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Kantola V, Karjalainen J, Jaakola T, Leskinen HPP, Nissi MJ, Casula V, Nieminen MT. Anisotropy of T 2 and T 1ρ relaxation time in articular cartilage at 3 T. Magn Reson Med 2024; 92:1177-1188. [PMID: 38558167 DOI: 10.1002/mrm.30096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Revised: 03/14/2024] [Accepted: 03/15/2024] [Indexed: 04/04/2024]
Abstract
PURPOSE The anisotropy of R2 and R1ρ relaxation rates in articular cartilage contains information about the collagenous structure of the tissue. Here we determine and study the anisotropic and isotropic components of T2 and T1ρ relaxation parameters in articular cartilage with a clinical 3T MRI device. Furthermore, a visual representation of the topographical variation in anisotropy is given via anisotropy mapping. METHODS Eight bovine stifle joints were imaged at 22 orientations with respect to the main magnetic field using T2, continuous-wave (CW) T1ρ, and adiabatic T1ρ mapping sequences. Relaxation rates were separated into isotropic and anisotropic relaxation components using a previously established relaxation anisotropy model. Pixel-wise anisotropy values were determined from the relaxation-time maps using Michelson contrast. RESULTS The relaxation rates obtained from the samples displayed notable variation depending on the sample orientation, magnetization preparation, and cartilage layer. R2 demonstrated significant anisotropy, whereas CW-R1ρ (300 Hz) and CW-R1ρ (500 Hz) displayed a low degree of anisotropy. Adiabatic R1ρ was largely isotropic. In the deep cartilage regions, relaxation rates were generally faster and more anisotropic than in the cartilage closer to the tissue surface. The isotropic relaxation rate components were found to have similar values regardless of measurement sequence. CONCLUSIONS The fitted relaxation model for T2 and T1ρ demonstrated varying amounts anisotropy, depending on magnetization preparation, and studied the articular cartilage layer. Anisotropy mapping of full joints showed varying amounts of anisotropy depending on the quantitative MRI parameter and topographical location, and in the case of T2, showed systematic changes in anisotropy across cartilage depth.
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Affiliation(s)
- Ville Kantola
- Research Unit of Health Sciences and Technology, University of Oulu, Oulu, Finland
- Medical Research Center, University of Oulu, Oulu University Hospital, Oulu, Finland
| | - Jouni Karjalainen
- Research Unit of Health Sciences and Technology, University of Oulu, Oulu, Finland
- Medical Research Center, University of Oulu, Oulu University Hospital, Oulu, Finland
| | - Tomi Jaakola
- Research Unit of Health Sciences and Technology, University of Oulu, Oulu, Finland
| | - Henri P P Leskinen
- Department of Technical Physics, University of Eastern Finland, Kuopio, Finland
| | - Mikko J Nissi
- Department of Technical Physics, University of Eastern Finland, Kuopio, Finland
| | - Victor Casula
- Research Unit of Health Sciences and Technology, University of Oulu, Oulu, Finland
- Medical Research Center, University of Oulu, Oulu University Hospital, Oulu, Finland
| | - Miika T Nieminen
- Research Unit of Health Sciences and Technology, University of Oulu, Oulu, Finland
- Medical Research Center, University of Oulu, Oulu University Hospital, Oulu, Finland
- Department of Diagnostic Radiology, Oulu University Hospital, Oulu, Finland
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Aptekarev T, Furman G, Badar F, Sokolovsky V, Xia Y. Study of the collagen tissue nanostructure by analyzing the echo decay obtained using the MRI technique. SOFT MATTER 2024; 20:4282-4290. [PMID: 38757720 PMCID: PMC11211971 DOI: 10.1039/d4sm00312h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2024]
Abstract
The multicomponent relaxation observed in nuclear magnetic resonance experiments in biological tissues makes it difficult to establish a correlation between specific relaxation times and tissue structural parameters. The analysis of a nanostructure (the characteristic size of 10-1000 nm) is usually based on formulas for relaxation times which depend on structural parameters at the atomic or molecular levels in the size range of 0.1-5 nm. We have recently developed an analysis method in which relaxation times' anisotropy in a sample is explicitly related to its structure of nanocavities containing a liquid or gas. However, the method is based on the analysis of experimental data on the anisotropy of relaxation times obtained by using the standard NMR technique and rotating the sample relative to a magnetic field and requires a series of experiments. In the present study, to address this challenge, we develop a new method of analysis of a multi-exponential magnetic resonance signal that does not require determining relaxation times and eliminates the sample rotation and the necessity of a series of experiments. Using the magnetic resonance imaging (MRI) technique, the total signal from the whole sample was obtained as a sum of the signals (echo decays) from all voxels. In contrast to previous research, the volumes of nanocavities and their angular distribution can be obtained by analyzing a single total signal for the entire cartilage. In addition, within the framework of this approach, it is possible to identify the reason for the multicomponent nature of relaxation. The proposed method for analyzing a single multi-exponential signal (transverse relaxation) was implemented on cartilage. Using the signal, three anatomical zones of cartilage were studied, revealing significant structural differences between them. The proposed method not only avoids the need for sample rotation but also enables repeated application of layer-by-layer magnetic resonance imaging with micron resolution. The study results allow us to suggest that water molecules contributing to the echo decay are more likely located in nanocavities formed by the fibrillar structure rather than inside the fibrils.
