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SIMPLE METHOD TO MEASURE MAGNETIC RESONANCE ANISOTROPIC T2 RELAXATION TIMES IN HUMAN KNEE CARTILAGE

20190313936 ยท 2019-10-17

    Inventors

    Cpc classification

    International classification

    Abstract

    Technology for measuring clinically relevant Magnetic Resonance (MR) anisotropic water proton transverse relaxation rates of cartilage in human knees and other joints is provided. A single sagittal T2-weighted magnetic resonance image of a cartilage associated with a human knee or other joint may be acquired, and an internal reference signal may be measured from this acquired sagittal image. The internal reference signal is a signal intensity (S())from the cartilage with its collagen fiber orientated approximately 54.7 to the main magnetic field. An anisotropic R.sub.2 relaxation rate (R().sub.2.sup.a) may be calculated for the cartilage using the following equation: R().sub.2.sup.a={log(S(=54.7))log(S())}/TE. Accordingly, an indication of a degeneration of the cartilage may be determined using the calculated anisotropic R2 relaxation rate.

    Claims

    1. A computer-implemented method, comprising: acquiring a single sagittal T2-weighted magnetic resonance image of cartilage associated with a human joint; measuring an internal reference signal in the acquired sagittal image, wherein the internal reference signal is a signal intensity (S()) from the cartilage with its collagen fiber orientated approximately 54.7 to the main magnetic field; calculating an anisotropic R.sub.2 relaxation rate (R().sub.2.sup.a) for the cartilage, using the following equation: R().sub.2.sup.a={log(S(=54.7))log(S())}/TE; and determining an indication of a degeneration of the cartilage using the calculated anisotropic R.sub.2 relaxation rates.

    2. The method of claim 1, wherein the cartilage is associated with a human knee joint.

    3. The method of claim 1, wherein the cartilage is associated with a human hip joint.

    4. The method of claim 1, wherein the cartilage is associated with a human elbow joint.

    5. The method of claim 2, wherein the cartilage is femoral cartilage.

    6. The method of claim 2, wherein the cartilage is tibial cartilage.

    7. The method of claim 2, wherein the cartilage is patellar cartilage.

    8. A system, comprising: one or more processors; and one or more memories storing instructions that, when executed by the one or more processors, cause the one or more processors to: acquire a single sagittal T2-weighted magnetic resonance image of cartilage associated with a human joint; measure an internal reference signal in this acquired sagittal image, wherein the internal reference signal is a signal intensity (S()) from the cartilage with its collagen fiber orientated approximately 54.7 to the main magnetic field; calculate an anisotropic R.sub.2 relaxation rate (R().sub.2.sup.a) for the cartilage, using the following equation: R().sub.2.sup.a={log(S(=54.7))log(S())}/TE; and determine an indication of a degeneration of the cartilage using the calculated anisotropic R.sub.2 relaxation rates.

    9. The system of claim 8, wherein the cartilage is associated with a human knee joint.

    10. The system of claim 8, wherein the cartilage is associated with a human hip joint.

    11. The system of claim 8, wherein the cartilage is associated with a human elbow joint.

    12. The system of claim 10, wherein the cartilage is femoral cartilage.

    13. The system of claim 10, wherein the cartilage is tibial cartilage.

    14. The system of claim 10, wherein the cartilage is patellar cartilage.

    15. A tangible, non-transitory computer-readable medium storing executable instructions that when executed by at least one processor of a computing device, cause the computing device to: acquire a single sagittal T2-weighted magnetic resonance image of cartilage associated with a human joint; measure an internal reference signal in this acquired sagittal image, wherein the internal reference signal is a signal intensity (S()) from the cartilage with its collagen fiber orientated approximately 54.7 to the main magnetic field; calculate an anisotropic R.sub.2 relaxation rate (R().sub.2.sup.a) for the cartilage, using the following equation: R().sub.2.sup.a={log(S(=54.7))log(S())}/TE; and determine an indication of a degeneration of the a degeneration of the cartilage using the calculated anisotropic R.sub.2 relaxation rates.

    16. The tangible, non-transitory computer-readable medium of claim 15, wherein the cartilage is associated with a human knee joint.

    17. The tangible, non-transitory computer-readable medium of claim 15, wherein the cartilage is associated with a human hip joint.

    18. The tangible, non-transitory computer-readable medium of claim 15, wherein the cartilage is associated with a human elbow joint.

