T 2 orientation anisotropy mapping of articular cartilage using qMRI

Objective. To provide orientation-independent MR parameters potentially sensitive to articular cartilage degeneration by measuring isotropic and anisotropic components of T 2 relaxation, as well as 3D fiber orientation angle and anisotropy via multi-orientation MR scans. Approach. Seven bovine osteochondral plugs were scanned with a high angular resolution of thirty-seven orientations spanning 180° at 9.4 T. The obtained data was fitted to the magic angle model of anisotropic T 2 relaxation to produce pixel-wise maps of the parameters of interest. Quantitative Polarized Light Microscopy (qPLM) was used as a reference method for the anisotropy and fiber orientation. Main results. The number of scanned orientations was found to be sufficient for estimating both fiber orientation and anisotropy maps. The relaxation anisotropy maps demonstrated a high correspondence with qPLM reference measurements of the collagen anisotropy of the samples. The scans also enabled calculating orientation-independent T 2 maps. Little spatial variation was observed in the isotropic component of T 2 while the anisotropic component was much faster in the deep radial zone of cartilage. The estimated fiber orientation spanned the expected 0°–90° in samples that had a sufficiently thick superficial layer. The orientation-independent magnetic resonance imaging (MRI) measures can potentially reflect the true properties of articular cartilage more precisely and robustly. Significance. The methods presented in this study will likely improve the specificity of cartilage qMRI by allowing the assessment of the physical properties such as orientation and anisotropy of collagen fibers in articular cartilage.


Introduction
In magnetic resonance imaging (MRI), orientation anisotropy refers to the dependence of the MR signal on the orientation of the material or tissue in the main magnetic field (B0). Anisotropic properties of T 2 relaxation have been reported in highly organized tissues such as tendons (Fullerton et al 1985, Erickson et al 1991, Navon et al 2007, white matter (Knight et al 2015), meniscus (Szeverenyi and Bydder 2011), and articular cartilage (Henkelman et al 1994, Xia 1998, Hänninen et al 2017.
Articular cartilage is a soft tissue covering the ends of bones in all joints. It enables the nearly frictionless movement of joints, and functions as a shock-absorbing medium distributing stress (Benninghoff 1925, Mow 2005. Articular cartilage consists mainly of collagen, proteoglycans (PG), water, and chondrocytes (Benninghoff 1925, Mow et al 2005. The bulk of articular cartilage is hyaline cartilage. Below it, next to the subchondral bone, is a layer of calcified cartilage anchoring the soft cartilage tissue to the bone. The non-calcified articular cartilage can be divided into three distinct zones based on the collagen fibril orientation: superficial zone (SZ), transitional zone (TZ), and deep radial zone (RZ). The organization of the collagen fibers in cartilage is the highest in the radial zone, in which the fibers are oriented perpendicularly to the surface. In the superficial zone, collagen fibers are oriented parallel to the surface. In the transitional zone between SZ and RZ, the fibers are oriented more randomly (Buckwalter and Mankin 1998, Xia et al 2002, Rieppo et al 2008, Hänninen et al 2017. Anisotropic effects can be seen in articular cartilage, especially in the deep zone, where the tissue is the most organized (Xia 1998, Rieppo et al 2008. Osteoarthritis (OA) is a progressive joint disease that affects a growing number of people (Kloppenburg and Berenbaum 2020). Idiopathic OA is strongly associated to the elderly population, at variable disease severities and including multiple joints, features which can further complicate the assessment of biomarkers (Buckwalter and Mankin 1997). The two risk factors frequently associated with OA are obesity and mechanical overloading typical in many athletic sports (Pappas et al 2016). OA is estimated to affect over 300 million people globally and it is the second largest cause of years lived with disability (James et al 2017, Kloppenburg and Berenbaum 2020). OA causes progressive, irreversible degeneration of articular cartilage. It is generally identified by detecting gross morphological changes, namely loss of hyaline cartilage in a joint, leading to joint space narrowing (Guermazi et al 2015). Articular cartilage is avascular and has a very limited capability to repair damage, especially in advanced OA. If OA is detected at an early enough stage, the progress can be slowed down by weight management and conservative therapeutic intervention, as OA typically develops over decades (Chu et al 2012). In the early stages of OA, molecular, chemical, and enzymatic changes occur in cartilage, accompanied by changes in the bone structure (Buckwalter and Mankin 1997). The most significant of these changes are PG loss and fibrillation of the collagenous network and changes in subchondral bone plate and trabecular bone volume (Orava et al 2022). A potential diagnosis method ought to be very sensitive to these early changes to be able to detect early-stage OA.