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Affiliation(s)
- Theodore Aptekarev
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel.
| | - Gregory Furman
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel.
| | - Farid Badar
- Physics Department, Oakland University, Rochester, MI, USA
| | | | - Yang Xia
- Physics Department, Oakland University, Rochester, MI, USA
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Furman G, Sokolovsky V, Panich A, Xia Y. Nanostructure of hydrogenated amorphous silicon (a-Si:H) films studied by nuclear magnetic resonance. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2023; 350:107434. [PMID: 37080070 DOI: 10.1016/j.jmr.2023.107434] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Revised: 03/29/2023] [Accepted: 03/31/2023] [Indexed: 05/03/2023]
Abstract
The aim of this work is to investigate the nanostructures of nanoporous materials by studying the anisotropy of the nuclear spin-spin and spin-lattice relaxations of the guest molecules trapped in the pores. The nuclear magnetic resonance (NMR) data are analyzed in the framework of the theory of the nuclear relaxation dominated by the dipole-dipole interactions in gas or liquid species contained in nanopores. A distinctive feature of this theory is the establishment of a relationship between the degree of orientation ordering of nanopores in the host matrix and their characteristic volume and the anisotropy of the NMR relaxation times. In this work the complex experimental and theoretical approach was applied to study the nanostructure of hydrogenated amorphous silicon (a-Si:H) films. A feature of this study is the simultaneous investigation of the three (T1, T1ρ, and T2) NMR relaxation times, for the same sample. This allows us to determine not only the degree of orientation ordering of nanopores but also to estimate their size (∼1 nm) and correlation times of the nanopore fluctuations. The obtained results demonstrate that the developed approach is effective in studying details of nanostructure of different nanoporous materials.
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Affiliation(s)
- Gregory Furman
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel; Education Department, Tel Hai College, Tel Hai, Upper Galilee, Israel.
| | | | - Alexander Panich
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel
| | - Yang Xia
- Physics Department, Oakland University, Rochester, MI, United States
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Pan RL, Martyniak K, Karimzadeh M, Gelikman DG, DeVries J, Sutter K, Coathup M, Razavi M, Sawh-Martinez R, Kean TJ. Systematic review on the application of 3D-bioprinting technology in orthoregeneration: current achievements and open challenges. J Exp Orthop 2022; 9:95. [PMID: 36121526 PMCID: PMC9485345 DOI: 10.1186/s40634-022-00518-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Accepted: 08/08/2022] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Joint degeneration and large or complex bone defects are a significant source of morbidity and diminished quality of life worldwide. There is an unmet need for a functional implant with near-native biomechanical properties. The potential for their generation using 3D bioprinting (3DBP)-based tissue engineering methods was assessed. We systematically reviewed the current state of 3DBP in orthoregeneration. METHODS This review was performed using PubMed and Web of Science. Primary research articles reporting 3DBP of cartilage, bone, vasculature, and their osteochondral and vascular bone composites were considered. Full text English articles were analyzed. RESULTS Over 1300 studies were retrieved, after removing duplicates, 1046 studies remained. After inclusion and exclusion criteria were applied, 114 articles were analyzed fully. Bioink material types and combinations were tallied. Cell types and testing methods were also analyzed. Nearly all papers determined the effect of 3DBP on cell survival. Bioink material physical characterization using gelation and rheology, and construct biomechanics were performed. In vitro testing methods assessed biochemistry, markers of extracellular matrix production and/or cell differentiation into respective lineages. In vivo proof-of-concept studies included full-thickness bone and joint defects as well as subcutaneous implantation in rodents followed by histological and µCT analyses to demonstrate implant growth and integration into surrounding native tissues. CONCLUSIONS Despite its relative infancy, 3DBP is making an impact in joint and bone engineering. Several groups have demonstrated preclinical efficacy of mechanically robust constructs which integrate into articular joint defects in small animals. However, notable obstacles remain. Notably, researchers encountered pitfalls in scaling up constructs and establishing implant function and viability in long term animal models. Further, to translate from the laboratory to the clinic, standardized quality control metrics such as construct stiffness and graft integration metrics should be established with investigator consensus. While there is much work to be done, 3DBP implants have great potential to treat degenerative joint diseases and provide benefit to patients globally.
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Affiliation(s)
- Rachel L Pan
- College of Medicine, University of Central Florida, Orlando, FL, USA
| | - Kari Martyniak
- Biionix Cluster, College of Medicine, University of Central Florida, 6900 Lake Nona Blvd, Orlando, FL, 32827, USA
| | - Makan Karimzadeh
- Biionix Cluster, College of Medicine, University of Central Florida, 6900 Lake Nona Blvd, Orlando, FL, 32827, USA
| | - David G Gelikman
- College of Medicine, University of Central Florida, Orlando, FL, USA
| | - Jonathan DeVries
- College of Medicine, University of Central Florida, Orlando, FL, USA
| | - Kelly Sutter
- College of Medicine, University of Central Florida, Orlando, FL, USA
| | - Melanie Coathup
- Biionix Cluster, College of Medicine, University of Central Florida, 6900 Lake Nona Blvd, Orlando, FL, 32827, USA
| | - Mehdi Razavi
- Biionix Cluster, College of Medicine, University of Central Florida, 6900 Lake Nona Blvd, Orlando, FL, 32827, USA
| | - Rajendra Sawh-Martinez
- College of Medicine, University of Central Florida, Orlando, FL, USA.,Plastic and Reconstructive Surgery, AdventHealth, Orlando, FL, USA
| | - Thomas J Kean
- Biionix Cluster, College of Medicine, University of Central Florida, 6900 Lake Nona Blvd, Orlando, FL, 32827, USA.