    19. The tangible, non-transitory computer-readable medium of claim 16, wherein the cartilage is femoral cartilage.

    20. The tangible, non-transitory computer-readable medium of claim 16, wherein the cartilage is tibial cartilage.

    Description

    BRIEF DESCRIPTION OF THE DRAWINGS

    [0015] FIG. 1 illustrates an exemplary schematic diagram of femoral articular cartilage with angular-radial segmentations, anatomical annotations and collagen fiber orientations. The deep and superficial zones are divided by a red dash-dot line. An ROI, at a magic-angle of 54.7 with an angular width of 5 in the deep zone, is represented by a red square. The main magnetic field B.sub.0 points downwards.

    [0016] FIG. 2 illustrates an exemplary segmented T2W signal (in a logarithmic scale) intensity map for a whole deep cartilage from the one knee (b). A white arrow points to the spatial location of an angular-radial segmentations in a lateral T2W image (a), and two horizontal dashed lines cross the segmented angles of 54.7.

    [0017] FIG. 3 illustrates exemplary (a) R.sub.2, (b) R.sub.1, (c) R.sub.2R.sub.1 and (d) R().sub.2.sup.a pixel maps for the image in FIG. 2a. An internal reference of 5.52 and TE of 48.8 ms was used in derivingR().sub.2.sup.a. All color bars are in the same scale.

    [0018] FIG. 4 illustrates exemplary comparisons between orientation-dependent relaxation rate profiles of R.sub.2 (blue circles) and R.sub.1 (red squares) in the deep (a) and superficial (b) zones, and the similar comparisons between R().sub.2.sup.a (red squares) and R.sub.2R.sub.1 (blue circles) in the deep (c) and the superficial (d) zones. Each point in the plots was an averaged relaxation rate from a segmented ROI in the corresponding relaxation rate maps shown in FIG. 3.

    [0019] FIG. 5 illustrates exemplary whole relaxation rate (s.sup.1) maps for (a, e) R.sub.2, (b, f) R.sub.1, (c, g) R.sub.2R.sub.1 and (d, h) R().sub.2.sup.a in the deep (a-d) and superficial (e-h) cartilage from one subject. All color bars are in the same scale.

    [0020] FIG. 6 illustrates exemplary correlations between R.sub.2R.sub.1 from FIG. 5c,g and R().sub.2.sup.a from FIG. 5d,h in the deep (a) and superficial (b) cartilage, with the linear Pearson correlation coefficients (r) included. Data ellipses are shown in red dashed lines, with the means of R.sub.2R.sub.1 and R().sub.2.sup.a highlighted by the horizontal and the vertical green dashed lines.

    [0021] FIG. 7 illustrates exemplary comparisons of the whole-knee averaged relaxation rates (s.sup.1) between R().sub.2.sup.a (circle and square) and R.sub.2R.sub.1 (triangle and diamond) in the deep (solid line) and superficial (dashed lines) cartilage for five knees.

    [0022] FIG. 8 illustrates exemplary comparisons of the normalized whole-knee averaged relaxation rates (%) between R().sub.2.sup.a (yellow) and R.sub.2R.sub.1 (blue) for examined five knees. The normalized quantity (%) was defined as (DEEP-SUPF)/DEEP*100, with DEEP and SUPF representing relaxation rates in the deep and superficial cartilage.

    [0023] FIG. 9 illustrates an exemplary computer system that may be used for analysis as described here and connected to a medical imaging system.

    [0024] FIG. 10 illustrates a flow diagram of an exemplary method for measuring clinically relevant Magnetic Resonance (MR) anisotropic water proton transverse relaxation rates of cartilage in human knee and other joints.

    DETAILED DESCRIPTION

    [0025] The present disclosure provides an efficient method to measure the collagen orientation-dependent anisotropic transverse water proton relaxation rates in human knee cartilage. Advantageously, this method may reduce clinical MR scan times significantly and may allow clinicians and researchers to derive more relevant and sensitive information on collagen integrity of both knees and other joints.

    [0026] The present disclosure first demonstrates theoretically that the R.sup.a.sub.2 () of cartilage at 3T was partially and inefficiently separated in the reported composite relaxation metric. The prolonged image acquisition protocol and demanding pulse sequences standardization across different MR systems have prevented the reported method from being favorably accepted by the clinical community. Hence, an efficient method is proposed here to derive R.sup.a.sub.2 () based on a single T2W sagittal image, by eliminating an assumed constant isotropic R.sub.2 contribution derived from the magic angle locations in the deep cartilage. The new method is a unique Anisotropic R.sub.2 of CollAgen DEgeneration (ARCADE) mapping to emphasize its straightforward association with the integrity of collagen fibers. The derived femoral cartilage R.sup.a.sub.2 () values in five knees from four volunteers were compared with those of R.sub.2R.sub.1. The results demonstrate that the proposed ARCADE mapping is an efficient alternative to the conventional approach, holding great promise in providing both high-resolution morphological and more sensitive R.sup.a.sub.2 () imaging from a single T2W scan in clinical studies on joint cartilage.

