

The publications selected in this dissertation are original research papers on the development and application of segmentation and finite element modelling methods for predicting knee osteoarthritis. The author was the main contributor to all studies.

The author participated in study planning, performed all segmentations and finite element analyses in studiesIand IIIand approximately half of the segmentations and analyses in study II. The author did not collect magnetic resonance imaging data in studiesIandII, while in studyIIIimaging data was collected by the author.

In study I, segmentation algorithm was built by the co-author. In study III, gait analysis and physical performance test were mainly carried out by the co-authors, but the author participated in the measurements in the gait laboratory. The author was the main writer in all studies.

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1 Introduction

The knee joint is one of the strongest joints in the human body. It is a synovial joint connecting the femur to the tibia and allowing movement of lower leg relative to thigh. The joint-forming surfaces of the bones are covered with a hyaline cartilage, which protects the underlying bones, providing a smooth, nearly frictionless, movement between the bones [1]. If cartilage breaks down, the normal function of the knee joint may be disturbed leading to OA [2, 3]. One of the main reasons for cartilage breakdown and the onset of OA is increased loads within cartilage caused by abnormal mechanics [4, 5]. At the tissue level, OA affects predominantly articular cartilage, although other tissues, such as bones, menisci, ligaments and synovium, are also involved [6]. Once OA has developed, it continues until the whole cartilage has worn away, causing bone-on-bone contact. This results in knee pain and stiffness, leading to an inability to cope with daily activities. These symptoms may lead to social isolation, a decrease in work ability, depression, i.e., a decrease in the patient’s quality of life [7].

Obesity is one of the major risk factors for causing excessive loads and developing OA [8–10]. The World Health Organization (WHO) has classified body weight based on body mass index (BMI) into four different categories:

Underweight (BMI < 18.5 kg/m²), normal weight (BMI = 18.5-24.99 kg/m²), overweight (BMI = 25-29.99 kg/m²) and obese (BMI ≥30 kg/m²) [11]. In 2014, 39

% of adults (40 % of women and 38 % of men) worldwide were overweight, and 13

% were obese (15 % of women and 11 % of men) [11]. It is also predicted that the numbers of obese people will increase in the future [11].

Globally, prevalence of knee OA was more than 250 million in 2010 [12]. In the US during 2013-2015, more than 50 million adults had doctor-diagnosed arthritis [13] and in Europe, 5-15 % of people aged between 35-74 years suffer from knee OA [14]. In Finland, 5-7 % of people over 30 years have knee OA [15]. The prevalence of OA is increasing due to the aging of the population and the increasing incidence of obesity all around the world. In Finland, knee OA is responsible for more than half a million doctor appointments in a year [15]. These numbers will be increased in the future due to the increased prevalence of OA.

Osteoarthritis causes a huge economic burden for societies. Direct and indirect yearly costs of OA are near 1 billion EUR in Finland [15] and more than USD $303 billion in US in 2013 [16]. Despite extensive global research efforts, there is no cure for OA, and consequently, the best and most cost-effective treatment option at the moment would be prevention.

The diagnosis of OA is usually based on the patient’s symptoms and traditional radiography [17], but it has a limited capacity of detecting soft tissues. In order to improve diagnostics, magnetic resonance imaging methods have been used. MRI is a non-invasive method to detect the macroscopic lesions in articular cartilage and evaluate cartilage composition [17, 18]. This method does not cause any radiation

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Computational mechanical models have been utilized in the analysis of cartilage and menisci contact mechanics [19], and in describing how they relate to the onset and progression of OA [20, 21]. In order to generate subject-specific geometries for biomechanical knee joint models, it is necessary to have an accurate segmentation of tissues from medical images. Automatic segmentation methods have been developed for assessing cartilage morphology [22, 23], but there is still a lack of automatic methods for computational modelling purposes. Gait analysis can be used for estimating knee kinetics and kinematics during daily physical actions, such as walking and stair climbing [24, 25]. This information can be implemented into the knee joint models to increase their subject-specificity as well as being advantageous when investigating the effect of different interventions on a subject’s kinetics, kinematics and contact mechanics.

The aim of this thesis was to improve and speed up the workflow of FE model generation, in order to transfer computational modelling into clinical use as a way to improve the diagnostics and treatment of osteoarthritis. Moreover, another aim was to investigate the effect of obesity and weight loss on OA progression using a novel cartilage degeneration algorithm. In study I, a semi-automatic radial intensity based segmentation method was developed and validated against manual segmentation. FE models were created for both manually and semi-automatically segmented geometries and the simulation results with the different models were compared. In the modelling part, geometry meshing, material model, loading and boundary conditions were selected such that model creation and simulation would be as quick as possible, which is an important feature in clinical use. In study II, the ability of the novel FE modelling based cartilage degeneration algorithm to differentiate between patients with different levels of OA was tested with a large patient group. In study III, the algorithm was applied for clinical patients with weight loss to examine the effect of weight loss on cartilage degeneration. In addition, subject-specific gait data was obtained and added to the FE models in studyIII.

The results obtained in this thesis have added knowledge about overloading based progression of OA and the importance of taking account of subject-specificity when investigating of different interventions in OA patients. The presented methodologies and approaches could be useful in the future in the diagnosis of OA and could be helpful in identifying improved subject-specific treatment methods for preventing or decelerating the progression of OA.