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Orozco GA, Tanska P, Gustafsson A, Korhonen RK, Isaksson H. Crack propagation in articular cartilage under cyclic loading using cohesive finite element modeling. J Mech Behav Biomed Mater 2022; 131:105227. [DOI: 10.1016/j.jmbbm.2022.105227] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 03/01/2022] [Accepted: 04/02/2022] [Indexed: 11/28/2022]
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Szarek P, Lilledahl MB, Emery NC, Lewis CG, Pierce DM. The zonal evolution of collagen-network morphology quantified in early osteoarthritic grades of human cartilage. OSTEOARTHRITIS AND CARTILAGE OPEN 2020; 2:100086. [DOI: 10.1016/j.ocarto.2020.100086] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Accepted: 07/14/2020] [Indexed: 10/23/2022] Open
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Batool S, Mahar R, Badar F, Tetmeyer A, Xia Y. Quantitative µMRI and PLM study of rabbit humeral and femoral head cartilage at sub-10 µm resolutions. J Orthop Res 2020; 38:1052-1062. [PMID: 31799697 PMCID: PMC7162717 DOI: 10.1002/jor.24547] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 11/30/2019] [Indexed: 02/04/2023]
Abstract
This study aimed to establish the baseline characteristics in humeral and femoral cartilage in rabbit, using quantitative magnetic resonance imaging (MRI) relaxation times (T2, T1ρ, and T1) at 9.75 and 70-82 µm pixel resolutions, and quantitative polarized light microscopy (PLM) measures (retardation, angle) at 1.0 and 4.0 µm pixel resolutions. Five intact (i.e., unopened) shoulder joints (the scapula and humeral heads) and three femoral heads of the hip joints from five healthy rabbits were imaged in MRI at 70-82 µm resolution. Thirteen cartilage-bone specimens were harvested from these joints and imaged in µMRI at 9.75 µm resolution. Subsequently, quantitative PLM study of these specimens enabled the examination of the fibril orientation and organization in both intact joints and individual specimens. Quantitative MRI relaxation data and PLM fibril structural data show distinct features in tissue properties at different depths of cartilage, different in individual histological zones. The thicknesses of the histological zones in µMRI and PLM were successfully obtained. This is the first correlated and quantitative MRI and PLM study of rabbit cartilage at sub-10 µm resolutions, which benefits future investigation of osteoarthritis using the rabbit model. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 38:1052-1062, 2020.
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Affiliation(s)
| | | | | | | | - Yang Xia
- Corresponding Author and Address: Yang Xia, Ph.D., Department of Physics, Oakland University, 244 Meadow Brook Road, Rochester, Michigan 48309, USA, Phone: (248) 370-3420, Fax: (248) 370-3408,
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Jerban S, Chang EY, Du J. Magnetic resonance imaging (MRI) studies of knee joint under mechanical loading: Review. Magn Reson Imaging 2019; 65:27-36. [PMID: 31670237 DOI: 10.1016/j.mri.2019.09.007] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Revised: 08/17/2019] [Accepted: 09/15/2019] [Indexed: 02/07/2023]
Abstract
Osteoarthritis (OA) is a very common disease that affects the human knee joint, particularly the articular cartilage and meniscus components which are regularly under compressive mechanical loads. Early-stage OA diagnosis is essential as it allows for timely intervention. The primary non-invasive approaches currently available for OA diagnosis include magnetic resonance imaging (MRI), which provides excellent soft tissue contrast at high spatial resolution. MRI-based knee investigation is usually performed on joints at rest or in a non-weight-bearing condition that does not mimic the actual physiological condition of the joint. This discrepancy may lead to missed detections of early-stage OA or of minor lesions. The mechanical properties of degenerated musculoskeletal (MSK) tissues may vary markedly before any significant morphological or structural changes detectable by MRI. Recognizing distinct deformation characteristics of these tissues under known mechanical loads may reveal crucial joint lesions or mechanical malfunctions which result from early-stage OA. This review article summarizes the large number of MRI-based investigations on knee joints under mechanical loading which have been reported in the literature including the corresponding MRI measures, the MRI-compatible devices employed, and potential challenges due to the limitations of clinical MRI sequences.
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Affiliation(s)
- Saeed Jerban
- Department of Radiology, University of California, San Diego, CA, USA.