Quantitative magnetic resonance imaging (qMRI) provides information about the tissue beyond what it is possible to obtain with only anatomical imaging. T 2 relaxation time is a qMRI parameter that has been extensively used to study cartilage and has been linked to its biomechanical properties; particularly to the properties of the collagen network of articular cartilage (Nieminen et al 2000, Xia et al 2002, Mosher and Dardzinski 2004, Nissi et al 2006. Elevated T 2 relaxation time has been reported in mild and severe OA (Dunn et al 2004, Li et al 2007. Nieminen et al (2000) demonstrated in 2000 that T 2 is sensitive to collagen integrity but fairly insensitive to changes in the proteoglycan content. In early OA, PGs and glycosaminoglycans leak out from cartilage, and the integrity of the collagen fibers is compromised in such a way that water can more freely diffuse into and within cartilage (Oei et al 2014). Additionally, changes in the orientation and integrity of collagen occur (Buckwalter and Mankin 1998). However, T 2 relaxation is greatly dependent on the orientation of highly organized structures or tissues in the magnetic field. Thus, it can be prone to misinterpretation and be unreliable without either rotation measurements or precise a priori knowledge of the properties of the oriented structures within the tissues (Xia et al 2002, Mosher and Dardzinski 2004, Momot et al 2010, Furman et al 2016, Hänninen et al 2017. Since T 2 relaxation is very sensitive to these changes, an orientation-independent method for T 2 mapping would be highly useful.
While T 2 relaxation has been proven anisotropic in articular cartilage, T 1 is shown to be orientationindependent (Xia 1998, Hänninen et al 2017, and many other relaxation times, such as T 1ρ are somewhere in between the two extremes (Hänninen et al 2017). The orientation dependence of T 2 relaxation is caused by the non-averaging residual dipolar coupling of 1 H nuclei (Erickson et al 1993, Akella et al 2004, Furman et al 2016.
In an unorganized or structurally loose medium, the water molecules can move in all directions equally, allowing the dipolar interactions to average out. However, the inner structures of organized tissues, such as the helical polypeptide chains in collagen fibrils, restrict the motion of water molecules, resulting in non-averaging residual dipolar interaction (Erickson et al 1993, Akella et al 2004.
The strength of the dipolar interactions between two nuclei is proportional to the term ( ) q -3 cos 1, 2 where θ is the angle between the internuclear vector and the external magnetic field, B0 (Erickson et al 1993). A result of this proportionality is that the dipolar interaction vanishes when ( ) q -= 3 cos 1 0, 2 a condition which is satisfied when θ = 54.74°, known as the magic angle (Andrew et al 1959, Erickson et al 1991, Momot et al 2010, Furman et al 2016. The T 2 relaxation time reaches its maximum at the magic angle, and thus the most signal is produced with typical T 2 -weighted MR imaging sequences at this angle. By symmetry, the magic angle conditions are met at cones that are 54.74°away from either the positive or negative field direction The transverse relaxation rate R 2 (=1/T 2 ) can be divided into an isotropic (R 2,i ) and an anisotropic part (R 2,a ) where only the anisotropic part is affected by the orientation-dependent dipolar interaction (Momot et al 2010, Furman et al 2016. T 2 relaxation time mapping has been proven to have great potential in collagen fiber mapping and assessment of collagen network integrity (Nieminen et al 2000, Mosher andDardzinski 2004). The observed T 2 relaxation time shows a distinct laminar pattern, dependent on the collagen anisotropy, when the surface of the cartilage is perpendicular to the direction of the main magnetic field (Xia 1998). However, due to the anisotropic component of T 2 diminishing at the magic angle, depth-wise changes in the collagen anisotropy are not visible in the T 2 relaxation time at this orientation. This introduces challenges in applying T 2 mapping to the assessment of collagen integrity, since an increase in the relaxation time might be due to the orientation rather than compromised integrity (Xia 1998). Because MRI voxel size greatly exceeds the diameter of an individual collagen fiber, the fibers cannot be distinguished from a morphological MR image, necessitating a different approach to obtain information on collagen orientation.