    [0027] Theory

    [0028] For knee cartilage water proton MR relaxation study at 3T, only the intramolecular dipolar interaction between two protons in water will be considered to interpret the observed MR relaxation rates of R.sub.1, R.sub.2, and R1.sub.. In general, these relaxation rates could be characterized using a two-pool fast exchange model, i.e., rapid water exchange between the free and bound pools, and thus represented as the weighted averages of two pools, as shown in Equation 1,


    R.sub.m=fi*R.sup.i.sub.m+fb*R.sup.a.sub.m () (1)

    [0029] with m=1, 2 and 1.sub.; f.sub.i and f.sub.b the molecular fractions of water in the free and bound pools, with fi+fb=1; R.sup.i.sub.m and R.sup.a.sub.m () the contributions from a fast isotropic and a slow anisotropic molecular reorientation, which could be characterized, respectively, by a smaller effective isotropic correlation time (r.sub.f) and a larger apparent isotropic correlation time (.sub.b.sub.f). To simplify the discussion, R.sup.i.sub.m and R.sup.a.sub.m () can absorb corresponding f.sub.i and f.sub.b, to denote the apparent relaxation rates in the following unless stated otherwise.

    [0030] The molecular anisotropic reorientation of the bound water in cartilage can be characterized using an axially symmetric model, with a correlation time .sub. assigned to one rotation about the symmetry axis along the collagen fiber, and another correlation time .sub. to the rotation about an axis perpendicular to the symmetry axis. If .sub. is set to .sub.f and much smaller than .sub. (i.e. .sub..sub.)), corresponding to the bound water preferential alignments, the effective correlation time .sub.b of the bound water could be determined only by .sub. leading to .sub.b.sub.f. This conclusion had been long before stated that the preferential alignments of water molecules could effectively have their otherwise-short correlation times amplified by many orders of magnitude. Therefore, it would not be surprising to see a significantly larger .sub.b for the restricted water in the bound pool.

    [0031] R.sup.a.sub.2 () can be explicitly written as R.sup.a.sub.2*(3 cos.sup.2 1).sup.2/4, where R.sup.a.sub.2 denotes the maximum anisotropic relaxation rate and an angle subtending the dipolar interaction vector and the B.sub.0 direction. R.sup.a.sub.2 () reportedly could be effectively suppressed in R.sub.1 measurements if using a stronger (.sub.1/2>2.0 kHz) spin-lock RF strength. Accordingly, an effective isotropic correlation time .sub.b for the bound water could be estimated to be at least larger than 0.5/.sub.1. On the other hand, the corresponding .sub.f for the free water should be at least larger than 0.62/.sub.0, given that R.sub.2R.sub.1. The Larmor frequency is denoted by .sub.0/2 and equal to 128 MHz at 3T.

    [0032] According to the classical MR relaxation theories, water proton relaxation rates of R.sub.1, R.sub.2, and R.sub.1 could be expressed in terms of an effective isotropic rotational correlation time .sub.c using Equations 2-4, and profiled correspondingly at 3T,

    [00001] R 1 = K .Math. { c 1 + 0 2 .Math. c 2 + 4 .Math. c 1 + 4 .Math. 0 2 .Math. c 2 } ( 2 ) R 2 = K .Math. { 3 .Math. .Math. c 2 + 2.5 .Math. .Math. c 1 + 0 2 .Math. c 2 + c 1 + 4 .Math. 0 2 .Math. c 2 } ( 3 ) R 1 .Math. .Math. = K .Math. { 1.5 .Math. .Math. c 1 + 4 .Math. 1 2 .Math. c 2 + 2.5 .Math. .Math. c 1 + 0 2 .Math. c 2 + c 1 + 4 .Math. 0 2 .Math. c 2 } ( 4 )

    [0033] where K is a constant of 1.056*10.sup.10 (s.sup.2) assuming a distance of 1.59 () between two proton nuclei in water. If .sub.c0.62/.sub.0 (0.8*10.sup.9 s), all relaxation rates will become 5K.sub.c, which describes a scenario for water molecules rotating freely in nonviscous liquids. In cartilage, however, water can attain a longer .sub.c, depending on both interactions with its neighboring macromolecules and their relative orientations to B.sub.0.

