Orientation anisotropy of quantitative MRI relaxation parameters in ordered tissue

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.

progression of the disease may be slowed down by dietary choices and weight management 20 . Thus, diagnosing OA at the earliest possible stage is essential in preventing the progression and minimizing the symptoms 20 . While numerous quantitative MRI methods have been proposed and established for early diagnosis of OA [21][22][23][24] , a significant issue persists that the results of many of those (particularly T 2 relaxation time) are susceptible to orientation anisotropy 1,25,26 .
In almost every joint of the human body, articular cartilage is naturally at variable orientations, causing different regions of cartilage to be scanned at different angles with respect to the MRI scanner's magnetic field; thus yielding potentially variable results for the different regions of otherwise similar cartilage. In practice, the measurement geometry due to joint shapes cannot be controlled and, therefore, orientation-independent MRI methods or detailed understanding of the dependence would be necessary to avoid possible false diagnoses and to allow realistic analysis of the structure and state of the health of cartilage.
The sensitivity of different quantitative MRI (qMRI) parameters to relaxation anisotropy varies. T 1 has been shown not to be sensitive to orientation 7 , whereas T 2 and continuous wave (CW)-T 1ρ have been shown to have excessive sensitivity to orientation [27][28][29] . For CW-T 1ρ , reduction of orientation sensitivity in cartilage has been reported for increasing spin-lock powers 27,30 .
Orientation dependence of T 2 relaxation time in articular cartilage has been ascribed to residual dipolar interactions (RDI) of water protons due to their restricted spatial arrangement within the collagen fibres 17,26 . In addition to water proton intramolecular dipolar interactions, intermolecular dipolar couplings between water and biopolymer protons have also been suggested as a source of T 2 anisotropy 10,31 . Dipolar interaction between two nuclei is directly proportional to the factor (3 cos 2 θ − 1), where θ is the angle between the direction of the magnetic field and a vector joining the nuclei 8 . Dipolar interaction is one of the predominant relaxation mechanisms and is generally noticed as a signal reduction except at θ angles near or at so called "magic angle" of 54.74° where (3 cos 2 θ − 1) = 0 and the dipolar interaction vanishes 8 . Thus, qMRI relaxation time parameters affected by dipolar interaction reach maximum values at this specific angle and show a (3 cos 2 θ − 1)-dependence on the sample orientation 7 .
Practical value of qMRI parameters depends on their potential and accuracy for diagnosis of diseases, such as OA. Recently, T 1ρ and T 2 32 , and rotating frame relaxation (RFR) methods including adiabatic T 1ρ , adiabatic T 2ρ and T RAFF2 24,33 , have been reported to be sensitive for cartilage degeneration 24,33 . Orientation sensitivities of these parameters have been investigated in a preliminary study; adiabatic T 2ρ and T RAFF2 were observed to have a similar orientation sensitivity as T 2 , whereas adiabatic T 1ρ was shown to be less sensitive to orientation than T 2 , both in ex vivo and in vivo measurements 34,35 .
The aim of the experimental part of this study was to investigate the orientation dependence of several quantitative MRI parameters (T 1, T 2, T 2 *, CW-T 1ρ , adiabatic T 1ρ , adiabatic T 2ρ and T RAFF2 ) and evaluate the findings against the collagen fibre orientation and anisotropy, measured by the gold standard reference technique, i.e., quantitative polarized light microscopy (qPLM). As a secondary aim, the usefulness of the aforementioned parameters for OA diagnostics, as described and reported in the literature, was evaluated against the orientation sensitivity determined in the experimental part.

Results
qPLM revealed the typical tri-laminar collagen orientation in all the samples, starting with fibres oriented along the cartilage surface and arching towards radial orientation at the cartilage-bone interface (Fig. 1a). Similar to qPLM anisotropy, optical retardation was lowest in the transitional zone and increased towards the deep tissue, indicating increasing anisotropy (Fig. 1b,c).