| | - Eric Y Chang
- Department of Radiology, University of California, San Diego, CA, USA; Radiology Service, VA San Diego Healthcare System, San Diego, CA, USA
| | - Jiang Du
- Department of Radiology, University of California, San Diego, CA, USA
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9
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Wang N, Badar F, Xia Y. Compressed sensing in quantitative determination of GAG concentration in cartilage by microscopic MRI. Magn Reson Med 2018; 79:3163-3171. [PMID: 29083096 PMCID: PMC5843514 DOI: 10.1002/mrm.26973] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2017] [Revised: 09/06/2017] [Accepted: 09/26/2017] [Indexed: 12/19/2022]
Abstract
PURPOSE To evaluate the potentials of compressed sensing (CS) in MRI quantification of glycosaminoglycan (GAG) concentration in articular cartilage at microscopic resolution. METHODS T1 -weighted 2D experiments of cartilage were fully sampled in k-space with five inversion times at 17.6 μm resolution. These fully sampled k-space data were re-processed, by undersampling at various 1D and 2D CS undersampling factors (UFs). The undersampled data were reconstructed individually into 2D images using nonlinear reconstruction, which were used to calculate 2D maps of T1 and GAG concentration. The values of T1 and GAG in cartilage were evaluated at different UFs (up to 16, which used 6.25% of the data). K-space sampling pattern and zonal variations were also investigated. RESULTS Using 2D variable density sampling pattern, the T1 images at UFs up to eight preserved major visual information and produced negligible artifacts. The GAG concentration remained accurate for different sub-tissue zones at various UFs. The variation of the mean GAG concentration through the whole tissue depth was 1.20%, compared to the fully sampled results. The maximum variation was 2.24% in the deep zone of cartilage. Using 1D variable density sampling pattern, the quantitative T1 mapping and GAG concentration at UFs up to 4 showed negligible variations. CONCLUSION This study demonstrates that CS could be beneficial in microscopic MRI (µMRI) studies of cartilage by acquiring less data, without losing significant accuracy in the quantification of GAG concentration. Magn Reson Med 79:3163-3171, 2018. © 2017 International Society for Magnetic Resonance in Medicine.
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Affiliation(s)
- Nian Wang
- Center for In Vivo Microscopy, Department of Radiology, Duke University, Durham, NC 27710
| | - Farid Badar
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309
| | - Yang Xia
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309
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High-resolution Imaging of Myeloperoxidase Activity Sensors in Human Cerebrovascular Disease. Sci Rep 2018; 8:7687. [PMID: 29769642 PMCID: PMC5956082 DOI: 10.1038/s41598-018-25804-y] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2018] [Accepted: 04/26/2018] [Indexed: 01/23/2023] Open
Abstract
Progress in clinical development of magnetic resonance imaging (MRI) substrate-sensors of enzymatic activity has been slow partly due to the lack of human efficacy data. We report here a strategy that may serve as a shortcut from bench to bedside. We tested ultra high-resolution 7T MRI (µMRI) of human surgical histology sections in a 3-year IRB approved, HIPAA compliant study of surgically clipped brain aneurysms. µMRI was used for assessing the efficacy of MRI substrate-sensors that detect myeloperoxidase activity in inflammation. The efficacy of Gd-5HT-DOTAGA, a novel myeloperoxidase (MPO) imaging agent synthesized by using a highly stable gadolinium (III) chelate was tested both in tissue-like phantoms and in human samples. After treating histology sections with paramagnetic MPO substrate-sensors we observed relaxation time shortening and MPO activity-dependent MR signal enhancement. An increase of normalized MR signal generated by ultra-short echo time MR sequences was corroborated by MPO activity visualization by using a fluorescent MPO substrate. The results of µMRI of MPO activity associated with aneurysmal pathology and immunohistochemistry demonstrated active involvement of neutrophils and neutrophil NETs as a result of pro-inflammatory signalling in the vascular wall and in the perivascular space of brain aneurysms.
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Mailhiot SE, Zong F, Maneval JE, June RK, Galvosas P, Seymour JD. Quantifying NMR relaxation correlation and exchange in articular cartilage with time domain analysis. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 287:82-90. [PMID: 29306110 DOI: 10.1016/j.jmr.2017.12.014] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Revised: 12/18/2017] [Accepted: 12/19/2017] [Indexed: 06/07/2023]
Abstract
Measured nuclear magnetic resonance (NMR) transverse relaxation data in articular cartilage has been shown to be multi-exponential and correlated to the health of the tissue. The observed relaxation rates are dependent on experimental parameters such as solvent, data acquisition methods, data analysis methods, and alignment to the magnetic field. In this study, we show that diffusive exchange occurs in porcine articular cartilage and impacts the observed relaxation rates in T1-T2 correlation experiments. By using time domain analysis of T2-T2 exchange spectroscopy, the diffusive exchange time can be quantified by measurements that use a single mixing time. Measured characteristic times for exchange are commensurate with T1 in this material and so impacts the observed T1 behavior. The approach used here allows for reliable quantification of NMR relaxation behavior in cartilage in the presence of diffusive fluid exchange between two environments.
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Affiliation(s)
- Sarah E Mailhiot
- Department of Mechanical Engineering, Montana State University, Bozeman, MT 59715, USA
| | - Fangrong Zong
- School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, NZ 6140, USA
| | - James E Maneval
- Chemical Engineering, Bucknell University, Lewisburg, PA 17837, USA
| | - Ronald K June
- Department of Mechanical Engineering, Montana State University, Bozeman, MT 59715, USA
| | - Petrik Galvosas
- School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, NZ 6140, USA
| | - Joseph D Seymour
- Department of Chemical and Biological Engineering, Montana State University, Bozeman, MT 59715, USA.