    [0034] For the free water (0.62/.sub.0<.sub.f<0.5/.sub.1) in cartilage, R.sup.j.sub.1 is equal to R.sup.j.sub.2, while R.sup.j.sub.1 becomes progressively smaller than R.sup.j.sub.2 as .sub.f increases. Notably, R.sup.a.sub.1 for the bound water becomes insignificant, implying that the R.sub.1 relaxation metric would be orientation-independent and only sensitive to the free water. For the bound water (.sub.b>0.5/.sub.1) in cartilage, R.sup.a.sub.1() is progressively decreased relative to R.sup.a.sub.2 () as .sub.b grows. In this case, R.sup.a.sub.1 () can be recast by R.sup.a.sub.2 ()/1+4 .sub.1.sup.2.sub.c.sup.2) because of the dominant first term on the right side of Equations 3-4. It is worth mentioning that R.sub.1 will turn into R.sub.2 (i.e. R.sup.j.sub.2+R.sup.a.sub.2 ()) and R.sup.j.sub.2, respectively, when a spin-lock RF is absent and a stronger (.sub.1.sup.2.sub.c.sup.20.5) spin-lock RF is present. Consequently, the reported composite relaxation metric R.sub.2R.sub.1 can be expressed in terms of R.sup.a.sub.2 () as shown in Equation 5, predicting that R.sub.2R.sub.1 would be a partial R.sup.a.sub.2 () if a spin-lock RF strength is limited in clinical R.sub.1 mapping.


    R.sub.2R.sub.1=R.sub.2.sup.a()*{4.sub.1.sup.2.sub.c.sup.2/(1+4.sub.1.sup.2.sub.c.sup.2)}(5)

    [0035] The present disclosure provides an efficient alternative to derive R.sup.a.sub.2 () from one T2W sagittal image, assuming constant proton density (S.sub.0) and R.sup.j.sub.2 in cartilage. Typically, an orientation-dependent signal intensity S() in T2W could be written as shown in Equation 6, including both free and bound water contributions, with TE being an echo-time.


    S()=S.sub. exp(TE*R.sub.2.sup.iTE*R.sub.2.sup.a()) (6)


    S(=54.7)=S.sub. exp(TE*R.sub.2.sup.1) (7)


    R.sub.2.sup.a()={log(S(=54.7))log(S())}/TE (8)

    [0036] As collagen fibers in the DZ are oriented predominately perpendicular to the cartilage surface, R.sup.a.sub.2 () will become zero at the magic angles of 54.7. In this case, Equation 6 will reduce to Equation 7, which represents the free water contribution as an internal reference of the assumed constant S.sub.0 exp (TE*R.sup.j.sub.2) in the deep cartilage. Combining Equation 6 and Equation 7, R.sup.a.sub.2 () can be computed using Equation 8. This proposed method has leveraged the specific femoral cartilage geometric information that can substitute the otherwise-required additional T2W measurement in conventional R.sub.2 mapping.

    [0037] The preliminary comparative results from five knees in a study described below demonstrate that a higher quality relaxation metric map with an enhanced contrast and less motion artifacts could be obtained with a minimum cost to clinical MR scan time. The proposed method could be potentially applied to other human joint cartilage studies such as in hips and elbows.

    Materials and Methods

    Volunteer Subjects

    [0038] Four volunteers (S1-S4) were enrolled in a study in which each volunteer had a single knee scanned (except for S4, who had both knees studied). Five datasets were labeled according to the subject's sex (M/F), age, knee (L/R), and health status (symptomatic [S], asymptomatic [A] or ACL repaired [P]), i.e. S1 M52RA, S2M47LS, S3F41 LA, S4F20LP and S4F20RA. The study was approved by the local institutional review board (IRB) and compliant with the Health Insurance Portability and Accountability Act (HIPAA). Each volunteer was informed about the study and signed a consent form.

    MR Imaging Protocols

    [0039] Both R.sub.2 and R.sub.1 mappings were performed using a dedicated 16 Channel T/R Knee Coil on a 3T MR scanner. 3D images with various spin-echo times (TEs) in R.sub.2 mapping and spin-lock durations (TSLs) in R.sub.1 mapping were collected in sagittal planes. A fast parallel imaging with an acceleration factor of 2 was used in both data acquisitions.

    [0040] R.sub.2 Mapping:

    [0041] An interleaved multi-slice (=43) multi-echo (=8) turbo spin-echo (TSE) pulse sequence was used to collect 3D T2W images (FOV=128*128*128 mm.sup.3) with a voxel size of 0.6*0.6*3.0 mm.sup.3 covering entire tibiofemoral compartments. The reconstructed images were interpolated to a final voxel resolution of 0.24*0.24*3.00 mm.sup.3. An effective TE for volumetric image data of each was n*6.1 ms, with n=1, 2, 3, 4, 5, 6, 7, 8. The pulse repetition time was 2500 ms, and a total scan time was about 9 minutes per knee.