Different sensitivities of the parameters to sample orientation with respect to B 0 were observed (Figs 2 and 3). Orientation dependence was absent or minimal for T 1 , adiabatic T 1ρ with HS1 pulse and CW-T 1ρ at 2 kHz spin-lock amplitude. On the other hand, using HS4 or HS8 pulses for adiabatic T 1ρ , or decreasing the spin-lock power of CW-T 1ρ increased the orientation dependence. T 2 , T 2 *, adiabatic T 2ρ and T RAFF2 had the highest sensitivity to orientation, visualized by the largest changes over the orientation, especially in the deep tissue. Identical behaviour was observed with all the samples. The regional minimum, maximum and mean values of the relaxation times over all the measurements reflected the same observations on orientation sensitivities ( Table 1).
Analysis of the depth-wise MR anisotropy, as determined using the Michelson contrast parameter, revealed distinctive differences between the relaxation times (Fig. 4). For those parameters that demonstrated sensitivity, the anisotropy changed as a function of depth: the minimum was observed at the transitional zone, higher relaxation anisotropy at the surface and the maximum in the radial zone, closely resembling the qPLM anisotropy of the collagen network (Fig. 1c). Relaxation anisotropy of the MRI parameters was assessed as a bulk value in the radial zone with the expected most uniform collagen architecture and the highest qPLM anisotropy. T 1 relaxation anisotropy in this region had the lowest correlation with qPLM anisotropy (r = 0.03) and retardation (r = −0.10), followed by adiabatic T 1ρ with HS1 pulse (r = 0.09/−0.10), whereas the anisotropies of T 2 and T 2 * relaxation times had the highest correlations (r = 0.87/−0.88 and r = 0.87/−0.86, respectively) ( Table 2).
Assessing the anisotropies of the MRI parameters in the radial zone enabled sorting the parameters by their respective sensitivities to the specimen orientation in the main field (Fig. 5, Table 2). Based on values reported in the literature, relative differences between "normal" or "intact" and variably degenerated or degraded ("OA") animal and human tissue were evaluated and plotted together with the estimated orientation anisotropies (Fig. 5). Broadly, parameters with higher sensitivity to orientation anisotropy also demonstrated largest relative differences between intact and degenerated articular cartilage (Fig. 5).

Discussion
Orientation dependence of several quantitative traditional and rotating frame MRI parameters in ordered tissue was investigated in this study. The findings on the MR anisotropy of several quantitative relaxation time parameters were compared to measurements of structural anisotropy of cartilage tissue by qPLM. Furthermore, literature-reported relative differences for the investigated MR parameters between intact and degenerated tissue were evaluated against the assessed orientation sensitivities.
In this study, we selected articular cartilage as a model tissue that has both highly anisotropic and also relatively isotropic regions 7 . The current findings confirmed earlier reports on the orientation sensitivity of T 1 and T 2 relaxation times 7,17,36 , and the reduction of the orientation sensitivity with increasing spin-lock power for CW-T 1ρ 27,30 . Orientation dependence was observed also for other relaxation parameters, and was the most significant for T 2 , T 2 *, adiabatic T 2ρ and T RAFF2 .
As previously demonstrated in multiple studies, T 2 relaxation time along with T 2 * was the most sensitive to orientation of the sample, a phenomenon ascribed to the residual dipolar interaction in cartilage and other similar highly organized tissues 17,27,37,38 . T 2 relaxation time is sensitive to dipolar interactions and, thus, this was an expected finding. T 2 *, on the other hand, might be sensitive also to field inhomogeneity contributions from anisotropic susceptibility of the collagen fibres in the cartilage 39,40 , since it carries not only T 2 but also the inhomogeneity related component. However, very similar relaxation anisotropy to T 2 was noted for T 2 *.
The orientation dependencies of adiabatic T 1ρ , adiabatic T 2ρ and T RAFF2 have been briefly investigated previously for articular cartilage 34 . The present results demonstrated the orientation dependence of T RAFF2 and adiabatic T 2ρ to be very similar to that of T 2 or T 2 *, as was noted in the preliminary findings 34 . Furthermore, an increase in the dependence for adiabatic T 1ρ was observed with increasing pulse stretching factor n 41 . Three different pulse modulations using hyperbolic secant function with stretching factors of 1, 4 and 8 were tested. To allow comparison, the RMS powers and bandwidths of the pulse modulations were kept the same (approximately equal to 906 Hz CW-pulse power). As the pulse is stretched further, the shape approaches that of a CW-pulse and the time the magnetization spends in the vicinity of the xy-plane is increased, i.e. the contributions from off-resonance T 1ρ relaxation are reduced and more dipolar relaxation is allowed, explaining the observed change in anisotropy [41][42][43][44] . However, even with the HS8 pulse modulation, the relaxation was nearly orientation-independent.