The anisotropy of T 2 in cartilage arises from the parallelly organized collagen fiber mesh restricting 1 H nuclei movement (Xia 1998). Hence, T 2 anisotropy can be assumed to reflect the collagen anisotropy. Utilizing multiangle measurements allows obtaining precise information about the properties of the collagen network in cartilage, independent of the orientation of the tissue in the magnetic field. In OA, the collagen network integrity is often compromised first at the cartilage surface, and as the disease progresses, the damage extends towards the bone-cartilage interface (Nieminen et al 2000, Rautiainen et al 2015. Direct information on the integrity and preferably also on the orientation of the collagen fiber network could be utilized for a more accurate diagnosis of OA and for more precise modeling of cartilage. The aim of this study was to develop a method to determine the orientation-independent isotropic and anisotropic components of T 2 relaxation using high angular resolution qMRI measurements for estimating the properties of the collagen network in articular cartilage. The study further aims to assess the effect of the number of scanned orientations on the accuracy of the determined parameters.

Methods
Articular cartilage-bone plugs (d = 6 mm, n = 7) were prepared from various surfaces of bovine knee joints. The joints were purchased from a local supermarket. The samples were stored at −22°C prior to the MRI experiments. For the measurements, the samples were immersed in perfluoropolyether (Galden HS 240, Solvay Solexis, Italy) to provide a clean 1 H signal-free background, and placed in a 3D printed holder and test tube that allowed reorientation of the samples from outside the magnet via a carbon fiber rod. The holder was further coupled to a motorized Arduino (Arduino Micro A000053) controlled device that was triggered by the pulse sequence to rotate the specimen by a pre-defined angle against the B0 direction at given steps during the scan protocol.
The scanning was conducted at 9.4 T using VnmrJ 3.1 Varian/Agilent DirectDrive console (Varian Associates Inc., Pala Alto, CA, USA) and a 19 mm quadrature RF volume transceiver (RAPID Biomedical GmbH, Rimpar, Germany). With the automated rotation device, the samples were scanned at 37 orientations along a single plane, spanning approximately 0°-180°with respect to B0 (figure 1(A)). All the samples were scanned with MESE-T2 sequence for T 2 mapping with either 256 × 256 px or 192 × 192 px matrix size, resulting in pixel sizes of 66.4 μm and 88.5 μm, respectively (table 1). Echo times of 8. 1, 16.3, 24.4, 32.6, 40.7, 48.8, 57, 65.1, 73.3, and 81.4 were used for the 256 × 256 images. Echo times of 7. 4, 14.7, 22.1, 29.4, 36.8, 44.1, 51.5, 58.8, 66.2 and 73.6 were used for the 192 × 192 images. A field of view of 17 mm × 17 mm and slice thickness of 0.5 mm were used. Additionally, B0 maps were collected at each orientation with a WASSR-prepared FSE sequence (Kim et al 2009) utilizing an off-resonance range of −300 to 300 Hz with 30 Hz spacing. The total scan times for all orientations varied between 16 and 23 h. One of the samples was rotated through the 180°range in a tilted orientation of about 45°(figure 1(B)) to simulate a situation where the collagen fibers are not parallel with the MRI slice (nor parallel with the B0 direction). Manual shimming was performed with approximately 10°spacing prior to the scan. The shimming parameters were saved, and the corresponding shimming values were loaded at the appropriate points during the scan.