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2 Knee joint

The knee joint is one of the largest and the most complex joints in the human body including two articulating joints: tibio-femoral and patello-femoral joint. The knee consists of bones (femur, tibia and patella), cartilages (femoral, tibial and patellar), menisci (medial and lateral), ligaments (anterior and posterior cruciate and lateral and medial collateral), tendons and muscles (Figure 2.1). The main role of the knee joint is to allow locomotion and to absorb, transmit and redistribute the forces caused during daily activities [26]. Bones make up the main body of the joint where the muscles attach through the tendons. Articular cartilage covers the ends of the articulating bones, distributing and transmitting forces to the entire articulating surfaces minimizing stress and strain concentrations within cartilage.

In conjunction with synovial fluid and menisci, articular cartilage provide nearly frictionless movements between the bones. Ligaments restrict the motion of the joint providing stability to the joint [1, 26, 27].

Figure 2.1:Antero-medial (left) and axial (right) view of the knee joint.

2.1 ARTICULAR CARTILAGE

Articular cartilage is an avascular, biphasic connective tissue, consisting of cartilage cells (chondrocytes) surrounded by a multicomponent extracellular matrix (ECM) [1]. ECM is composed of fluid (interstitial fluid) and solid (collagen and proteoglycan (PG)) matrices (Figure 2.2) [1]. In the healthy human knee joint, articular cartilage is ∼1.5-5 mm [28–30] thick and the thickness varies depending on the location of the knee (tibia, femur, patella) or site of the cartilage (anterior, middle, posterior) [29, 31, 32], being thickest on the cartilage-on-cartilage contact area (high load area) and thinnest on the regions without contact [33]. Structure

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2.1.1 Structure and composition

Interstitial fluid is the most abundant component of cartilage, accounting for about 80 % of its wet weight. The fluid content is at its highest (∼85 %) in the superficial zone decreasing linearly to∼ 75 % in the deep zone [35, 36] (Figure 2.2). However, the site of cartilage, the age of subject or the presence of pathology in cartilage (e.g.

healthy versus osteoarthritic conditions) may cause differences in the water content [36–38]. Most fluid and ions can flow freely in and out of the tissue [1, 39]

and this fluid flow through cartilage is needed for transporting and distributing nutrients to chondrocytes [39–41].

The main role of highly specialized cartilage cells, i.e. the chondrocytes, is to develop, maintain and repair the ECM of the cartilage by producing collagen, proteoglycan and other components of the cartilage tissue [1]. The chondrocyte content is only 1 % of the volume of human cartilage [42] meaning that metabolism is slow. For this reason, cartilage regenerates and repairs very slowly.

Chondrocytes from different cartilage zones differ in size, shape and activity (Figure 2.2). In the superficial zone, cells are flat and lie in parallel to the tissue surface. In the middle zone, the cell shape is spherical and cells are present in groups of a few cells. In the deep zone, cells are spheroidal shaped and they are oriented in columns perpendicular to the cartilage surface [43, 44].

Collagen is a rod-shaped protein contributing about 15-22 % of the wet weight of cartilage (∼60 % of the dry weight) [1, 27]. The main type of collagen in articular cartilage is type II (90-95 % of the collagen), but also other types (e.g. VI, IX, XI, XII and XIV) exist [45, 46]. Type II collagen forms an organized network and the other collagen types help to form and stabilize this network [45]. The collagen content decreases from the superficial zone towards the middle zone and increases again towards the deep zone [47, 48] (Figure 2.2). Collagen fibrils have an arcade-like orientation throughout the cartilage depth (Figure 2.2). In the superficial zone, a densely packed collagen fibril network is oriented in parallel to the joint surface. In the middle zone, fibrils start to turn towards the bone and they are perpendicular to the subchondral bone in the deep zone [49].

Proteoglycans are formed by a core protein and covalently attached glycosaminoglycan (GAG) chains contributing about 5-10 % of the wet weight of cartilage [1, 50]. The proteoglycan content increases from the superficial zone towards the deep zone of cartilage [47, 48], and is opposite to the interstitial fluid content (Figure 2.2). The most prominent proteoglycan in cartilage is negatively charged aggrecan, which is mainly enclosed by the thick collagen mesh causing fixed charge density (FCD) in the cartilage [1]. This leads to increased osmotic pressure causing a fluid flow to the tissue. This fluid flow results in swelling, which is resisted by the collagen network [1].

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Figure 2.2: Depth-wise structure and composition of the articular cartilage of the knee.

2.1.2 Biomechanical properties

Articular cartilage has to withstand multiple static and dynamic mechanical loads during daily activities, where high dynamic peak stresses with low compressive strains as well as low static stresses with high strains exist. The ability to withstand such changing loading conditions is attributable to the poroelastic properties of the articular cartilage [1, 51–53]. The interstitial fluid, collagen network and proteoglycan have their own characteristics; these are the factors that determine the biomechanical properties of the cartilage [1, 54]. In addition, the response of cartilage to mechanical loading is highly depth-dependent due to the depth-dependently varying composition and structure of cartilage.

Proteoglycans together with the collagen network control the permeability of the cartilage tissue, thus controlling the fluid flow of cartilage [34, 40, 55, 56].

During a dynamic, impact load, fluid flow out of the tissue is almost negligible;

thus fluid has a significant role in controlling the dynamic and impact loading properties of cartilage [57, 58]. During static (creep) load, fluid has time to flow out of the tissue and cartilage tissue starts to compress [1]. In the unloaded condition, fluid flows back to cartilage. Hence, interstitial fluid provides viscoelastic stress-relaxation and creep behaviour of cartilage [59].