Native (non-contrast enhanced) T 1 relaxation time and adiabatic T 1ρ with HS1 pulses were found to be essentially independent of the tissue orientation. Adiabatic T 1ρ and T 2ρ have been shown to be sensitive to changes in cartilage even in vivo, and adiabatic T 1ρ seems promising also with clinical MRI equipment 45,46 . The independence of T 1 and adiabatic T 1ρ parameters on the orientation of the tissue promotes them as suitable parameters to be applied in vivo for assessing tissue status. For quantitative MR imaging of articular cartilage, this also implies that the dGEMRIC method 47 , while requiring exogenous contrast agent, should provide orientation-independent assessment. Similar orientation-independence is expected for other T 1 -based contrast-enhanced imaging methods. Assuming dipolar interaction is the main contributor to spin relaxation in cartilage, both longitudinal T 1 and transverse T 2 relaxation depend on molecular fluctuations introducing field perturbations driving the relaxations 7 . Compared with T 1 , T 2 relaxation has an additional contribution from the secular component of the dipole-dipole interaction (relaxation depending on the spectral density at zero frequency, which does not affect the T 1 relaxation). This additional component brings about the orientation sensitivity to T 2 relaxation. In sufficiently organized matter, such as cartilage, this orientation dependent component may not completely vanish by random molecular motion and represents itself as orientation-dependent T 2 relaxation. Since T 1 relaxation does not have this component, it is not orientation dependent. This also suggests an explanation for the orientation insensitivity of the adiabatic T 1ρ relaxation. With an adiabatic pulse, the magnetization follows the trajectory of the RF field; this results in the magnetization relaxing along the RF field. The RF modulation of the adiabatic Figure 2. Relaxation parameter maps for one representative sample at different angles with respect to B 0 (arrows above). Orientation anisotropy is clearly seen for T 2 , T 2 *, Ad-T 2ρ and T RAFF2 . Articular surface and cartilage-bone interface are marked with arrowheads.
Scientific REPORts | 7: 9606 | DOI:10.1038/s41598-017-10053-2 HS-pulse is such that the effective field starts along the Z-axis, halfway through the pulse traverses through the transverse plane and ends along the opposite direction of the Z-axis 41,44 . Thus the relaxation during an adiabatic HS-pulse can be viewed as a combination of longitudinal and transverse relaxations, with the amounts of the respective components dependent on the pulse shape. This is also evidenced by the increased orientation sensitivity of adiabatic T 1ρ when the pulse is stretched, making the effective field (and the magnetization) spend more time in the transverse plane and thus experiencing more T 2 -like relaxation.
For all the parameters with clear anisotropy along the cartilage depth, the minimal orientation dependence was detected in the transitional zone, at approximately 12-14% of depth from the articular surface. This is the zone in which the anisotropy of the collagen fibres is also at its minimum. Above this zone, in the superficial cartilage, the anisotropy is higher due to the preferential arrangement of the fibres along the surface. However, collagen fibres in the superficial cartilage are also distributed at multiple orientations along the plane parallel to the surface 48,49 . Thus, orientation dependent relaxation times depend also on the rotation angle about the axis of the surface normal. In the radial zone, however, the collagen fibres are more uniformly oriented along the axis of the surface normal and relaxation is less affected by the rotation about this axis. This also explains the observed maximum of the qMRI anisotropy in the radial zone. The overall average relaxation times and their ranges in the different zones generally reflect the same observations, although the averages can only be considered indicative and descriptive of the measurements due to the different orientation sensitivities of the parameters.
Since the deep cartilage has the most uniform collagen fibre structure 13,17 (see also Fig. 1), it was chosen as a region to represent the overall orientation sensitivity of the relaxation parameters. Orientation anisotropy in the radial zone was calculated for all the parameters as the average value from the depth of 40% to 80%. According to The results of the qPLM orientation and retardation are in accordance with the results of Xia et al. 50 and Rieppo et al. 13 on mature articular cartilage. On average, the difference between orientations of fibres in the superficial and radial zone was approximately 75 degrees, which is less than the theoretical value of 90 degrees. This likely reflects the actual variations in the fibre orientation in the deep zone, as well as the possibility that the primary orientation can differ from the angle exactly perpendicular to the cartilage-bone interface or cartilage surface 51 .