The data obtained at the different orientations were co-registered to the first orientation using Elastix software (Klein et al 2010) and using the first echoes of the T 2 weighted series for each sample. A mutual cost function and a rigid transformation (Euler transformation) were used in the registration. A rigid transformation was chosen because the images were only expected to rotate and translate and not to change scale, shear, or deform. The result of the registration was confirmed visually. The parameter file used with Elastix can be found in the open data set of this study (Leskinen et al 2023). Pixel-wise T 2 relaxation time maps for each orientation were calculated using mono-exponential fitting after first evaluating against bi-exponential fitting via Akaike information criteria (Akaike 1973) and then rotated to the first orientation using the transform parameters obtained from the registration process. From the relaxation time maps, pixel-wise relaxation anisotropy maps were calculated using the Michelson contrast (Rieppo et al 2008, Hänninen et al 2017. Regions of interest (ROIs) were manually defined for the SZ, TZ, and RZ of cartilage, based on the anisotropy values (figure 1). In addition to the zone-wise ROIs, depth-wise relaxation time profiles over the cartilage were calculated approximately at the center of the cartilage plug using approximately 0.34 mm wide columns. The T 2 relaxation rate components (R 2i , R 2a ) and fiber angle (θ) were then estimated pixel-wise and ROI-wise with model presented by Momot et al (2010), augmenting it with a phase shift term f to account for the initial orientation of the anisotropic structures: The fit was performed using nonlinear least-squares estimation, which was minimized using a default MATLAB function fminsearch. The multi-orientation scans performed in the study allowed the estimation of the T 2 components and anisotropy independent of the initial orientation of the sample. The obtained anisotropy and fiber angle maps were compared to the respective maps of quantitative polarized light microscopy (qPLM) scans of the same samples in slices matching the MRI slices as well as possible. All ROI and data analysis was performed using in-house developed scripts and plugins for Aedes (http://aedes.uef.fi) in MATLAB (MATLAB R2019b, MathWorks, Natick, MA). While the angle between each scan was obtained in the co-registration process, the collagen fibers were allowed to have an angle also off from the plane of rotation. i.e. the model assumed θ = θ(α, β), where α is the nominal sample orientation from the co-registration and β is a free parameter describing the off-plane tilt angle obtained in the fitting process. Using basic trigonometry, this can be expressed as Including β influences the spread of the angles θ, and accounting for it in the model allows describing the collagen fiber-to-field angle rather than the nominal sample angle. To analyze the sensitivity of the number of orientations used in the fitting process, the fitting was repeated to all samples with successive reduction in the number of angles used in the fit. The accuracy of this sparse fit was assessed via the normalized standard error  using the full data set as reference. The standard errors were calculated pixel-wise, which enabled forming error maps to assess the reliability of the data throughout the cartilage. After the qMRI scans were performed, the samples were fixed in 10% neutral buffered formalin for 48 h and decalcified in EDTA for histological processing. After the fixation, the samples were embedded in paraffin and unstained histological slices of 5 μm were prepared from the same locations with the MRI slices using landmark cuts in the samples as guidelines.
Histology-based orientation and the anisotropy of the collagen fibers were measured following Mehta et al (2013) using Leitz Ortholux II POL (Leitz Wetzlar, Wetzlar, Germany) microscope body equipped with a monochromatic light source (λ = 630 ± 30 nm, Edmund Optics Inc., Barrington, NJ, USA), crossed polarizers (Techspec optics ® XP42-200, Edmund Optics, Barrington, NJ, USA) and a monochrome camera (pixel size 3, 5 μm, BFS-U3-88S6M-C FLIR Blackfly ® S, FLIR Systems Inc., Wilsonville, OR, USA ) with a 2.5× magnification lens. The setup consists of a polarizer and an analyzer at a 90°angle to each other, with the sample in between. Sample slices were measured at 21 orientations spanning 180°. qPLM measurements were performed using a monochromatic light source to avoid wavelength-dependent phase dispersion in a birefringent material. The polarizer and the analyzer were rotated in sync using Newport PR50 rotator mounts (Newport Corporation, Irvine, CA, USA). With this setup, all the light detected with the camera could be assumed to be birefringed by the sample. The fibrous collagen network structure of articular cartilage imposes an angle dependence on the intensity of the observed light. This allows anisotropy to be defined using Michelson contrast as described previously (Rieppo et al 2008). This type of linear polarization enabled the use of Stokes parameters in the calculation of the mean fiber angle in each individual pixel. The fiber angle was calculated with the equation where j is the orientation of the birefringent structures (i.e. collagen fibers) and I x are the recorded signal intensities in each pixel at the given orientations.