    [0042] R.sub.1 Mapping:

    [0043] A spin-lock prepared T.sub.1-enhanced 3D turbo gradient-echo sequence (T.sub.1-TFE) was used to acquire T1-weighed images through a segmented elliptic-centric k-space acquisition. The specific k-space trajectories moved along radial directions in a zigzag pattern starting from the center to optimally sample the spin-lock prepared signals before a steady-state was established. The spin-lock RF field strength (.sub.1=B.sub.1/2) was 500 Hz, and TSL were 0, 10, 20, 30 and 40 ms, respectively. A field of view was 130*130*130 mm.sup.3 (an acquired voxel size of 0.40*0.40*3.00 mm.sup.3 and interpolated to 0.24*0.24*3.00 mm.sup.3). The total scan duration was about 11 minutes per knee.

    MR Image Post-Processing

    Image Co-Registrations:

    [0044] A free software Elastix was used for intraseries and interseries image coregistrations. The T2W or T1 3D images with different TE and TSL were first aligned within time series; then, the aligned T1 3D images were further coregistered to the aligned T2W 3D images. The coregistration scheme was based on a published protocol for human knee cartilage, including a multiresolution approach and a rigid transformation model. The coregistration was optimized over 1,000 iterations using a localized mutual information (MI) as a similarity metric, and mutual information was progressively maximized by minimizing its negative values in the optimization process.

    Angular-Radial Segmentation:

    [0045] First, a whole femoral cartilage was manually delineated using a free software ITK-SNAP for each slice in T2W and T1 3D data. Region of interest (ROI) vertices were placed along cartilage boundaries, with the vertex path defined as smoothly as possible. Furthermore, nonoverlaid cartilage areas (due to motion or misalignment) in both T2W and T1 images were minimized in delineating cartilage ROI.

    [0046] Second, the localized cartilage partitions were accomplished by an angular and radial segmentation method. Specifically, the vertices (x and y coordinates) from a predefined cartilage ROI were used to fit (by a nonlinear least-squares fitting) a virtual circle in each image slice, with the circle center located in the femoral condyle. Relative to a vertical line, an angle of a spoke connecting each vertex and the virtual center could be calculated; subsequently, the whole cartilage was subdivided angularly into 5 partitions based on the range of calculated spoke angles. A reference angle (0) was chosen as the B.sub.0 direction in a sagittal image, with the negative angles pointing to the anterior direction and the positive angles to a posterior direction (see FIG. 1).

    [0047] Third, as the shape of femoral cartilage deviates from an ideal half-circle, especially on the lateral sides, a segmented angle () had to be recomputed using only adjacent (=10) vertices to generate a new angle () to represent collagen fiber orientation closely in the deep cartilage.

    [0048] Finally, the femoral cartilage was further subdivided radially into two zones, i.e. the deep zone (DZ) and the superficial zone (SZ), with a shared border line equidistant to opposite boundaries. This segmented SZ actually covers at least both the histologically defined SZ and the transition zone (TZ).

    R.sub.2R.sub.1 Parametric Map:

    [0049] Both R.sub.2 and R.sub.1 maps were fitted pixel by pixel from coregistered multiple 3D data using an exponential relaxation decay model, i.e., S(t.sub.i)=S.sub.0 exp(t.sub.i*P), where P=R.sub.2 or R.sub.1, and t.sub.i=[6.1, 12.2, 18.3, 24.4, 30.5, 36.6, 42.7, 48.8] or [0, 10, 20, 30, 40] (ms), respectively. The corresponding parametric error maps were also created by adjusting fitted parameter uncertainties so that the reduced .sup.2 was equal to 1. A composite metric R.sub.2R.sub.1 3D parametric map was merely a difference between the fitted R.sub.2 and R.sub.1 3D maps. All data analysis and image visualization were performed using an in-house software developed in IDL 8.5 (Harris Geospatial Solutions, Inc., Broomfield, Colo.).

    [0050] R().sub.2.sup.a Parametric Map from ARCADE:

    [0051] A single T2W (TE=48.8 ms) 3D dataset from R.sub.2 mapping was used. An internal reference corresponding to the free water contribution for each image slice was estimated using Equation 6. Specifically, the average T2W pixel values (in logarithmic scale) within each of segmented ROIs in the DZ were fitted to a function of collagen fiber orientations () as shown in Equation 9, with parametric bound constraints.


    y=AB*(3 cos.sup.2(+C)1).sup.2 (9)

    [0052] The model parameter A was not constrained; however, B and C were limited to the ranges of [0, 10] and [10, +10], respectively. The limited freedom introduced for was to account for potential systematic errors in collagen fiber orientations.

    [0053] The nonlinear curve fitting was performed slice by slice. The optimal fits were determined using goodness of fits characterized by .sup.2 test statistics with a significant level of P>0.95. Finally, the mean of those determined optimal A values was used as a global internal reference, i.e., log (S(=54.7) in Equation (8).