The change in orientation anisotropy for CW-T 1ρ followed the previously reported change: increasing spin-lock amplitude reduced the sensitivity 27 , with the conclusion that spin-lock amplitude greater than 500 Hz starts to overpower the RDI at 1.5 T. Here it was found that 500 Hz already reduces the sensitivity to orientation (i.e. to RDI), but does not remove it; the sensitivity is further reduced with 1 kHz and 2 kHz amplitudes (see also Fig. 4). Mlynarik et al. tested CW-T 1ρ at two different B 0 field strengths and concluded that dipolar interaction is a major factor in T 1ρ relaxation especially at lower field strengths 26 . However, in practice the increasing SAR values of increasing spin-lock amplitude (and often also hardware limitations) prevent the clinical use at high frequencies (typically up to ~500 Hz is clinically applicable) 52 .
The maximum values for the relaxation times (Fig. 3) were found at sample orientations of 59°, 56°, 69° and 72°. Theoretically, the dipolar relaxation vanishes at the magic angle, which is 54.7°8. The observed small deviations are probably reflective of the small variations in the actual fibre angles in deep cartilage with respect to the sample itself, as the orientations of the specimens were determined from the scout images based on the  orientation of the cartilage surface 15 . Recognizing this possibility, there was no specific attempt to scan the specimens exactly at the magic angle, potentially also allowing missing of the true maximum, which might lie between the measured angles. As a step forward from standard anatomical imaging, qMRI has a huge potential to provide improved diagnostics and objective, quantitative information of tissue properties at the molecular level. However, in clinical MRI, the measurement geometry often cannot be altered. Thus, orientation independent MRI methods, or understanding of the dependence, is necessary to avoid possible false diagnoses and to allow realistic analysis of the structure and of the state of the tissue being imaged 53 . The correlation (or lack of it) of the anisotropy of the qMRI parameters with the PLM anisotropy effectively indicates the sensitivity of the different parameters to orientation and further to the geometry of the scan setup. To precisely characterize relaxation changes in ordered tissue, more orientations are required for those parameters that correlate with structural anisotropy. From the literature comparison (Fig. 5) it can be seen that the parameters with the best sensitivity in detecting tissue changes related to OA also tend to have the highest sensitivity to orientation anisotropy. This suggests that the methods sensitive to the orientation are thus also sensitive to changes in the orientation, i.e. sensitive to the properties of the collagen fibre network, which is one of the primary components of articular cartilage. Thus, sensitivity to orientation anisotropy may have a role in the sensitivity of the parameters for detecting differences between "intact" or "normal" and "degenerated" tissue. However, the optimal qMRI parameter would exhibit zero sensitivity to orientation while having the maximum sensitivity to tissue degeneration or changes in tissue, i.e., parameters approaching lower right corner in Fig. 5 would be generally preferred. While a number of different MRI parameters were  Table 2. Average anisotropy of the relaxation parameters in deep cartilage (average of four samples and range (min/max)) and the coefficients of correlation for the depth-wise MRI anisotropy with depth-wise PLM anisotropy and PLM retardation. Averages for correlation coefficients have been calculated using Fisher's z transform. The parameters are ordered in the table based on their anisotropy. studied, yet more possibilities exist: for example, magnetization transfer experiments have been demonstrated to have minimal or no orientation dependence 54 . On the other hand, sensitivity to orientation changes could provide an alternative means to analyse tissue structure and properties at the molecular level.

Conclusion
In conclusion, adiabatic T 1ρ , also reported sensitive to cartilage degeneration 24,33,55 , appeared as a promising, minimally orientation-dependent quantitative MRI parameter for the articular cartilage. Additionally, adiabatic pulses provide flexibility with respect to overcoming SAR issues. While limited and somewhat variable results have been reported for native T 1 , it appears as the most promising parameter out of the investigated in terms of SAR and orientation (in)dependence. This finding also suggests that other measurements based on estimating T 1 relaxation time (such as contrast enhanced methods) would be promising. The practical usefulness of qMRI parameters depends on how well they can be used in diagnosis of diseases, such as OA. Based on the literature findings and the measured relaxation anisotropies, parameters with higher sensitivity to orientation anisotropy generally also demonstrated larger relative differences between intact and degenerated articular cartilage. The best-suited MRI parameter for diagnostics in ordered tissues remains uncertain.  Table 1. All measurements were repeated for every orientation. After the MRI studies, the samples were fixed in 10% neutral buffered formalin for 48 hours and then decalcified in EDTA for histology processing.

Methods
Histology and quantitative polarized light microscopy (qPLM). After decalcification, the samples were cut in the same plane that was used in MR imaging utilizing 3-D reconstructions of the MRI data as visual guides. Subsequently, the samples were dehydrated and embedded in paraffin. Unstained histological sections were prepared from the locations of the MRI slices and placed on the standard microscope slides. The sections were digested with hyaluronidase enzyme for 18 hours to remove proteoglycans before quantitative polarized light microscopy (qPLM) measurements (pixel size 2.53 × 2.53 µm). The optical retardation and collagen fibre orientation in the sections were measured according to Rieppo et al. 13 using quantitative Abrio PLM imaging system. Abrio PLM system (CRi, Inc., Woburn, MA, USA) is mounted on a conventional light microscope (Nikon Diaphot TMD, Nikon, Inc., Shinagawa, Tokyo, Japan) and consists of a green bandpass filter, a circular polarizer, a computer-controlled analyser composed of two liquid crystal polarizers and a CCD camera.
Data Analysis. In MRI analyses, to obtain relaxation time maps, relaxation time constants were fitted in a pixel-wise manner using the respective signal equations: T RAFF was fitted using exponential decay and approach to steady state 57 , CW-T 1ρ using 2-parameter exponential with baseline and the rest of the parameters were fitted using 2-parameter monoexponentials with noise floor subtraction before fitting, using in-house developed Matlab (Matlab R2015b, Mathworks, Natick, MA, USA) plugin functions for Aedes (http://aedes.uef.fi) (examples of fit curves and values can be found in the supplementary Figure S1 and Table S1). Depth-wise profiles of 1.75 mm width from the cartilage surface to bone interface were calculated at the centres of the specimens. The profiles were then depth-normalized for comparison and averaging between specimens. In qPLM analyses, anisotropy of the collagen fibres was calculated by applying an entropy filter of size 5 × 5 pixels (entropyfilt, Matlab) to the orientation angle images obtained from the qPLM. The anisotropy is represented by the inverse of the entropy + 1 to constrain the values to the range [0, 1]. The orientation, retardation and anisotropy profiles were calculated separately for each sample along cartilage depth and averaged point-by-point for mean profile and depth-normalized for comparison. Average values and ranges for the relaxation times over the samples and orientations were calculated in the three structural zones, SZ, TZ and RZ (regions shown in Fig. 3).
Scientific REPORts | 7: 9606 | DOI:10.1038/s41598-017-10053-2 Parallelism, or anisotropy of the collagen fibres, can be defined as Michelson contrast 13, 58 : where min and max are the minimum and maximum measured intensity R i over the different physical orientations of the specimen. Here, this formalism was used to calculate the depth-wise MR anisotropy profiles for the relaxation parameters using the relaxation rates at different sample orientations as the measured intensities.
To quantitatively analyse relaxation anisotropy of the MRI parameters as a bulk property, an average value for the depth of 40% to 80% was calculated, since the deep cartilage, i.e., radial zone has relatively constant fibre orientation with the highest anisotropy (Fig. 4, ROI region shown with dashed line).
Correlations between the MR anisotropy profiles and PLM measurements were calculated per sample and then averaged using Fisher's z transform 59 . Matlab was used for all calculations and analyses.
To assess the orientation dependence versus relative sensitivity of the parameters, the average anisotropies of the MR parameters were plotted against relative difference of the same parameters between early OA and advanced OA, or intact and degenerated tissue, taken from multiple previous studies reporting different OA cases or OA models 24, 33, 45, 55, 60, 61 . Data Availability. All of the raw data, documentation and analysis codes of the study are available for download at Zenodo (doi:10.5281/zenodo.519752).