The main role of collagen network is to provide the tensile, dynamic and shear properties of cartilage [34, 54, 60, 61]. Collagen fibrils can resist the tissue tensile deformations effectively in the direction of the fibrils [62]. The tensile stiffness of cartilage is at its highest in the superficial zone due to surface-oriented collagen fibrils. In the middle zone, the orientation of collagen fibrils is optimal for resisting

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swelling of cartilage and protect it from large tensile and shear strains, especially at the cartilage-bone interface [54, 63]. In addition, the fibril orientation has a significant role in nutrient transportation from the deep zone towards the superficial zone [56].

In the equilibrium state, compressive properties of articular cartilage are mainly produced by proteoglycans [53, 64]. During the compressive deformation of cartilage, osmotic pressure is increasing due to increase in the fixed charge density.

Together these factors resist fluid flow out from the tissue increasing its effective stiffness.

2.2 MENISCUS

Menisci are two crescent shaped wedges of fibrocartilaginous tissue located on the medial and lateral side of the knee joint between femoral condyles and tibial plateaus (Figure 2.1). The medial meniscus is semicircular (∼40-45 mm long and

∼27 mm wide) covering ∼60 % of the medial tibial plateau surface, while the lateral meniscus is almost circular (∼32-35 mm long and ∼26-29 mm wide) covering ∼80 % of the lateral tibial plateau surface [65, 66]. Menisci horns are attached to the tibial bone via insertional ligaments [67, 68]. The other stabilizing ligaments are medial collateral, transverse, and meniscofemoral ligaments [67].

Due to the differences in the ways of attachments of medial and lateral meniscus, the lateral meniscus is more mobile than the medial meniscus [66]. The purpose of the menisci is to decrease cartilage stresses by increasing tibiofemoral contact area within the knee joint. In addition to load transmission, the menisci contribute to knee joint stability and shock absorption [67, 69].

Similarly to cartilage, the meniscus consists of ECM and cells [1]. The most abundant component of ECM is water, contributing 60-70 % of the wet weight. The remaining tissue is mainly composed of collagen (15-25 % of wet weight) and proteoglycan (1-2 % of wet weight) [1, 67]. Most of the collagen in meniscus is type I although types II, III, IV, VI, and XVIII are also known to be present [68].

Collagen fibers are mainly oriented circumferentially conferring high tensile strength in the circumferential direction and transferring vertical compressive loads into circumferential "hoop" stresses [68, 70]. Circumferential fibers are tied with radially oriented fibers providing better structural integrity [68, 70]. The relatively higher portion of proteoglycans are located in the inner two-thirds of meniscus than in the outer one-third [71]. Their main function is to increase compressive strength of the meniscus.

Unlike cartilage, menisci contains blood vessels and nerves, but it is fully vascularized only at birth [66]. At maturity, only 10-30 % of the peripheral menisci have blood vessels and nerves [66, 72, 73]. Thus, only the outer area of the menisci possesses a healing capability.

2.3 LIGAMENTS

Ligament is a connective tissue mainly consisting of collagen fibers [1]. In general, ligaments connect bones to other bones, limit the mobility of articulations and provide stability to the joint [1]. Primary ligaments in the knee joint are anterior cruciate ligament (ACL), posterior cruciate ligament (PCL), medial collateral ligament (MCL) and lateral collateral ligament (LCL) (Figure 2.1).

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The ACL is attached to the posterior part of the inner surface of the lateral femoral condyle and to the medial part of the anterior intercondylar eminence of the tibia [74]. The PCL crosses the ACL attaching posteriorly to the intercondylar notch of the medial femur and to the posterior intercondylar eminence of the tibia [75]. The main role of ACL is to resist anterior translations and medial rotations of the tibia with respect to the femur [74], while PCL resists posterior translations and lateral rotations [75]. It is the interaction between ACL and PCL during activities (different flexion and extension angles) that provides dynamic stability to the knee joint.

The MCL is attached proximally to the medial femoral epicondyle, while it is distally attached to the medial side of the proximal tibia ∼5 cm below the joint line [76]. Moreover, the LCL is attached on the lateral femoral epicondyle and on the head of the fibula [77]. MCL and LCL restrict primarily valgus and varus rotations, respectively [76, 77].

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3 Knee osteoarthritis

Osteoarthritis is a degenerative joint disease characterized by a progressive loss of articular cartilage, subchondral bone sclerosis and remodelling and formation of subchondral bone cysts and osteophytes [3]. Overall, OA affects all of the synovial joint tissues: cartilages, bones, menisci, ligaments, synovium, and muscles, causing joint pain, joint effusion and crepitus during motion [2, 6, 78]. Osteoarthritis can occur in any synovial joint, but most frequently it is encountered in the foot, knee, hip, spine, and hand joints [2, 79].

The main risk factors for knee OA are aging, female gender, abnormal knee alignment, knee injury, occupational overuse and obesity [80]; with the exception of age and female gender, these factors are mainly related to mechanical overloading of the knee. On the other hand, it has been suggested that ACL laxity may change during the menstrual cycle [81] causing changes in knee joint loading. Thus mechanical overloading may have a role in an onset of OA in women. Obesity is responsible for chronic excessive impact and cumulative loading while a knee injury is typically related to focal impact overload.

One of the first signs of OA is fibrillation in the superficial zone of articular cartilage which progresses into the middle and deep zones when OA progresses [2, 3, 47, 82] (Figure 3.1). Other changes are proteoglycan loss in the superficial zone, subchondral bone remodeling and increase in water content [2, 3, 47, 83]. These changes in cartilage composition increase the permeability and decrease the stiffness of the cartilage matrix [2, 84]. Some investigators believe that articular cartilage loss increases peak stresses on subchondral bone leading to bone remodeling, while others have postulated that it is the stiffening of subchondral bone that causes articular cartilage degeneration [85–87]. As OA progresses, the surface of cartilage becomes rough and irregular and cartilage starts to tear (Figure 3.1). Free cartilage fragments are released into the joint space and cartilage become thinner. At the end stage of the disease, cartilage is fully degenerated and bone-on-bone contact exists causing pain and stiffness in the joint [83].

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Figure 3.1: Top row: Progression of radiological knee OA. Bottom row: Structural changes in the knee cartilage during OA.

The diagnosis of OA is traditionally based on clinical examination and radiography [17, 88, 89]. Unfortunately, those diagnostic methods are insensitive at detecting early OA changes [17, 88]. This means that patient is often only diagnosed with OA after it has progressed and caused prominent changes at the joint level. Magnetic resonance imaging (MRI) can be used for OA diagnostics, since it may reveal earlier OA changes than the conventional methods [17, 18, 88].

The level of OA severity is normally classified using Kellgren-Lawrence (KL) grading criteria [90], which are based on inspections of radiographs. This grading method is a five-step scale, which focuses on joint space narrowing and the presence of osteophytes in the entire knee joint (Table 3.1) [90]; the grading is not directly measuring the extent of cartilage degeneration. The Osteoarthritis Research Society International -atlas is another, less widely used, radiography based classification scale in clinical practice [91]; this classifies individual grades for medial and lateral compartments. Long-lasting knee pain, stiffness, and physical function of patients with knee OA can be evaluated using The Western Ontario and McMaster Universities Arthritis Index (WOMAC) [92]. In addition, prevailing pain 10

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can be quantified using the Visual Analog Scale for Pain (VAS) [93]. The drawbacks of these methods are that they are subjective and in no way related to medical images or perception of clinicians. It is also important to notice that there is often a poor correlation between radiographic measures of OA and symptomatic pain [94].

Table 3.1: Kellgren-Lawrence grading system [90]

Grade Radiographic findings

0 No OA changes

1 Doubtful joint space narrowing and possible osteophytes 2 Possible joint space narrowing and definite osteophytes 3 Definite joint space narrowing, moderate multiple osteophytes,

some sclerosis and possible deformity of bone ends 4 Marked joint space narrowing, large osteophytes,

severe sclerosis and definite deformity of bone ends

Attempts have been made to devise OA classification systems also for MR images. The two most widely used semi-quantitative grading systems are Boston-Leeds Osteoarthritis Knee Score (BLOKS) [95] and Whole-Organ Magnetic Resonance Imaging Score (WORMS) [96]. Both methods examine OA related abnormalities in various structures such as cartilages, menisci, ligaments and bones at different anatomical regions. The scoring of certain abnormalities is similar between these methods, with the most prominent differences being detected in the evaluation of cartilage defects, subchondral bone marrow lesions and meniscal tears [97]. In order to avoid having to choose between these two instruments, the MRI Osteoarthritis Knee Score (MOAKS) has been developed [98]. This method improves the assessment of meniscal tears and bone marrow lesions. In the MOAKS grading system, the whole knee is divided into 14 sub-regions and the evaluation is made for all regions separately. The femoral cartilage is divided into six sub-regions: medial and lateral anterior, central and posterior femur (Figure 3.2). Similar division is defined for tibial cartilage. The definitions utilized in the evaluation of cartilage are presented in Figure 3.2.

Currently there is no cure for OA and traditionally pain medication, rehabilitation and physical activity have been used for maintaining the quality of life [89, 99]. Surgical treatments for relieving OA symptoms are cartilage repair, knee joint distraction, realignment of the knee (osteotomy) and knee joint replacement (knee arthroplasty) [89, 100, 101]. Repair techniques for focal cartilage defects are bone marrow stimulating techniques, replacement techniques or grafting or a combination of these techniques [89, 100]. In knee joint distraction, the ends of femoral and tibial bones are gradually separated from each other for a fixed time using an external fixation frame [101]. Osteotomy is the method where the knee joint is realigned such that joint load is transferred from a diseased compartment to a healthier one [102]. Ultimately, when the pain becomes intolerable, total knee replacement is the only feasible solution for treating knee OA [89, 100]. In this respect, the best option for the treatment of OA must be its prevention.

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Figure 3.2: Top left: Delineation of femur and tibia into anterior (A), central (C) and posterior (P) regions. Top right: Division of femur and tibia into medial (Med) and lateral (Lat) compartments and subspinous (SS) region. Bottom row: Grading criteria for cartilage [98].

3.1 OBESITY AND OSTEOARTHRITIS

Obesity is the most important modifiable risk factor for knee OA [8–10, 103]. It has been postulated that the earlier in adult life an individual becomes obese with the resulting increase in the loads placed on the knee joint increases her/his risk for developing OA [104]. Obese individuals have a 7 times greater risk to suffer knee OA than normal weight subjects [9]. It has also been shown that a 5-unit increase in BMI increases the risk for knee OA by about 35 % with this relationship being higher in women than men [105, 106]. Moreover, the knee OA encountered in obese individuals is more severe than in normal weight people [107].

Obesity does not only cause structural joint damage due to increased joint loads, decreased muscle strength and altered biomechanics, but it also triggers metabolic changes causing inflammation of the joint e.g. as a result of the elevated insulin levels [108]. There is also evidence that the amount of pro-inflammatory cytokines increases in the knee joint due to the increased load [109] and that their levels can predict the incidence of OA [110]. Obesity also increases the risk of OA in non- weight-bearing joints such as hands [111], which indicates that OA is not purely a mechanical disease. Nonetheless, the mechanisms behind the connection between obesity and OA are poorly understood [112].

The primary and most effective intervention for obese OA patients is weight loss [113]. It has been shown that∼2 unit reduction in BMI leads to a 50 % decrease in the probability of developing knee OA in women [114]. One major reason for 12

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that may be that the weight loss reduces both the extent of inflammation and the joint loads in the knee joint [113,115–117]. For example, it has been calculated that a weight loss of 1kg results in a 4 kg reduction in the mechanical knee joint loads [118].

Weight loss also alleviates knee pain and improves function [119] increasing the patient’s quality of life. A weight loss of 10 % has been claimed to be the threshold for experiencing a significant improvement in knee pain levels [120,121]. It has been suggested that weight loss decreases the muscle strength in the lower extremities and thus exercise is needed to restore the strength [122]. Thus, weight loss should be accomplished by combining diet and exercise, not diet or exercise alone, to achieve a better outcome in knee pain and joint function [123]. For some patients, exercise and diet based weight loss does not produce the desired results, especially if long- term lifestyle changes are not achieved. In those cases, weight loss can be induced by bariatric surgery (i.e. weight loss surgery) or pharmacotherapy [113].

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4 Knee joint imaging, segmentation and gait analysis

Radiography (x-ray) is the primary imaging method when evaluating knee OA [17, 88, 89], it is mainly based on estimating the joint space narrowing, the amount of osteophytes, subchondral sclerosis and subchondral cysts [90]. Since cartilage is not directly detectable in traditional x-ray, cartilage thickness is estimated based on joint space width [124]. This estimation may be inaccurate, e.g.

possible meniscal extrusion may also cause joint space narrowing [125–127].

Traditional radiography is fast, cheap, widely available, well understood, repeatable and simple, supporting its use in the diagnosis of OA. On the other hand, traditional radiography is limited to 2D images, which also makes it almost impossible for use in biomechanical applications.

Since x-ray reveals only bony structures, the evaluation of soft tissues is almost impossible. To improve the evaluation of knee joint disorders, contrast-enhanced computed tomography (CECT) and MRI techniques have been developed since these can reveal the structure, composition and condition of cartilage [18, 88, 98, 128, 129]. However, these methods are slower, more expensive and not as widely available as traditional x-ray.

Segmentation is a method in which regions of interest (ROIs) are delineated from images into non-overlapping homogeneous regions based on specific features such as intensity or texture [130]. In clinical and musculoskeletal applications, segmentation is often used for differentiating between different anatomical regions (for example bones, cartilages and muscles). Manual segmentation, considered as the gold standard, is accurate and a widely used method [131–136], but it suffers from intra- and inter-observer variability and is rather time-consuming [137–139].

Automatic segmentation methods are faster and less affected by user variability, but developing those kinds of methods for medical images is challenging.

Furthermore, reliable segmentation procedures are needed not only for assessing morphological changes (changes in cartilage thickness and volume) but also for generating subject-specific geometries as a basis for adopting different computational modelling approaches [140, 141]. Automatic procedures could also make it possible to develop a standardized practice for identifying biomarkers as well as being essential when analyzing large datasets.

Gait analysis can be used for evaluating gait patterns (e.g. step length, gait speed and cadence), joint kinetics (forces and moments) and kinematics (rotations and translations) during human movement (e.g. walking, running and jumping) [142, 143]. Gait analysis is used in sports biomechanics to improve athletes’ sports performance, but it is clinically less available. Gait analysis could be a useful complementary technique for improving medical diagnostics and rehabilitation.

In the following sections, knee joint imaging, segmentation and gait analysis methods are discussed especially from the point of view of knee joint biomechanics and with respect to the ways of evaluating of knee OA in clinical and research

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4.1 MAGNETIC RESONANCE IMAGING

Magnetic resonance imaging is a non-invasive imaging technique which enables superior soft tissue contrast [18], thus, being advantageous for imaging articular cartilages and other soft tissues in the knee joint. Compared to traditional radiographs, MRI is more sensitive at detecting osteoarthritic changes in the knee [17].

MRI has been widely been used for studying cartilage morphology, as well as for revealing cartilage lesions and composition [18, 98, 144]. The main pulse sequences used for imaging cartilage morphology and lesions are T2-weighted or proton-density (PD) Fast Spin Echo (FSE), 3D T1-weighted Spoiled Gradient Echo (3D SPGR) and 3D Double Echo Steady State (3D DESS) [145–147]. Nonetheless, in order to assess cartilage composition, more specialized methods are needed [18, 145, 148]. The cartilage proteoglycan content can be evaluated using delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) [149, 150] or T1ρ-sequence [151], while the water content and orientation of the collagen fibers of cartilage can be examined using T2 mapping techniques [18, 152, 153].

A local decrease in dGEMRIC index has been associated with a loss of glycosaminoglycan [154], while an increase in the T2 relaxation time was linked with the degeneration of cartilage due to collagen fibrillation and an increase in the water content [155, 156]. The T2 relaxation time has been shown to associate with the subject’s age and BMI [157–159] and weight loss has been shown to decrease cartilage T2 time [160]. The dGEMRIC index and T2 relaxation time may predict the onset of radiographic knee OA [156, 159, 161]. In biomechanical applications, MRI is widely used for creating subject-specific knee joint geometries [131, 133, 134, 162] and for evaluating cartilage composition (such as collagen orientation and FCD) [162, 163] in computational models.

4.2 SEGMENTATION METHODS FOR CARTILAGE

Important features, i.e. biomarkers, from the knee joint can be extracted with segmentation. Those markers are crucial for studying the development and progression of OA. For example, cartilage thickness and volume as well as knee bone shape have been proposed to predict the progression of OA [164–167]. Many different semi-automatic and automatic segmentation methods applicable to the knee joint have been developed for clinical or research use [22], but there is no perfect method suitable for all kinds of images and tissues. In addition, it is difficult to develop a segmentation method that works well for both healthy and diseased knee joints. The main challenges encountered in knee joint segmentation are the low contrast between different structures, intrinsic image intensity heterogeneity, image artefacts (e.g. motion and field inhomogeneity artefact), and the partial volume effect [22].

When validating automatic segmentation methods, manual segmentation is usually considered as the gold standard and accuracy of the method is tested by calculating similarity values of the automatic method against manual segmentation [138, 168–173]. The Jaccard index (J) and the Dice Similarity Coefficient (DSC) have been used for calculating the overlapping of the segmented masks [22]. The Jaccard index is the intersection of the segmented masks (A∩B) divided by the union of the masks (A∪B):

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J= ^A∩B

A∪B. (4.1)

The Dice Similarity Coefficient can be calculated from the Jaccard index as follows:

DSC= ^2J

1+J. (4.2)

In addition, other metrics such as sensitivity, specificity, and coefficients of variation can be calculated to assess the accuracy of the segmentation method [22].

Moreover, statistical correlation coefficients can be used for estimating the accuracy of the method’s repeatability [174].

A prior knowledge required cartilage segmentation methods can be divided into the three catogories: model-based [168, 175–179], atlas-based [169, 170, 180–182], and machine learning-based [171, 172, 183–187]

methods. Model- and atlas-based methods have shown promising results, but both methods tend to fail when there is a high variability between subjects [22].

Moreover, all three approaches need prior knowledge about the shapes of the segmented tissues and training of the method is usually time consuming and may suffer from user-dependent variability [22, 137].

In the model-based methods, training sets are used for creating shape models from objects, which are then fitted to match the target image [188]. In one of the first model-based knee cartilage segmentation approaches, femoral cartilages were segmented using 2D active shape models (2D-ASM) [175]. Vincent et al. [168]

proposed a fully automatic 3D Active Appearance Model (3D-AAM) based segmentation method for knee cartilages and bone. The average Dice Similarity Coefficients between automatic and manual segmentations for femoral and tibial cartilage segmentations were 0.78 and 0.79, respectively.

In the atlas-based methods, one or multiple, usually manually segmented, references are registered on the target image [130]. Tamez-Peña et al. [169] devised a multi-atlas segmentation algorithm, in which five manually segmented knee MRI series were used as reference atlases, while Lee et al. [170] compared multi-atlas segmentation with the region adjustment counterpart. When compared to manual segmentations, DSC values of cartilages were∼0.86 and∼0.72 in the first [169] and second [170] method, respectively.

Machine-learning based segmentation methods are sets of methods that can detect statistical patterns from the data and use that knowledge to predict future data [130]. Machine-learning based algorithms can be either supervised (training data is needed) or unsupervised (training data is not needed). However, unsupervised methods have not been proposed for knee cartilage segmentation.

The K-nearest neighbour classification has been successfully used for segmenting medial tibio-femoral cartilages from low-field MR images [171]. The similarity between manually and automatically segmented cartilages was shown to be∼0.79.

Ambellan et al. [172] combined Convolutional Neural Networks (CNNs) with 3D Statistical Shape Models (SSM). This method achieved high accuracy between the manual and automatic segmentation method (DSC∼88 %).

There are also multiple segmentation methods for knee cartilage in the literature, which do not need prior knowledge, such as region growing [189], edge

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methods, but they require a significant amount of user interaction. One promising method for segmenting knee joint cartilage without any prior knowledge is the graph-cut method [138]. A comparison between manual and semi-automatic segmentation methods revealed an average similarity coefficient of 87.8 %. When using the watershed method, a similarity coefficient of ∼49 % was observed [192], but combining watershed with atlas registration the similarity improved to 89.5

% [173].

Although multiple segmentation approaches have been developed for measuring biomarkers from healthy and diseased knee joints, only a few of those have involved geometry creation of biomechanical knee joint models [129, 193].