    Statistical Analysis:

    [0054] The differences and associations between two relaxation metrics were, respectively, quantified using a Student paired t test (a two-tailed distribution) and a Pearson correlation coefficient (r), where the statistical significance was considered at P<0.05. Scatterplots were used to demonstrate the potential correlation between two parameters; additionally, data ellipses with a 95% confidence level were included for visual enhancement. A normalized relaxation metric, in terms of zonal contrast, was generated as (DEEPSURF)/DEEP*100%, with DEEP and SURF representing R().sub.2.sup.a or R.sub.2R.sub.1 in the DZ and SZ, respectively. All measurements are shown as meanSD unless stated otherwise.

    Results:

    [0055] A schematic sketch in FIG. 1 illustrates orientations of collagen fibers in the deep and the superficial zones, anatomical locations and angular-radial segmentations on a perfectly circular femoral cartilage in a sagittal plane. A red square at a magic-angle in the deep cartilage is highlighted where resides an internal reference signal.

    [0056] A segmentation example of a lateral image from one subject's right knee (S1M52RA) is shown in FIG. 2a, which overlays its corresponding T2W image. An exact spatial location of this image is specified by a white arrow on a whole deep cartilage T2W intensity (in a logarithmic scale) map as shown in FIG. 2b. The two horizontal dashed lines represent segmented angles of 54.7. The internal reference signal for this knee was estimated to be 5.52.

    [0057] FIG. 3d shows R().sub.2.sup.a pixel map derived using Eq. 3 for the image in FIG. 2a, and was compared to a composite relaxation metric of R.sub.2R.sub.1 in FIG. 3c. Clearly, R().sub.2.sup.a qualitatively reproduced its counterpart of R.sub.2R.sub.1 with less motion artifacts, thanks to a significant fast (i.e. 1.2 vs. 20 minutes) acquisition of one T2W 3D image data. As a reference, original R.sub.2 and R.sub.1 pixel maps are listed respectively in FIG. 3a and FIG. 3b, which primarily resonated with previous findings in that the relaxation anisotropy was largely suppressed in R.sub.1.

    [0058] The relaxation anisotropy profiles are plotted in FIG. 4, which were obtained by averaging ROI values in the angular-radial segmentations in FIG. 3. As expected, R().sub.2.sup.a values were significantly higher than those of R.sub.2R.sub.1 in both the deep (9.174.26 vs. 7.583.43, <0.001, see FIG. 4c) and the superficial (8.354.36 vs. 7.634.12, p=0.04, se FIG. 4d) zones. On the other hand, R.sub.1, relative to R.sub.2, had been significantly suppressed in both the deep (22.725.43 vs. 15.142.28, p<0.001, see FIG. 4a) and the superficial (23.774.79 vs. 16.141.75, p<0.001, see FIG. 4b) zones.

    [0059] Moving forward, the complete whole knee maps of R.sub.2 (FIG. 5a,e), R.sub.1 (FIG. 5b,f), R.sub.2R.sub.1 (FIG. 5c,g) and R().sub.2.sup.a (FIG. 5d,h) in the deep (FIG. 5a-d) and the superficial (FIG. 5e-h) zones are presented in FIG. 5. On a global scale, R().sub.2.sup.a qualitatively resembled R.sub.2R.sub.1 in both cartilage zones and all four relaxation rates were relatively higher in the deep zone (FIG. 5a-d vs. FIG. 5e-h). It is worth noting that R.sub.1 maps, on the same color scales, were much more featureless compared with R.sub.2 maps.

    [0060] Quantitatively, R().sub.2.sup.a in this exampled cartilage highly correlated with R.sub.2R.sub.1, as shown in FIG. 6, in both the deep (r=0.83 in FIG. 6a) and the superficial (r=0.88 in FIG. 6b) zones. The averaged R().sub.2.sup.a values were slightly higher than those of R.sub.2R.sub.1 in the deep (9.92 vs. 8.57 s.sup.1) and the superficial (6.84 vs. 5.95 s.sup.1) zones as specified by the data ellipse centroids.

    [0061] The relationship between an averaged R().sub.2.sup.a and an averaged R.sub.2R.sub.1 for five knees are presented in FIG. 7, indicating a highly positive correlation (r=0.830.07) in both subdivided cartilage zones. Although R().sub.2.sup.a was slightly but not significantly higher than or hardly differentiated from R.sub.2R.sub.1 in the deep (8.381.31 vs. 7.251.89, p=0.26) and the superficial (3.632.47 vs. 4.461.61, p=0.44) zones, the corresponding averaged relaxation metrics normalized between the two subdivided zones, defined as (DEEPSUPF)/DEEP*100% as shown in FIG. 8, was significantly higher for R().sub.2.sup.a relative to R.sub.2R.sub.1 (i.e. 5923% vs. 3917%, p<0.04), implying an enhanced image contrast in the derived relaxation metric using the developed method.

    [0062] In summary, the comparative relaxation results on five femoral cartilages have demonstrated that R().sub.2.sup.a derived from the proposed method could be an efficient alternative to R.sub.2R.sub.1, which could provide a higher quality diagnostic-relevant relaxation parametric map at a minimum cost to routine clinical MR scan time.

    Discussion:

    [0063] In the present disclosure, it was established that the composite relaxation metric (R.sub.2R.sub.1) actually measures inefficiently a partial anisotropic R.sub.2 (R().sub.2.sup.a) in clinical knee cartilage studies at 3T. Accordingly, the present disclosure introduces a new method to extract an un-compromised R().sub.2.sup.a based on a single T2W sagittal image. The comparable results between the derived R().sub.2.sup.a and the measured R.sub.2R.sub.1 on five femoral cartilages demonstrate that the developed method can be an efficient alternative to the conventional approach.

    [0064] A key assumption in the new method was a uniform proton density S.sub.0 and a constant isotropic R.sub.2 (R.sub.2.sup.i) regardless of its locations and health status in articular cartilage, where the differences in observed R.sub.2 relaxation rates stemmed solely from the bound water on differently orientated collagen fibers. This oversimplified view on the free water was mainly based on previous observations in that the estimated water content and the observed R.sub.2 values at the magic angle (MA) orientations were all nearly uniform across different zones in cartilage.

    [0065] For example, one ex vivo study showed that S.sub.0 was marginally larger in the SZ than in the DZ (i.e. 903% vs. 884%) at a location near the MA. Xia reported an approximately constant T.sub.2 (596 ms) in cartilage specimens when orientated at the MA in a high-resolution MRI study. Xia also found that T.sub.1 was orientation-independent and almost constant (1.720.11 sec), as was confirmed recently by Hnninen et al. Based on MR relaxation theories, both isotropic R.sup.j.sub.2 and R.sup.j.sub.1 have nearly linear relationships albeit opposite with an effective correlation time .sub.f of the free water in tissue. Thus, a uniform R.sub.1 could be reasonably interpreted as a constant R.sup.j.sub.2, as the observed R.sub.1 in cartilage is predominantly contributed from R.sup.j.sub.1.

    [0066] As articular cartilage has a similar biochemical composition and structural network in extracellular matrix, the free water contribution to R.sub.2 should not substantially fluctuate in different cartilages; in other words, the internal reference derived from the deep femoral cartilage is applicable to the tibial and patellar cartilages as well. The preliminary data (not shown) indicated that comparable correlations between R().sub.2.sup.a and R.sub.2R.sub.1 were found in the femoral, tibial, and patellar cartilages, and an average R().sub.2.sup.a in the tibial was almost three times larger than those found in the femoral and patellar cartilages.

    [0067] The assumption used in ARCADE is no exception for an OA population. The integrity of collagen fibers could be compromised as a result of pathology leading to less preferentially orientated water, and the amount of released free water would be very small compared to an existing large pool of free water. Although the free water contribution to T2W signal should not be altered in OA subjects, the observed T.sub.2 at the locations other than the MA orientations could be increased and could adversely impact optimal curve fittings in some image slices and thus potentially lead to a biased internal reference. On the other hand, if localized OA happens to be at the MA sites, the internal reference would not be altered unless an insignificant (<4% at 3T) chemical exchange effect associated with GAG loss were taken into account.

    [0068] Had the assumption been violated, the derived R().sub.2.sup.a would have been offset systematically from its true value as the R().sub.2.sup.a computation was just a simple subtraction in logarithmic scale. In this work, the measured R.sub.2R.sub.1 was expected to be smaller than R().sub.2.sup.a because of a limited spin-lock RF strength used in R.sub.1 mapping. According to previous reports, a spin-lock RF strength of 2.0 kHz could adequately (99%) suppress R().sub.2.sup.a, leading to R.sub.2R.sub.1=99%*R().sub.2.sup.a. In clinical R.sub.1studies at 3T, however, the spin-lock RF strength is usually limited to 0.5 kHz, which would translate into R.sub.2R.sub.186%*R().sub.2.sup.a. On the other hand, the observed R.sub.2R.sub.1 could be erroneously increased due to different data acquisitions, where R.sub.2 derived from a multiecho pulse sequence tends to be more overestimated than R.sub.1 from a pulse sequence similar to 3D-MAPSS. Consequently, the enhanced R.sub.2R.sub.1 could compensate for the loss due to a limited spin-lock RF power, which might justify the comparable R().sub.2.sup.a and R.sub.2R.sub.1 observed for some subjects in the current study.

    [0069] The derived R().sub.2.sup.a values generally agreed with the prediction in the DZ except for the first knee (S1). It was quite likely that the determined internal references for S1 in the DZ and for others in the SZ were underestimated, leading to an unexpected smaller R().sub.2.sup.a. However, when using a normalized relaxation metric in terms of zonal contrast, all systematic errors associated with the internal reference and pulse sequences became irrelevant, and the derived normalized R().sub.2.sup.a from ARCADE was significantly larger than the normalized R.sub.2R.sub.1 as predicted. Furthermore, the observed variations in both R().sub.2.sup.a and R.sub.2R.sub.1 might reflect collagen fiber unique arrangements due to the volunteers' different ages (20-52 years old), sexes (M/F), and knee health statuses (ACL repaired, asymptomatic, or symptomatic). Even though their true relaxation rates might be systematically offset, the reported significant correlations should not be impaired.

    [0070] R().sub.2.sup.a was found to be qualitatively comparable to R.sub.2R.sub.1 as shown in FIG. 3 and FIG. 5; quantitatively, both were highly correlated as demonstrated in FIG. 6 and FIG. 7, where a relatively larger R().sub.2.sup.a was detected for the majority of five deep cartilage as illustrated in FIG. 7. Additionally, the proposed method was shown providing a higher contrast R().sub.2.sup.a map with less motion artifacts. Accordingly, a significant time saving in clinical MR scans and much less efforts in the image post-processing adds a strong impetus for further validating the new method in a lager clinical study.

    [0071] Currently, it usually takes about 20 minutes to complete both R.sub.2 and R.sub.1 mapping acquisitions for just one knee. During this lengthy scan duration, patients face a notable challenge of keeping their knees still. Consequently, the motion artifacts induced during data acquisitions and later image post-processing (i.e. co-registrations) were inevitable as shown in FIG. 3c. In contrast, the proposed method depends only on one T2W 3D image acquisition that cost just 1.2 minutes in the study, thus, the potential motion artifacts were significantly reduced as demonstrated in FIG. 3d. With the proposed method, an isotropic high-resolution R().sub.2.sup.a map could be obtained, which could further improve sensitivities of the compositional MR imaging to cartilage degenerative changes.

    [0072] In articular cartilage, collagen fibers are orientated predominantly perpendicular to and parallel to cartilage surface in the deep and the superficial zones, respectively. On the contrary, collagen fibers have no preferential orientations in the transitional zone. In our subdivided superficial zone, the majority of collagen fibers was essentially located in the histologically defined transitional zone, thus, the magic angle effect was relatively small. This was the very reason why a comparatively similar anisotropic R.sub.2 values in the superficial zone in FIG. 7, and an amplified contrast within cartilage in FIG. 8 were observed.

    [0073] As demonstrated in FIG. 7, the majority (4 out 5) of whole knee averaged R().sub.2.sup.a was larger than those obtained using the conventional approach in the deep cartilage. It is worth noting that the subjects 2 and 4 (i.e. S2M47LS and S4F20LP) had either knee pain or ACL repair surgery history, whose R().sub.2.sup.a values happened to be relatively smaller in the deep cartilage. According to a recent study, R().sub.2.sup.a seems to have a best sensitivity in detecting tissue changes related to OA. To draw a meaningful conclusion, a larger sample size in measured R().sub.2.sup.a would be needed in the future investigations.

    [0074] R.sub.2 and R.sub.1 mappings are the most widespread pre-structural and compositional MR techniques in evaluating knee early cartilage degeneration in an expanding aging population and young athletes after sport injuries and surgical reconstruction. Although these advanced MR imaging techniques have been available for more than two decades, they are still not favorably accepted in the routine clinical practice due mainly to MR technical challenges. The proposed approach is basically an internal reference method; hence, all systemic errors reported in R.sub.2 and R.sub.1 mappings induced by various pulse sequence implementations on different platforms will vanish in the new method, making it a standardized R().sub.2.sup.a measurement much easier in a multi-center trial. Finally, this developed MR method to extract a meaningful relaxation metric could be applied equally to other human joint cartilage such as those in hips and elbows.

    [0075] As an internal reference method, the developed ARCADE mapping should alleviate any systematic errors known for both R.sub.2 and R.sub.1 mappings due to different pulse sequence implementations on multiple platforms, making it easier to standardize R().sub.2.sup.a measurement in a multicenter trial and be integrated in clinical studies. This new method is independent of the pulse sequence implementation as long as the image pixel intensities are spin-echo weighted, which is inherently insensitive to B.sub.0 inhomogeneity. