Applied Science, Faculty of
Biomedical Engineering, School of
DSpace
UBCV
Sullivan, Emily
Master of Applied Science - MASc
University of British Columbia
Introduction: Osteoarthritis (OA) is a debilitating disease caused by abnormal joint mechanics. There is a need for a non-invasive method to identify the specific mechanical changes that lead to OA. Magnetic resonance imaging (MRI) techniques such as T2 and T1ρ have shown sensitivity to mechanical changes in cartilage. However, the response is depth-dependent, and clinical MRI scanners with lower image resolutions cannot detect such specific changes. The magnetization transfer ratio (MTR) is a newer MRI metric that has shown promise as a measure of cartilage strain and stiffness. This research aimed to validate MTR as a robust method to measure loaded deformation and stiffness of knee cartilage. Methods: Three phases of work are described: first, an electropneumatic compressive loading device was developed and validated to apply step compressive forces to cartilage specimens in a high-resolution small-bore 9.4 Tesla MRI scanner. Second, bovine tibiofemoral osteochondral samples were compressed using this device while acquiring MTR and T2 data, and the correlations between cartilage strain and MTR/T2 were analyzed to determine any significant relationships. Finally, instantaneous stiffness maps were acquired across the same specimens via indentation testing. The relationship between local instantaneous modulus and local MTR/T2 were then assessed. Results: The loading device was successfully developed and validated to apply step compressive loads to cartilage samples in a small-bore MRI. Uniform MTR differences were observed through the cartilage thickness with increasing strain, whereas the T2 reaction to strain was regionally dependent. The relationship between MTR and strain was also found to be less specimen dependent (rrm = -0.25 to -0.36) than the relationship between T2 and strain (rrm = -0.28 iv to 0.21). When assessing correlations between local MTR/T2 and local instantaneous modulus, neither MRI metrics were found to be strong predictors of cartilage stiffness (rrm = 0.06 to 0.35). However, both measurements showed promise as indicators of mean cartilage stiffness when averaged across the cartilage plate. Conclusion: Our results suggest MTR could be useful in future in vivo cartilage studies in clinical MRI scanners, which may further our understanding of the mechanical changes that occur in cartilage during OA initiation and progression.
ASSESSMENT OF KNEE CARTILAGE MECHANICS USING THE MAGNETIZATION TRANSFER RATIO by EMILY SULLIVAN BASc, The University of British Columbia, 2020 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Biomedical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) March 2023 © Emily Sullivan, 2023 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Assessment of knee cartilage mechanics using the magnetization transfer ratio submitted by Emily Sullivan in partial fulfilment of the requirements for the degree of Master of Applied Science in Biomedical Engineering Examining Committee: Dr. David Wilson, Professor, Department of Orthopaedics, UBC Supervisor Dr. Thomas Oxland, Professor, Departments of Orthopaedics and Mechanical Engineering, UBC Supervisory Committee Member Dr. Jessica Kupper, Post Doctoral Fellow, Department of Orthopaedics, UBC Supervisory Committee Member Dr. Roger Tam, Associate Professor, Departments of Radiology and Biomedical Engineering, UBC Supervisory Committee Member iii Abstract Introduction: Osteoarthritis (OA) is a debilitating disease caused by abnormal joint mechanics. There is a need for a non-invasive method to identify the specific mechanical changes that lead to OA. Magnetic resonance imaging (MRI) techniques such as T2 and T1ρ have shown sensitivity to mechanical changes in cartilage. However, the response is depth-dependent, and clinical MRI scanners with lower image resolutions cannot detect such specific changes. The magnetization transfer ratio (MTR) is a newer MRI metric that has shown promise as a measure of cartilage strain and stiffness. This research aimed to validate MTR as a robust method to measure loaded deformation and stiffness of knee cartilage. Methods: Three phases of work are described: first, an electropneumatic compressive loading device was developed and validated to apply step compressive forces to cartilage specimens in a high-resolution small-bore 9.4 Tesla MRI scanner. Second, bovine tibiofemoral osteochondral samples were compressed using this device while acquiring MTR and T2 data, and the correlations between cartilage strain and MTR/T2 were analyzed to determine any significant relationships. Finally, instantaneous stiffness maps were acquired across the same specimens via indentation testing. The relationship between local instantaneous modulus and local MTR/T2 were then assessed. Results: The loading device was successfully developed and validated to apply step compressive loads to cartilage samples in a small-bore MRI. Uniform MTR differences were observed through the cartilage thickness with increasing strain, whereas the T2 reaction to strain was regionally dependent. The relationship between MTR and strain was also found to be less specimen dependent (rrm = -0.25 to -0.36) than the relationship between T2 and strain (rrm = -0.28 iv to 0.21). When assessing correlations between local MTR/T2 and local instantaneous modulus, neither MRI metrics were found to be strong predictors of cartilage stiffness (rrm = 0.06 to 0.35). However, both measurements showed promise as indicators of mean cartilage stiffness when averaged across the cartilage plate. Conclusion: Our results suggest MTR could be useful in future in vivo cartilage studies in clinical MRI scanners, which may further our understanding of the mechanical changes that occur in cartilage during OA initiation and progression. v Lay Summary With nearly five million Canadians suffering from osteoarthritis, there is a pressing need to identify the specific mechanical changes, particularly cartilage strain and stiffness, that lead to the disease. Magnetic resonance imaging (MRI) has been used to study these changes under applied load, however the methods used cannot be reproduced in clinical MRI scanners due to low image resolution. This thesis investigates a new MRI technique to measure knee cartilage strain and stiffness compared to other common MRI techniques. This research will establish this new technique’s utility to identify how injuries and deformities affect joint mechanics, which can then help us better understand how effectively treatments such as joint replacement surgery can correct osteoarthritis. vi Preface A version of Chapter 3 of this thesis has been submitted for publication. The following individuals contributed to Chapter 3: Dr. Jessica Küpper (mechanical design, validation testing and analysis, drafting and editing of manuscript), Dr. Robin Coope (mechanical design, manufacturing, manuscript editing), and Dr. David Wilson (senior author, manuscript editing). I contributed to the mechanical design along with Dr. Küpper and Dr. Coope, designed and assembled the electro-pneumatic system, conducted validation testing and resulting data analysis with Dr. Küpper, and drafted and edited the manuscript with Dr. Küpper. The following individuals contributed to Chapter 4: Dr. Jessica Küpper (specimen preparation, MRI data collection, chapter editing), Andrew Yung (development and application of MRI sequence protocols), Kirsten Bale (MRI data acquisition), Charlene Harasym (MRI/CECT thickness measurement comparison), and Dr. David Wilson (interpretation of results, chapter editing). I was responsible for protocol development, specimen collection and preparation, data collection and analysis, and the writing and editing of this chapter. The following individuals contributed to Chapter 5: Dr. Jessica Küpper (specimen preparation, MRI data collection, chapter editing), Andrew Yung (development and application of MRI sequence protocols), Kirsten Bale (MRI data acquisition), Carly Jones (indentation testing protocol development), Shawna Naderi (indentation testing, MATLAB code to define regions of interest), Charlene Harasym (indentation testing), and Dr. David Wilson (interpretation of results, chapter editing). I was responsible for protocol development, specimen collection and preparation, data collection (MRI and indentation data) and analysis, and the writing and editing of this chapter. vii Table of Contents Abstract ...................................................................................................................................................... iii Lay Summary ............................................................................................................................................... v Preface ......................................................................................................................................................... vi Table of Contents .......................................................................................................................................vii List of Tables ............................................................................................................................................... xi List of Figures ............................................................................................................................................xii List of Abbreviations ................................................................................................................................ xiv Acknowledgements ................................................................................................................................... xvi Dedication .................................................................................................................................................xvii 1 Introduction ......................................................................................................................................... 1 1.1 Motivation ....................................................................................................................... 1 1.2 Objectives ....................................................................................................................... 3 2 Literature Review ............................................................................................................................... 4 2.1 Relevant Anatomy .......................................................................................................... 4 2.2 Biomechanics of Articular Cartilage .............................................................................. 6 2.3 Effect of Osteoarthritis on Mechanical Behaviour ....................................................... 10 2.4 Biomechanics Assessment Techniques......................................................................... 12 2.5 Magnetic Resonance Imaging (MRI) of the Knee ........................................................ 14 2.5.1 Principles of MRI ................................................................................................................... 14 2.5.2 MRI for Knee Articular Cartilage in Literature .................................................................... 18 viii 2.6 Summary ....................................................................................................................... 21 3 Design and validation of a MRI-compatible pneumatic compressive loading device for articular cartilage ...................................................................................................................................... 22 3.1 Introduction ................................................................................................................... 22 3.2 Methods......................................................................................................................... 24 3.2.1 Design Criteria (DC) ............................................................................................................. 24 3.2.2 Cartilage Compressive Actuator (CCA) Design .................................................................... 26 3.2.3 Force vs. Pressure Calibration .............................................................................................. 30 3.2.4 Fibre Bragg Grating (FBG) Sensor Calibration ................................................................... 31 3.3 Results ........................................................................................................................... 33 3.4 Discussion ..................................................................................................................... 35 4 Analysis of the magnetization transfer ratio as a surrogate measure for axial compressive strain in tibiofemoral articular cartilage ................................................................................................. 40 4.1 Introduction ................................................................................................................... 40 4.2 Methods......................................................................................................................... 41 4.2.1 Loading Device Design .......................................................................................................... 41 4.2.2 Sample Preparation ............................................................................................................... 42 4.2.3 Image Acquisition .................................................................................................................. 44 4.2.4 Image Processing ................................................................................................................... 48 4.2.5 Data Modelling ...................................................................................................................... 49 4.2.6 Statistics ................................................................................................................................. 52 4.3 Results ........................................................................................................................... 53 4.4 Discussion ..................................................................................................................... 66 ix 5 Validating the magnetization transfer ratio as an indicator of cartilage health through stiffness testing .......................................................................................................................................................... 74 5.1 Introduction ................................................................................................................... 74 5.2 Methods......................................................................................................................... 75 5.2.1 Sample Preparation ............................................................................................................... 76 5.2.2 MRI Imaging .......................................................................................................................... 76 5.2.3 Mechanical Testing ................................................................................................................ 76 5.2.4 Data Processing ..................................................................................................................... 82 5.2.5 Statistics ................................................................................................................................. 83 5.3 Results ........................................................................................................................... 84 5.4 Discussion ..................................................................................................................... 90 6 Integrated Discussion ........................................................................................................................ 96 6.1 Overview ....................................................................................................................... 96 6.2 Contributions................................................................................................................. 96 6.3 Strengths ....................................................................................................................... 99 6.4 Limitations .................................................................................................................. 100 6.5 Clinical Utility ............................................................................................................ 103 6.6 Future Directions ........................................................................................................ 106 6.7 Conclusion .................................................................................................................. 107 Bibliography ............................................................................................................................................. 108 Appendices................................................................................................................................................ 120 Appendix A: Images of specimen preparation........................................................................ 120 x Appendix B: Investigation of the inter-rater and intra-rater reliability for cartilage segmentation in 3D Slicer ....................................................................................................... 124 Appendix C: Validation of 9.4T MRI thickness measurements using CECT ........................ 127 Appendix D: Specimen-specific mean strains and MRI metrics for full contact area ............ 135 Appendix E: Manual femoral compression measurements in 3D Slicer ................................ 138 Appendix F: Specimen-specific correlation plots comparing ΔMTR and strain .................... 139 F.1: Full contact area MTR correlations.......................................................................................... 140 F.2: Refined contact area MTR correlations .................................................................................... 146 Appendix G: Specimen-specific correlation plots comparing ΔT2 and strain ....................... 152 G.1: Full contact area T2 correlations ............................................................................................. 153 G.2: Refined contact area T2 correlations ....................................................................................... 158 Appendix H: Repeatability of registration between indentation test points and MRI image sets................................................................................................................................................. 163 Appendix I: Specimen-specific correlation plots comparing local instantaneous modulus and MTR/T2 .................................................................................................................................. 166 xi List of Tables Table 3.1: Design criteria and comparison to similar published devices ..................................... 25 Table 3.2: Ranking of design criteria ............................................................................................ 26 Table 4.1: T2 and MTR Sequence Parameters ............................................................................. 46 Table 4.2: Femoral mean and maximum strains in full contact area and refined contact area ..... 54 Table 4.3: Tibial mean and maximum strains in full contact area and refined contact area......... 55 Table 4.4: Full contact region average compressive strain and mean normalized change in MTR and T2 by load .............................................................................................................................. 57 Table 4.5: Refined contact region average compressive strain and mean normalized change in MTR and T2 by load ..................................................................................................................... 58 Table 4.6: Repeated measures correlation modelling outputs when comparing strain and normalized change in MTR .......................................................................................................... 65 Table 4.7: Repeated measures correlation modelling outputs when comparing strain and normalized change in T2 ............................................................................................................... 66 Table 5.1: Femoral specimen mean MTR, T2, mechanical measurements, and thickness .......... 85 Table 5.2: Tibial specimen mean MTR, T2, mechanical measurements, and thickness .............. 86 Table 5.3: T2 versus IM repeated measures correlation outputs at each region of interest .......... 88 Table 5.4: MTR versus IM repeated measures correlation outputs at each region of interest ..... 88 xii List of Figures Figure 2.1 Basic anatomy of the human knee ................................................................................. 4 Figure 2.2: Collagen fibril orientation in zones of cartilage ........................................................... 6 Figure 2.3: Viscoelastic behaviour of cartilage .............................................................................. 8 Figure 2.4: Common cartilage compression methodologies........................................................... 8 Figure 2.5: MT pulse application relative to the spectral lines of the bound and free pools ........ 15 Figure 2.6: Two-pool cross-relaxation model for magnetization transfer .................................... 17 Figure 3.1: The Cartilage Compression Actuator (CCA) ............................................................. 27 Figure 3.2: Pneumatic system schematic with functionality for a future double-acting pneumatic configuration ................................................................................................................................. 30 Figure 3.3: Specimen mounted in the water-tight specimen chamber .......................................... 32 Figure 3.4: Force vs. pressure relationship for the CCA for three trials showing quality of logarithmic fit (R2) ........................................................................................................................ 33 Figure 3.5: Wavelength vs. displacement for the FBG sensor measured with calipers and MR iamges showing quality of linear fit (R2) ...................................................................................... 34 Figure 3.6: Creep test showing wavelength vs. time in the MRI .................................................. 35 Figure 4.1: Prepared femoral and tibial osteochondral blocks fixed onto polycarbonate plates (top) and secured in the holding chamber of the CCA (bottom) .................................................. 43 Figure 4.2: The 9.4 Tesla MRI Scanner ........................................................................................ 44 Figure 4.3: Cartilage "flattening" methodology ............................................................................ 51 Figure 4.4: Definitions of zonal regions of interest (ROIs) .......................................................... 52 Figure 4.5: MTR (left) and T2 (right) for each applied load ........................................................ 59 Figure 4.6: Axial projections of mean strain, normalized change in MTR, and normalized change in T2 per column of cartilage ........................................................................................................ 60 Figure 4.7: Mean regional normalized change in MTR compared to mean compressive strain for each zonal region of interest ......................................................................................................... 61 Figure 4.8: Mean regional normalized change in T2 copmared to mean compressive strain for each zonal region of interest ......................................................................................................... 62 Figure 4.9: Repeated measures correlation plots illustrating the relationship across the full contact area between strain and A) normalized change in MTR, and B) normalized change in T2....................................................................................................................................................... 63 xiii Figure 4.10: Repeated measures correlation plots illustrating the relationship across the refined contact area between strain and A) normalized change in MTR, and B) normalized change in T2....................................................................................................................................................... 64 Figure 5.1: Axial view of tibial osteochondral block mounted to sample holder in high walled chamber ......................................................................................................................................... 77 Figure 5.2: Mechanical indentation testing equipment and data collection set up ....................... 79 Figure 5.3: Generated indentation testing points for a femoral specimen in the Mach-1 software....................................................................................................................................................... 80 Figure 5.4: Mean IM versus mean (A) MTR, and (B) T2 ............................................................ 87 Figure 5.5: Repeated measures correlation plots illustrating the relationship between IM and T2....................................................................................................................................................... 89 Figure 5.6: Repeated measures correlation plots illustrating the relationship between IM and MTR .............................................................................................................................................. 90 xiv List of Abbreviations 3D Three-dimensional ACL Anterior cruciate ligament AP Anterior-posterior B1 Radiofrequency field BMI Body mass index CBI Cartilage-bone interface CT Computerized tomography DC Design criteria DZ Deep zone DENSE Displacement encoding with stimulated echoes ECM Extracellular matrix FLASH Fast low angle shot FOV Field of view HR-pQCT High-resolution peripheral quantitative computed tomography ML Medial-lateral MR Magnetic resonance MRI Magnetic resonance imaging MSME Multi-slice multi-echo MT Magnetization transfer MTR Magnetization transfer ratio NA Number of acquisitions NRRD Nearly raw raster data xv PBS Phosphate-buffered saline PG Proteoglycans PLA Polylactic acid RF Radiofrequency ROI Region of interest S0 MTR image volume with saturation S+ MTR image volume without saturation SI Superior-inferior SZ Superficial zone T1 Spin-lattice relaxation time T1ρ Spin-lock relaxation time T2 Spin-spin relaxation time TE Echo time TR Repetition time TZ Transitional zone UTE Ultra-short echo time xvi Acknowledgements My sincere gratitude goes to my supervisor, Dr. David Wilson, for his endless expertise and encouragement. Dr. Wilson introduced me to the world of joint biomechanics when I was just a co-op student, and it has been an honour to learn from him over the past five years. I am grateful for Dr. Jessica Küpper, who has been such a supportive and knowledgeable mentor. I thank her for the hours spent together designing systems over Zoom during quarantine, troubleshooting outdated software, and preparing dozens of specimens. I thank my supervisory committee, Dr. Thomas Oxland and Dr. Piotr Kozlowski, for their invaluable feedback throughout this research. I am also grateful for Dr. Jane Desrochers, who taught me everything I know and ignited in me a true passion for cartilage research. I thank Dr. Robin Coope for his mechanical design expertise, and Scott Young and Jugoslav Kitanovic for all the hours put into manufacturing. I also thank Andrew Yung for his expertise in MRI protocol development, and Kirsten Bale for her assistance in image acquisition. I want to acknowledge all of those at the Wilson lab for their support and comradery. I thank Carly Jones for her guidance regarding indentation testing, and Adam Yu, Shawna Naderi, William Hornaday, and Charlene Harasym for their support with various tasks. Finally, I thank my family, friends, and loved ones, for their endless love and support throughout all the trials and breakthroughs. This work would not be possible without all of them. Funding for this work was received from the Natural Sciences and Engineering Research Council of Canada (NSERC) and Arthritis Society Canada. xvii Dedication To my father, Greg, who taught me the importance of true grit (even if I didn’t like the movie), My mother, Elese, who reminded me to be kind to myself in times of stress, and drove food over to me when I wasn’t taking that advice, And my grandparents, Connie, Paul, Glo, and Ed, who instilled in me a love for learning from an age before I can even remember. 1 1 Introduction 1.1 Motivation Osteoarthritis (OA) is a progressive and debilitating disease that affects over 13% of Canadians over the age of 20, increasing with age to 28% of Canadians over the age of 65 [1]. OA, which impacts joints such as the knee and hip, causes gradual degradation of joint cartilage, the bone underneath, and surrounding connective tissues such as the muscle and synovium. This leads to joint pain and reduced mobility, which detrimentally impacts quality of life [2]. With an aging population, OA prevalence is projected to increase to over 18% of all Canadians by 2031, and annual related costs are expected to rise from 2.9 billion CAD (in 2010) to 7.6 billion CAD (in 2031) [3]. OA is understood to be caused by abnormal joint mechanics, which can be initiated by factors such as joint injury and obesity [1]. However, it is still unclear which mechanical parameters best describe abnormal joint loading conditions. Stiffness [4]–[6] and strain [7]–[9] have both been associated with OA and abnormal joint loading, however there is a strong need for more accurate measurements of these parameters in cartilage to better understand localized mechanical changes. A major objective in cartilage research is to develop techniques that can eventually be used to directly assess these mechanical parameters in vivo in cartilage. Although many ex vivo cadaver studies [10]–[14] and computational models [15]–[19] have furthered our understanding of joint load distribution, these techniques cannot connect mechanical findings to clinical symptoms such as pain and restricted motion. Medical imaging tools allow researchers to create this connection non-invasively. Magnetic resonance imaging (MRI) has been used extensively in cartilage 2 mechanics research to study both cartilage stiffness [20] and strain [21]–[24], as it can directly visualize small morphological changes in the tissue. MRI sequences such as transverse relaxation time (T2) and spin-lattice relaxation time in the rotating frame (T1ρ) have been used extensively in cartilage mechanics literature. T2 and T1ρ have shown sensitivity to changes in cartilage strain patterns in both ex vivo [23], [25], [26] and in vivo [27]–[29] experiments. However, these sensitivities are depth-dependent, and the mean response of the cartilage does not show the same sensitivity. This is an issue in clinical MRIs, as they only have the resolution to detect the overall response of the tissue, rather than the localized changes through the depth of the tissue. There is very limited work studying the correlation between T2/T1ρ and stiffness, but the work conducted has generally concluded a non-significant correlation [20], [30]. Magnetization transfer (MT) is a newer MRI method that was originally developed to improve image contrast [31]. Rather than measuring the relaxation times of protons in the tissue, which is how T2 and T1ρ are determined, MT is measured by saturating only the macromolecular components of cartilage via off-resonance radiofrequency (RF) pulses, which can then be measured by the MRI when the macromolecules exchange energy with the surrounding water. This effect is quantified by calculating the normalized difference between the signal before and after the macromolecules are saturated. This difference is known as the magnetization transfer ratio (MTR). Previous work studying MTR in cartilage has shown it is sensitive to stiffness, and more specifically the Hayes instantaneous modulus [20]. MTR was also shown to have a strong relationship with axial compressive strain in a pilot study conducted by our lab, with significant changes through the overall thickness of the cartilage [32]. However, the research investigating 3 MTR and cartilage mechanics is extremely limited, and no studies currently exist that directly compare MTR’s sensitivity to cartilage strain to that of other MRI parameters such as T2. 1.2 Objectives The goal of this work was to validate MTR as a robust method for measuring loaded deformation and stiffness of knee cartilage, for future application in studying the prevention and treatment of OA. Previous work did not compare MTR to other relevant MRI metrics, nor did it consider depth dependency. To compare MTR more accurately with cartilage mechanics, we required a system that would consistently load the cartilage while inside the MRI scanner. The specific aims of this research are as follows: 1. Design and validate an MRI-compatible pneumatic compressive loading rig to apply load to cartilage specimens in a high field, small bore 9.4 Tesla MRI scanner. 2. Validate MTR as a measure of axial compressive strain in healthy cartilage and compare it to T2 measurements. 3. Determine the relationship between MTR values and cartilage stiffness in healthy specimens. 4 2 Literature Review 2.1 Relevant Anatomy The knee joint is a weight-bearing joint that allows for motion in all six degrees of freedom between the thigh and the shank. Three bones meet at the joint: the patella, the femur, and the tibia. The lateral and medial femoral condyles articulate with the tibial plateaus, and the posterior side of the patella articulates with the distal femur. To guide motion and transmit load between these bones, the knee joint also includes muscles, tendons, ligaments, meniscus, and articular cartilage (Figure 2.1). Figure 2.1 Basic anatomy of the human knee (© Reproduced with permission from [33]) 5 Articular cartilage thinly covers the articulating surfaces of synovial joints such as the knee, with an average human cartilage thickness typically ranging from 1.65 – 2.65 mm [34]. Its two main functions are to (1) reduce friction in the joint by providing a smooth and lubricated surface for bone contact, and (2) transmit load across the surface area of the joint to the subchondral bone [35]. Articular cartilage is avascular and is made up of an extracellular matrix (ECM), chondrocytes (specialized cells), and water. In healthy human cartilage, chondrocytes make up less than 10% of the tissue. The ECM is responsible for the mechanical functions of the tissue and is composed primarily of collagen fibrils (75% dry weight) and proteoglycans (PGs) (20-30% dry weight) [35], [36]. PGs are hydrophilic macromolecules that work with the collagen fibrils so that the ECM can withstand stresses on the tissue [37]. It has been discovered through empirical evidence that PGs are the primary source of resistance during static compression, whereas collagen fibrils are the primary source of resistance during tension and dynamic compression [38], [39]. Articular cartilage can be divided into four zones: the superficial zone (just under the surface), the transitional zone, the deep zone, and the calcified zone, which is closest to the bone (Figure 2.2). In the superficial zone, collagen fibrils are oriented parallel to the surface, which counteract the swelling pressure created in the cartilage by the PGs when under loading [40]. It is often in the superficial zone that the first signs of degeneration appear. The transitional zone is the first point of major resistance against compression, due to a higher concentration of PGs compared to the superficial zone and thicker collagen fibrils that are oriented obliquely. In the deep zone, fibrils are oriented perpendicular to the surface and PG concentration is the highest, providing the highest resistance to compressive force [35]. Under the deep zone is a layer of calcified cartilage that secures the articular cartilage to the subchondral bone [41]. PG and collagen 6 concentrations both increase deeper in the cartilage towards the cartilage-bone interface [42]. Because of this, observed strain under loading is inhomogeneous throughout healthy cartilage, with the largest strains observed in the superficial zone and the smallest in the deep zone [42], [43]. Under uniaxial compression, the orientation of the collagen fibrils changes in all zones but the calcified zone. When loaded, fibrils in the superficial zone remain parallel to the surface. Deep zone collagen fibrils, however, drastically change from a perpendicular to parallel orientation [36]. Figure 2.2: Collagen fibril orientation in zones of cartilage (© Reproduced with permission from [44]) 2.2 Biomechanics of Articular Cartilage Articular cartilage behaves viscoelastically and can be best understood when viewing cartilage as a biphasic structure, a theory developed by Mow et al. [45]. According to this theory, cartilage is described as two phases: a solid phase (the porous and permeable ECM), and a fluid phase (primarily water). In this theory, three forces are at play in the tissue under load: (1) stress in the compressed ECM, (2) a pressure gradient in the fluid phase, and (3) a frictional force created by 7 the fluid phase flowing through the ECM. Because all three of these forces work together to counteract the external load, a viscoelastic effect is observed [46]. Cartilage mechanics under loading have often been studied through creep and stress relaxation tests (Figure 2.3) during confined compression, unconfined compression, and indentation (Figure 2.4) [46]. In creep tests, a step compressive load or stress is applied to the cartilage, which causes a fast increase in deformation and water to quickly flow out of the tissue (Figure 2.3B). Over time, the rate of deformation decreases, as the water takes longer to flow out of the ECM. This eventually results in an equilibrium state. In stress relaxation tests, a step compressive displacement or strain is applied to the cartilage. Stress quickly rises to a peak, followed by a slow relaxation. Water continues to flow out of the ECM until equilibrium is reached [37] (Figure 2.3A). The bi-phasic model was expanded upon by Lai et al., who developed a tri-phasic model to account for an additional ionic phase [46]. 8 Figure 2.3: Viscoelastic behaviour of cartilage (A) When a step displacement d is applied, a response known as stress relaxation is observed. (B) When a step load P is applied, a response known as creep is observed. Figure 2.4: Common cartilage compression methodologies (A) Indentation, (B) confined compression, and (C) unconfined compression. © Reproduced from [48] with permission 9 Indentation testing is the most common method for testing cartilage mechanical properties compared to unconfined or confined compression. Indentation testing does not require preparing specialized samples like the cylindrical cartilage plugs required for confined compression, and indentation testing can be conducted in situ with the cartilage on the bone, while obtaining data that more closely matches that of the natural physiological environment [46]. Several numerical models [49]–[51] have been developed specifically for the indentation testing of cartilage to calculate stiffness values from the collected indentation data. One model of particular importance was derived by Hayes et al., which described various boundary conditions for cartilage indentation using either a spherical or end-plate indenter. This model assumes an infinite, isotropic, and elastic layer of cartilage to be rigidly attached to an underlying layer of hard subchondral bone [52]. The Hayes formula predicts the instantaneous elastic modulus (𝐼𝑀) for the indented point of interest. The equation considers peak normal indentation force (𝐹), the normal displacement of the indenter (𝑑), the Poisson ratio (𝑣), the radius of the indenter (𝑅), the indentation depth (𝑡), the indentation area radius (𝑎) cartilage thickness (ℎ), and a correction factor (𝜅): 𝐼𝑀 = 𝐹𝑑(1 − 𝑣2)2𝑎 𝜅(𝑎ℎ,𝑣) Models like the Hayes equation are necessary to calculate desired parameters (such as various moduli) from indentation test measurements such as force and displacement. The Hayes equation solves the issue of boundary conditions that previous models did not consider [53]. 10 2.3 Effect of Osteoarthritis on Mechanical Behaviour Osteoarthritis (OA) is a degenerative joint disease that affects almost five million Canadians [1], and is most commonly seen in the knee, followed by the hip and the hand [54]. Risk factors for OA include age, gender, genetic factors, obesity, previous joint injuries, and occupational factors [2], [55]. With an aging population and the growing obesity epidemic, OA incidence is expected to grow [54]. OA can cause debilitating pain for the patient, thereby leading to detrimental impacts in daily life. Therefore, it is critical to improve the prevention and treatment of OA. Although nonsurgical treatments for OA do exist, such as exercise programs and pharmacologic solutions [56], many patients do not experience satisfactory pain relief without surgical intervention [57]. It is widely accepted that joint mechanics impact the initiation and progression of OA [58]. One well established hypothesis focused around cartilage is that a shift in contact location or increase in loading in the joint can trigger the initiation of OA. Prior studies have shown that in a healthy joint, increased loading either improves or has no long-term impact on the thickness of cartilage [59]–[61], indicating that loading does not damage healthy cartilage under normal conditions. It is widely thought that in OA initiation, factors such as trauma or overuse alter the mechanics of the joint, which the cartilage cannot adapt to [62]. This then leads to a structural breakdown of the chondrocytes and ECM, as well as a reduction in PGs (which are critical to load-bearing in the tissue) [58]. In OA progression, the damaged cartilage cannot support the load that it previously could, which leads to further structural breakdown. During this phase, more loading will cause a more rapid progression, whereas less loading will slow the progression [62]. 11 Although it is agreed upon that joint mechanics play an important role in OA, there has been debate over which mechanical quantities are most relevant. Cartilage strain is one quantity that is thought to be important in OA. Causes of cartilage damage in early OA have been indirectly studied by quantifying strain during joint loading [9]. A strong correlation has been seen between abnormally high nominal cartilage strains under loading with eventual fibrillation and softening, and abnormally low nominal cartilage strains with osteophyte formation and cartilage stiffening [24]. Increased axial compressive cartilage strains have been observed using medical imaging techniques in patients with anterior cruciate ligament (ACL)-deficient knees (compared to each patient’s unaffected knee) [7], [63] and patients with high body mass index (BMI) (compared to patients with a lower BMI) [8], [21]. ACL damage or rupture and high BMI are both known risk factors for OA. This further suggests a strong relationship between cartilage health and strain. Cartilage stiffness has also been linked to tissue health and degeneration. As described above, PG concentration decreases significantly during OA initiation and progression. This increases the permeability of the ECM, thereby reducing the pressure gradient and eventually the compressive stiffness of the cartilage [6]. Indentation testing conducted by Kempson et al. on articular cartilage of varying quality revealed a strong relationship between cartilage stiffness parameters and areas of fibrillation, where cartilage is less stiff [5]. Further research has shown that the instantaneous stiffness (stiffness immediately after loading) of cartilage is a better indicator of degeneration than equilibrium stiffness (stiffness after cartilage has had sufficient time to reach an equilibrium state after loading) and is more sensitive than equilibrium stiffness to cartilage regions that are softening [64]. 12 Although these studies and numerous others have furthered our understanding of OA, much is still left unknown regarding the relationship between OA and mechanics. Most of the work done to understand this relationship has been done in animals, and little has been done using intact joints. This means most of the literature is not necessarily transferable to the in vivo environment in humans. Unfortunately, most in vivo studies are expensive, time consuming, and at times too invasive for a clinical population. These limitations prevent in vivo studies in large, clinically-relevant populations, which is needed for statistical relevance [58]. 2.4 Biomechanics Assessment Techniques Numerous studies have been conducted to better understand the relationship between joint load distribution and OA, with most of these studies having been conducted with ex vivo models. Pressure sensors have been used in several of these ex vivo models to measure joint loading mechanics. Kubota et al. observed contact pressure and contact area changes using a pressure mapping sensor while positioning porcine knee joints at various degrees of flexion, finding that contact pressure generally increased with increased flexion [14]. Black et al. cycled cadaveric knee specimens (n = 7) equipped with pressure sensors and infrared motion capture sensors through flexion and extension and discovered that changes to tibial slope during osteotomy will significantly impact the centre of pressure and therefore joint kinematics [11]. Contact pressure distributions have been further studied in other cadaveric models [12], [13]. Mechanical testing machines (i.e. compression rigs) have also been utilized to gather joint mechanics data under loading. Cartilage strain was mapped across porcine knee joints after local compression in a mechanical testing apparatus [14]. Although ex vivo studies provide valuable, anatomically relevant information about joint reaction to load, they cannot link these observed mechanics with 13 clinical symptoms, which is critical in furthering our understanding of cartilage degeneration. Furthermore, ex vivo studies cannot be used to study OA progression over time. Many variations of computational models have also been utilized to study load distribution in cartilage. Several studies have used motion capture technology and other gait analysis techniques to collect biomechanical data, which is then used to create three-dimensional (3D) musculoskeletal models and study cartilage load distribution in different joint alignments [17], [65]–[67]. Others have utilized discrete element [16] or finite element [18], [19], [68] modelling to describe mechanical parameters of the cartilage surface under pressure. Many of these models help inform how surgical decisions (such as in ACL reconstructions) might impact cartilage mechanics and the development of OA [15], [18]. Unfortunately, these models rely on several assumptions and often simplifications regarding the surrounding joint tissues and load behaviour, such as simplifying or negating the effects of muscle tension on load distribution, range of motion limitations for different patients, and patient-specific contact force distribution changes. In vivo studies allow us to investigate cartilage mechanics while observing clinical symptoms. This is commonly done with various medical imaging modalities. Dual fluoroscopy was used to study cartilage thickness at the contact area in the tibiofemoral joint in patients 6 months after successful ACL reconstruction [69]. Another study used biplanar radiography and computerized tomography (CT) to predict patellofemoral force magnitude and location when walking [70]. Modalities like radiography and CT, however, expose the participants to radiation, and must be used sparingly. These approaches also rely on assumptions about cartilage to predict strain, and cartilage cannot be visualized with radiography. MRI can directly visualize cartilage morphology, which has led to its rise in popularity in studying cartilage mechanics. 14 2.5 Magnetic Resonance Imaging (MRI) of the Knee 2.5.1 Principles of MRI Magnetic resonance imaging (MRI) is a method of non-invasive imaging that is commonly used in both clinical and research contexts. The strong magnetic field in the MRI causes the protons in tissues to align accordingly. When a radiofrequency (RF) pulse is sent to the tissue, this causes the protons to spin out of field alignment. Physicians and researchers can measure the time it takes for the protons to relax, as well as the energy released through this process. These properties are different for each type of tissue and can also change due to conditions such as OA [71]. The phase and frequency of signals sent from these protons are used for localization, eventually creating an image visualized in 3D space [72]. By changing the RF pulses sent and collected, different types of images can be developed. T1-weighted and T2-weighted scans are the most common MRI sequences. T1, or the spin-lattice relaxation time, is the time constant that describes the relaxation of spinning protons as they realign with the magnetic field after excitation. T2, or the spin-spin relaxation time, is the time constant that describes the decay of spins from the rotating frame of reference (the transverse plane) [73]. T2 and T1ρ are very commonly used sequences when imaging cartilage. T1ρ, or spin-lock relaxation time, combines both T1 and T2 principles, as it is the time constant that describes the relaxation of “spin-locked” protons along the rotating frame of reference [10]. T1ρ has shown to have a strong correlation with PG content in cartilage [10], [74]–[76]. Since PG depletion is one of the first signs of OA, this makes T1ρ a potentially useful technique to study cartilage. Increasing T2 values have been related to ECM degeneration, likely due to the sequence’s sensitivity to water content and collagen structure [74], [75], [77], [78]. 15 Magnetization transfer (MT) is a newer MRI technique that has been developed to improve image contrast. Rather than measuring proton relaxation time, the technique is based on applying off-resonance RF pulses to the tissue’s macromolecules [79]. MT can be best explained as a two-pool cross-relaxation model, consisting of a “free pool” and a “bound pool”. The “free pool” contains mobile protons, most importantly in water, that rotate quickly and take a while to relax (therefore the T2 of the free pool protons is quite long). The “bound pool” contains mostly macromolecules, with some layers of water molecules that are restricted in motion. The protons in this pool have a short enough T2 relaxation time that the protons cannot be directly recorded in MRI. However, these bound protons have an important indirect effect on MT. By using an off-resonance RF pulse, it is possible to excite only the bound pool protons. This is because the protons in the free pool have a very narrow lineshape, compared to the much broader absorption lineshape of the bound pool protons [80] (Figure 2.5). Figure 2.5: MT pulse application relative to the spectral lines of the bound and free pools The off-resonance RF pulse hardly impacts the free pool and only saturates the bound pool. The narrow line of the free pool indicates a long T2, and the broad line of the bound pool indicates a very short T2 (adapted from [81]). 16 During the MT sequence, this off-resonance RF pulse is sent only to the bound pool. This energy is then partially transferred to the protons in the free pool, which is then detectable by MRI. This transfer of energy between the two pools is what we know as MT. The exchange rate between the two pools is dependent on the tissue’s macromolecular content (more sites to exchange with will result in a higher MT). Using this, two pseudo-first-order rate constants can be derived as follows: 𝑘𝐹 = 𝑅𝑀0,𝐹 Where: • 𝑘𝐹 is the rate constant describing the MT rate from the free pool to the bound pool • 𝑅 is the exchange rate between pools • 𝑀0,𝐹 is the number of spins in the free pool (conventionally normalized to equal 1) 𝑘𝐵 = 𝑅𝑀0,𝐵 Where: • 𝑘𝐵 is the rate constant describing the MT rate from the bound pool to the free pool • 𝑅 is the exchange rate between pools • 𝑀0,𝐵 is the number of spins in the bound pool (conventionally given as the relative fraction of spins compared to the free pool) Figure 2.6 below illustrates the two-pool model and the relevant variables [80]. 17 Figure 2.6: Two-pool cross-relaxation model for magnetization transfer The free pool (M0,F) and bound pool (M0,B) exchange energy between each other (R). RF and RB refer to the energy released from the free pool and bound pool, respectively. Adapted from [80]. To quantify the effects of MT, the magnetization transfer ratio (MTR) is calculated. MTR is the normalized difference between the signal before excitation and after excitation (i.e. before and after the off-resonance RF pulse is emitted), making the value dependent on the macromolecular concentration as well as the exchange rate (𝑅) between pools. MTR can be described by the following equation [79]: 𝑀𝑇𝑅 =𝑀0 − 𝑀𝑆 𝑀0 Where: • 𝑀0 is the signal intensity before excitation • 𝑀𝑆 is the signal intensity after excitation 18 2.5.2 MRI for Knee Articular Cartilage in Literature MRI has long been used to assess cartilage degeneration, as it allows for non-invasive tissue visualization. Measurements can be made from MRI scans to study cartilage swelling [82], [83], fissures [84], [85], decreased cartilage thickness [86], and other morphological indicators of OA. Newer MRI methods assess various structural and biochemical properties in cartilage which may be stronger biomarkers for degeneration, such as PG content, collagen content and orientation, and water mobility [87]. T2 [88] and T1ρ [89] have both been validated in detecting osteoarthritic degeneration in cartilage. Subburaj et al. used T2 and T1ρ relaxation times in 3T MRI to investigate loaded knee cartilage in female participants with (n1 = 10) and without (n2 = 10) OA, with significantly elevated relaxation times observed in the OA group [90]. Several other MRI methods exist that are used to quantify cartilage degeneration. For example, delayed gadolinium enhanced MRI of cartilage (dGEMRIC) has shown strong correlations with cartilage health due to its strong relationship with PG content [91]. MRI has also been used to measure cartilage mechanics and further investigate joint load distribution. Conventionally, MRI has been used to study morphologic changes in the tissue. Song et al. validated and applied a 3D thickness mapping technique for a loaded sheep knee joint pre- and post-meniscectomy using images collected from a 4.7T MRI scanner. These results showed average cartilage strain to decrease by over 5% after surgery and maximum strain to increase by over 13% [24]. Greaves et al. measured human cadaveric hip cartilage thickness and strain in a 7T scanner to compare how labral resection and labral repair impact 3D cartilage strain pattens in human cadaveric hips. They found a 2% decrease in mean cartilage strain after labral repair and a 4% increase in mean cartilage strain after labral resection [22]. Cartilage morphology has also been studied when the tissue is loaded cyclically in MRI to better simulate 19 the in vivo loading environment. Neu et al. validated a new technique (coined “cartilage deformation by tag registration”) to noninvasively measure articular cartilage deformation when both loaded and unloaded throughout several load cycles in a 7T MRI [92]. In a similar experiment, Chan et al. cyclically loaded intact porcine tibiofemoral joints to investigate in vitro cartilage deformation and strain, finding axial compressive strains in the range of -9.8% to 0.7% when applying approximately one times body weight dynamically [85]. Unfortunately, the techniques described above rely on high resolution scanners (above clinical levels) for detailed morphologic images, and these morphologic changes are only associated with later stages of OA progression. T2 and T1ρ have been used to quantify cartilage mechanics quite extensively. Souza et al. discovered decreasing T2 and T1ρ under loading in both healthy and OA cartilage in a study of 137 participants when knees were unloaded and loaded to 50% body weight [29] . However, the responses of T2 and T1ρ to compression have been shown as highly depth dependent [90], [93], [94], and these localized changes cannot always be picked up on low field strength or clinical scanners. Desrochers et al. found the local change in T2 to vary significantly with depth when applying various levels of axial compressive strain to human tibial and femoral cartilage. Average T2 of the tissue did not change significantly with axial compressive strain and was therefore deemed unsuitable to quantitatively describe strain, as it masks important local changes [23]. There are also inconsistencies in literature regarding T1ρ. Some studies have shown T1ρ decreasing with load [29], [95], whereas others have shown it increases [25], [94], [96]. T2 and T1ρ are also affected by the “magic angle” effect, which is an MRI artifact that occurs due to changes in dipole-dipole interactions and is centralized when molecules (collagen fibrils and 20 PGs) are oriented 54.7° with respect to the main magnetic field. The magic angle effect causes signals to appear more intense than they are, causing error in the collected data [97]. Contrastingly, MTR quantifies the concentration of macromolecules in articular cartilage relative to water concentration [31]. A positive correlation was found between stiffness and MTR in human patellar cartilage [98] and tibiofemoral cartilage [20]. MTR values increase with depth towards the cartilage-bone interface as macromolecular concentration increases [75]. MTR has been shown to increase under loading (due to an increased MT exchange rate) ex vivo in intervertebral discs [99]. There is limited work assessing MTR’s response to load, and none describing the relationship with morphological strain in cartilage. Our lab previously assessed the relationships between cartilage axial compressive strain and MTR in a pilot study where 3 bovine knees were loaded uniaxially while measuring MTR in a 30 cm bore, 7T scanner (Bruker Biospec 70/30 USR system, Ettlingen, Germany). MTR was averaged across the depth of the cartilage, and morphologic axial compressive strain was calculated. The relationship between axial compressive strain and ΔMTR showed a linear response (R2 = 0.45 and R2 = 0.68 for the tibia and femur, respectively). The slope of this response was consistent and had a high range (0.6% change in ΔMTR for every 1% change in axial compressive strain), allowing us to conclude that MTR may be a better alternative to existing MRI sequences (like T2 and T1ρ) that quantify cartilage strain [32]. However, this work did not consider depth dependency throughout the varying regions of cartilage, was not directly compared to other MRI sequences, and only considered one specimen. Further investigation is required to understand the utility of MTR in mapping localized strain patterns throughout articular cartilage. 21 2.6 Summary • OA is a prevalent and debilitating joint disease related to joint mechanics. Early intervention and effective protection of the joint are critical, however, there is currently no method to assess joint load distribution in vivo under physiological loading. Strong correlations between abnormal strain patterns and cartilage damage have been discovered, making strain a promising candidate for cartilage health measurement. Increased cartilage stiffness has been recognized as an early feature of OA due to cartilage softening and fibrillation. • Ex vivo studies and computational modelling have been used to further our understanding of joint mechanics under loading. However, neither of these techniques can link clinical symptoms with the mechanical changes observed. • MRI has become a powerful technique to assess cartilage quantitatively, as it is non-invasive and can directly visualize the tissue’s morphology, making it extremely useful in mapping morphologic strain. T2 and T1ρ have been successful in assessing cartilage health and cartilage behaviour under load, but both sequences are highly depth-dependent, and these local changes cannot always be detected on clinical MRI scanners of lower field strength. • More recently, MTR has been used to study cartilage load distribution and health. A pilot study recently discovered MTR had a linear relationship with axial compressive strain when averaged across the depth of the tissue, suggesting that MTR has potential for use in a low field clinical scanner. 22 3 Design and validation of a MRI-compatible pneumatic compressive loading device for articular cartilage 3.1 Introduction OA is a joint disease affecting over 525 million people globally [100], with significant effects on patient health and wellbeing including comorbidities [101]. One theory for OA progression is that changes to joint mechanics initiate and hasten a breakdown of tissue [62], however, it is still unclear what specific mechanical changes are important. One variable of interest is cartilage strain, which has been identified as relevant to OA cartilage damage [58] and a potential imaging biomarker [9]. Strain is a measure of how much a material deforms, normalized to the initial thickness. Magnetic resonance (MR) imaging has been used to measure cartilage strain non-invasively, and new MR-based approaches are under development. Cartilage strain quantification is commonly done using a morphological approach [102], where segmented voxels are used to reconstruct the tissue volume. The change in morphology from unloaded to loaded tissue can then be quantified. Other potential approaches rely on the information MR provides about tissue composition. For example, MR imaging measures such as T2 and T1ρ give indications of cartilage collagen organization and PG content, respectively [103]. When combined with tissue loading, correlations can be obtained between strain and cartilage composition measures [23], [32]. If these correlations can be reliably established, the implications for in-vivo research studies are that non-invasive imaging could be used to explore how cartilage strain patterns change with OA in living humans, with potential to study mechanical relationships with early OA. 23 Assessing relationships between strain and changes in MR parameters in cadaver specimens requires a device to hold the specimen in an appropriate orientation and to apply load. Compression devices used in MR scanners must also be MR compatible. This means that they must not have ferromagnetic components that will interfere with the MR signal or pose a safety hazard. A number of designs have been put forward in the literature for this purpose, with a variety of approaches to applying controlled forces or displacements. Manual adjustment via screw [23], [93], [104] is mechanically straightforward but requires an individual to enter the scanner room to change the applied load and strain. The process of manual adjustment may cause the orientation of the specimen to change with respect to the imaging system. Electro-pneumatic controls may be used for remote actuation [96], [105]–[107], applying desired loads using calibrated relationships between displacement or load and pressure. This does not account for varying mechanical properties between specimens nor consistent strain throughout the duration of the scan. Existing systems have also been designed for either (1.5-3 Tesla) clinical [96], [105], [107] or wide bore [106] MR imaging, with bore diameters of approximately 60-70 cm, and are not compatible with 7-9 Tesla research MR scanners with bore/coil diameters smaller than 15 cm. The objective of this work was to design and validate a small-bore MR-compatible loading apparatus, called the cartilage compressive actuator (CCA), for measurement of varying levels of axial strain in cartilage-on-cartilage samples. During MR imaging, displacement is measured independent of MR scans to target approximate strains and ultimately enable real time position feedback. Although a high Tesla MR scanner allows for high resolution scans (e.g. < 70um), its small-bore size prevents larger sample geometry such as intact specimens of larger joints. 24 The goal in this design was to be able study cartilage at specific strain levels, but also to be able to fully load the tissue in future studies. Knee articular cartilage thickness ranges across the contact area, but the mean thickness ranges between 1.60 and 2.65 mm [108]. Articular cartilage strain in the knee during the stance phase of walking ranges between 7-23% [28]. This apparatus must therefore achieve at least 0.6 mm of displacement to reflect the situation in-vivo. The approximate loading on one knee during walking is 2.5 times body weight [109]. Assuming a body mass of 80 kg, and that the subsection of knee specimen under load accounts for one-third of the joint contact area, the required maximum force applied would be 650N. This calculation provides an upper limit for the device from a design perspective. Additionally, a simplified calculation was completed to estimate the lower requirements of the device for strain studies. Assuming a contact area of 1 cm2, a Young’s Modulus for the cartilage of 12 MPa [110] and strains of 10, 20 and 30%, the forces needed to act on the cartilage would be, respectively, 120 N (47 kPa), 240 N (94 kPa) and 360 N (141 kPa). It is important to note that this is a simplified equation that assumes linear elastic behavior and does not account for the non-linear and viscoelastic properties of cartilage. 3.2 Methods 3.2.1 Design Criteria (DC) A literature review (multifield search using the OVID Medline database with keywords: articular cartilage AND compression AND magnetic resonance imaging) was conducted to identify key design criteria for a new CCA. These are summarized in Table 1. This new device combines the features seen in previous devices, with small bore MR compatibility and real time displacement feedback. 25 Table 3.1: Design criteria (DC) and comparison to similar published devices Device Type of Specimen Tested Compression Application Mechanism DC1 DC2 DC3 DC4 DC5 DC6 DC7 Desrochers 2020 [23] Articular cartilage Manual (screw) ✓ ✓ x x ✓ ✓ x Chan 2009 [106] Whole knee joint Electropneumatic ✓ x ✓ ✓ x x x Nebelung 2020 [105] Meniscus Electropneumatic ✓ x ✓ ✓ ✓ x x Freutel 2014 [107] Meniscus Pneumatic ✓ x ✓ ✓ ✓ x x Truhn 2020 [96] Articular cartilage Electropneumatic ✓ x ✓ ✓ ✓ x x Nebelung 2017 [93] Whole knee joint Manual (screw) ✓ x x ✓ ✓ x x Shiomi 2010 [104] Whole knee joint Manual (screw) ✓ x x ✓ x x x CCA Articular cartilage Electropneumatic ✓ ✓ ✓ ✓ ✓ ✓ ✓ DC1. Material Compatibility: Device components that will be in the scanner room must be compatible with MRI DC2. Compatible with Small Bore MRI: The device must be able to fit inside a small-bore MRI (i.e. ≤70mm diameter) DC3. Remote Control: The system must be controllable from outside the scanner room DC4. Constant Load: The load applied to the specimen must remain consistent throughout the scanning period. DC5. Incremental Strain Capabilities: The system must allow for multiple loads/displacements to obtain varying levels of compressive strain DC6. Watertight Holding Chamber: The chamber that will hold the specimen must be watertight to allow for fluid submersion DC7. Real Time Displacement Feedback: The system must have capabilities to give real-time displacement feedback The key design criteria were qualitatively ranked according to how important it was to incorporate each element (i.e., essential, highly desirable, and desirable). This ranking was referred to throughout the design process as design decisions were made and finalized. Essential 26 items (Level I) were prioritized, and design specifications were optimized to achieve Levels II and III. A consensus between two engineers was used to determine the rankings. Table 3.2: Ranking of design criteria (DC) Design Criteria Ranking Description Design Criteria as described in Table 1 Level I Essential DC1, DC2, DC5 Level II Highly Desirable DC4, DC6, DC7 Level III Desirable DC3 3.2.2 Cartilage Compressive Actuator (CCA) Design Details of the CCA are shown in Figure 3.1. Each design specification was selected to meet a design requirement. For DC1 – material compatibility (MR safe), the apparatus is made mostly from Delrin™ (acetal co-polymer) with acrylic piston and test chamber cylinders, which had the added benefit of specimen visibility. Nylon screws and Buna-N O-rings are used and the arch upon which the fiber Bragg grating (FBG) sensor (explained below) is mounted is 0.64 mm (0.025”) thick polycarbonate. All plastics, seals and fittings were purchased from McMaster-Carr (Cleveland Ohio). 27 Figure 3.1: The Cartilage Compression Actuator (CCA) Figure showing A) the completed device and B) a cross sectional rendering of the internal components. The CCA is composed of Delrin™ and acrylic, with nylon screws and Buna-N O-rings (McMaster-Carr; Cleveland Ohio). The sensor arch (polycarbonate) holds an FBG sensor to monitor displacement. The CCA was manufactured at the BC Cancer Department of Medical Physics machine shop (Vancouver, BC, Canada). 28 For DC2 – compatible with small bore MR imaging, the entire apparatus needed to be no more than 70 mm in diameter so as to fit within the borehole of a 9.4 Tesla MR scanner (Bruker Biospec 94/30 USR system, Ettlingen, Germany), lined with a quadrature volume radiofrequency (RF) coil insert (Bruker Biospin Ltd., Ettlingen, Germany). For DC3 – remote control capabilities, the system was selected to be electropneumatic rather than manual. This allowed for pressure to be controlled outside of the MR scanner, while changing the loading at the specimen. The specific components of the pneumatic system were defined based on the requirements outlined in DC4 as follows. For DC4 – constant load application, we required pressure to be constantly applied to the specimen throughout the scan duration. To address this design requirement, a pneumatic system was designed. The pneumatic system moves the actuating piston (Figure 3.2) and includes 1) an air compressor (MAC2400, Makita, Anjo, Japan) as the source of pressurized air, 2) a particle filter to remove particulates including water to protect the components (F03-02-000, Wilkerson, Richland, MI, USA), 3) an electronic pressure regulator (500-EH, ControlAir Inc., Amherst, NH, USA; output range of 20-830 kPa) to control the downstream pressure seen by the device, 4) pressure gauges (MGA-300, SSI Technologies, Janesville, WI, USA) to monitor/record pressures and ensure a constant pressure in the system, and 5) a relief valve on either side of the piston to prevent the system from over pressurizing (ST25, Control Devices LLC, Fenton, MO, USA). Constant load application was validated as described below in the ‘Force vs. Pressure Calibration’ section. For DC 5 – incremental strain capabilities, the regulator and the control system are the two key elements that allow this DC to be met. The apparatus and experiments are controlled by a lab 29 made LabView program (DC5; v10.0.1, National Instruments, Austin, TX, USA). The software directly controls the regulator by modulating the amount of voltage being sent to the regulator, which changes the pressure in the device. To confirm a predictable regulator pressure-voltage relationship, the pressures output by the regulator and the duty cycle input into the software were confirmed to be highly linearly related (R2 = 0.99). For DC6 – water-tight holding chamber, O-rings were used at junctions between system components where air or water leakage could occur. Further, this system was designed in a modular way, so the specimen chamber was separated from the rest of the components. For DC7 – real time displacement feedback, we selected an FBG sensor. FBG sensors reflect light back down a fiber with a strain-dependent wavelength. This sensor was used to measure displacement of the actuator on the sample as it is MR compatible and can detect small displacements. The T10 FBG sensor (Technica Optical Components, Atlanta, USA) has a strain response time of 0.01 ms, strain range of greater than 15000 microstrain with a sensitivity of 1.2 pm per microstrain. Measurements were made via a National Instruments PXIe-4844 4-Channel FBG Interrogator Module. The device was modelled in Solidworks CAD software1 (Dassault Systèmes, Vélizy-Villacoublay, France) and manufactured at the BC Cancer Department of Medical Physics machine shop in Vancouver Canada. 1 Drawings are available in the repository located at: wilsonbiomechanicslab.com/downloads 30 Figure 3.2: Pneumatic system schematic with functionality for a future double-acting pneumatic configuration 3.2.3 Force vs. Pressure Calibration The force vs pneumatic pressure relationship was calibrated by having the apparatus apply force to a 1110 N load cell (Sensotec Model 75/C8 63-01, Honeywell, Charlotte, NC, USA) with a reported non-linearity of 0.1%, recorded by an Instron 8800 controller (Instron, Norwood, MA, USA). This was done by applying incremental pressures between 70 kPa and 515 kPa in increments of 35 kPa. This experiment was repeated three times. The CCA was clamped to a bench and acted through the distal end of the test chamber on the load cell via a Delrin extension rod. This allowed calibration with all the sources of friction in the CCA to be included. Loading consistency was assessed by holding a set pressure level for 30 minutes and recording force values over time. Thirty minutes was chosen to account for creep in cartilage, as Kempson et al. demonstrated that this period consistently brings the sample within 10% of equilibrium for displacement [5]. Pressures were held at approximately 175 kPa, 345 kPa, and 515 kPa and repeated in triplicate. 31 3.2.4 Fibre Bragg Grating (FBG) Sensor Calibration The first test to evaluate the FBG sensor wavelength relationship to displacement was set up using a synthetic “specimen”. A 3D-printed bone model made from polylactic acid (PLA) was used with a ~3mm silicone pad substituting for cartilage. The CCA was clamped to the bench and a digital caliper was clamped and extended into the specimen chamber such that it was in contact with the specimen mandrel. As the specimen mandrel translated under the applied pressure, the calipers were also displaced. The pressure applied was between 70 kPa and 515 kPa with steps of 35 kPa. This experiment was repeated in triplicate. The wavelength of the FBG sensor was recorded at each step. To confirm the FBG sensor worked correctly in the MR and to calibrate an ex vivo sample against the ground truth established by the caliper measurement, a second test was completed in the MR scanner. A bovine osteochondral sample of both tibial and femoral cartilage was loaded into the specimen chamber (Figure 3.3) and submerged in phosphate-buffered saline (PBS) buffer. The distance between tibial and femoral mounting plates was measured from three-minute scan MR images via the MR software. Target strains of approximately 10%, 20% and 30% based on FBG values from the first test were applied and the resulting FBG wavelength was recorded at 5-minute intervals over 45 minutes in this creep test. For each set pressure at the 30-minute time point an MR image was taken [3D fast low angle shot (FLASH) (echo time (TE)/repetition time (TR) = 3.323/65 ms, flip angle = 10 degrees, matrix size = 832x160x17, FOV=52x40x27.2 mm, resolution = 62.5x250x1600 microns, scan time = 2 x 8 min 50 sec 400 ms)]. The highest resolution was along the longitudinal axis of the CCA (proximal to distal). 32 Figure 3.3: Specimen mounted in the water-tight specimen chamber Tibial specimen is on the left, and femoral specimen is on the right. The mean tibial and femoral cartilage thicknesses were then measured from the high-resolution MR images using the following method in a MATLAB script (MATLAB 2020b, Mathworks, Massachusetts, USA) [23]. In brief, normal vectors were drawn from a fourth order polynomial function that was fitted to the cartilage-bone interface. The lengths of these vectors were defined as cartilage thickness and were averaged to determine bulk mean cartilage thickness. The MR-based strain measurement errors have been reported previously to be within 3 voxels [23] (equating to 0.19 mm at a resolution of 62.5 µm and strains of 4-6% across tibiofemoral specimens that are 3-5 mm thick). For all results (force calibration and FBG sensor calibration), medians, ranges, and quality of fit (R2 values) are reported. 33 3.3 Results The force-pressure calibration followed a nearly perfect logarithmic fit (R2 = 0.99; Figure 3.4). At the set peak output pressure of 550 kPa, a resultant median output force of 654 N (range 652-656 N) was measured. Repeated force measurements taken at 175 kPa, 345 kPa, and 515 kPa resulted in output forces of 348 N (range 342-355 N), 531 N (range 528-532 N), and 636 N (range 635-639 N), respectively. When held at these pressures for 30 minutes, force deviated by 15 N (range 9-21 N), 3 N (range 1-5 N), and 9 N (range 5-12 N), respectively. Figure 3.4: Force vs. pressure relationship for the CCA for three trials showing quality of logarithmic fit (R2) For the validation of the FBG sensor wavelength with the 3D printed ‘bones’ and silicone ‘cartilage’, the wavelength-displacement relationship was highly linear (R2=0.99; Figure 3.5). 34 Based on a caliper accuracy of 0.02 mm, a change of this magnitude in the caliper displacement corresponds to a change in FBG wavelength of 0.086 nm (Figure 3.5). Figure 3.5: Wavelength vs. displacement for the FBG sensor measured with calipers and MR images showing quality of linear fit (R2) For the bovine specimen in the MR scanner, average applied tibiofemoral strain was 8.2% (34 kPa), 17.1% (41 kPa), and 21.4% (48 kPa). The FBG wavelength vs. displacement slope was comparable to the slopes found with the caliper test (-4.2 nm/mm vs. -4.3 to -4.5 nm/mm). There was an offset of <1 nm of the x-intercept (MRI: 1559.2 nm vs. Calipers: 1558.4 to 1558.6 nm). The FBG wavelength creep study result demonstrated a decreasing value over time in response to each set input pressure (Figure 3.6). 35 Figure 3.6: Creep test showing wavelength vs. time in the MRI 3.4 Discussion The objective of this study was to design and validate the CCA for use in ex-vivo cartilage studies. The design criteria outlined in Table 1 were all successfully met through iterative mechanical design. The validation included a force calibration, a sensor calibration, and assessment of the FBG sensor creep response. The requirement for a positional feedback sensor is the driving feature of the CCA’s layout. The sensor must be mounted between the fixed housing and the moving sample mandrel (Figure 3.1) in a manner that provides measurable strain. This sensitive device must be connected to its fixed and moving references in such a way as not to stress the sensor or disturb the sample during the connection process. This was addressed by separating the actuator, sensor and sample chamber into independent sections and then connecting them after the sample was mounted in its chamber. The actuator and sample chamber were arrived at as follows. The requirement for constant force application and MRI compatibility naturally suggested the use of an all-plastic pneumatic 36 cylinder, which readily fit the sub 70 mm diameter requirement, and otherwise could mimic conventional double acting cylinders of this size. The sample chamber, adapted from Desrochers et al. [23], is already 70 mm in diameter and water-tight through the use of fixed and sliding O-rings. The latter seals the moving sample mandrel, to which the femoral side of a knee specimen is mounted. The tibial side of a knee specimen is attached to a plate at the distal cap. The chamber has internal D-shaped profiles to prevent the mandrel and distal plate from rotating. This allows the sample components to be mounted in the correct orientation and be constrained to only axial movement. The FBG sensor is mounted on a plastic arch (Figure 3.1), screwed to the actuator body at one end, and attached to the piston shaft with a two-part collar clamp on the other end. The arch allows several millimeters of axial movement without over straining the sensor. The sensor and mount are surrounded by a cylindrical “connecting chamber” of two halves with rabbet joints at either end that connect to rabbets on the actuator and sample chamber caps. During assembly, with the sample already mounted, the system is as shown in Figure 3.1 on its support stand. One half of the connecting chamber cylinder is engaged, holding the actuator and sample chamber fixed. With the collar clamp loose, the piston rod is extended to meet the sample mandrel and the two are connected using a captive threaded coupling (Figure 3.1B). The FBG sensor arch is then clamped to the piston rod by tightening the collar clamp and then the other half of the connecting chamber cylinder is screwed on, locking the whole system together. In this way the components can be assembled without disturbing the sample or the FBG sensor. The electro-pneumatic control system was selected as it improves the ease and precision of load and displacement application, and has proven a successful choice for several other systems [96], [105]–[107]. As an example, Neu et al. were able to achieve precision up to 1.8% of a 400 N 37 load compressing a juvenile porcine joint [111]. Pneumatics allow remote control, removing the need for registration between image sets, thus eliminating a potential source of error in analysis. Compression via manually rotated lead screws has been used [23], [93], [104], but this introduces repositioning errors, and such designs do not allow for cyclical loading studies. Our finding of a logarithmic relationship between force and pressure is consistent with earlier work with similar devices. Truhn et al. discovered that the force-pressure curve for their pneumatic compression device began to flatten as load increased [96]. The authors attributed this reaction to air leakage within their system. Our CCA design shows minimal air leakage. We instead attribute the flattening of the force-pressure curve in this study to the non-linearity of the pressure gauges (1% of full-scale), which corresponds to an error of up to 20 kPa. More precise instruments would likely result in a more linear relationship between force and pressure. Frictional forces also oppose the direction of compression, which may further contribute to the logarithmic response. The implication of this relationship between force and pressure on the operation of the device is that the error in target pressure as a percent of the target pressure decreases as pressure increases. Practically, when testing at higher loads the operator must be aware that lower force increments will be achieved. Our previous calculations for estimation of the pressure needed for 20% overall strain was found to be greater than the pressure needed during MR testing (i.e., 94 kPa vs. 48 kPa, respectively). This decrease in required pressure is likely due to a smaller contact area between tibial and femoral cartilage than the 1 cm2 that was assumed. However, the CCA will be used in future studies for other specimens that require higher loads (such as hip joint tissue), making the higher loading capabilities a robust feature of the apparatus. It should be noted that MR-based strain measurements can have errors as high as 3 voxels [23] (4-6% strain), which could have 38 implications of measurement error being within the same magnitude as the target change in strain. The FBG sensor demonstrated a highly linear relationship between wavelength and displacement, both for the test with calipers and the test with the MR scanner [112]. In addition, we measured the change in FBG wavelength over time for a set input pressure (Figure 3.6), with the wavelength showing a typical response to creep in the tissue [113]. Assessing the creep response in tissue may elucidate the patterns of water transport in cartilage. Composition and structure of the cartilage ECM are linked to water transport, and investigation of this aspect, although challenging with MR imaging, could be a contribution to the study of OA with the CCA. The curve in Figure 3.6 also provides justification for future imaging protocols where we want to image the cartilage after the viscoelastic response of the cartilage has approached equilibrium. Specifically, waiting 20 minutes is ample time to be displaced within 0.03-0.05 mm (1-1.6% strain change for 3 mm bulk tibiofemoral cartilage thickness) of the final position at 45 minutes (based on the 4.3 nm/mm slope shown in Figure 3.5). One design feature is that the FBG sensor is mounted a distance away from the specimen. The FBG sensor is mounted in the connecting chamber of the CCA because the specimen is immersed in PBS and the FBG sensor is temperature sensitive. Therefore, strain measurements assume that displacement in the mounting chamber is equal to displacement of the specimen mount in the specimen chamber (but not of the cartilage itself). Although this allows for potential error in strain measurement, it should be noted that the FBG sensor is used to achieve a target strain. The measured strain comes from the MR-based morphological scans. 39 There are several limitations to this design that should be considered for future CCA design iterations and other loading rig designs. First, the pressure regulator used here cannot output less than 34 kPa, making it challenging to produce small initial strains. Estimates of joint loading used to find target maximum loads for the device could be conservative, as more recent research measured higher loads [114]. Additionally, the current capabilities of the CCA do not allow for cyclical or dynamic loading, which better simulates the biomechanical environment of joint cartilage [115]. However, the CCA is currently equipped with additional components (Figure 3.2) that would allow for future cyclical application (discussed further in Chapter 6). With these capabilities, the CCA has potential to be the first design of its kind to allow for incremental strain control during cyclic loading. The CCA successfully applies increasing levels of compression to femoral-tibial cartilage samples in a small-bore 9.4T MRI scanner. The device has performed as expected and the initial tests described here were executed without any issues for the sensor or sample, or leaks. While similar electro-pneumatic systems depend on previously calibrated pressure-displacement relationships to determine target strain levels, the CCA employs an optical sensor to track displacement independently throughout the scanning period. The system could be modified in the future to incorporate a closed-loop feedback system (using methods such as a PID control) to allow for dynamic loading. 40 4 Analysis of the magnetization transfer ratio as a surrogate measure for axial compressive strain in tibiofemoral articular cartilage 4.1 Introduction MRI has been used in a number of studies to measure cartilage mechanics, due to its non-invasive nature and its ability to detect small morphologic changes in the tissue [22], [24], [92]. More recently, the relationship between various MRI parameters and cartilage mechanics has been studied in more detail, as these parameters are sensitive to various structural and biochemical tissue properties [87]. Using MRI to quantify cartilage strain has been of particular interest, as strain has been associated with abnormal joint loading that may lead to OA [7], [8]. T2 and T1ρ have been studied most in cartilage mechanics literature, and both MRI metrics have shown some sensitivity to compressive cartilage strain [23], [26], [29], [94]–[96]. However, the T2 response to compression is highly depth-dependent [23], [90], [94], and both positive and negative correlations have been observed between T1ρ and cartilage compression [25], [29], [95]. Both metrics also tend to be sensitive to the magic angle effect [97], which can significantly impact MRI measurements. MTR measurements may be related to cartilage strain, due to its high dependence on the tissue’s macromolecular concentration [31]. A previous pilot study determined MTR was sensitive to overall axial compressive cartilage strain, with a robust dynamic range that suggests suitability for use in a low-field clinical MRI [32]. However, only one specimen was used for this study, and depth dependency was not considered, which could mask important zone-specific changes. MTR’s sensitivity to axial compressive strain has yet to be compared to commonly used sequences in cartilage research, such as T2. 41 This chapter addresses the second objective of this thesis: to determine the relationship between axial compressive strain and MTR in healthy cartilage and compare it to T2. 4.2 Methods This study builds on the previous pilot work by studying the effect of axial compressive strain on MTR and T2 values through the depth of ex vivo cartilage. To apply various levels of compression to the cartilage, an MRI-compatible compressive loading device was designed, manufactured, and validated, as detailed in Chapter 3. Healthy bovine tibiofemoral osteochondral samples were prepared and compressed to several physiological loading levels while acquiring MTR and T2 data in a small-bore research MRI. The resulting image volumes were then analyzed to assess associations between axial compressive cartilage strain and the collected MRI data. 4.2.1 Loading Device Design A cartilage compression actuator (CCA) was designed and manufactured to apply controlled compression to knee cartilage samples in a small-bore MRI. The details of the design, manufacture, and validation of the CCA can be found in Chapter 3 of this thesis. Compression was achieved in the CCA with a double-acting pneumatic cylinder that was controlled by an electropneumatic system. The pneumatic components of the system included an air compressor (OF45200SS, RIDGID, Elyria, Ohio, USA), a particle filter (F03-02-000, Wilkerson, Richland, MI, USA), a pressure regulator (500-EH, Amherst, NH, USA), pressure gauges (MGA-300, SSI Technologies, Janesville, WI, USA), and a relief valve on either side of the piston (ST25, Control Devices LLC, Fenton, MO, USA). A rod attached to the pneumatic cylinder loaded the prepared femoral specimen fixed in the water-tight specimen chamber, in the axial direction of 42 the prepared tibial specimen (discussed subsequently). Pressure (and therefore the amount of force) applied to the specimen was controlled using a custom LabView program (v10.0.1, National Instruments, Austin, TX, USA). Note that the FBG sensor described and validated in Chapter 3 was not used as part of the CCA in this study. 4.2.2 Sample Preparation Six previously frozen intact bovine knees were obtained from a local butcher for this study. Intact knees were required 1) so that the cartilage would not be damaged by prolonged exposure to air, and 2) to ensure that the femoral and tibial cartilage were from the same animal. Prior to preparation, the intact knees were thawed for at least 24 hours in a refrigerator at 4° Celsius. Specimens were prepared one day before scanning at the MRI. First, each intact knee was carefully cleaned and disarticulated using a scalpel and scissors. All surrounding soft tissue (including muscle, tendons, and ligaments) was removed while taking care not to damage the cartilage. The menisci were also removed as they were not of interest for this study. Osteochondral blocks corresponding to regions of contacting cartilage in standing were then removed from the medial femoral condyle and medial tibial plateau using a surgical oscillating saw (Hall MPower2, ConMed Linvatec, Utica, NY, USA) and cut down further with a hand saw (Appendix A). Blocks were approximately 30 mm x 20 mm in the anterior-posterior (AP) and medial-lateral (ML) directions, and at least 20 mm thick. Images of the specimen preparation process can be found in Appendix A. For each femoral/tibial condyle pair, the femoral block and tibial block were oriented on separate polycarbonate plates such that contact surface area between the femoral and tibial cartilage was maximized. The AP and ML directions were kept consistent between the femoral and tibial block 43 alignment relative to each other. Each block was then attached to its corresponding polycarbonate plate using cyanoacrylate adhesive. The plate with the femoral block attached was screwed to the actuating mandrel of the CCA, and the plate with the tibial end was placed on the distal cap of the CCA (Figure 4.1). Once secured, the actuator of the CCA was manually adjusted so that the femoral and tibial blocks were less than 2 mm apart (without touching). Finally, the holding chamber was filled with phosphate-buffered saline (PBS) to keep the cartilage hydrated. Once completed, the CCA with the submerged cartilage samples was stored for approximately 20 hours in a refrigerator at 4° Celsius. Figure 4.1: Prepared femoral and tibial osteochondral blocks fixed onto polycarbonate plates (top) and secured in the holding chamber of the CCA (bottom) The next day, after transportation to the MRI facility, the femoral and tibial blocks were re-examined to ensure correct initial positioning (< 2 mm apart) and that there was sufficient PBS in 44 the holding chamber of the CCA. One of the plugs on the distal end of the CCA was then replaced with the balloon component (see section 3.2.2 in Chapter 3) to avoid an increase in pressure in the holding chamber. 4.2.3 Image Acquisition All specimens were scanned in a 9.4 Tesla MRI scanner (Bruker Biospec 94/30 USR system, Ettlingen, Germany) at the Centre for Comparative Medicine at the University of British Columbia (Figure 4.2). For each specimen, the CCA containing the specimen was placed into a quadrature volume RF coil insert (Bruker Biospin Ltd., Ettlingen, Germany), with foam taped around the circumference of the CCA to minimize empty space between the CCA and RF coil to prevent movement during scanning. The CCA was then inserted with the coil into the scanner. Figure 4.2: The 9.4 Tesla MRI Scanner 45 A standard multi-echo spin-echo MSME (multi-slice multi-echo) sequence was used for T2 mapping (Table 4.1). Only three slices were acquired during the T2 scan to reduce signal attenuation observed in cartilage during 2D multi-slice imaging due to magnetization transfer effects [116]. The MTR sequence was optimized over several sessions of protocol development to meet the following criteria: 1. A sufficient signal-to-noise ratio so that the interface between tibial cartilage, femoral cartilage, and PBS is easily distinguishable. 2. A short enough scan time to ensure that there is enough time to run through the protocol with the specimen unstrained and at 3 different axial compressive strain levels. 3. Power reduced enough so that the temperature does not increase by more than 1°C by the end of the entire scan protocol. MTR requires two image volumes, one with saturation and one without (S0 and S+, respectively). The readout sequence chosen was a 3D snapshot fast low angle shot (FLASH) sequence, with each saturation period followed by four linearly encoded FLASH readouts. Saturation before S+ used a 10 ms Hanning pulse, which is simply a constant RF pulse sent to the tissue (Table 4.1) 46 Table 4.1: T2 and MTR Sequence Parameters TE: echo time, TR: repetition time, NA: number of acquisitions, FOV: field of view, SI: superior-inferior, AP: anterior-posterior, ML: medial-lateral, B1: radiofrequency field Parameter T2 Value MTR Value General TE 9.22 ms 5.079 ms TR 4000 ms 65 ms (between saturations) 12.05 ms (between FLASH readouts in same snapshot) TE/TR ---- 3.323/65 ms Number of echoes 36 ---- Flip angle ---- 10° NA 3 4 Scan time 32 minutes 2 x 2.95 minutes Geometry FOV (SI x AP x ML directions) 40x43.75x27.2 mm 40x40x27.2 mm Matrix size (SI x AP directions) 640x160 640x160 In plane resolution (SI x AP directions) 62.5x250 microns 62.5x250 microns Number of slices 3 17 Slice thickness 1.6 mm 1.6 mm Saturation before S+ (Hanning pulse) – MTR sequence only Pulse duration ---- 10 ms Flip angle ---- 3250° Peak B1 ---- 42.41 uT Frequency offset ---- 2500 Hz 47 Each specimen was scanned in the original uncompressed position, then three more times with the cartilage compressed to approximately 10%, 20%, and 30% tibiofemoral overall axial compressive strain. These desired strain levels were achieved by adjusting pressure accordingly. Approximate axial compressive strain levels were confirmed by measuring the approximate tibiofemoral cartilage thickness with a ruler tool directly in the MRI software from a short three-minute scan taken before image acquisition for each load. Estimated axial compressive strain was then calculated from these scans by comparing to the uncompressed tibiofemoral thickness, using the following equation: 𝜀𝑒𝑠𝑡 = 𝑡𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 − 𝑡𝑢𝑛𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑𝑡𝑢𝑛𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 Where: • 𝜀𝑒𝑠𝑡 is the estimated axial compressive cartilage strain; • 𝑡𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 is the estimated cartilage thickness after compression • 𝑡𝑢𝑛𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 is the estimated cartilage thickness before compression These axial compressive strain levels were achieved with pneumatic pressures of approximately 41 kPa, 48 kPa, and 55 kPa, respectively, in the CCA. Scanning began twenty minutes after load was applied at each step load to account for creep [51]. 48 4.2.4 Image Processing To process the MTR data, S0 and S+ image volumes were first denoised using nonlocal mean denoising [117] and then corrected for Gibbs artifact [118]. S0 and S+ were then used to calculate MTR using the following equation: 𝑀𝑇𝑅 = 1 − 𝑆+𝑆0 T2 data were denoised [119], and mean T2 for each pixel was calculated using non-negative least squares fitting with stimulated echo correction [120]. To calculate axial compressive strain in the cartilage and determine the femoral-tibial cartilage contact area, three dimensional (3D) volumes (nearly raw raster data, or NRRD, files) of the cartilage at each strain level (including the unstrained level) for each MRI sequence were imported into 3D Slicer [121] (Version 4.11, Boston, MA, USA) for segmentation. The tibial and femoral cartilage were manually segmented as two separate masks. To minimize any error due to partial volume effects, voxels that could not confidently be deemed as containing only cartilage were excluded from the segmentation masks. Segmentation was completed by one rater, and a repeatability analysis was conducted with two raters to assess inter-rater and intra-rater segmentation error (Appendix B). Two specimens were studied in this repeatability analysis, with the primary rater segmenting each specimen 3 times and the secondary rater segmenting each specimen twice. Full cartilage contact area was defined as the voxels with direct contact between the segmented femoral cartilage and segmented tibial cartilage. A “refined cartilage contact area” was defined as a region 2.4 mm in length and width centred around the voxel where the highest axial compressive strain was observed. This refined contact area was defined 49 to study the cartilage that would be primarily undergoing axial compressive strain. The length and width of 2.4 mm was chosen based on observation of where axial compressive strain transitioned to zero strain when looking at the cartilage axially. 4.2.5 Data Modelling Strain calculations All data modelling was completed in MATLAB (v. 2020b, Mathworks, Massachusetts, USA). To generate axial heat maps of strain across the contact area, the axial compressive component of strain, 𝜀𝑐𝑜𝑙,𝑖, was calculated from MTR scans for each “column” (column of voxels in the axial direction) of cartilage using the following equation: 𝜀𝑐𝑜𝑙,𝑖 = 𝑡𝑖,𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 − 𝑡𝑖,𝑢𝑛𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑𝑡𝑖,𝑢𝑛𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 Where: • 𝑡𝑖,𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 is the thickness of each “column” of cartilage after compression; and • 𝑡𝑖,𝑢𝑛𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 is the thickness of each “column” of cartilage before compression A validation study was conducted to assess accuracy of cartilage thickness measurements by comparing to contrast-enhanced CT (CECT) measures, which have been validated to measure articular cartilage thickness to within 8% [122] (Appendix C). Three lateral tibial and femoral osteochondral blocks (prepared the same as the specimens described above) were scanned unloaded in the 9.4T MRI, then in a high-resolution peripheral quantitative computed tomography (HR-pQCT) imaging system (XtremeCT, Scanco Medical AG, Switzerland, 50 resolution 41 microns isotropic) after submersion in CA4+ contrast agent for 64 hours. Cartilage in both image sets was manually segmented, and thickness was calculated as described above. Thickness of corresponding voxel columns between MRI and CECT datasets were directly compared. Cartilage map flattening To allow us to compare depth-specific changes as specimen geometry changed due to added compression, flattened cartilage maps for femur and tibia were developed using a previously published methodology [23] that is similar to other published models [123]–[125]. A fourth order polynomial was fit through the cartilage-bone interface (CBI) for each segmented slice of femoral and tibial cartilage (Figure 4.3). Tangent lines were determined at each voxel centroid along the polynomial fit, and perpendicular vectors were then drawn from the CBI voxel centroids to the intersecting voxels at the cartilage surface. The lengths of these perpendicular vectors were taken as cartilage thickness. MTR and T2 maps of this now “flattened cartilage” were created using the “improfile” function in MATLAB (Mathworks, Massachusetts, USA) (Figure 4.3). This function uses nearest neighbour interpolation, which assumes the intensity value of each point is that of the nearest neighbouring voxel. 51 Figure 4.3: Cartilage "flattening" methodology The segmented cartilage map (A) is input into the algorithm, where a fourth order polynomial is fit to the cartilage bone interface (CBI) (B; blue line shows fourth order polynomial). Tangent lines (black dotted lines) are determined across the polynomial, and normal vectors are drawn from the CBI to the cartilage surface (black arrows). Note that normal vectors were generated at each voxel column, however only seven normal vectors are drawn in this image for clarity. (C) The resultant “flattened” cartilage map was then used in the analysis of zonal regions of interest and axial compressive strain versus MRI correlations. Three zonal regions of interest (ROIs) were defined in the flattened cartilage (Figure 4.4): the superficial zone (SZ) (0-15% of cartilage thickness), the transitional zone (TZ) (15%-70% of cartilage thickness), and the deep zone (DZ) (70%-100% of cartilage thickness) [44]. 52 To determine correlations between strain and each MRI metric, axial compressive strain for each column was calculated as described above in the “Strain Calculations” section, but this time from the flattened cartilage masks. Average axial compressive strain for each specimen at each step load was calculated by averaging 𝜀𝑐𝑜𝑙,𝑖 across all columns of cartilage considered part of the cartilage contact area. MTR and T2 were averaged across each column of the flattened cartilage masks to obtain a single MTR and T2 value for each column. Figure 4.4: Definitions of zonal regions of interest (ROIs) The superficial zone (SZ) was defined as the most superficial 15% of the cartilage depth. The deep zone (DZ) was defined as the 30% of the cartilage depth closest to the cartilage bone interface (CBI). The transitional zone (TZ) was defined as the 55% of the cartilage depth between the SZ and DZ. 4.2.6 Statistics Summary statistics were collected for axial compressive strain, MTR and T2 values for tibial and femoral cartilage. Average MTR and T2 were calculated across the entire depth for femoral and tibial cartilage at each strain level (including unstrained), as well as across each of the three ROIs (SZ, TZ, and DZ). Repeated measures correlation [126] was used to test the null hypothesis that there is no linear relationship between change in MTR values (ΔMTR) and axial compressive strain. This was also done to assess the relationship between ΔT2 and axial compressive strain. Repeated measures correlation is used in this instance to avoid biased results due to violation of 53 independence that would otherwise arise if data from multiple specimens was combined. Estimated slope ß, which defines the estimated linear relationship between axial compressive strain and each MRI metric change, and repeated measures correlation coefficient rrm, which defines the strength of linearity between the two variables, were the two outputs of this statistical model. A confidence interval of 0.95 was used for this analysis. Statistical analysis was completed in RStudio (R Core Team 2022, Vienna, Austria). Correlations were defined as weak (rrm < 0.3), moderate (0.3 < rrm < 0.5), or strong (rrm > 0.5). 4.3 Results Mean femoral axial cartilage strain observed due to each step load ranged from +12.1 to -6.1% when averaged across the full contact area and ranged from -0.6 to -16.9% when averaged across the refined contact area (2.4 mm length and width) (Table 4.2, Appendix D). In the tibial cartilage, mean axial strain ranged from -5.2 to -25.3% when averaged across the full contact area and ranged from -10.5 to -37.1% when averaged across the refined contact area (Table 4.3, Appendix D). Segmentation repeatability analyses (Appendix B) found an average intra-rater repeatability error of 2.2 voxels in the tibial cartilage and 1.3 voxels in the femoral cartilage, corresponding to approximately 6% and 7% overall axial compressive strain, respectively. Average inter-rater repeatability error was found to be 2.3 voxels in the tibial cartilage and 1.6 voxels in the femoral cartilage, corresponding to approximately 6% and 9% axial compressive strain, respectively. The average difference in cartilage thickness measurement between MTR and CECT cartilage scans was 4.6% in the tibia and 5.6% in the femur (Appendix C). In many cases, a mean positive axial strain was observed in the femoral cartilage when averaged across the full contact area (Table 4.2). A manual measurement test conducted with the ruler tool in Slicer confirmed that when averaged across the full contact area, femoral cartilage was only 54 deforming under compression within the height of two voxels (0.125 mm, equivalent to approximately 10% axial strain), indicating that the positive axial strains recorded in the femur across the full contact area may be partially due to segmentation error and MRI resolution limitations (Appendix E). When only the refined contact area was considered, however, a mean negative (compressive) axial strain was observed. Table 4.2: Femoral mean and maximum axial compressive strains in full and refined contact areas Negative strain indicates average strain in the axial compressive direction. Maximum strain corresponds to the largest axial compressive strain calculated from a single voxel. Specimen Load 1 Load 2 Load 3 Mean±SD (%) Maximum (%) Mean±SD (%) Maximum (%) Mean±SD (%) Maximum (%) Full Contact Area Refined Contact Area Full Contact Area Refined Contact Area Full Contact Area Refined Contact Area 1 5.2 ±3.3 -0.6 ±6.1 -18.5 -6.1 ±8.5 -3.4 ±9.5 -25.8 -3.0 ±9.2 -13.8 ±7.8 -24.0 2 10.3 ±15.2 -5.2 ±12.5 -33.3 9.1 ±15.6 -8.2 ±10.6 -41.2 4.7 ±12.6 -16.9 ±8.1 -29.4 3 6.7 ±13.6 -8.1 ±8.1 -23.1 -5.4 ±11.2 -7.8 ±8.5 -28.6 -3.5 ±16.7 -8.1 ±11.8 -33.3 4 10.4 ±10.2 -2.8 ±5.6 -20.0 8.6 ±9.1 -8.8 ±6.6 -33.3 6.1 ±9.4 -14.0 ±6.4 -35.7 5 4.2 ±14.3 -2.1 ±1.3 -4.2 7.5 ±17.2 -2.2 ±14.5 -13.6 9.7 ±20.3 -8.2 ±18.9 -16.7 6 10.7 ±14.7 -3.2 ±6.5 -22.2 9.3 ±6.1 -10.5 ±5.6 -31.3 2.1 ±7.2 -12.2 ±16.6 -33.3 All specimens 10.3 ±4.4 -3.0 ±8.6 -20.2 ±9.4 -4.9 ±5.3 -6.8 ±9.2 -29.0 ±9.1 6.0 ±6.2 -10.5 ±11.6 -28.7 ±7.2 55 Table 4.3: Tibial mean and maximum axial compressive strains in full and refined contact areas Negative strain indicates average strain in the axial compressive direction. Maximum strain corresponds to the largest axial compressive strain calculated from a single voxel. Specimen Load 1 Load 2 Load 3 Mean±SD (%) Maximum (%) Mean±SD (%) Maximum (%) Mean±SD (%) Maximum (%) Full Contact Area Refined Contact Area Full Contact Area Refined Contact Area Full Contact Area Refined Contact Area 1 -5.1 ±13.3 -15.7 ±7.8 -36.4 -11.6 ±9.4 -24.6 ±5.2 -40.9 -13.2 ±7.2 -27.9 ±5.7 -43.2 2 -5.1 ±8.2 -11.1 ±4.1 -27.1 -8.1 ±12.7 -12.1 ±6.6 -29.8 -15.4 ±9.3 -24.2 ±3.0 -37.5 3 -10.9 ±12.1 -15.6 ±3.7 -34.2 -12.5 ±13.5 -16.8 ±3.4 -33.3 -14.7 ±9.2 -21.4 ±2.9 -35.7 4 -14.7 ±15.8 -25.3± 6.9 -50.0 -19.9 ±9.6 -32.5 ±5.5 -48.6 -25.2 ±12.2 -37.1 ±5.6 -52.6 5 -18.4 ±8.5 -27.3 ±2.5 -38.7 -23.9 ±7.2 -32.0 ±2.5 -44.4 -25.3 ±10.3 -36.5 ±3.2 -48.4 6 -8.8 ±11.8 -10.5 ±6.1 -40.0 -12.2 ±8.1 -15.3 ±4.6 -42.5 -15.5 ±14.5 -17.2 ±7.4 -42.4 All specimens -11.6 ±8.5 -17.6 ±5.2 -37.7 ±7.5 -15.3 ±4.4 -22.2 ±4.6 -39.9 ±7.1 -19.2 ±3.1 -27.4 ±4.6 -43.3 ±6.4 MTR increased throughout both tibial and femoral cartilage with each step load increase (Tables 4.4 and 4.5, Figure 4.5). ΔMTRnorm, the average normalized change in MTR for a full thickness “column” of cartilage, increased across the entire surface of the cartilage, including in regions that did not undergo substantial axial compressive strain (Figure 4.6B). The response to axial strain was depth dependent, with MTR increasing most in the superficial zone (Figure 4.7). 56 These larger changes in the superficial zone resulted in more uniformly distributed MTR values throughout the cartilage depth with each step load increase. There were significant correlations between ΔMTR and axial compressive strain using repeated measures correlation in both tibial (rrm = -0.36 across all loads) and femoral (rrm = -0.28 across all loads) cartilage (Table 4.6). Correlations between femoral axial strain and ΔMTR were similar in the refined contact area (rrm = -0.15 to -0.30) and the full contact area (rrm = -0.20 to -0.33), as were the correlations between tibial axial strain and ΔMTR (rrm = -0.12 to -0.25 for full contact area, rrm = -0.17 to -0.36 for refined contact area) (Table 4.6, Figures 4.8 and 4.9). T2 results were not considered for one specimen (specimen 2) due to technical issues during image acquisition. For all applied loads, T2 increased under the loaded region only, and at only some depths (Figure 4.5). T2 changes varied more with depth compared to MTR (Figure 4.5), although the largest changes in T2 were also observed in the superficial zone (Figure 4.8). ΔT2norm, the average normalized change in T2 for a full thickness “column” of cartilage, showed a more focal response in the tibial cartilage, with higher ΔT2norm seen in areas of higher axial compressive cartilage strain (Figure 4.6C). However, cartilage columns with significantly high ΔT2norm are observed randomly across the cartilage contact area, particularly in the femoral cartilage. ΔT2norm displayed a more variable and specimen dependent relationship with axial compressive strain compared to ΔMTRnorm (Figure 4.9), with negative correlations observed in the tibial cartilage and positive correlations observed in the femoral cartilage (Table 4.7). Correlations were stronger between femoral axial strain and ΔT2 in the refined contact area (rrm = 0.31 to 0.46) than the full contact area (rrm = 0.19 to 0.25). In contrast, correlations between tibial axial strain and ΔT2 were stronger in the full contact area (rrm = -0.23 to -0.37) than the refined contact area (rrm = -0.01 to -0.14) (Table 4.7, Figures 4.8 and 4.9). Average MTR and T2 57 values for each specimen at each step load are in Appendix D. Correlation plots describing the relationship between axial compressive strain and ΔMTR and ΔT2 for each individual specimen can be found in Appendix F (MTR) and Appendix G (T2). Table 4.4: Full contact region average axial compressive strain and mean normalized change in MTR and T2 by load All changes are compared to the uncompressed state. Denoted as mean (standard deviation). Negative strain indicates average strain in the axial compressive direction. Averages only include cartilage within the full contact region. Average Strain % ∆MTRnorm % ∆T2norm % Load # Tibial Femoral Tibial Femoral Tibial Femoral 1 -11.6 (8.5) 10.3 (4.4) 27.2 (5.6) 25.5 (5.6) 22.9 (18.4) -9.2 (13.4) 2 -15.3 (4.4) -4.9 (5.3) 34.7 (5.9) 33.3 (4.7) 30.9 (31.3) -6.0 (17.2) 3 -19.2 (3.1) 6.0 (6.2) 38.6 (6.5) 36.9 (4.2) 32.9 (27.5) 4.9 (21.8) 58 Table 4.5: Refined contact region average axial compressive strain and mean normalized change in MTR and T2 by load All changes are compared to the uncompressed state. Denoted as mean (standard deviation). Negative strain indicates average strain in the axial compressive direction. Averages only include cartilage within the refined contact region. Average Strain % ∆MTRnorm % ∆T2norm % Load # Tibial Femoral Tibial Femoral Tibial Femoral 1 -17.6 (5.2) -3.0 (8.6) 30.2 (7.5) 30.7 (8.4) 39.4 (26.0) -6.8 (16.5) 2 -22.2 (4.6) -6.8 (9.2) 37.6 (7.5) 38.8 (6.4) 44.2 (34.7) 3.5 (20.3) 3 -27.4 (4.6) -10.5 (11.6) 42.9 (9.2) 44.2 (8.8) 44.7 (32.2) 14.7 (25.5) 59 Figure 4.5: MTR (left) and T2 (right) for each applied load Specimen #4 displayed. Load 0 represents the case in which no pressure has been introduced to the system, therefore there is no load and no strain. 60 Figure 4.6: Axial projections of mean axial compressive strain, normalized change in MTR, and normalized change in T2 per column of cartilage Means are representative of the full tissue depth (specimen #4 displayed). 61 Figure 4.7: Mean regional normalized change in MTR compared to mean axial compressive strain for each zonal region of interest Error bars represent standard deviation at each load for both strain (horizontal) and the normalized change in MTR (vertical). Means and standard deviations are representative of all tested specimens. Means represent the full contact area. 62 Figure 4.8: Mean regional normalized change in T2 compared to mean axial compressive strain for each zonal region of interest Error bars represent standard deviation at each load for both strain (horizontal) and the normalized change in T2 (vertical). Means and standard deviations are representative of all tested specimens. Means represent the full contact area. 63 Figure 4.9: Repeated measures correlation plots illustrating the relationship across the full contact area between axial compressive strain and A) normalized change in MTR, and B) normalized change in T2 Each colour represents one specimen, and each point represents the average value across the full tissue depth for one column of cartilage. rrm values represent the repeated measures correlation coefficient. All tests show statistical significance (p < 0.001). 64 Figure 4.10: Repeated measures correlation plots illustrating the relationship across the refined contact area between axial compressive strain and A) normalized change in MTR, and B) normalized change in T2 Each colour represents one specimen, and each point represents the average value across the full tissue depth for one column of cartilage. rrm values represent the repeated measures correlation coefficient. 65 Table 4.6: Repeated measures correlation modelling outputs when comparing axial compressive strain and normalized change in MTR * indicates statistical significance (p < 0.001). Type of tissue and load level(s) considered Estimated Slope 𝛽ΔMTRε Repeated measures correlation coefficient rrm Full contact area Refined contact area Full contact area Refined contact area Femoral cartilage: all loads -0.16 -0.26 -0.28* -0.30* Femoral cartilage: load 1 -0.10 -0.21 -0.20* -0.27* Femoral cartilage: load 2 -0.11 -0.22 -0.23* -0.28* Femoral cartilage: load 3 -0.16 -0.13 -0.33* -0.15* Tibial cartilage: all loads -0.24 -0.07 -0.36* -0.25* Tibial cartilage: load 1 -0.09 -0.02 -0.17* -0.15 Tibial cartilage: load 2 -0.17 -0.04 -0.29* -0.23 Tibial cartilage: load 3 -0.28 -0.06 -0.36* -0.12* 66 Table 4.7: Repeated measures correlation modelling outputs when comparing axial compressive strain and normalized change in T2 * indicates statistical significance (p < 0.001). Type of tissue and load level(s) considered Estimated Slope 𝛽ΔT2ε Repeated measures correlation coefficient rrm Full contact area Refined contact area Full contact area Refined contact area Femoral cartilage: all loads 0.91 1.30 0.21* 0.34* Femoral cartilage: load 1 0.91 0.98 0.24* 0.31* Femoral cartilage: load 2 0.84 1.62 0.19* 0.38* Femoral cartilage: load 3 1.28 2.25 0.25* 0.46* Tibial cartilage: all loads -0.91 -0.24 -0.28* -0.07 Tibial cartilage: load 1 -1.38 -0.57 -0.37* -0.14* Tibial cartilage: load 2 -0.75 -0.55 -0.23* -0.01 Tibial cartilage: load 3 -0.84 -0.3 -0.27* -0.08 4.4 Discussion We studied changes in MTR and T2 in bovine knee specimens under loading to assess any relationships that may be present between axial compressive cartilage strain and changing MR metrics. Overall differences in MTR were observed with each step load, whereas this pattern was not observed in T2 due to its regional dependency throughout the cartilage depth. The correlation between changes in MTR averaged across the cartilage depth and axial compressive strain were consistent between specimens, compared to a more variable and specimen dependent correlation in T2. 67 It was expected that average axial compressive strain would increase more in the tibial cartilage than the femoral cartilage, as tibial cartilage is less stiff than femoral cartilage [127]. The positive axial strains observed in the femoral cartilage when averaged across the full contact area were unexpected. The positive axial strain could be related to “bulging”, which can occur in cartilage when only a certain area is compressed. In bulging cartilage, the collagen fibers adjacent to the compressed area curve laterally away from the centre of loading in the transitional zone and converge back to the centre of loading in the superficial zone [128]. This results in both tensile and shear stresses in the cartilage which counteract the axial compressive strain caused by loading. This is supported by the negative femoral axial strains we observed in the refined contact area compared to the positive axial strains observed in the full contact area (Tables 4.2 and 4.3), suggesting that there is a central mean axial compressive strain directly under the centre of loading surrounded by an adjacent area under net tensile axial strain due to the bulging collagen fibres. It is important to note however that manual segmentation errors could have resulted in large strain errors due to thin femoral cartilage specimens and little measurable deformation in the femoral cartilage when averaged across the full contact area (Appendix E). Therefore, the quantitative correlations observed between axial compressive strain and MTR/T2 (Figures 4.7, 4.8, 4.9) in the femoral cartilage cannot be deemed sufficiently accurate when averaged across the full contact area. The correlation observed between axial compressive strain and MTR in this study may be related to the decrease in water content as compression is increased. Although it is unclear what physiological mechanisms determine MTR in cartilage, it is likely that the decrease in water content under load leads to increased magnetization transfer between free and bound pools in the cartilage, thereby increasing the MTR. This inverse relationship between MTR and water content 68 has been qualitatively observed in liver [129] and cerebral matter [130], [131], and has been quantified in bone marrow (r = -0.432) [132], which suggests a similar relationship exists in articular cartilage. The differences in tibial MTR, both in the unloaded state and under loading, are similar to what has been observed in other knee cartilage studies. Unloaded, Namiranian et al. found a lower ultrashort echo time (UTE) MTR in the superficial half of ten tibiofemoral cartilage specimens (29 ± 3 %) compared to the deeper half (36 ± 2 %) [20]. Although our protocol did not utilize UTE methodologies, we saw a similar pattern of higher MTR in unloaded (load 0) tibial and femoral cartilage in the deeper cartilage regions than the regions closer to the articular surface (Figure 4.5). Regatte et al. compressed eight bovine patellar cartilage plugs in a 2T MRI and found that MTR increased throughout the cartilage depth with increasing load, with the most dramatic changes observed in the superficial zone [75]. Although our study used a high resolution 9.4T (resolution 0.0625 mm axially) scanner rather than the 2T (resolution approximately 0.25 mm axially) scanner utilized by Regatte et al., and we used large cartilage samples still attached to the bone rather than small, detached cartilage plugs, their results closely match our findings in tibial cartilage as described in Figure 4.7. However, Regatte et al. only studied the average changes in MTR at one level of compression (rather than at several step loads) and did not quantify the resulting strain. Little other work has been conducted studying the effects on MT in cartilage under loading, however a recently published study found increased MT (measured by the macromolecular proton fraction, which estimates macromolecular matrix density) in healthy human cadaver knees under 300 N and 600 N of load, compared to the unloaded state [133]. This result is consistent with our finding of increased MTR with increased compression. However, this earlier study only compared average MT metrics to the amount of 69 force applied to the entire specimen, whereas our current work directly compares the axial strain observed locally across the cartilage to the local ΔMTRnorm. Overall, T2 patterns in the tibial cartilage were similar to what has been reported in literature. Unloaded, we observed a mean T2 of 25.1±6.5 ms and 22.0±9.7 ms in the femoral and tibial cartilage, respectively. This is lower than what has been measured in bovine cartilage with high-field MRI in the literature, with reported mean values ranging from 30-80 ms [134]–[136]. However, T2 values are highly dependent on collagen fibril orientation and the magic angle effect, which may cause variation in T2 measurements by up to 60% [137]. The zonal variation of T2 observed across the depth of the cartilage is consistent with other work [77], [136], [138]–[141], with much higher values up to the order of 100 ms recorded in the superficial zone and decreasing values as depth increases. The depth-dependent response of T2 to axial compressive strain observed in the tibial cartilage, with the majority of T2 changes occurring in the superficial zone, supports what has been observed in previous studies. In a study conducted on human cadaveric tibiofemoral specimens in 7T MRI, no obvious pattern was detected in mean ΔT2 across the cartilage volume with axial compressive strain [23]. However, the highest T2 values shifted deeper into the tissue as compression increased, as we also observe in the current study (Figure 4.5) [23]. Nebelung et al. similarly found the only significant changes in T2 to be in the superficial zone of cartilage when applying unconfined compression to ex vivo femoral cartilage specimens in 3T MRI [94]. Our finding of a mean increase of T2 in the superficial zone by 25% is consistent with findings in the literature (ranges approximately 17–38%) [23], [66], [90], [94], [104]. Several ex vivo and in vivo studies have found no consistent change in mean T2 values when averaged across the cartilage volume under loading [28], [29], [90], [142], which supports our mean results (Table 4.6, Figure 4.8). 70 The relationship between ΔMTR and axial compressive strain appears much less specimen dependent than the relationship between ΔT2 and axial compressive strain (Figure 4.9). However, with an estimated slope of -0.24 for tibial cartilage when averaged across the full contact area, the relationship between ΔMTR and axial compressive strain does not appear very sensitive. Repeated measures correlation coefficients are also moderate at best (-0.36 for tibial cartilage), which is only slighter higher than the coefficients observed in T2 (-0.28 for tibial cartilage), indicating that the relationship between ΔMTR and axial compressive strain is not strongly linear. These moderate correlations may be due to water redistributing evenly by the time scans were taken at equilibrium, and it is possible that correlations could be stronger if MTR data were collected immediately after loading. T2 has much higher estimated slope values (-0.91 and 0.91 for tibial and femoral cartilage, respectively), however this is due to the large spread of ΔT2 values across the same axial strain levels. This variability seen in the repeated measures correlation analysis indicates that ΔT2 may not be a reliable surrogate measure of axial compressive strain in cartilage. It is possible that this variability is due to the complex dependence that T2 has on collagen fibril orientation and the change in orientation that occurs during compression [75]. This dependence on collagen orientation could explain why the strength of linearity increased between ΔT2 and axial compressive strain when only the refined contact area (0.34 in the femoral cartilage) was considered compared to the full contact area (0.21 in the femoral cartilage), as the largest changes in femoral T2 are observed at the centre of contact (Figure 4.6). There were several strengths to this study that should be noted. First, this research used osteochondral blocks of cartilage and bone. Using these larger samples rather than cartilage plugs allowed us to observe the MRI metric response in cartilage that was both within the contact 71 region and outside the contact region (as shown qualitatively in Figure 4.5) and is more representative of the physiological contact scenario. This is more easily translatable to what we could expect under loading in vivo. This study also used a high field strength 9.4T scanner, which allowed for a high voxel resolution of 62.5 microns in the axial direction. This higher resolution meant that axial strain could be measured more accurately than on a low field or clinical scanner at 1.5T or 3T, in which articular cartilage is only a few voxels thick due to an in-plane resolution of approximately 0.5 mm [94], [104], [143]. The depth-dependent responses in MTR and T2 could also be observed in more detail, including the centralized response seen in the T2 scans (Figure 4.5). Additionally, a validated pneumatic compressive device (see Chapter 3) was used to apply remote controlled loading to each specimen, so that specimen repositioning was not required at each load. This eliminated any error seen in similar studies caused by repositioning between loads [23]. Limitations to this study included the inability to study fully intact knee joints under loading. Because of the geometrical limitations of the MRI bore diameter (70 mm), an intact bovine knee joint could not be studied in this scanner. However, the results from this study can inform future work regarding which MRI metrics may be appropriate to utilize when investigating intact joints in lower resolution scanners with larger bore diameters, based on the aims of the study. Six bovine samples were included in the analysis for this work (five for T2), but a larger sample size of human cadaveric samples would be required to generalize any findings. Although bovine articular cartilage has been shown to behave more similarly than other animal models compared to human articular cartilage in ex vivo studies, there are still many differences between bovine and human cartilage behaviour [144]. Bovine cartilage dynamic stiffness has been recorded as over 1.5 times greater than human cartilage, with bovine femoral cartilage 20% thinner than 72 human femoral cartilage [110]. Third, the T2 times observed in this work (25.1±6.5 ms and 22.0±9.7 ms in the femoral and tibial cartilage, respectively) are shorter than those typically reported in the literature for articular cartilage (30 – 80 ms) [134]–[136]. These differences are likely due to differences in field strengths compared to other literature, which certainly also impacts T2 length [145]. It is important to note, however, that the main variables analyzed in this study are the normalized change in T2 and MTR rather than the original values of each metric. It is a fair assumption that the normalized changes in T2 would be minimally impacted by the lower T2 values. A further limitation was that only 3 slices were acquired for T2, which was done to reduce signal attenuation. Although this was a necessary decision, it does limit the comparison that can be made between ΔT2 and axial strain across the cartilage volume. Additionally, the axial compressive strain under steady, static load observed at equilibrium in this work may not truly represent the in vivo environment, as load is typically applied dynamically in the knee during activities such as walking. Although we waited for twenty minutes to allow the cartilage to reach approximately 90% of equilibrium [51], it is still likely that the cartilage morphology was changing during image acquisition (6 minutes for MTR, 32 minutes for T2). An instantaneous image is more ideal, and certain UTE methodologies may be able to acquire images much more quickly. UTE also allows us to acquire MT and T2 data in structures with short T2, such as the collagen-dense deep and calcified zones of articular cartilage. Furthermore, this work assumed a uniform axial strain throughout the cartilage depth for each column. Cartilage strain is depth-dependent, due to the differences in cartilage composition throughout each zone. Previous models have been developed to describe the local strain changes throughout the cartilage depth [125]. However, these models are extremely sensitive to partial volume effects and segmentation errors, which can cause surface strain 73 measurement errors twice the size of average strain measurement errors [23]. Finally, as discussed above, the two validation studies conducted in this work indicate some possible error in axial strain measurement due to technological limitations and human error, particularly in the femoral cartilage. Due to thin femoral cartilage specimens, with several under 1 mm thick, an error of less than two voxels during segmentation can result in an axial strain calculation error of almost ten percent. Correlations between local column strain and MTR or T2 therefore cannot be properly analyzed in specimens this thin. The results of this work suggest that MTR may be a less specimen dependent surrogate measure of average axial compressive cartilage strain, although it does not appear to match the spatial pattern of local axial strain that T2 mimics in tibial cartilage. It may be easier to measure strain-related changes in MTR in lower field strength clinical scanners due to the simpler changes that are easily noticeable throughout the cartilage volume. MTR may also be more useful in a clinical setting due to its short scan time and simplicity in application. High-resolution measurements of T2 could prove useful as a technique to further investigate local cartilage strain patterns, however this requires a more detailed understanding of how the collagen network orientation changes under loading and the impact of those changes on T2 measurements. 74 5 Validating the magnetization transfer ratio as an indicator of cartilage health through stiffness testing 5.1 Introduction Knee OA is linked to altered or abnormal mechanics in the joint tissue [62], specifically the cartilage and underlying bone. Changes in cartilage mechanical properties are detectable in the early stages of tissue degeneration due to early changes in cartilage structure and biochemistry [146]. Cartilage compressive stiffness is a mechanical parameter of particular importance since one purpose of articular cartilage is to transmit high compressive forces across the joint surface area [35]. Specifically, instantaneous cartilage stiffness has been an identifier for regions of cartilage that have softened due to OA [64]. Currently, in vivo cartilage stiffness is most often measured using invasive arthroscopic techniques, for which measurements have low repeatability, with inter-observer variations ranging from 17-20% [147]. MRI allows us to study cartilage non-invasively; however, it is unclear what the mechanical implications are of the changes we can observe in MRI scans. The relationship between cartilage stiffness and quantitative MRI techniques such as T2, T1ρ and dGEMRIC has been investigated in the literature. Correlations between T2 or T1ρ and stiffness have been conducted primarily in cartilage plugs removed from the bone [76], [148], [149], which drastically changes the cartilage response to compression from the intact condition. Additionally, these studies used either confined or unconfined compression, so correlations between these MRI metrics and stiffness have only been assessed when averaged across the cartilage volume. dGEMRIC is the only MRI parameter that has been studied as a predictor of local stiffness across the cartilage, with strong correlations (ranging from r = 0.64-0.90) observed when only the superficial cartilage layer is 75 considered in analysis [150], [151]. However, no significant relationship has been found between dGEMRIC and local cartilage stiffness when the full cartilage depth is considered. MTR may be a more suitable and repeatable surrogate measure of cartilage mechanics than T2, T1ρ, or dGEMRIC because it has minimal sensitivity to the magic angle effect and does not require the use of contrast agents. Two recent studies have found moderately linear positive correlations (ranging from r = 0.38-0.52) between cartilage stiffness and MTR [20], [98]. However, these studies utilized UTE techniques during image acquisition, which are susceptible to image distortion and require more complicated post-processing corrections that conventional MT techniques do not. To date no studies have compared cartilage stiffness and MTR values obtained through conventional (non-UTE) methods, and no studies have mapped stiffness and MTR across the cartilage surface to compare any local relationships between the two variables. This chapter addresses the third and final objective of this thesis: to determine the relationship, if any, between MTR and cartilage stiffness in healthy ex vivo bovine cartilage specimens. The relationship between T2 and cartilage stiffness is also assessed as a comparison. 5.2 Methods We assessed the relationships between MTR and stiffness by mechanically testing the specimens that we had previously imaged to map MTR and T2 (as described in Chapter 4). We used indentation testing with a spherical indenter to measure instantaneous compressive stiffness. This section outlines the indentation device and methodology, the registration techniques used to directly compare MRI metrics with stiffness values, and how regions of interest were defined in order to average MRI metrics at each testing location. 76 5.2.1 Sample Preparation Six bovine femoral and tibial osteochondral blocks were imaged and mechanically tested for this study. These samples were the same as those studied in Chapter 4 of this thesis. The specimen preparation methodology is detailed in Section 4.2.4. During sample preparation, three MRI-compatible fiducial markers were adhered to the D-shaped mounting plate of each specimen to serve as origin markers. 5.2.2 MRI Imaging Image acquisition and processing (including segmentation) were completed as part of Chapter 4 of this thesis. To summarize, a MSME sequence was used for T2 mapping of cartilage, with only three slices acquired to reduce signal attenuation. To obtain saturated and unsaturated image volumes (S0 and S+, respectively) for MTR, a 3D snapshot FLASH sequence was used, with each saturation period followed by four linearly encoded FLASH readouts. MTR was then calculated using the following equation: 𝑀𝑇𝑅 = 1 − 𝑆+𝑆0 Refer to Sections 4.2.3 and 4.2.4 for sequence details. Note that the aims of this current chapter are only concerned with the uncompressed MRI images of each specimen. Mean cartilage thickness was calculated from the segmented cartilage scans by averaging the thickness of each column of segmented voxels. 5.2.3 Mechanical Testing After MRI scanning, the femoral and tibial specimens were removed from the CCA and stored overnight in a 4º C refrigerator while submerged in PBS. Approximately 16 hours later, the 77 specimen was mounted to the testing device’s sample holder with set screws, placed into a high-walled chamber, and once again submerged in PBS to prepare for mechanical testing (Figure 5.1). Femoral and tibial specimens were tested separately. Figure 5.1: Axial view of tibial osteochondral block mounted to sample holder in high walled chamber Mechanical indentation testing was completed using the Mach-1 V500CSS micro-mechanical system (Biomomentum, Montreal, Canada) (Figure 5.2). This system includes a test frame, three motorized stages (two horizontal for the x and y directions and one vertical for the z direction), and a six-axis load cell. This load cell measures force (calibrated to range = 70 N, resolution = 3.5 mN) and torque (calibrated to range = 0.5 Nm, resolution = 25 μNm) in the x, y, and z directions. The load cell passed a detailed calibration inspection by ATI Industrial Automation in 2013, with a reported measurement accuracy of 1.5% of full-scale load (at a 95% confidence 78 interval) [122]. The load cell is calibrated prior to every indentation test using the “Calibrate” function in the Mach-1 control software (LabView, National Instruments, Austin, USA). The motorized stages have a displacement accuracy of 0.5 μm [122]. A nonporous spherical indenter 1 mm in diameter was rigidly attached to the load cell for specimen testing, and indenter orientation and velocity were controlled through software. This software also recorded load and displacement as a function of time throughout the entirety of testing. Indentation testing parameters were determined in a previous pilot study assessing stiffness in human articular cartilage [152]. An indentation depth of approximately 10% of cartilage thickness was chosen based on Hertz’s theory of contact mechanics, which states that the depth of cartilage affected by indentation is nine times the indentation depth [153]. This indentation depth was set at 0.2 mm based on the assumption that mean bovine cartilage thickness is 2 mm [144], as our exact specimen thicknesses could not easily be determined a priori. Previous work has shown no significant correlation was observed between local cartilage stiffness measurements from indentation testing and the range of thickness of cartilage in a typical specimen (r = 0.11, p > 0.05) [122], so the protocol was not altered for varying thicknesses across specimens. 79 Figure 5.2: Mechanical indentation testing equipment and data collection set up Prior to indentation testing, the location of each fiducial marker was determined by placing the indenter on each marker and manually recording the coordinates. The z coordinate of the D-shaped endplate surface was also recorded. Black waterproof India ink was injected before PBS submersion at two random points on the cartilage surface to act as reference origin points, and the x and y translational stages were adjusted so that the indenter was directly above the marked points. The coordinates of the reference points were then localized by lowering the indenter with the “Find Contact” function in the Mach-1 LabView software (which detects an increase in force that is defined as contact force), until a threshold load of 0.3 N was reached. Once completed, a grid of indentation testing points was generated in the Mach-1 software (Figure 5.3), with points approximately 3 mm apart on the cartilage surface. Surface orientation was determined and stiffness data were subsequently collected at each testing point using the “Normal Indentation” testing sequence programmed in the Mach-1 LabView software [122]. This sequence first identifies the surface orientation at the testing point by measuring the coordinates of 4 points that 80 are each 1 mm from the testing point. The direction of indentation is defined as the vector normal to the resultant plane. The repeatability and accuracy of surface orientation determination have both been validated in previous work at our lab. To assess repeatability, surface orientation was determined four times at eight random testing locations on a lamb knee cartilage specimen. An intraclass correlation of 0.977 was calculated from this test, with a standard deviation of the mean error for each measurement of 1.54º [152]. To assess accuracy, the recorded normal displacement of the indenter was compared to the normal axis calculated by the “Normal Displacement” function in human cartilage samples. The maximum error between the two was found to be 1.2º [122]. Figure 5.3: Generated indentation testing points for a femoral specimen in the Mach-1 software To collect mechanical data, the indenter tip was lowered normal to the resultant plane, towards to cartilage surface, until the defined maximum contact load of 0.3 N is reached to localize the testing point. The three mechanical stages were then translated to lower the tip normal to the surface, at a constant velocity of 0.5 mm/s until an indentation depth of 0.2 mm was achieved. 81 This velocity was chosen based on previous work that has suggested a minimum velocity of 0.3 mm/s is required to ensure the cartilage response to indentation is elastic [151]. Instantaneous stiffness was recorded at each testing point in the Mach-1 software using the following equation: 𝑆 = 𝐹𝑛𝑜𝑟𝑚,𝑝𝑒𝑎𝑘𝑑𝑛𝑜𝑟𝑚 Where: • 𝑆 (N/mm) is the instantaneous stiffness of the cartilage at the selected indentation point; • 𝐹𝑛𝑜𝑟𝑚,𝑝𝑒𝑎𝑘 (N) is the peak normal force; and • 𝑑𝑛𝑜𝑟𝑚 (mm) is the normal displacement Instantaneous stiffness measurement repeatability on the Mach-1 indentation testing system has been validated in a previous study [122]. 16 testing locations were randomly selected on an intact human cadaveric cartilage specimen, and instantaneous stiffness measurements were collected six times at each location. The root mean square of the resultant coefficients of variation was 8%. The instantaneous elastic modulus (IM) was also calculated at each indentation point. This was done using an equation developed by Hayes et al. for articular cartilage indentation with a spherical indenter, which expands on the simple stiffness measurement described above [52]: 𝐼𝑀 = 𝐹𝑛𝑜𝑟𝑚,𝑝𝑒𝑎𝑘𝑑𝑛𝑜𝑟𝑚(1 − 𝑣2)2𝑎 𝜅(𝑎ℎ,𝑣) Where: • 𝐼𝑀 (MPa) is the instantaneous elastic modulus; 82 • 𝐹𝑛𝑜𝑟𝑚,𝑝𝑒𝑎𝑘 (N) is the peak normal indentation force; • 𝑑𝑛𝑜𝑟𝑚 (mm) is the normal displacement; • 𝑣 is the Poisson ratio for cartilage, assumed to be 0.5 (perfectly incompressible) [152]; • 𝑎 (mm) is the indentation area radius – which is calculated as √𝑅𝑑, where 𝑅 (mm) is the radius of the indenter (1 mm) and 𝑑 (mm) is the indentation depth (0.2 mm); • 𝜅 is a correction factor dependent on 𝑎 (indentation area radius), ℎ (cartilage thickness), and 𝑣 (Poisson ratio); and • ℎ (mm) is the thickness of the cartilage The Hayes equation assumes an infinitely long and thick layer of elastic cartilage that is perfectly adhered to the bone. It also assumes that the cartilage is perfectly isotropic, has a frictionless surface, and that any energy dissipation is negligible. 5.2.4 Data Processing Defining regions of interest for analysis: To determine the indentation testing locations on the MRI scans, rigid registration was conducted in Analyze (14.0, AnalyzeDirect, Overland Park, KS, USA) using the manual registration feature. This feature allows for visual manipulation of the “match” data (the segmented MRI scan – see Section 4.2.4 for segmentation details) to align geometrically to the “base” data (the image collected during indentation testing). The geometry of the plate below the specimen and fiducial markers visible in the indentation data and MRI data were used as references for this registration. The resulting transformation matrix was inverted and applied to the coordinates of each indentation testing location. This converted these coordinates from “physical space” to “imaging space”. A repeatability test was conducted to assess errors associated with this 83 registration method (Appendix H), for which the registration technique described above was repeated three times each for two specimens (one femoral and one tibial). Resultant errors in region of interest (ROI, described below) location for ten randomly chosen testing points were compared. ROIs in the quantitative imaging data (MTR and T2) were defined for each indentation point, perpendicular to the cartilage surface. To determine surface orientation, a fourth order polynomial was fit to the most superficial layer of cartilage (i.e. the cartilage-PBS interface) for each segmented MRI slice of femoral and tibial cartilage. At each indentation point along this polynomial fit, the tangential slope was calculated, which was defined as the surface orientation at each point. Once orientation was confirmed, the ROI was then defined on the cartilage surface at each point as a 1 mm circle (to match the indenter size) centred around the testing location. ROI depth was defined in the normal direction as two times the indentation depth (i.e. 0.4 mm), which has been used in a similar indentation study [122]. The ROI depth definition is based on a finite element modelling study that found indentation stress to decrease by 50% at double the indentation depth [154]. Average MTR and T2 were averaged across each superficial ROI and each full depth ROI. 5.2.5 Statistics Summary statistics were collected for MTR, T2, instantaneous modulus, instantaneous stiffness, and thickness for each tibial and femoral cartilage specimen. These summary statistics were collected for all ROIs (i.e. 1 mm circle) defined at a depth of 0.4 mm, as well as for all ROIs across the full depth of the cartilage. Repeated measures correlation [126], which is explained in more detail in Section 4.2.6, was utilized to test the null hypothesis that there is no linear relationship between MTR values and cartilage stiffness. This analysis was also repeated to test 84 the null hypothesis that there is no linear relationship between T2 values and cartilage stiffness. As in Chapter 4, estimated slope ß (the estimated linear slope between each MRI metric and stiffness) and repeated measures correlation coefficient rrm (the strength of linearity between each MRI metric and stiffness) were the two outputs of this statistical model, calculated using a confidence interval of 0.95. All repeated measures correlation analyses were conducted in RStudio (R Core Team 2022, Vienna, Austria). For this analysis, correlations were defined as weak (rrm < 0.3), moderate (0.3 < rrm < 0.5), or strong (rrm > 0.5). 5.3 Results The repeatability error associated with registration between mechanical indentation points and the MR images ranged from 0.26 – 1.03 mm, with a median error of 0.64 mm. Errors in the slice direction were all zero, due to a low resolution in the slice direction (1.6 mm). Median error in the column direction was 2 voxels (maximum 4 voxels), and median error in the row direction was 2 voxels (maximum 4 voxels). Detailed results of this repeatability analysis can be found in Appendix H. Generally, the tibial cartilage specimens were thicker (ranges 1.06 – 4.13 mm) than the femoral cartilage specimens (ranges 0.69 – 3.13 mm) (Tables 5.1, 5.2). Large IM ranges were observed across specimens, with the calculated IM at each indentation point ranging from 0.30 MPa to 14.3 MPa (mean and standard deviation: 4.10±3.34 MPa) in the femoral specimens, and from 0.020 MPa to 8.6 MPa (mean and standard deviation: 0.85±1.11 MPa) in the tibial specimens. T2 varied more than MTR, with standard deviations of T2 values corresponding to variations as high as 40% across specimens compared to a maximum of 25% in MTR values across specimens. Specimen 3 was excluded from analysis in this chapter due to corruption of the 85 mechanical testing data. As mentioned in Chapter 4, one specimen (specimen 2) was not included in T2 analysis due to technical errors during image acquisition. Table 5.1: Femoral specimen mean MTR, T2, mechanical measurements, and thickness Mean MTR and T2 are reported for each superficial ROI (defined as a 1 mm diameter circle centred around the indentation point, with a depth of 0.4 mm below the cartilage surface) as well as for each ROI across the full depth of the cartilage. All values are reported as mean ± standard deviation. T2 values are not reported for specimen 2 due to technical error during image acquisition. Sample Superficial ROI Full Depth ROI Mechanical Measurements Cartilage Thickness (mm) MTR (%) T2 (ms) MTR (%) T2 (ms) IM (MPa) S (N/mm) 1 31.9±8.7 42.7±2.5 39.8±2.1 14.6±3.6 1.48±1.15 1.40±1.11 1.66±0.20 2 39.7±2.9 N/A 50.4±1.8 N/A 7.89±3.03 9.83±4.20 0.90±0.39 4 42.9±1.5 50.5±32.3 45.5±2.8 25.4±1.5 3.75±2.85 4.66±3.93 1.06±0.37 5 44.3±7.6 40.4±10.4 45.1±3.3 41.3±1.0 1.57±0.52 1.46±0.52 1.73±0.44 6 34.1±3.1 59.6±61.4 45.3±1.7 44.2±7.9 6.19±2.35 7.28±3.02 0.89±0.13 All specimens 38.2±7.9 56.9±35.0 43.1±7.1 32.1±6.4 4.10±3.34 4.87±4.43 1.20±0.39 86 Table 5.2: Tibial specimen mean MTR, T2, mechanical measurements, and thickness Mean MTR and T2 are reported for each superficial ROI (defined as a 1 mm diameter circle centred around the indentation point, with a depth of 0.4 mm below the cartilage surface) as well as for each ROI across the full depth of the cartilage. All values are reported as mean ± standard deviation. T2 values are not reported for specimen 2 due to technical error during image acquisition. Sample Superficial ROI Full Depth ROI Mechanical Measurements Cartilage Thickness (mm) MTR (%) T2 (ms) MTR (%) T2 (ms) IM (MPa) Stiffness (N/mm) 1 41.0±6.1 53.4±7.0 56.1±6.8 22.3±3.7 0.76±0.37 0.58±0.31 1.87±0.38 2 36.0±9.5 N/A 51.5±7.7 N/A 1.35±1.62 1.40±2.02 2.20±0.64 4 34.7±10.3 61.4±9.4 54.8±4.0 41.3±19.5 0.84±1.24 0.89±1.42 2.56±0.61 5 34.7±3.3 32.9±12.1 43.7±3.9 24.4±2.2 0.36±0.32 0.30±0.29 2.99±0.53 6 45.1±2.4 59.7±8.9 61.0±9.1 34.7±7.0 1.03±1.05 0.98±1.14 2.51±0.66 All specimens 38.0±7.1 52.9±11.1 53.7±8.6 30.8±13.0 0.85±1.11 0.83±1.30 2.43±0.37 Mean T2 correlated more strongly with mean IM than mean MTR correlated with mean IM (Figure 5.4). The strongest relationship between mean T2 and mean IM was observed when only the superficial ROIs were considered (R2 = 0.98 and R2 = 0.53 for femoral and tibial cartilage respectively) versus the ROIs including the full depth of cartilage (R2 = 0.26 and R2 = 0.35 for femoral and tibial cartilage respectively). The opposite was seen in mean MTR, where a moderate correlation with mean IM was seen for ROIs considering the full depth of the cartilage (R2 = 0.65 and R2 = 0.28 for femoral and tibial cartilage respectively). When only the superficial 0.4 mm was considered, mean MTR could not confidently predict mean IM (R2 = 0.003 and R2 = 0.059 for femoral and tibial cartilage respectively). 87 Figure 5.4: Mean IM versus mean (A) MTR, and (B) T2 Each point represents the mean values for one specimen, with femoral specimens represented in the left column and tibial specimens represented in the right column. Blue data represents mean MTR or T2 data averaged for only the top 0.4 mm of cartilage, and orange data represents mean MTR or T2 data averaged across the full depth of the cartilage. Equations and R2 values for linear correlation are displayed. Neither MTR nor T2 were strong predictors of IM at local testing points across the surface of the cartilage (Figures 5.5, 5.6). With a few exceptions, a positive correlation was observed between either MRI metric and IM, however the slope of this relationship changed significantly between specimens. Specimen-specific correlation plots can be found in Appendix I. The repeated measures correlation analysis similarly shows weak (less than 0.3) to moderate (0.3 – 0.5) correlations between each MRI metric and IM at local testing points. In both the 88 superficial ROIs and the full depth ROIs, rrm values were higher for all T2 analyses (Table 5.3) compared to all MTR analyses (Table 5.4). Stronger sensitivity (larger slopes) were observed between each MRI metric and IM in the femoral specimens than in the tibial specimens (Tables 5.3, 5.4). Generally, T2 values had a larger spread both within and between specimens (Figure 5.5) compared to MTR values (Figure 5.6). All correlations were statistically significant (p < 0.001). Table 5.3: T2 versus IM repeated measures correlation outputs at each region of interest Type of tissue and region of interest Estimated Slope 𝛽𝐼𝑀𝑇2 (MPa/ms) Repeated measures correlation coefficient rrm p-value ( p < 0.001 indicates statistical significance) Femoral cartilage: superficial 0.097 0.35 < 0.001 Femoral cartilage: full depth 0.086 0.27 < 0.001 Tibial cartilage: superficial 0.018 0.25 < 0.001 Tibial cartilage: full depth 0.019 0.26 < 0.001 Table 5.4: MTR versus IM repeated measures correlation outputs at each region of interest Type of tissue and region of interest Estimated Slope 𝛽𝐼𝑀𝑀𝑇𝑅 (MPa) Repeated measures correlation coefficient rrm p-value ( p < 0.001 indicates statistical significance) Femoral cartilage: superficial 4.46 0.18 < 0.001 Femoral cartilage: full depth 6.28 0.23 < 0.001 Tibial cartilage: superficial 0.59 0.11 < 0.001 Tibial cartilage: full depth 0.50 0.06 < 0.001 89 Figure 5.5: Repeated measures correlation plots illustrating the relationship between IM and T2 Each colour represents one specimen, and each point represents the one indentation testing point with T2 averaged across the corresponding ROI at (A) a superficial depth of 0.4 mm, or (B) the full depth of the cartilage. rrm values represent the repeated measures correlation coefficient. All tests show statistical significance (p < 0.001). 90 Figure 5.6: Repeated measures correlation plots illustrating the relationship between IM and MTR Each colour represents one specimen, and each point represents the one indentation testing point with MTR averaged across the corresponding ROI at (A) a superficial depth of 0.4 mm, or (B) the full depth of the cartilage. rrm values represent the repeated measures correlation coefficient. All tests show statistical significance (p < 0.001). 5.4 Discussion To our knowledge, this is the first study to assess the strength of local MTR and local T2 as predictors of local cartilage stiffness across the surface. Positive correlations were observed between mean MTR and mean IM when averaged across the full depth of the cartilage (R2 = 0.65 and 0.28 in the femoral and tibial cartilage respectively), and stronger positive correlations were observed between mean T2 and mean IM when only considering the superficial region of the 91 cartilage (R2 = 0.98 and 0.53 in the femoral and tibial cartilage respectively). However, neither local MTR nor local T2 were found to be strong predictors of local IM in femoral or tibial specimens. Tibial cartilage was overall thicker and had a lower IM than femoral cartilage, which is consistent with what has been reported in the literature. Previous studies have measured mean bovine femoral cartilage thickness to range between 0.50 – 1.28 mm [110], [144], whereas mean bovine tibial cartilage thickness was measured previously to be 2.19±0.67 mm [144]. These values support our thickness measurements of 1.20±0.39 mm (femoral) and 2.43±0.37 mm (tibial). Although the Hayes equation has not been frequently used to calculate IM for bovine knee cartilage, one recent study did use this methodology to calculate IM via indentation testing (indenter diameter = 8 mm) on healthy bovine knee cartilage plugs [155]. They reported IM ranges between 0.5 – 12.0 MPa, similar to our calculated IM values and ranges. The correlations observed between mean T2 and mean instantaneous cartilage stiffness in this study are consistent with similar relationships reported in the literature. Nissi et al. used unconfined compression testing to compare the dynamic modulus of bovine cartilage samples to mean T2 (measured in unloaded cartilage), finding a positive linear correlation between the two (R2 = 0.879) [148]. In a similar study using compression testing to assess the relationship between T2 and Young’s modulus of bovine patellofemoral cartilage, comparable relationships were observed (R2 = 0.62–0. 