Baldwin et al. [193] proposed a statistical shape model to generate automatically subject-specific geometries and hexahedral meshes for finite element modelling applications from MR images. Differences between contact pressures of manually and semi-automatically segmented cartilages were ∼5 %. The disadvantage of the method was that it required manually segmented prior knowledge from knee joint cartilages. Myller et al. [129] developed a semi-automatic knee cartilage segmentation method utilizing CT images. In their method, cartilages are segmented based on prior knowledge about the knee bones. Their results showed that the new segmentation approach was >90 % faster than the manual method [129]. They also tested the validity of the segmentation method for creating knee joint geometries for FE modelling. The average differences of tensile stresses between manually and semi-automatically segmented geometries were almost zero, but standard deviations were higher, especially in the medial compartment of the knee [194]. Even though these two methods showed promising results in terms of computational modelling outcomes, there still exists a need for a clinically appropriate segmentation method, which would be fast and not require any prior knowledge about knee joint tissues. That kind of method would help to convert computation modelling into a clinical tool and assist in improving decision making for clinicians struggling to treat the OA patient.

4.3 GAIT ANALYSIS

Human gait can be divided into two parts: stance phase (the first 60 % of the gait cycle) and swing phase (the last 40 % of the gait cycle). In healthy normal subjects eight specific events can be observed from the gait cycle: 1) initial contact (0 %), 2) loading response (0-10 %), 3) midstance (10-30 %), 4) terminal stance (30-50 %), 5) preswing (50-60 %), 6) initial swing (60-70 %), 7) midswing (70-85 %), and terminal swing (85-100 %) [195].

Different kinds of measurement techniques have been used in assessing knee joint kinematics (rotations and translations) [196–203]. Perhaps the most commonly used method for gait analysis is stereophotogrammetry in which instantaneous position of skin markers located in the different parts of the body is obtained with conventional photography or optoelectric sensors [196, 204]. Markers are located based on specific landmarks of the body, so that they represent the movement of certain bones. Major limitations in marker-based methods are misplacements of the marker, errors in estimation of marker location, and soft tissue artefacts (i.e. the motion of the markers with respect to the underlying bones) [205]. In order to minimize this error, model-based methods have been developed; in these a geometrical multisegment model has been fitted to the markers being observed

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during the experiment [206, 207]. One of the proposed methods for fitting the model to observations has been a Kalman filter, which estimates the pose of the model based on the estimation of the marker position during a previous step [207, 208]. In order to remove the errors caused by the soft tissues, bone pins and fluoroscopic methods have been proposed [197, 198]. In the fluoroscopic methods, single or multiple fluoroscopic systems are used for monitoring the movement of bones with respect to each other. There are also some other markerless motion capture methods described in the literature, such as an electrogoniometry method [199, 200], visual hull method [201, 202], structured light and time-of-flight methods [203].

External forces (ground reaction forces, GRFs) can be measured using force plates. Combining kinematic data obtained with marker-based or markerless methods with GRFs, joint moments can be estimated using inverse dynamics [209].

In addition, electromyography can be used for measuring the electrical activity of muscles and that knowledge can be exploited in the inverse dynamic analysis.

Individual muscle tension can be measured using invasive methods such as optic fibers [210] or estimated indirectly from tendon loads [211]. Moreover, joint contact forces can be measured with an implanted prosthesis [212]. Musculoskeletal models have been proposed as a way of avoiding invasive methods [213]. In the musculoskeletal models, the human body has been considered as rigid body segments controlled by muscle activation. Muscle, ligament and joint contact forces of the human joints can then be estimated using either forward (motion calculated based on the forces applied to the system) or inverse dynamics (forces solved from the motion) [209, 214].

Gait analysis has been used for assessing the effect of different knee joint disorders (such as OA [215], ACL-rupture [216, 217] and meniscectomy [218]) or treatment methods (e.g. osteotomy [219, 220] and total knee replacement [221]) to human gait. In addition, the effect of obesity [222] and weight loss [223] has been studied using gait analysis. Patients with severe knee OA have been shown to have increased knee adduction moments when compared to individuals with less severe OA or control subjects [224, 225]. The OA patients were also shown to have smaller knee flexion angles compared to healthy patients and furthermore being obese with OA has been shown to decrease those angles even more [226]. It has been proposed that obese patients [227] as well as patients with knee OA [228] have a smaller range of motion. Weight loss has been shown to decrease significantly absolute ground reaction forces [117, 206, 229, 230]. In addition, decreases of axial and posterior ground reaction forces were also seen after normalization to subjects’

body weight [229]. Weight loss has shown to increase extension moment and decrease normalized abduction moment [229]. On the other hand, decreased absolute knee joint moments after weight loss has also been reported [206]. It is also observed that weight loss in OA patients can reduce knee joint compressive forces and abduction and external rotations [115, 118, 231].

It may be possible to use subject-specific gait analysis to identify specific features in gait for different subject groups, to evaluate possible risk factors for knee disorders or the effect of rehabilitation. Subject-specific gait together with joint geometry is also an important input for biomechanical modelling purposes to evaluate stress and strain distributions within the knee joint as well as to predict

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5 Finite element modelling of the knee joint

Although there are multiple methods for assessing knee joint morphology, function and development of OA, none of those can directly estimate stresses and strains within the knee joint and predict the onset and development of OA.

Musculoskeletal models have been used for estimating individual muscle forces and joint contact forces [214, 232–236]. However, they usually simplify the joint geometry and mechanics. In order to gather more detailed information about contact behaviour (e.g. cartilage stresses, strains, pore pressures and fibril strains) Finite Element Method (FEM) is needed. FEM has been applied for studying joint, tissue and cell level biomechanics [19, 237]. Even though FE analysis is time consuming and challenging, especially if subject-specific features such as geometry, tissue composition, material properties and movement have been taken into account, it has been widely used for assessing the progression of OA and estimating the effect of different surgeries and disorders [20, 21, 132, 238, 239]. One of the first FEM based biomechanical applications was published in the beginning of 70s [240] and nowadays it can be used for analyzing subject-specific cases.

5.1 KNEE JOINT MODELS

One of the first knee joint models was proposed by Chand et al. [241]. They studied contact stresses between femur and tibia bones with a 2D FE model without soft tissues. Subsequently, hundreds of papers have been published describing contact mechanics of the knee joint [19, 237]. In many knee joint studies, bones were considered as rigid [131–133, 136, 242–244] due to their high elastic modulus as compared to cartilage tissue and since it has been shown that the rigid bone assumption is valid for simple axial load [245]. Only in a couple of studies bones were considered as non-rigid [245–249]. In many reports, ligaments have been considered as linear or nonlinear springs or completely excluded [131, 134, 244, 250, 251]. Some investigators have compared FE models with solid ligaments to models with spring ligaments [136, 252]; it was observed that knee models with simpler materials for ligaments may give results similar to those with more sophisticated materials. They also stated that a proper material model for ligaments should be selected based on the purpose of the study.

Knee joint models have been used for assessing the effect of different interventions such as meniscectomy [20, 131, 132, 239] and prosthetics [253] to stresses and strains of cartilage. Pena et al. [254] proposed that increased cartilage shear stress after meniscectomy could be the reason for cartilage damage. They observed an almost 250 % increase in shear stress in the lateral tibial surface after lateral meniscectomy [255]. After bilateral meniscectomy, stresses and strains increased considerably in the lateral tibial cartilage [131].

The effect of different disorders such as ACL rupture [256–258] or cartilage

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estimated using knee joint models [134, 251]. When estimating the risk of a cartilage defect in the progression of knee OA, it has been suggested that the defect size could be used as a threshold to guide clinical decision-making [259, 260, 263].

One previous study by Boyd et al. [134] suggested that obesity increases stresses in the extended knee in the medial tibial cartilage, possibly being a reason for medial OA. FE models have also been applied to predict bone adaptation [264–266] and OA progression [267, 268] (see more from the section 5.3).

5.1.1 Workflow for creating knee joint models

The workflow for finite element knee joint models can be divided into five parts: 1) geometry creation, 2) mesh creation, 3) defining boundary and loading conditions, 4) defining material properties, and 5) simulating the model [19, 250]. In the subject-specific knee joint models, 3D geometries are traditionally generated from MRI or CT image stacks with some image processing software using manual segmentation [20, 247, 256, 259, 268]. In the post-processing phase, sharp edges and incorrect cavities are removed from the geometry. Finally, the geometries are smoothed to improve the functioning of the final model, especially when different contacts between tissues exist.

A suitable FE mesh can be generated using FE analysis software, third party meshing software or some built-in functions of the image processing software. The element types used in 3D models are commonly tetrahedral or hexahedral elements. Usually the generation of a tetrahedral mesh is fully automatic while in the generation of a hexahedral mesh more user intervention is needed, thus, tetrahedral meshing is faster and may be more suitable for clinical use. Currently, only a few automatic hexahedral meshing tools are available [193, 269], although hexahedral elements have been shown to be more stable and less influenced by mesh refinement [270]. The construction of a proper FE mesh with reasonable mesh quality, especially when multiple contacts, complex loading and large deformations exist, can be a demanding and time-consuming task.

When attempting to achieve reasonable simulation results, realistic boundary and loading conditions should be implemented into the model [19, 237]. For example, simulated movements can be walking, running, jumping or squatting and those movements can be evaluated using gait analysis [142, 143]. Moreover, simpler loads such as axial impact load or standing (creep) can also be simulated. Another crucial step is to define reasonable material properties for the models. Nonetheless, it is complicated and almost impossible to define subject-specific material properties for knee joint tissues, thus, most commonly used way is to use general, experimentally observed material properties [237]. The selection of a suitable material constitutive model is as important as the selection of realistic material properties. The basic concept is that the selected constitutive model should mimic the real behaviour of the tissues in a chosen loading configuration so that the final FE model (and its results) realistically represents a human knee joint.

5.2 MATERIAL MODELS OF CARTILAGE AND MENISCUS

Many previous knee joint studies use simple, single-phase constitutive models for cartilages and menisci [19, 237], but nowadays even more complicated material models have been investigated [132, 163, 271]. The models being used at present 22

Predicting knee osteoarthritis : development and application of segmentation and finite element modelling methods

uef.fi

Dissertations in Forestry and Natural Sciences

MIMMI LIUKKONEN

PREDICTING KNEE OSTEOARTHRITIS

MIMMI LIUKKONEN

Mimmi Liukkonen

PREDICTING KNEE OSTEOARTHRITIS

DEVELOPMENT AND APPLICATION OF SEGMENTATION AND FINITE ELEMENT MODELLING METHODS

TABLE OF CONTENTS

1 Introduction

2 Knee joint

3 Knee osteoarthritis

4 Knee joint imaging, segmentation and gait analysis

5 Finite element modelling of the knee joint