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Hänninen N, Rautiainen J, Rieppo L, Saarakkala S, Nissi MJ. Orientation anisotropy of quantitative MRI relaxation parameters in ordered tissue. Sci Rep 2017; 7:9606. [PMID: 28852032 PMCID: PMC5574987 DOI: 10.1038/s41598-017-10053-2] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2017] [Accepted: 08/02/2017] [Indexed: 12/04/2022] Open
Abstract
In highly organized tissues, such as cartilage, tendons and white matter, several quantitative MRI parameters exhibit dependence on the orientation of the tissue constituents with respect to the main imaging magnetic field (B0). In this study, we investigated the dependence of multiple relaxation parameters on the orientation of articular cartilage specimens in the B0. Bovine patellar cartilage-bone samples (n = 4) were investigated ex vivo at 9.4 Tesla at seven different orientations, and the MRI results were compared with polarized light microscopy findings on specimen structure. Dependences of T2 and continuous wave (CW)-T1ρ relaxation times on cartilage orientation were confirmed. T2 (and T2*) had the highest sensitivity to orientation, followed by TRAFF2 and adiabatic T2ρ. The highest dependence was seen in the highly organized deep cartilage and the smallest in the least organized transitional layer. Increasing spin-lock amplitude decreased the orientation dependence of CW-T1ρ. T1 was found practically orientation-independent and was closely followed by adiabatic T1ρ. The results suggest that T1 and adiabatic T1ρ should be preferred for orientation-independent quantitative assessment of organized tissues such as articular cartilage. On the other hand, based on the literature, parameters with higher orientation anisotropy appear to be more sensitive to degenerative changes in cartilage.
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Affiliation(s)
- Nina Hänninen
- Department of Applied Physics, University of Eastern Finland, POB 1627, FI-70211, Kuopio, Finland
- Research Unit of Medical Imaging, Physics and Technology, University of Oulu, POB 5000, FI-90014, Oulu, Finland
| | - Jari Rautiainen
- Department of Applied Physics, University of Eastern Finland, POB 1627, FI-70211, Kuopio, Finland
| | - Lassi Rieppo
- Research Unit of Medical Imaging, Physics and Technology, University of Oulu, POB 5000, FI-90014, Oulu, Finland
- Medical Research Center Oulu, Oulu University Hospital and University of Oulu, Oulu, Finland
| | - Simo Saarakkala
- Research Unit of Medical Imaging, Physics and Technology, University of Oulu, POB 5000, FI-90014, Oulu, Finland
- Medical Research Center Oulu, Oulu University Hospital and University of Oulu, Oulu, Finland
- Department of Diagnostic Radiology, Oulu University Hospital, Oulu, Finland
| | - Mikko Johannes Nissi
- Department of Applied Physics, University of Eastern Finland, POB 1627, FI-70211, Kuopio, Finland.
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Tourell MC, Momot KI. Molecular Dynamics of a Hydrated Collagen Peptide: Insights into Rotational Motion and Residence Times of Single-Water Bridges in Collagen. J Phys Chem B 2016; 120:12432-12443. [DOI: 10.1021/acs.jpcb.6b08499] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Monique C. Tourell
- School
of Chemistry, Physics and Mechanical Engineering and ‡Institute of
Health and Biomedical Innovation, Queensland University of Technology (QUT), GPO Box
2434, Brisbane, Queensland 4001, Australia
| | - Konstantin I. Momot
- School
of Chemistry, Physics and Mechanical Engineering and ‡Institute of
Health and Biomedical Innovation, Queensland University of Technology (QUT), GPO Box
2434, Brisbane, Queensland 4001, Australia
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Wright AC, Yoder JH, Vresilovic EJ, Elliott DM. Theory of MRI contrast in the annulus fibrosus of the intervertebral disc. MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE 2016; 29:711-22. [PMID: 26755061 DOI: 10.1007/s10334-015-0522-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2015] [Revised: 12/02/2015] [Accepted: 12/18/2015] [Indexed: 12/21/2022]
Abstract
OBJECTIVE Here we develop a three-dimensional analytic model for MR image contrast of collagen lamellae in the annulus fibrosus of the intervertebral disc of the spine, based on the dependence of the MRI signal on collagen fiber orientation. MATERIALS AND METHODS High-resolution MRI scans were performed at 1.5 and 7 T on intact whole disc specimens from ovine, bovine, and human spines. An analytic model that approximates the three-dimensional curvature of the disc lamellae was developed to explain inter-lamellar contrast and intensity variations in the annulus. The model is based on the known anisotropic dipolar relaxation of water in tissues with ordered collagen. RESULTS Simulated MRI data were generated that reproduced many features of the actual MRI data. The calculated inter-lamellar image contrast demonstrated a strong dependence on the collagen fiber angle and on the circumferential location within the annulus. CONCLUSION This analytic model may be useful for interpreting MR images of the disc and for predicting experimental conditions that will optimize MR image contrast in the annulus fibrosus.
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Affiliation(s)
- Alexander C Wright
- Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA.
| | - Jonathon H Yoder
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA
| | - Edward J Vresilovic
- Department of Orthopaedics and Rehabilitation, Pennsylvania State University, Hershey, PA, USA
| | - Dawn M Elliott
- Department of Biomedical Engineering, University of Delaware, Newark, DE, USA
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Wang N, Xia Y. Experimental issues in the measurement of multi-component relaxation times in articular cartilage by microscopic MRI. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2013; 235:15-25. [PMID: 23916991 PMCID: PMC3775938 DOI: 10.1016/j.jmr.2013.07.001] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2013] [Revised: 07/02/2013] [Accepted: 07/03/2013] [Indexed: 05/21/2023]
Abstract
A number of experimental issues in the measurement of multi-component T2 and T1ρ relaxations in native and enzymatically digested articular cartilage were investigated by microscopic MRI (μMRI). The issues included the bath solutions (physiological saline and phosphate buffered saline (PBS)), the imaging resolution (35-140 μm), the specimen orientations (0° and 55°), and the strength of spin-lock frequencies (0.5-2 kHz) in the T1ρ experiments. In addition to cartilage, the samples of agar gel and doped water solution were also used in the investigation. Two imaging sequences were used: CPMG-SE and MSME. All raw data were analyzed by the non-negative least square (NNLS) method. The MSME sequence was shown to result in the observation of multi-component T2, even in the gel and liquid samples, demonstrating the artificial uncleanness of this sequence in the multi-component measurements. The soaking of cartilage in PBS reduced the observable T2 components to one at both 0° and 55°, suggesting the effect of phosphate ions on proton exchange between different pools of water molecules. The cartilage orientation with respect to the external magnetic field and the spin-lock strengths in the T1ρ experiment both affected the quantification of the multi-component relaxation. The transitions between a mono-component and multi-components in cartilage under various experimental conditions call for the extra caution in interpreting the relaxation results.
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Affiliation(s)
| | - Yang Xia
- Corresponding Author and Address: Yang Xia, PhD, Department of Physics, Oakland University, Rochester, Michigan 48309, USA, Phone: (248) 370-3420, Fax: (248) 370-3408,
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Hanifi A, McGoverin C, Ou YT, Safadi F, Spencer R, Pleshko N. Differences in infrared spectroscopic data of connective tissues in transflectance and transmittance modes. Anal Chim Acta 2013; 779:41-9. [PMID: 23663670 PMCID: PMC3900307 DOI: 10.1016/j.aca.2013.03.053] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2012] [Revised: 03/17/2013] [Accepted: 03/20/2013] [Indexed: 10/27/2022]
Abstract
Fourier transform infrared imaging spectroscopy (FT-IRIS) has been used extensively to characterize the composition and orientation of macromolecules in thin tissue sections. Earlier and current studies of normal and polarized FT-IRIS data have primarily used tissues sectioned onto infrared transmissive substrates, such as salt windows. Recently, the use of low-emissivity ("low-e") substrates has become of great interest because of their low cost and favorable infrared optical properties. However, data are collected in transflectance mode when using low-e slides and in transmittance mode using salt windows. In the current study we investigated the comparability of these two modes for assessment of the composition of connective tissues. FT-IRIS data were obtained in transflectance and transmittance modes from serial sections of cartilage, bone and tendon, and from a standard polymer, polymethylmethacrylate. Both non-polarized and polarized FTIR data differed in absorbance, and in some cases peak position, between transflectance and transmittance modes. However, the FT-IRIS analysis of the collagen fibril orientation in cartilage resulted in the expected zonal arrangement of fibrils in both transmittance and transflectance. We conclude that numerical comparison of FT-IRIS-derived parameters of tissue composition should account for substrate type and data collection mode, while analysis of overall tissue architecture may be more invariant between modes.
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Affiliation(s)
- Arash Hanifi
- Tissue Imaging and Spectroscopy Lab, Department of Bioengineering, Temple University, Philadelphia, PA, USA. Fax: (215)204-4956; Tel: (215)204-4280
| | - Cushla McGoverin
- Tissue Imaging and Spectroscopy Lab, Department of Bioengineering, Temple University, Philadelphia, PA, USA. Fax: (215)204-4956; Tel: (215)204-4280
| | - Ya-Ting Ou
- Tissue Imaging and Spectroscopy Lab, Department of Bioengineering, Temple University, Philadelphia, PA, USA. Fax: (215)204-4956; Tel: (215)204-4280
| | - Fayez Safadi
- Department of Anatomy and Neurobiology, Northeast Ohio Medical University, Rootstown, OH, USA
| | - Richard Spencer
- Magnetic Resonance Imaging and Spectroscopy Section, National Institute on Aging, National Institutes of Health, Baltimore, MD, USA
| | - Nancy Pleshko
- Tissue Imaging and Spectroscopy Lab, Department of Bioengineering, Temple University, Philadelphia, PA, USA. Fax: (215)204-4956; Tel: (215)204-4280
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Lee JH, Xia Y. Quantitative zonal differentiation of articular cartilage by microscopic magnetic resonance imaging, polarized light microscopy, and Fourier-transform infrared imaging. Microsc Res Tech 2013; 76:625-32. [PMID: 23533143 DOI: 10.1002/jemt.22209] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2013] [Revised: 02/26/2013] [Accepted: 03/03/2013] [Indexed: 11/07/2022]
Abstract
This study aimed to synchronize the zonal differentiation of the full-thickness articular cartilage by three micro-imaging techniques, namely microscopic magnetic resonance imaging (µMRI), polarized light microscopy (PLM), and Fourier-transform infrared imaging (FTIRI). Eighteen cartilage-bone blocks from three canine humeral joints were imaged by: (a) µMRI T2 relaxation at 0° and 55° orientations in a 7 T magnetic field, (b) PLM optical retardation and azimuthal angle, and (c) FTIRI amide I and amide II anisotropies at 0° and 90° polarizations relative to the articular surface. In addition, µMRI T1 relaxation was imaged before and after the tissue being immersed in gadolinium (contrast agent) solution, to calculate the proteoglycan concentration. A set of previously established criteria in cartilage imaging was revised. The new criteria could simultaneously correlate the thicknesses of the three consecutive subtissue zones in articular cartilage among these imaging techniques.
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Affiliation(s)
- Ji Hyun Lee
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, Michigan 48309, USA
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Abstract
This review briefly summarises some of the definitive studies of articular cartilage by microscopic MRI (µMRI) that were conducted with the highest spatial resolutions. The article has four major sections. The first section introduces the cartilage tissue, MRI and µMRI, and the concept of image contrast in MRI. The second section describes the characteristic profiles of three relaxation times (T1, T2 and T1ρ) and self-diffusion in healthy articular cartilage. The third section discusses several factors that can influence the visualisation of articular cartilage and the detection of cartilage lesion by MRI and µMRI. These factors include image resolution, image analysis strategies, visualisation of the total tissue, topographical variations of the tissue properties, surface fibril ambiguity, deformation of the articular cartilage, and cartilage lesion. The final section justifies the values of multidisciplinary imaging that correlates MRI with other technical modalities, such as optical imaging. Rather than an exhaustive review to capture all activities in the literature, the studies cited in this review are merely illustrative.
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Affiliation(s)
- Y Xia
- Oakland University, 276 Hannah Hall, Department of Physics, Rochester, Michigan 48309, USA
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19
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Bowles RD, Gebhard HH, Dyke JP, Ballon DJ, Tomasino A, Cunningham ME, Härtl R, Bonassar LJ. Image-based tissue engineering of a total intervertebral disc implant for restoration of function to the rat lumbar spine. NMR IN BIOMEDICINE 2012; 25:443-451. [PMID: 21387440 DOI: 10.1002/nbm.1651] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2010] [Revised: 09/16/2010] [Accepted: 11/03/2010] [Indexed: 05/30/2023]
Abstract
Nonbiological total disc replacement is currently being used for the treatment of intervertebral disc (IVD) disease and injury, but these implants are prone to mechanical wear, tear and possible dislodgement. Recently, tissue-engineered total disc replacement (TE-TDR) has been investigated as a possible alternative to more fully replicate the native IVD properties. However, the performance of TE-TDRs has not been studied in the native disc space. In this study, MRI and microcomputed tomography imaging of the rat spine were used to design a collagen (annulus fibrosus)/alginate (nucleus pulposus) TE-TDR to a high degree of geometric accuracy, with less than 10% difference between TE-TDR and the native disc dimensions. Image-based TE-TDR implants were then inserted into the L4/L5 disc space of athymic rats (n = 5) and maintained for 16 weeks. The disc space was fully or partially maintained in three of five animals and proteoglycan and collagen histology staining was similar in composition to the native disc. In addition, good integration was observed between TE-TDR and the vertebral bodies, as well as remnant native IVD tissue. Overall, this study provides evidence that TE-TDR strategies may yield a clinically viable treatment for diseased or injured IVD.
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Affiliation(s)
- Robby D Bowles
- Department of Biomedical Engineering, Cornell University, Ithaca, NY 14853, USA
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Rössler E, Mattea C, Mollova A, Stapf S. Low-field one-dimensional and direction-dependent relaxation imaging of bovine articular cartilage. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2011; 213:112-118. [PMID: 21962910 DOI: 10.1016/j.jmr.2011.09.014] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2011] [Revised: 09/01/2011] [Accepted: 09/06/2011] [Indexed: 05/31/2023]
Abstract
The structure of articular cartilage is separated into three layers of differently oriented collagen fibers, which is accompanied by a gradient of increasing glycosaminoglycan (GAG) and decreasing water concentration from the top layer towards the bone interface. The combined effect of these structural variations results in a change of the longitudinal and transverse relaxation times as a function of the distance from the cartilage surface. In this paper, this dependence is investigated at a magnetic field strength of 0.27 T with a one-dimensional depth resolution of 50 μm on bovine hip and stifle joint articular cartilage. By employing this method, advantage is taken of the increasing contrast of the longitudinal relaxation rate found at lower magnetic field strengths. Furthermore, evidence for an orientational dependence of relaxation times with respect to an axis normal to the surface plane is given, an observation that has recently been reported using high-field MRI and that was explained by preferential orientations of collagen bundles in each of the three cartilage zones. In order to quantify the extent of a further contrast mechanism and to estimate spatially dependent glycosaminoglycan concentrations, the data are supplemented by proton relaxation times that were acquired in bovine articular cartilage that was soaked in a 0.8 mM aqueous Gd++ solution.
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Affiliation(s)
- Erik Rössler
- Fachgebiet Technische Physik II/Polymerphysik, Institute of Physics, Technische Universität Ilmenau, PO Box 100 565, 98684 Ilmenau, Germany
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Xia Y, Zheng S, Szarko M, Lee J. Anisotropic properties of bovine nasal cartilage. Microsc Res Tech 2011; 75:300-6. [PMID: 21823202 DOI: 10.1002/jemt.21058] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2011] [Accepted: 06/10/2011] [Indexed: 12/21/2022]
Abstract
To investigate the structural anisotropy in bovine septal cartilage, quantitative procedures in microscopic magnetic resonance imaging (μMRI), polarized light microscopy (PLM), and mechanical indentation were used to measure the tissue in three orthogonal planes: vertical, medial, and caudocephalic. The quantitative T2 imaging experiments in μMRI found strong anisotropy in the images of both vertical and caudocephalic planes but little anisotropy in the images from the medial plane. The PLM birefringent experiments found that the retardation values in the medial section were only about 10% of these in the vertical and caudocephalic sections and that the angle values in all three sections followed the rotation of the tissue section in the microscope stage. The stress relaxation experiments in mechanical indentation showed reduced stiffness in the medial plane compared to stiffness in either the vertical or caudocephalic planes. Collectively, the results in this project coherently indicate a marked structural anisotropy in cartilage from the nasal septum, where the long axis of the collagen fibrils is oriented in parallel with the medial axis.