73) [149]. Our current study differs by testing cartilage still intact with the underlying bone, whereas both mentioned studies used detached cartilage samples, which may impact cartilage physiological properties and therefore correlations observed. The previous studies mentioned calculated dynamic modulus [148] or equilibrium modulus [149] rather than the IM calculated in our current work. These three moduli measure cartilage stiffness 92 under different loading conditions, which will result in different values and therefore different correlations with mean T2. However, previous work has found the immediate stiffness of cartilage to be significantly correlated with equilibrium stiffness (r = 0.82 – 0.84) and dynamic stiffness (r = 0.79 – 0.82) [122]. MTR has not been studied extensively as a predictor of cartilage stiffness, but our results can be compared to two recent studies that both utilized Hayes’ equation to calculate IM (averaged across the cartilage surface). Namiranian et al. compared mean UTE-MTR to mean IM when measured via indentation testing across 40 human tibiofemoral specimens. A statistically significant relationship was found between mean MTR and mean IM in both the superficial zone of the cartilage (R2 = 0.49) and throughout the full depth of the cartilage (R2 = 0.52) [20]. A similar study utilizing UTE-MTR to study cadaveric human patellar cartilage in 3T MRI found slightly weaker correlations between mean MTR and mean IM (r = 0.379) [98]. This is consistent with our findings of R2 = 0.65 (femoral cartilage) and 0.28 (tibial cartilage) when MTR was averaged across the full depth of the cartilage (Figure 5.4). Unfortunately, we cannot directly compare the correlations reported in these studies to those observed in our current work, as both studies use human cadaveric samples that likely have substantial cartilage degeneration compared to the healthy bovine samples used in our current study. This has a significant impact on the calculated IM (0.07 – 0.9 MPa in the above studies) and mean MTR (17 – 37 % in the above studies), and likely also impacts the correlations between the two. The above studies also used UTE techniques, which may impact MTR measurements due to the lower TE used during image acquisition. The weak correlations observed between both T2 and IM and MTR and IM when comparing local testing points indicates that neither metric is suitable for mapping stiffness across the 93 cartilage surface. T2 analyses did result in stronger rrm values (rrm = 0.25 – 0.35) than MTR analyses (rrm = 0.06 – 0.23). This could be due to the dependency that T2 has on the collagen fibril network, as the properties of this network have been shown to change across the articular cartilage within a single specimen [156]. MTR is believed to depend on the overall macromolecular concentration (primarily collagen and PGs) of the cartilage relative to the water concentration. The weak correlations between local IM and local MTR imply that local stiffness and local macromolecular concentration may not be significantly related. Previous studies investigating the relationship between local dGEMRIC and local cartilage stiffness through indentation testing have reported stronger correlations (R2 = 0.55 – 0.90) [150], [151], as has previous work assessing correlations between local CECT measurements and local cartilage stiffness (r = 0.37 – 0.73) [4]. Since both dGEMRIC and CECT are related to PG content, these previous results indicate that cartilage stiffness is highly dependent on PG concentration. It may be that MTR measures different features of the cartilage compared to dGEMRIC and CECT, as MTR can only detect the changes in overall macromolecular content. Further investigation would be required to assess this theory. Cartilage health quality and thickness differences in tibial and femoral cartilage specimens likely contributed to differences in the correlations observed in each type of specimen. Based on qualitative observation, tibial cartilage samples were more impacted by freezer storage prior to specimen preparation than femoral cartilage (see Figure 4.1 in Chapter 4), which may have led to some initial tissue softening and degeneration at the cartilage surface. This may explain the weaker correlations seen in the tibial cartilage compared to the femoral cartilage, as the IM values calculated from indentation testing may not be indicative of the tissue health during MRI image acquisition. Tibial cartilage was also generally thicker than femoral cartilage, however the 94 indentation depth was kept the same during indentation testing for both types of specimens. Therefore, a larger percentage of the femoral cartilage depth was loaded compared to tibial cartilage depth, which could have impacted IM values, as Hertz’s theory of contact mechanics suggests that cartilage up to nine times the indentation depth can be impacted by indentation testing [153]. A key strength of this study was the use of intact cartilage surface samples during imaging and mechanical testing. Many other studies comparing cartilage stiffness to imaging parameters use cartilage plugs that have been removed from the underlying bone [76], [148], [149], [157]. Using cartilage still attached to the bone more closely mimics the in vivo environment and preserves the physiological environment of the tissue [158]. Assessing the relationship between IM and MRI metrics rather than equilibrium modulus may also better represent the in vivo environment, since load is typically applied and removed quickly (within approximately 0.6 seconds [159]) in situations such as walking and running. However, as mentioned above, there is a strong correlation between equilibrium modulus and IM in cartilage [122]. Furthermore, this study is the first to study the local relationships across the cartilage surface area between cartilage stiffness and MRI parameters aside from dGEMRIC [150], [151]. Similar work has been conducted comparing stiffness with CECT measurements [4], however most studies comparing MRI and cartilage stiffness simply compare the overall mean values for each specimen. This work goes further by determining whether there is a more specific correlation at various points of interest across the cartilage. Finally, this work utilized a high field strength MRI scanner (9.4T), allowing for a high voxel resolution and more accurate MRI metric measurements for each ROI compared to what would be measured on a clinical scanner with a lower resolution. 95 It is important to also note the limitations of this work. First, only a small sample of bovine specimens was analyzed in this study (five joint samples for MTR, four joint samples for T2). A larger sample size outside the scope of this work would be required to generalize any reported results. Bovine tissue also behaves differently under loading to human tissue due to factors such as higher stiffness and differences in thickness [148], and the correlations between stiffness and MRI parameters may differ between species. It is also important to note that mechanical testing could not be conducted until approximately 48 hours after initial specimen preparation. Although specimens were stored at 4° Celsius submerged in PBS, this waiting time may have contributed to some specimen degeneration, particularly in the tibial cartilage. Additionally, the imaging time required for T2 (32 minutes) was significantly longer than MTR (6 minutes), making it less desirable for further cartilage mechanics investigation that are interested in the instantaneous response of cartilage. Future studies may want to consider UTE methodologies, as they can shorten scan time significantly [160]. Finally, errors associated with registration may have impacted the correlations observed between IM and each MRI parameter. The errors associated with registration were quantified to be within one millimetre, with repeatability remaining within four voxels. A higher resolution in the anterior-posterior direction of the scans would likely improve this repeatability. The results of this study indicate that there is some utility in using MTR and T2 as measures of overall cartilage stiffness, and therefore overall cartilage health. This could be useful in low field strength and clinical scanners where stiffness mapping is not as feasible. However, neither MTR nor T2 appear to be strong candidates to map cartilage stiffness across the tissue in MRI. 96 6 Integrated Discussion 6.1 Overview The overall goal of this work was to assess the relationship in cartilage between MTR and two mechanical parameters: strain and stiffness. We compared these relationships to those seen between T2 and strain as well as T2 and stiffness, as T2 has been studied more extensively in the cartilage mechanics literature. Understanding these relationships may be useful for future in vivo studies investigating cartilage and OA prevention and treatment. Our current findings indicate that compression produces a uniform change in MTR throughout the cartilage volume. The relationship between T2 and axial strain was highly depth dependent, which is consistent with findings in the literature [23], [66], [90], [94]. Additionally, our work suggests that both MTR and T2, averaged across the entire cartilage, may be useful as measurements of average cartilage stiffness, which could be utilized as a tool to assess overall cartilage health. However, neither MTR nor T2 were found to be strong predictors of local cartilage stiffness, which limits their utility for mapping cartilage stiffness. 6.2 Contributions 1. We developed and validated the CCA, an MRI-compatible electro-pneumatic loading device that applied uniaxial compression to cartilage samples while using an optical sensor to track displacement throughout scanning. The electro-pneumatic system allowed for remote controlled load application to each specimen to avoid specimen repositioning at each load. With manually controlled loading devices [23], [93], [104], users must reposition their specimen in the MRI scanner after each load application, which requires further registration between image sets, thereby introducing error. An advantage of the CCA is that it uses an FBG sensor to measure 97 displacement of the femoral specimen as it is compressed against the tibial specimen, which allowed us to target specific axial compressive strain levels throughout the scanning period based on the thickness of each cartilage specimen. This is an advantage over earlier electro-pneumatic systems that have been used to apply compression to cartilage in MRI [96], [105], [106], because these systems relied on previous calibrations between pressure and displacement to determine target axial compressive strain levels. The large stiffness differences between cartilage specimens, as were found in Chapter 5 of this work to vary by more than 6 MPa (approximately 75%) in healthy femoral bovine cartilage, mean that assuming equal stiffness between specimens would introduce substantial error. These stiffness differences impact the amount of pressure required to achieve a certain level of strain. The CCA also allows us to study larger osteochondral samples, with the cartilage still attached to the bone. These samples behave more similarly to the in vivo scenario physiologically, compared to smaller cartilage plugs that have been removed from the underlying bone. The CCA has strong potential for use in future ex vivo cartilage mechanics studies (described further in section 6.6). 2. We developed a MT sequence protocol on a high field strength 9.4T MRI scanner, using the CCA to optimize the sequence for ex vivo cartilage compression tests. This protocol was eventually used in hypothesis testing to obtain MTR measurements in unloaded and loaded cartilage. All previous work comparing MT parameters to cartilage mechanics in high-field MRI has utilized UTE-MT techniques [20], [98], [161], which require complex post-processing steps and corrections to address UTE image distortion. Our protocol utilizes conventional MT techniques, which do not require such corrections and are much simpler to implement. The MTR protocol was designed to be less than six minutes in duration, with a power low enough to minimize specimen heating but a signal-to-noise ratio high enough to distinguish between 98 cartilage boundaries. This quick and simple protocol could be useful for further cartilage mechanics investigation (detailed in section 6.6). 3. This was the first study to directly compare local axial compressive strain measured across the cartilage to local changes in MTR. We observed a uniform response in MTR across the cartilage volume as axial compressive strain increased, which resulted in a stronger and less specimen dependent correlation between ΔMTRnorm and axial compressive strain compared to ΔT2norm and axial compressive strain. Previous studies have only compared MT values (including MTR and the macromolecular proton fraction) averaged across the entire cartilage volume to the strain applied to the entire specimen [75], [133], rather than comparing local strain to local MTR changes. This MTR response to axial strain could be beneficial when imaging in vivo at lower field strengths (such as 1.5T or 3T), as the uniform reaction could still easily be seen at lower imaging resolutions (see section 6.5). 4. We built on a previous study comparing local T2 reactions to local axial compressive strain measured across the cartilage. We confirmed the findings of the only previous study to directly compare local strain to local T2 changes [23], and that study did not compare the T2 response to other MRI values. We directly compared the T2 and MTR responses to axial compressive strain, finding that the correlation between ΔT2norm and axial compressive strain was more specimen dependent compared to the correlation between ΔMTRnorm and axial compressive strain due to the zonal variations of T2. This was generally consistent with the zonal dependency of T2 that has been reported in the literature for both unloaded [77], [136], [138]–[141] and loaded [23], [94] cartilage. It is important to understand this difference in strain response, as it tells us that we may not be able to see T2 changes with axial compressive strain in low field strength or clinical scanners. The lower image resolution at such scanners will not 99 easily detect such depth-dependent changes. However, T2 could still be a practical tool in better understanding local cartilage structure changes under load in high-field strength MRI studies. 5. We established the strength of association between local MTR/T2 and local cartilage stiffness (specifically instantaneous modulus) across the cartilage surface. This local relationship between imaging parameters and cartilage stiffness has only been studied in the literature with imaging techniques requiring contrast: dGEMRIC [150], [151] and CECT [4]. Both MTR and T2 show promise when averaged across the cartilage as indicators of overall cartilage stiffness, which is consistent with previous studies in MTR [20], [98] and T2 [148], [149]. However, we found that MTR and T2 are weaker surrogate measurements of instantaneous cartilage stiffness compared to dGEMRIC or CECT when mapped locally across the cartilage surface (rrm < 0.25 in MTR, rrm < 0.5 in T2, r = 0.64-0.90 in dGEMRIC [150], [151], r = 0.37-0.69 in CECT [4]). It is important to note that CECT is not possible in vivo, and dGEMRIC is rarely used in modern in vivo studies due to the use of a controversial contrast agent. MTR and T2 carry minimal risk in vivo, as no contrast agent nor radiation is required. Both MTR and T2 therefore still show promise for low field and clinical MRI studies as measures of overall cartilage stiffness (discussed further in section 6.5). 6.3 Strengths One strength of this thesis is that osteochondral blocks of cartilage and bone were used throughout, rather than smaller cartilage plugs that have been separated from the bone. Only a handful of studies have used these types of samples [20], [23], [66], [94], and most of the literature studying the relationship between T2 and cartilage stiffness has used cartilage plugs [76], [148], [162]. There are several benefits to using intact articular cartilage in our work. First, these samples allowed us to observe MTR and T2 responses to axial compressive strain in 100 cartilage that was in contact with each other, as well as in cartilage that was outside of the contact region. This was especially important for MTR, as we observed uniform changes far away from the contact region. Additionally, keeping the cartilage attached to the bone ensured that the tissue responded similarly to how it does in the in vivo environment, while also preserving the physiological environment of the tissue [158] and minimizing any swelling that could occur due to PBS submersion [163]. A further strength is that utilizing a high field strength 9.4T MRI scanner allowed for a high voxel resolution in the axial direction (0.0625 mm). Low field and clinical scanners (0.5-3.0T) cannot typically obtain an in-plane resolution better than 0.4-0.5 mm [164], which limits the thickness of cartilage specimens to just a few voxels. Most studies studying cartilage under loading have been conducted in clinical 3T scanners [20], [26], [29], [93], [94], [98], [161], with only a few conducted at high field strengths of 7T – 9.4T [23], [66], [150], [151]. The high resolution in our current study allowed for a more accurate axial compressive strain measurement in the tibial cartilage compared to what could be measured in lower field scanners. It also provided important detailed information about the zone dependent T2 response to compression, which would not be clearly observable in a scanner with lower resolution. This high resolution was also very useful in mapping the relationship between cartilage stiffness and each MRI metric, as the mean MRI metric measurements for each region of interest could be calculated more accurately. 6.4 Limitations It is important to note the limitations of the work in this thesis. First, the FBG sensor described and validated as part of the CCA in Chapter 3 was not used to measure target axial strain levels during MRI scanning in Chapter 4. This was due to the sensor unfortunately breaking during a 101 scan and timing limitations preventing its replacement for this study. However, the nature of the work described in Chapter 4 did not require us to have the exact same mean target axial strain levels for each specimen, as we were studying the relationship between column-specific axial compressive strain and each MRI metric. The FBG sensor should be used in future studies when it is important to have the same target axial strain levels at each step load across specimens. A second limitation is that only the axial compressive component of strain was studied in Chapter 4 of this thesis. Strain is a tensor made up of six components (three normal and three shear), and the cartilage response to load requires all six components for a complete description. Although most of the strain observed in cartilage in vivo is compressive, significant shear strains have been found at higher levels of compression [101], with shear strains up to 10% measured in the in vivo human knee [165]. It is likely that shear strain and strains in other directions may be influencing MTR and T2 measurements. Shear strain has also been implicated in OA [166]–[168], making it an important consideration when studying changes in cartilage function throughout OA progression. However, axial compressive strain is a measurement that can be calculated simply from sagittal MRI images and is more easily translatable to future in vivo and clinical scenarios. The relationship between shear strain and MTR, T2, or other MRI metrics could be explored by expanding upon the methods described in Chapter 4, but this would require more complex analysis outside the scope of this work. Comparisons between MTR and other MRI parameters as surrogate measures of cartilage strain and stiffness were limited due to MRI scanner limitations. As mentioned in Chapter 4, only 3 slices could be acquired for the T2 scans, compared to the 17 acquired for MTR. This low slice number was necessary to reduce signal attenuation and acquire reliable T2 data, however it significantly reduced the T2 data collected, therefore limiting the comparisons that can be made 102 between MTR and T2. Faster sequences such as double echo steady state (DESS) have been used in previous work to collect 3D T2 image volumes of cartilage [23], however DESS is still an experimental sequence that requires further validation in T2 applications [169]. A further limitation is that no other MRI parameters were compared to MTR in this work. T1ρ was originally planned to be included in this thesis, and significant T1ρ sequence protocol development was conducted at the 9.4T MRI scanner. However, the sequence was too long (over 40 minutes) and required too much additional protocol development to be included in this study. It is important to note that because cartilage reacts dynamically to loading, all MRI studies will be limited in detecting cartilage behaviour due to the time required for image acquisition. Many MRI measures (such as T2) require several images, and cartilage creep may cause differences between each set of images, which could impact final T2 measurements. However, shorter scan protocols (such as the six-minute MTR protocol) are less affected by this trade-off. Future studies should include T1ρ as a key comparison, as it is used prominently in cartilage mechanics literature [26], [29], [90], [94], [95]. Another limitation was the small sample size of six bovine tibiofemoral specimens used for this work. This sample size was reduced further by one in collected T2 data due to technical issues during T2 image acquisition for one specimen and reduced further by one in Chapter 5 due to corruption of the collected indentation testing data for another specimen. This small study in bovine tissue was an important step to establish data collection and analysis methodologies. To fully understand the relationships between MRI and cartilage mechanics, we would require a larger sample size of human tissue with an appropriate range of age, sex, body mass index (BMI), degree of degeneration, and other factors. 103 6.5 Clinical Utility This research builds on the limited knowledge we have from previous MTR studies by providing clarity on the MTR relationship to cartilage axial compressive strain and stiffness. Only a few studies have investigated the relationship between MT parameters and strain [75], [99], [133] or stiffness [20], [98]. Our results help us better understand how we may be able to apply MTR clinically in future cartilage studies. The findings of this thesis indicate that MTR could be useful as a measure of cartilage mechanics in lower field strength clinical scanners. When averaged across the full depth of the cartilage volume, MTR showed promise as an indicator of mean cartilage stiffness. However, a poor correlation was found between local MTR and local instantaneous modulus when mapped across cartilage specimens. A similar full depth MTR response was observed in Chapter 4, where a uniform change in MTR was observed as axial compressive strain increased. This full thickness change in MTR is a stark contrast to T2, in which significant changes were primarily observed only in the superficial zone when comparing to both axial compressive strain and stiffness. These findings indicate that MTR may be useful in vivo when low field clinical scanners with poor image resolutions must be used. Localized and specific changes in cartilage cannot be observed at such resolutions, but MTR could prove advantageous as a preliminary indicator of overall cartilage response to load, which may be useful in assessing cartilage health in vivo. MTR also requires a much shorter scan time (less than six minutes), whereas the T2 image acquisition reported in this work was over thirty minutes long. A shorter scan time is ideal in clinical scenarios, as it minimizes the time required to scan each patient or participant. Both CECT and dGEMRIC have shown promise as predictors of local cartilage stiffness through indentation testing [4], [150], [151], but there are limitations preventing both imaging methods 104 from widespread use in clinical in vivo applications that do not apply to MTR. First, although the quality of CECT images allows for detailed cartilage analysis, the cationic contrast agent (specifically CA4+) used has not been approved for clinical use [170]. Although previous work has suggested that a lower dose of this contrast agent would be sufficient to study cartilage mechanics [122], no in vivo studies can be conducted in humans until the contrast agent’s approval. CECT also requires the use of ionizing radiation, whereas no radiation is required in MRI. As an MRI methodology, dGEMRIC does not require radiation, but it uses a gadolinium-based contrast agent that raises concerns for use in vivo [151]. dGEMRIC is also limited in its application due to long scan times and the complicated post-processing required to obtain useful T1 values after scanning [171]. With a total image acquisition time of less than six minutes, only one calculation needed to obtain MTR values, and no contrast agent required, the MT sequence described in this thesis may be a valuable alternative when studying knee cartilage under load in vivo. This research confirms that T2 is likely less valuable as a research tool in clinical scanners and is more useful in studying local cartilage changes at higher field strength scanners. Unlike MTR, the correlation between T2 and cartilage under load has been studied much more in previous work. The depth-dependent response of T2 to load seen in Chapter 4 supports other what has been reported qualitatively in previous studies [23], [66], [90], [94], [104], as do the positive linear correlations observed in Chapter 5 between mean T2 at the superficial layer and mean bovine cartilage stiffness (R2 = 0.53 – 0.98 in our study versus R2 = 0.62 – 0.88 in the literature) [148], [149]. The similarities in T2 between this thesis and the literature indicate that our methodologies were comparable to previous published studies, thereby also validating our findings regarding MTR. Although T2 changes may not be easily observed in low field strength 105 MRI, the localized T2 response to load could be useful in further ex vivo investigation when high image resolutions are possible. Understanding the physiology behind the changes seen in MTR and T2 when cartilage is compressed can provide insight into the clinical or research applications of each MRI metric. MTR is highly dependent on macromolecular concentration [31], but MTR does not describe any specific components of the macromolecular structure (such as collagen or PGs). As compression is added to the cartilage, water is pushed through the ECM and out of the tissue. As a result, the magnetization transfer between the free water and macromolecules increases, thereby increasing the MTR. This supports our findings in Chapter 4, where a distinct uniform increase in MTR is seen in the cartilage with compression. This MTR response could be useful in a clinical application to help us better understand the behaviour of free water in both healthy and degenerated cartilage. In contrast, T2 is known to be sensitive to water content and the orientation of the collagen architecture [136]. The “waveform” of increased T2 moving deeper into the cartilage that we observed in our results (see Figure 4.5) suggests that the collagen structure orientation is only affected by load at the superficial and upper transitional zones of the cartilage. We theorize this waveform indicates a “flattening” of the collagen fibrils away from the area of compression. T2 could be used in future high-resolution studies to assess cartilage fibril structure in degenerated cartilage. However, the utility of T2 in these studies may be limited due to its sensitivity to the magic angle effect [97], which can have a large impact on T2 measurements. 106 6.6 Future Directions The methodologies developed in this thesis provide a strong starting point for future cartilage mechanics studies in MRI. Our results provide preliminary evidence that there is a relationship between MTR and mechanical parameters in compressed cartilage. This work can be built on in the future by studying a large sample of human cartilage that accurately reflects population diversity (age, sex, BMI, etc.). We recommend that future work be conducted in human cadaveric specimens, as human cartilage has been shown to behave differently under loading compared to bovine cartilage [148]. Human cadaveric samples with cartilage degeneration will also likely show higher variation when studying correlations between MTR and mechanical parameters, which will be important to understand for future in vivo studies. Future studies should explore the relationship between cartilage strain and MTR (or other MRI measurements) under dynamic loading conditions. Instantaneous and dynamic strain patterns are important in understanding the mechanisms that may initiate and progress OA, as load is typically applied and removed quickly in vivo (such as while walking or running). The CCA is already equipped with pressure transducers (G27M0210N, Ashcroft, Stratford, CT, USA; specification reported accuracy of 1%) at either end of the piston and a 5/2 solenoid valve (V61R517A, Norgren, Birmingham, United Kingdom). Combined, these two components allow the capability to program a dynamic loading sequence via a double-acting actuator. This could be done either by toggling a switch in the software program to change loading direction, or by implementing a proportional-integral-derivative (PID) controller to allow for autonomous cyclic loading. The cartilage response to this cyclic loading could be observed through rapid MR acquisition, which is feasible through dynamic sequences such as DENSE (displacement 107 encoding with stimulated echoes). DENSE has been validated in previous ex vivo work to measure magnetization phase changes in cartilage throughout cyclic loading phases [172]. Finally, we recommend that MTR be compared to additional MRI parameters beyond T2 in future cartilage mechanics studies. The response of T1ρ in compressed cartilage has been studied numerous times in the literature [25], [29], [90], [94]–[96] , and has shown more significant changes than those seen in T2 when averaged across the cartilage depth. Additionally, dGEMRIC is the only MRI technique that has shown success in mapping stiffness across the cartilage [150], [151]. Both T1ρ and dGEMRIC are related to PG content [91], [173], and PG depletion is one of the first signs of OA. Comparing MTR to these MRI measurements would help us better understand the utility of MTR as a surrogate measure for cartilage mechanics, and furthermore, cartilage health. 6.7 Conclusion This thesis investigated the relationships between MTR and axial compressive strain and stiffness in cartilage and compared these to relationships between T2 and axial compressive strain and stiffness. This investigation was done using a novel electropneumatic loading rig, which allowed us to apply step compressive loads to specimens in a small-bore research MRI. Both MTR and T2 may be useful as measurements of mean cartilage stiffness in clinical scanners with low field strength. 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Grinstaff, “X-Ray Computed Tomography Contrast Agents,” Chem Rev, vol. 113, no. 3, pp. 1–64, 2013, doi: 10.1021/cr200358s. [171] T. C. Mamisch, M. Dudda, T. Hughes, D. Burstein, and Y. J. Kim, “Comparison of delayed gadolinium enhanced MRI of cartilage (dGEMRIC) using inversion recovery and fast T1 mapping sequences,” Magn. Reson. Med., vol. 60, no. 4, pp. 768–773, 2008, doi: 10.1002/MRM.21726. [172] L. Zevenbergen et al., “Cartilage-on-cartilage contact: effect of compressive loading on tissue deformations and structural integrity of bovine articular cartilage,” Osteoarthritis Cartilage, vol. 26, pp. 1699–1709, 2018, doi: 10.1016/j.joca.2018.08.009. [173] R. Reddy Regatte, S. V. S. Akella, A. Borthakur, J. B. Kneeland, and R. Reddy, “Proteoglycan Depletion-induced Changes in Transverse Relaxation Maps of Cartilage: Comparison of T2 and T1 1”. 120 Appendices Appendix A: Images of specimen preparation In-tact previously frozen bovine knee (left = proximal, right = distal, top = anterior, bottom = posterior) Removal of excess tissue with scalpel (pictured: patella removal) 121 Disarticulation of ligaments. Pictured: disarticulation of ACL. Bovine knee is bent in extreme flexion to create more tension on the ligament for ease of cutting. Caution is taken to ensure the cartilage is not nicked by the scalpel accidentally. Fully disarticulated tibia (left) and femur (right). Meniscus is later removed to expose tibial cartilage. 122 Femoral and tibial sides were lined up in the neutral standing position, and corresponding blocks of approximately 30 mm x 30 mm in AP and ML directions were extracted from the femur and tibia. Pictured above are initial cuts marked by a manual saw and surgical oscillating saw. Surgical oscillating saw was used to cut through the depth of the osteochondral block (at least 20 mm thick). Cut was done as parallel to the cartilage surface as possible. 123 Final osteochondral blocks (femur = left, tibia = right) adhered to plastic plates. A and M written on the cartilage represent the anterior and medial orientation of each block, respectively. 124 Appendix B: Investigation of the inter-rater and intra-rater reliability for cartilage segmentation in 3D Slicer A repeatability study was conducted to assess the reliability of the tibial and femoral cartilage segmentations completed in 3D Slicer. To assess intra-rater reliability, the primary rater (ES) segmented MTR scans from all loads (0, 1, 2, 3) for 2 specimens three times. To assess inter-rater reliability, a second rater (CH) segmented the same scans from the 2 specimens twice. A brief list of rules was determined before segmentation: 1) which slices were deemed relevant for segmenting; and 2) to include only voxels that were certainly cartilage (i.e., avoid voxels impacted by partial volume effects). All segmentation was completed as described in section 4.2.4. The resultant errors in terms of voxels for each specimen are described in the below tables. Table B.1: Intra-rater and inter-rater repeatability for specimen 1 Cartilage Type Load Number Intra-rater repeatability in voxels (mean ± SD) Inter-rater repeatability in voxels (mean ± SD) Tibia 0 0.6 ± 0.4 1.0 ± 0.6 Tibia 1 2.4 ± 0.2 2.5 ± 0.3 Tibia 2 2.2 ± 0.6 2.4 ± 0.4 Tibia 3 0.8 ± 0.8 2.0 ± 0.4 Femur 0 0.9 ± 0.2 1.6 ± 0.3 Femur 1 1.3 ± 0.3 1.4 ± 0.8 Femur 2 1.2 ± 0.5 1.8 ± 0.5 Femur 3 1.4 ± 0.3 1.5 ± 0.6 125 Table B.2: Intra-rater and inter-rater repeatability for specimen 3 Cartilage Type Load Number Intra-rater repeatability in voxels (mean ± SD) Inter-rater repeatability in voxels (mean ± SD) Tibia 0 1.5 ± 0.8 2.4 ± 0.5 Tibia 1 2.0 ± 0.5 2.0 ± 0.3 Tibia 2 2.1 ± 0.2 1.9 ± 0.6 Tibia 3 1.9 ± 0.4 2.1 ± 0.5 Femur 0 1.4 ± 0.4 1.7 ± 0.5 Femur 1 1.2 ± 0.2 1.2 ± 0.3 Femur 2 1.2 ± 0.3 1.7 ± 0.6 Femur 3 0.8 ± 0.4 1.4 ± 0.9 The resulting overall mean error and standard deviation found for each type of cartilage are shown below in voxels. Intra-rater repeatability in voxels (mean ± SD) Inter-rater repeatability in voxels (mean ± SD) Tibial 2.2 ± 0.8 2.3 ± 1.0 Femoral 1.3 ± 0.5 1.6 ± 0.7 With a mean cartilage thickness between the two specimens of 2.22 mm (tibial) and 1.10 mm (femoral), and a voxel height of 0.0625 mm, the % strain error is shown below: 126 Intra-rater repeatability in % strain error (mean ± SD) Inter-rater repeatability in % strain error (mean ± SD) Tibial 6.2 ± 2.3 6.4 ± 2.8 Femoral 7.4 ± 2.8 9.1 ± 3.9 The maximum mean repeatability error in manual segmentation through these methods was within 6.4% of the total cartilage thickness for the tibial cartilage, and within 9.1% of the total cartilage thickness for the femoral cartilage. It is important to note the potential errors in segmentation when assessing the relationship between MRI parameters and strain, as these errors could impact the correlation observed between the variables. 127 Appendix C: Validation of 9.4T MRI thickness measurements using CECT This validation study was conducted and written by Charlene Harasym under the supervision and guidance of Emily Sullivan. Introduction The objective of the present work was to validate MRI cartilage thickness measurements in bovine femora and tibiae, compared to the previously validated method of measuring from contrast enhanced computed tomography (CECT) [122]. Measurements of cartilage thickness were needed in our study to calculate the cartilage strain while under different levels of compression. Methods Three lateral tibial and femoral cartilage specimens were prepared as described in section x. These specimens were first scanned unloaded in the 9.4 Tesla MRI following the protocol described in section Y. The specimens were then soaked in CA4+ contrast agent for 64 hours before being scanned unloaded using CECT. The CT images were then resampled to have the same pixel dimensions as the MTR MRI images and were manually registered for the tibia and femur separately. The cartilage was manually segmented in each slice of the MRI and CECT images separately, and the thickness of each column of segmented pixels was calculated as done in section 4.2.5. Corresponding pixel columns between image sets were directly compared via mean and median differences, coefficients of variation and ranges, and linear correlation. All statistical analyses were completed using a custom script written in MATLAB (2020). 128 Results The mean thickness of the femur samples was observed as 1.37 and 1.38 mm by the CECT and MRI respectively. The mean thickness error for all femur samples was 0.077 mm with a coefficient of variation (CV) of 136%, corresponding to a 5.58% error of the mean thickness values. The median thickness of the femur samples was observed as 1.25 mm with a range of 0.62-2.94 mm and 1.25 mm with a range of 0.56-2.94 mm by the CECT and MRI respectively. The median thickness error for all femur samples was 0 mm with a range of -0.5-0.625 mm, corresponding to a 0% error of the median thickness values. Significant correlations (R²=0.93, p<0.001) were observed between the MRI and CECT measurements of thickness. Data for each femur sample can be seen in Table C1 and Figures C1-C3. Table C1: Results for each of the 3 femur samples for CECT versus MRI thickness measurement methods (Bovine femoral condyle). Sample Mean Difference (mm) Median Difference (mm) Coefficient of Variation (%) Difference Range (mm) R² A 0.11 0.0625 110.96 -0.4375-0.625 0.93 B 0.051 0 146.02 -0.4375-0.25 0.95 C 0.082 0 137.24 -0.5-0.5 0.95 All 0.077 0 136.24 -0.5-0.625 0.93 129 Figure C1: Thickness measurements from CECT method versus MRI method for Femur Sample A. 130 Figure C2: Thickness measurements from CECT method versus MRI method for Femur Sample B. 131 Figure C3: Thickness measurements from CECT method versus MRI method for Femur Sample C. The mean thickness of the tibia samples was observed as 1.31 and 1.29 mm by the CECT and MRI respectively. The mean thickness error for all tibia samples was 0.060 mm with a CV of 153%, corresponding to a 4.61% error of the mean thickness values. The median thickness of the tibia samples was observed as 1.25 mm with a range of 0.5-3 mm and 1.25 mm with a range of 0.5-3.12mm by the CECT and MRI respectively. The median thickness error for all tibia samples was 0 mm with a range of -0.56-0.62 mm, corresponding to a 0% error of the median thickness values. Significant correlations (R²=0.95, p<0.001) were observed between the MRI and CECT measurements of thickness. Data for each tibia sample can be seen in Table C2 and Figures C4-C6. 132 Table C2: Results for each of the 3 tibia samples for CECT versus MRI thickness measurement methods (Bovine tibial plateau). Sample Mean Difference (mm) Median Difference (mm) Coefficient of Variation (%) Difference Range (mm) R² A 0.029 0 200.64 -0.25-0.3125 0.90 B 0.016 0 254.48 -0.25-0.25 0.97 C 0.10 0.0625 107.18 -0.5625-0.625 0.95 All 0.060 0 153.18 -0.5625-0.625 0.95 Figure C4: Thickness measurements from CECT method versus MRI method for Tibia Sample A. 133 Figure C5: Thickness measurements from CECT method versus MRI method for Tibia Sample B. 134 Figure C6: Thickness measurements from CECT method versus MRI method for Tibia Sample C. Discussion The results of this experiment show that 9.4 Tesla MRI measures cartilage thickness with an error less than 0.078mm. Although large coefficients of variation and ranges are seen in this data, this was expected due to the small thicknesses of the cartilage and segmentation restrictions of 62.5 µm pixels. A key strength of this method is that the specimen preparation, data collection, and image processing methods are consistent with those used for hypothesis testing. This allows for a more accurate validation of the thickness measurements that are used to calculate strain. 135 Appendix D: Specimen-specific mean strains and MRI metrics for full contact area Specimen 1 Femur: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.35 0 15.1 0 Load 1 0.05 0.49 0.34 15.8 0.05 Load 2 -0.06 0.52 0.40 16.6 0.10 Load 3 -0.03 0.53 0.49 17.5 0.16 Tibia: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.44 0 20.8 0 Load 1 -0.05 0.50 0.12 26.0 0.15 Load 2 -0.11 0.52 0.16 26.9 0.20 Load 3 -0.14 0.53 0.18 27.5 0.23 Specimen 2 Femur: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.49 0 N/A N/A Load 1 0.10 0.68 0.34 N/A N/A Load 2 0.09 0.69 0.38 N/A N/A Load 3 0.04 0.70 0.39 N/A N/A Tibia: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.47 0 N/A N/A Load 1 -0.05 0.66 0.35 N/A N/A Load 2 -0.06 0.68 0.39 N/A N/A Load 3 -0.15 0.69 0.41 N/A N/A 136 Specimen 3 Femur: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.46 0 22.7 0 Load 1 0.07 0.56 0.18 22.1 -0.03 Load 2 0.05 0.60 0.25 23.7 0.04 Load 3 0.03 0.61 0.30 26.6 0.16 Tibia: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.48 0 22.8 0 Load 1 -0.10 0.59 0.20 22.1 -0.03 Load 2 -0.12 0.61 0.25 23.7 0.04 Load 3 -0.15 0.62 0.28 26.6 0.17 Specimen 4 Femur: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.42 0 29 0 Load 1 0.104 0.54 0.26 24 -0.14 Load 2 0.086 0.58 0.34 23 -0.19 Load 3 0.060 0.60 0.39 27 -0.05 Tibia: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.45 0 21 0 Load 1 -0.15 0.58 0.27 28 0.31 Load 2 -0.20 0.61 0.35 26 0.23 Load 3 -0.25 0.63 0.40 25 0.21 137 Specimen 5 Femur: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.45 0 26.6 0 Load 1 0.04 0.55 0.19 25.5 -0.04 Load 2 0.07 0.59 0.28 27.7 0.04 Load 3 0.09 0.61 0.32 33.5 0.26 Tibia: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.42 0 22.2 0 Load 1 -0.18 0.55 0.29 32.6 0.47 Load 2 -0.24 0.60 0.41 41.0 0.84 Load 3 -0.25 0.63 0.46 40.1 0.80 Specimen 6 Femur: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.42 0 32.0 0 Load 1 0.10 0.55 0.30 22.5 -0.30 Load 2 0.09 0.60 0.41 22.8 -0.29 Load 3 0.12 0.61 0.45 23.1 -0.28 Tibia: Strain MTR % Change MTR T2 (ms) % Change T2 Load 0 0 0.44 0 23.0 0 Load 1 -0.09 0.55 0.25 26.4 0.15 Load 2 -0.12 0.59 0.34 26.1 0.13 Load 3 -0.15 0.61 0.39 26.0 0.13 138 Appendix E: Manual femoral compression measurements in 3D Slicer To assess how much the femoral cartilage was deforming under load, or whether it was deforming at all, a “sanity check” was performed in 3D Slicer using the ruler tool. Specimen 1: Column 76 Column 84 Slice Load 0 Load 1 Load 2 Load 3 Load 0 Load 1 Load 2 Load 3 8 1.36 1.34 1.32 1.32 1.86 1.82 1.80 1.75 9 1.29 1.24 1.24 1.22 1.79 1.77 1.77 1.76 10 1.38 1.33 1.30 1.27 1.87 1.84 1.82 1.79 11 1.44 1.41 1.41 1.41 1.98 1.91 1.90 1.88 Specimen 4: Column 74 Column 92 Slice Load 0 Load 1 Load 2 Load 3 Load 0 Load 1 Load 2 Load 3 8 1.07 1.06 1.04 0.99 1.06 1.01 1.00 1.00 9 0.96 0.96 0.95 0.93 1.04 1.02 1.02 1.02 10 0.98 0.92 0.91 0.89 0.99 0.91 0.90 0.87 11 0.96 0.86 0.86 0.85 1.02 0.94 0.92 0.92 Based on the above data, in both specimens the maximum compression seen was within the difference of two voxels (0.125 mm). Therefore, any femoral cartilage strain observed is minimal, and correlations between femoral strain and MRI metrics cannot be deemed reliable. Qualitative responses observed in the femur are still of interest, as the femoral cartilage appears to be compressing slightly. 139 Appendix F: Specimen-specific correlation plots comparing ΔMTR and strain The scatterplots below describe the relationship between strain and normalized change in MTR for each step load compared to the uncompressed cartilage, for each individual specimen. Femoral cartilage relationships are shown in the top row, and tibial cartilage relationships are shown in the bottom row. Slopes (m) and coefficients of determination (R2) are reported. 140 F.1: Full contact area MTR correlations Figure F1: Plot of correlation between normalized change in MTR and strain – Specimen 1 141 Figure F2: Plot of correlation between normalized change in MTR and strain – Specimen 2 142 Figure F3: Plot of correlation between normalized change in MTR and strain – Specimen 3 143 Figure F4: Plot of correlation between normalized change in MTR and strain – Specimen 4 144 Figure F5: Plot of correlation between normalized change in MTR and strain – Specimen 5 145 Figure F6: Plot of correlation between normalized change in MTR and strain – Specimen 6 146 F.2: Refined contact area MTR correlations Figure F7: Plot of correlation between normalized change in MTR and strain in refined contact area– Specimen 1 147 Figure F8: Plot of correlation between normalized change in MTR and strain in refined contact area– Specimen 2 148 Figure F9: Plot of correlation between normalized change in MTR and strain in refined contact area– Specimen 3 149 Figure F10: Plot of correlation between normalized change in MTR and strain in refined contact area– Specimen 4 150 Figure F11: Plot of correlation between normalized change in MTR and strain in refined contact area– Specimen 5 151 Figure F12: Plot of correlation between normalized change in MTR and strain in refined contact area– Specimen 6 152 Appendix G: Specimen-specific correlation plots comparing ΔT2 and strain The scatterplots below describe the relationship between strain and normalized change in T2 for each step load compared to the uncompressed cartilage, for each individual specimen. Specimen 2 was not included in T2 analysis due to technical issues during image acquisition. Femoral cartilage relationships are shown in the top row, and tibial cartilage relationships are shown in the bottom row. Slopes (m) and coefficients of determination (R2) are reported. 153 G.1: Full contact area T2 correlations Figure G1: Plot of correlation between normalized change in T2 and strain – Specimen 1 154 Figure G2: Plot of correlation between normalized change in T2 and strain – Specimen 3 155 Figure G3: Plot of correlation between normalized change in T2 and strain – Specimen 4 156 Figure G4: Plot of correlation between normalized change in T2 and strain – Specimen 5 157 Figure G5: Plot of correlation between normalized change in T2 and strain – Specimen 6 158 G.2: Refined contact area T2 correlations Figure G6: Plot of correlation between normalized change in T2 and strain in refined contact area – Specimen 1 159 Figure G7: Plot of correlation between normalized change in T2 and strain in refined contact area – Specimen 3 160 Figure G8: Plot of correlation between normalized change in T2 and strain in refined contact area – Specimen 4 161 Figure G9: Plot of correlation between normalized change in T2 and strain in refined contact area – Specimen 5 162 Figure G10: Plot of correlation between normalized change in T2 and strain in refined contact area – Specimen 6 163 Appendix H: Repeatability of registration between indentation test points and MRI image sets A repeatability sub-study was conducted to assess the repeatability of the registration method (described in Chapter 5) between the testing points recorded from the Mach-1 indentation testing and the MRI images acquired at the 9.4T scanner. Registration was conducted three times for two specimens (one femoral specimen and one tibial specimen). Ten points were chosen for each specimen randomly, and the position of each point in imaging space was recorded for all three trials. The error across all trials was then defined for each point as the difference between the lowest and highest positions in imaging space for each of the three dimensions (columns, rows, and slices). Overall error was calculated for each point in millimetres by taking the square root of the sum of each dimension’s error squared. The tables below detail the registration errors found for each specimen. 164 Table H1: Registration Error for Specimen 2 Femur Testing Location Index Error (voxels) Overall Error (mm) Column (resolution 0.25 mm) Slice (resolution 1.6 mm) Row (resolution 0.0625 mm) 1 3 0 4 0.79 2 1 0 2 1.03 3 3 0 3 0.77 4 1 0 3 0.31 5 1 0 4 0.35 6 4 0 4 1.03 7 3 0 1 0.75 8 3 0 2 0.76 9 4 0 2 1.00 10 1 0 2 0.28 Maximum (mm) 1.00 0.00 0.25 165 Table H2: Registration Error for Specimen 6 Tibia Testing Location Index Error (voxels) Overall Error (mm) Column (resolution 0.25 mm) Slice (resolution 1.6 mm) Row (resolution 0.0625 mm) 1 1 0 2 0.28 2 3 0 2 0.76 3 2 0 2 0.52 4 2 0 2 0.52 5 2 0 3 0.53 6 2 0 2 0.52 7 1 0 1 0.26 8 3 0 3 0.77 9 2 0 2 0.52 10 3 0 2 0.76 Maximum (mm) 0.75 0.00 0.19 Errors ranged from 0.26 – 1.03 mm, with a median error of 0.64 mm. Errors in the slice direction were all zero, due to a low resolution in the slice direction (1.6 mm). Median error in the column direction was 0.50 mm (maximum 1.00 mm), and median error in the row direction was 0.13 mm (maximum 0.25 mm). With all planes considered, errors associated with registration repeatability were within one millimetre, which is the diameter of each testing point’s region of interest. It is important to note these limitations of the current registration method, as it could impact the correlations observed between cartilage stiffness and MRI metrics. 166 Appendix I: Specimen-specific correlation plots comparing local instantaneous modulus and MTR/T2 The scatterplots below depict the relationship between local instantaneous modulus and either MTR or T2 values for each individual specimen. Each point represents one testing location on the specimen. y1 and r1 are the equation and linearity associated with the trendline of the superficial ROI data, and y2 and r2 are associated with the trendline of the full depth ROI data. 167 MTR – Femoral Specimens Specimen 1: m1 = 5.70 e6, m2 = 1.03 e7, r1 = 0.30, r2 = 0.10 168 Specimen 2: m1 = 2.01 e7, m2 = 8.69 e6, r1 = 0.12, r2 = 0.01 169 Specimen 4: m1 = 9.50 e7, m2 = 2.60 e7, r1 = 0.20, r2 = 0.17 170 Specimen 5: m1 = 2.53 e6, m2 = 7.18 e6, r1 = 0.11, r2 = 0.16 171 Specimen 6: m1 = 1.90 e7, m2 = 5.28 e7, r1 = 0.13 , r2 = 0.34 172 MTR – Tibial Specimens Specimen 1: m1 = -2.20 e6, m2 = -2.04 e6, r1 = 0.10 , r2 = 0.09 173 Specimen 2: m1 = 6.09 e5, m2 = 3.22 e5, r1 = 0.53, r2 = 0.14 174 Specimen 4: m1 = 6.70 e5, m2 = 2.31 e5, r1 = 0.35, r2 = 0.06 175 Specimen 5: m1 = 1.42 e6, m2 = 1.78 e6, r1 = 0.27, r2 = 0.38 176 Specimen 6: m1 = 4.18 e5, m2 = 1.15 e7, r1 = 0.05, r2 = 0.04 177 T2 – Femoral Specimens Specimen 1: m1 = 7.45 e4, m2 = -4057 e7, r1 = 0.46, r2 = 0.13 178 Specimen 4: m1 = 1.22 e5, m2 = -3.085 e5, r1 = 0.14, r2 = 0.02 179 Specimen 5: m1 = 1.14 e4, m2 = -1186, r1 = 0.02, r2 = 0.001 180 Specimen 6: m1 = 2.92 e4, m2 = 9.47 e4, r1 = 0.14, r2 = 0.31 181 T2 – Tibial Specimens Specimen 1: m1 = 9777, m2 = 2.81 e4, r1 = 0.31, r2 = 0.25 182 Specimen 4: m1 = 2677, m2 = 2632, r1 = 0.35, r2 = 0.01 183 Specimen 5: m1 = 1.81 e5, m2 = 9.04 e4, r1 = 0.53, r2 = 0.52 184 Specimen 6: m1 = 4.65 e4, m2 = 7.81 e4, r1 = 0.32, r2 = 0.19
Thesis/Dissertation
eng
Biomedical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Wilson, David R.
Assessment of knee cartilage mechanics using the magnetization transfer ratio
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