Results
In comparison between mono-and bi-exponential models of T 2 relaxation, the Akaike information criteria was found to consistently value the 2-parametric fit with background correction as the best model for T 2 relaxation, and thus in the subsequent analysis, all the relaxation times were fitted using the 2-parametric monoexponential model. The relaxation times in the three different regions of interest over 0-180°exhibited the magic angle behavior depicted in figure 2, especially for the RZ, which showed the largest changes with respect to orientation (figures 2(A)-(C)). All samples demonstrated the typical laminar structure (Mow et al 2005, de Visser et al 2008). TZ had the least angular variation, and for the SZ, the spatial resolution was insufficient for precise evaluation of the anisotropy due to the thinness of the zone. The model (1) described the angular dependence of R 2 in a radial zone ROI in a precise manner for in-plane-rotation measurements. The average standard error of the fit over all samples was 0.17 ± 0.10 (data-normalized dimensionless error). For the measurement of a sample rotated in a strongly tilted orientation, the standard error values were higher (0.19 ± 0.13) but indicated successful estimation of the isotropic R 2 relaxation rate component R 2,i and the anisotropic component R 2,a in this condition as well (figures 2(B), (C), 1(B)). The reference parallelism index, i.e. the anisotropy maps produced using qPLM showed a high level of anisotropy in the superficial and radial zone with a distinct low anisotropy transitional zone in between. The image registration between qMRI and qPLM was performed by layering the images on top of each other based on the sample surface and landmarks. Some histology processing artifacts (tissue folds) were also visible in the qPLM anisotropy maps (figure 3). The anisotropy maps calculated from the T 2 relaxation rates appeared similar to the reference images of the same samples, measured from sections matching the MRI slices as closely as possible. The TZ of articular cartilage appeared as a band of low anisotropy in the relaxation anisotropy maps as well. The varying thickness of this low anisotropy band in the different samples was observed also in the depth-wise anisotropy profiles ( figure 3).
By fitting the relaxation model voxel-by-voxel, the spatial differences in the components of T 2 relaxation in cartilage were obtained. The isotropic R 2 component, R 2,i (figure 4(A)) was fairly homogenous throughout the whole cartilage with slight increase visible in the surface and close to bone-cartilage interface. The anisotropic R 2 relaxation component, R 2,a ( figure 4(B)) was the fastest in the deep cartilage and the slowest in the superficial and transitional zones. The combined isotropic + anisotropic T 2 relaxation time map ((R 2,a + R 2,i ) −1 ) (figure 4(C)) represents the overall orientation-independent T 2 relaxation time in cartilage. The orientation-independent T 2 was found to be closely similar to the T 2 map scanned at the a 0°(figure 4(D)) or 180°orientation, but not to the maps scanned at the other orientations (supplementary figure S1). The estimated fiber angles (figures 4(E), (F)) spanned the expected 0°-90°in the samples with the thickest SZ (figure 4(F)), visually matching the fiber orientation angles obtained for the same sample with qPLM measurements in the same zones ( figure 4(H)). In the samples with a thin SZ, the estimated fiber angle did not span the full range of angles visible in the respective qPLM maps.
The data analysis conducted with subsets of the orientation angles demonstrated similar results but with greater noise. Although reducing the number of orientations decreased the accuracy of the parameters determined using the least-squares fitting, similar results could be obtained with only 3 orientations ( Figure 5). A subset of 15 orientations spanning 0°-95°was found to be sufficient for decreasing the standard error to within 15% of the error of the full data set of 37 orientations in all scanned samples.