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Affiliation(s)
- Yang Xia
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, Michigan 48309, USA.
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Mittelstaedt D, Xia Y, Shmelyov A, Casciani N, Bidthanapally A. Quantitative determination of morphological and territorial structures of articular cartilage from both perpendicular and parallel sections by polarized light microscopy. Connect Tissue Res 2011; 52:512-22. [PMID: 21787136 PMCID: PMC3674864 DOI: 10.3109/03008207.2011.595521] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
In order to investigate the three-dimensional structure of the collagen fibrils in articular cartilage, full-thickness canine humeral cartilage was microtomed into perpendicular sections that included both the articular surface and the subchondral bone and approximately 100 successive parallel sections that were each 6 microm thick and from a different cartilage depth. Each section was imaged using polarized light microscopy with a 5x objective (2.0 microm pixel size), generating two quantitative images (angle and retardation). Selected sections were also imaged using a 40x objective (0.25 microm pixel size). At an increased depth from the articular surface, the angle and retardation results in the perpendicular sections showed the well-known 90 degrees change in fibril orientation between the surface and the deep cartilage. In contrast, the retardation results of the parallel sections decreased from the articular surface and remained approximately 0 through most of the radial zones, while the angle results of the parallel sections only changed about 30 degrees. The territorial matrix morphology surrounding 61 chondrocyte clusters was quantified by its length, aspect ratio, and orientation. The cellular clusters in the surface cartilage were ellipsoidal in both parallel and perpendicular sections. In the radial zone, the cellular clusters were oriented in vertical columns in the perpendicular sections and as circular groupings in the parallel sections. This orthogonal imaging technique could provide a better understanding of the three-dimensional territorial and interterritorial fibrils in articular cartilage, the disturbance of which could signify the onset of degenerative cartilage diseases such as osteoarthritis.
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Affiliation(s)
- Daniel Mittelstaedt
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309, USA
| | - Yang Xia
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309, USA
| | - Alex Shmelyov
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309, USA
| | - Nick Casciani
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309, USA
| | - Aruna Bidthanapally
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309, USA
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Zheng S, Xia Y, Badar F. Further studies on the anisotropic distribution of collagen in articular cartilage by μMRI. Magn Reson Med 2011; 65:656-63. [PMID: 20939069 PMCID: PMC3021642 DOI: 10.1002/mrm.22648] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2010] [Revised: 08/16/2010] [Accepted: 08/26/2010] [Indexed: 11/08/2022]
Abstract
To further study the anisotropic distribution of the collagen matrix in articular cartilage, microscopic magnetic resonance imaging experiments were carried out on articular cartilages from the central load-bearing area of three canine humeral heads at 13 μm resolution across the depth of tissue. Quantitative T2 images were acquired when the tissue blocks were rotated, relative to B0, along two orthogonal directions, both perpendicular to the normal axis of the articular surface. The T2 relaxation rate (R2) was modeled, by three fibril structural configurations (solid cone, funnel, and fan), to represent the anisotropy of the collagen fibrils in cartilage from the articular surface to the cartilage/bone interface. A set of complex and depth-dependent characteristics of collagen distribution was found in articular cartilage. In particular, there were two anisotropic components in the superficial zone and an asymmetrical component in the radial zone of cartilage. A complex model of the three-dimensional fibril architecture in articular cartilage is proposed, which has a leaf-like or layer-like structure in the radial zone, arises in a radial manner from the subchondral bone, spreads and arches passing the isotropic transitional zone, and exhibits two distinct anisotropic components (vertical and transverse) in the surface portion of the tissue.
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Affiliation(s)
| | - Yang Xia
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309
| | - Farid Badar
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309
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Xia Y, Mittelstaedt D, Ramakrishnan N, Szarko M, Bidthanapally A. Depth-dependent anisotropies of amides and sugar in perpendicular and parallel sections of articular cartilage by Fourier transform infrared imaging. Microsc Res Tech 2011; 74:122-32. [PMID: 21274999 PMCID: PMC3043386 DOI: 10.1002/jemt.20881] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Full thickness blocks of canine humeral cartilage were microtomed into both perpendicular sections and a series of 100 parallel sections, each 6 μm thick. Fourier transform infrared (IR) imaging was used to image each tissue section eleven times under different IR polarizations (from 0° to 180° polarization states in 20° increments and with an additional 90° polarization), at a spatial resolution of 6.25 μm and a wavenumber step of 8 cm⁻¹. With increasing depth from the articular surface, amide anisotropies increased in the perpendicular sections and decreased in the parallel sections. Both types of tissue sectioning identified a 90° difference between amide I and amide II in the superficial zone (SZ) of cartilage. The fibrillar distribution in the parallel sections from the SZ was shown to not be random. Sugar had a weak but recognizable anisotropy in the upper part of the radial zone (RZ) in the perpendicular sections. The depth-dependent anisotropic data were fitted with a theoretical equation that contained three signature parameters, which illustrate the arcade structure of collagens with the aid of a fibril model. Fourier-transform IR imaging of both perpendicular and parallel sections provides the possibility of determining the three-dimensional macromolecular structures in articular cartilage. Being sensitive to the orientation of the macromolecular structure in healthy articular cartilage aids the prospect of detecting the early onset of the tissue degradation that may lead to pathological conditions such as osteoarthritis.
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Affiliation(s)
- Yang Xia
- Department of Physics and Center for Biomedical Research, Oakland University, Rochester, Michigan 48309, USA.
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