Discussion
In this study, the T 2 relaxation anisotropy in articular cartilage was measured at a high angular resolution to estimate the physical properties of the tissue, such as the collagen fiber orientation and anisotropy, as well as to  separate the isotropic and anisotropic components of T 2 relaxation. We hypothesized that the calculated relaxation anisotropy map would be similar to the corresponding qPLM anisotropy or parallelism map. By utilizing the high angular resolution (planar) re-orientation measurements, we were able to extract multiple orientation-independent parameters describing the relaxation properties of cartilage (R 2,i , R 2,a , f) and compare them with the single-orientation T 2 measurements and qPLM reference measurements. The model used for relaxation anisotropy was able to describe the T 2 relaxation precisely especially in the deep zone of articular cartilage, capturing the theoretical orientation dependence in a highly ordered tissue. The accuracy of the model was significantly worse near the cartilage surface due to the partial volume effect and small inaccuracies in the coregistration, which may have led to the inclusion of background voxels in the SZ ROI. The anisotropic part of the R 2 was faster in the deep cartilage, decreasing towards the surface and diminishing to almost zero in the most randomly oriented transitional zone immediately below the superficial zone. The anisotropy maps generated from the rotation MRI measurements were strikingly similar to the corresponding anisotropy maps from the qPLM measurements, while the MRI-based orientation maps showed only moderate similarity to the qPLMorientation maps, differing the most in the superficial zone.
The work focused on measuring and modeling the relaxation anisotropy, which was assumed to follow the model in (1) (Momot et al 2010). The model was adapted to include the initial angle, reflecting the fiber-to-field orientation as well as the off-plane tilt, allowing fiber orientations out of the rotation plane. The orientationindependent parameters accounting for the isotropic and anisotropic relaxation rates R 2,i and R 2,a appeared highly feasible, although no comparison to previous literature could be done due to the lack of reported values. The 90°angle of SZ fibers was visible in the samples where the thickness of SZ was over 4 pixels. This suggests that MRI hardware capable of producing very high spatial resolution is required for an accurate fiber orientation mapping in all layers of cartilage via T 2 anisotropy. Models have been proposed for the superficial zone allowing fan-like or cone-like distributions of collagen fibers or assuming a homogenous fiber direction distribution in all directions in a plane (two degrees of freedom), which results in a different model (Gründer 2006, Zheng et al 2011. In reality there usually is a preferred orientation for the collagen fibers within the articular surface due to loading geometry. The orientation can be visualized as split lines on the cartilage surface by pricking it with an ink-tipped pointer (Meachim et al 1974, Zheng andXia 2009).
The model used in this work includes a phase shift term (f). The term was included to capture the initial orientation of the collagen fibers in each fitted voxel or ROI, which cannot be assumed to be in any given precise orientation with respect to the B0 field at the beginning of the measurements. Including this term allows the estimation of the initial angle of the collagen fibers with respect to the B0 field, and thus allows producing a fiber orientation map. At the lateral edges of the qMRI fiber orientation maps of some samples, deviation from the deep zone orientation and parallelism could be appreciated. The same angular deviation was seen in the qPLM fiber orientation maps, and thus can be assumed to represent the real fiber orientations in the sample, suggesting that the qMRI method correctly captured the orientation for the highly anisotropic parts of the tissue. The deviations in the fiber orientation were expected to be due to the loosening of the tissue matrix and collagen network after the sample excision.
Besides using the measurement setup described here, other possibilities for determining the collagen fiber orientation of articular cartilage exist. Significant advances in diffusion imaging, especially diffusion tensor imaging (DTI) have been made (Raya et al 2013, Ferizi et al 2018. Using high angular resolution DTI and tractography algorithms allows reliable mapping of the collagen fiber network and producing quantitative parameters which can also potentially be linked to cartilage degeneration (Ferizi et al 2017, Wang et al 2019. However, these sequences are slow due to the high number of diffusion directions to be scanned. The collagen network in articular cartilage most likely causes a significantly weaker diffusion barrier compared to the myelin sheathing in the brain white matter. The T 2 anisotropy is likely a more prominent effect than the diffusion anisotropy in cartilage, since the reported values for diffusion FA are higher in white matter (0.4-0.7 in white matter (Rimol et al 2019)) than in cartilage (0.2-0.3 in healthy cartilage (Raya 2015)), while T 2 relaxation anisotropy of up to about 80% has been reported in cartilage (Hänninen et al 2017).
The methods and models used in this work allow calculating and observing fiber orientation in a single plane. Calculating the fiber orientation in 3D would require rotating the sample over multiple axes and considering the measured quantities as 3D tensors. A method especially promising for the 3D fiber orientation imaging in cartilage is susceptibility tensor imaging (Wei et al 2017). Although the sample was rotated in a plane in this study, a 3D orientation of fibers was allowed in the model. If this was not included, the measured curve of T 2 versus angle would appear deformed ( figure 2(B)). This was demonstrated by rotating one sample tilted to approximately 45°( figure 1(B)). Including the off-plane orientation in the model, however, allowed obtaining the true fiber-to-field angle regardless of the initial orientation of the structures. The calculated orientation-independent overall T 2 relaxation time maps (i.e. 1/T 2,combined = R 2,i + R 2,a ) had a close resemblance to the maps scanned in the parallel orientation (i.e. 0°and 180°orientations) to the B0 field. Due to being a combination of fitted orientation-independent isotropic and anisotropic relaxation components, the overall T 2 relaxation is expected to represent the 'true' T 2 relaxation properties of cartilage, independent of the sample orientation and measurement geometry and interpreted as a fiber orientation-corrected T 2 map. Since the reference single-orientation T 2 map (figure 4(D)) is scanned approximately at the 0°orientation, where the anisotropic component of the relaxation is at its maximum, the similarities between the two maps can be expected. The 'true' T 2 relaxation time is expected to mainly reflect the biophysical and biochemical properties of cartilage that have been suggested by previous research for the orientation-dependent T 2 relaxation time measurements (collagen network integrity (Mosher and Dardzinski 2004), collagen content (Nieminen et al 2000), and water content (Lüsse et al 1995)). The results indicated the potential of multi-orientation scans for extracting physically meaningful information from cartilage in a non-invasive manner. The relaxation anisotropy, and to a lesser extent, the fiber orientation maps, appeared not only consistent with the previously reported PLM maps of articular cartilage (Rieppo et al 2008) but also to match with the qPLM of the same samples. Here, the anisotropy was calculated using Michelson contrast (Rieppo et al 2008, Hänninen et al 2017, but the relative anisotropy could be directly calculated from the model-fit relaxation components equally well. Conversely, also the relaxation rate envelope-approach of the Michelson contrast could be used to estimate the isotropic and anisotropic relaxation components directly, and possibly more robustly. The manual registration between qMRI and qPLM, utilizing anatomical landmarks was considered to be the best approach to enable comparing anisotropy, because the difference in the voxel/pixel size between the maps was substantial and the histological processing often introduces morphological changes to the sample slices. Anisotropy is directly linked to the structural integrity of the collagen network and thus to the integrity of the whole tissue (Rieppo et al 2008). This study confirms the previous findings on T 2 anisotropy in cartilage (Xia et al 2002, Hänninen et al 2017 and creates solid links between T 2 relaxation time and the structure of articular cartilage. The total scan time for a single specimen in this study was extreme, 16-22 h. In the data analysis, the scan time was assumed not to affect the sample, but it is possible that the relaxation properties of the samples differ between the start and end of the scan. The high number of orientations scanned in this study, as well as the long scan times, severely limit the reproducibility of the study in vivo as is. Due to the practical geometry and time constraints, an in vivo scan can only be done in a limited number and range of orientations. The need for scanning the subject with several different echo times, as required for qMRI, makes the scanning significantly slower than the weighted-only imaging. This is further extended by repeating the scans at multiple orientations. Similar results can be expected for T 2 weighted images with the fitting I = A exp(-R 2,a (3cos 2 (θ − 1)) 2 ), where A is a constant dependent on the R 2,i and signal intensity at TE = 0 (Szeverenyi and Bydder 2011). Similar measurements in the clinical environment are challenging also due to the geometric restrictions of the clinical systems.
There are studies showing relaxation anisotropy in highly organized collagenous tissues conducted in a variety of field strengths (Erickson et al 1993, Akella et al 2004, Mlynárik et al 2004, Szeverenyi and Bydder 2011. The results hint that the T 2 anisotropy depends on the field strength, but the evidence is not conclusive on different joint surfaces. Conducting these scans at a lower B0 field, and with larger RF coils typical to clinical scanners, would decrease the signal-to-noise ratio, which in turn would force an increase in the voxel size or scan time. A larger voxel size would most likely make the SZ nearly indistinguishable. However, we would expect to observe close to identical anisotropic behavior of T 2 in the radial zone also with lower field strength clinical systems. There are several limitations to the study. The shimming of the magnetic field had to be done prior to the actual scans due to technical limitations. Hence the shimmed orientations matched the actual scanned angles only approximately, introducing a potential source of errors in terms of B0 inhomogeneity. Based on the measured B0 maps (supplementary figure S2), it was estimated that a specific shim setting provided a good field homogeneity. The primary sources of error in the fits in this study are the relatively low signal intensity in the deep cartilage in some samples and the accuracy of the model itself. Furthermore, the registration process was not perfect down to a single voxel and thus introduces an additional source of errors into the fits, especially in the SZ. This limitation, in addition to not controlling for the split line orientation may explain the fiber angle maps not reaching the expected 90°in the SZ of all samples. Despite the potential issues, the fits were robust as indicated by the low standard error values and the good visual match between the measured data and fitted theoretical curves.
Seemingly contradictory to Xia et al (2002), the isotropic component of T 2 was found here to have little to no depth-wise variation in the bulk of the cartilage but a slight elevation in the superficial zone and near the cartilage-bone interface. However, here the total relaxation time T 2 is modeled based on summing up the components of the R 2 relaxation rate (equation (1)), while in the previous paper, components of T 2 were summed. This difference in the relaxation model likely explains the differences in the observations. The findings of this study suggest that by utilizing high angular resolution rotation measurements, the structurally anisotropic T 2 -relaxation of articular cartilage can be divided into anisotropic and isotropic components. Any single-orientation T 2 scan of articular cartilage always suffers from intensity changes by the magic angle phenomenon. Due to the orientation-independence of the parameters studied here, they are likely sensitive and specific to changes in the tissue itself, instead of being sensitive to the differences in the measurement setup. Furthermore, the methods presented in this study remove the major problem caused by the anisotropicity of T 2 and also enable analysis of its isotropic and anisotropic components. In the future, we aim to establish a solid connection between spontaneous cartilage degeneration and thereby altered properties of the tissue, and the orientation-independent qMRI parameters studied here, i.e. R 2,i , R 2,a , f, and anisotropy. Elevated T 2 values have been reported to have a link to a clinically moderate OA (David-Vaudey et al 2004, Hannila et al 2007, Apprich et al 2010, and we hypothesize to observe a decrease in either isotropic or anisotropic component of R 2 relaxation rate, or both, in degenerated cartilage. There are also results that demonstrate lower T 2 anisotropy in the degenerated articular cartilage when compared to the less degenerated samples (Hänninen et al 2021). Hence, relaxation anisotropy may serve as a biomarker for structural integrity of cartilage and thus as an indicator of degeneration and OA. The use of the qMRI for non-invasive measurement of local tissue anisotropy and the orientation of the collagen network is an interesting and promising topic of future research, especially if it can replace other invasive methods, such as standard histology. The possibilities of applying this method in the clinical environment with live patients are certainly worth exploring, but the method is probably the most suitable for ex vivo purposes, such as improving biomechanical models and assessing error sources in them. Unlike the previous studies that have looked into the anisotropic properties of T 2 in cartilage, this study allows the estimation of the 3D fiber-to-field angle with no prior assumptions of the distribution of orientations in the collagen network.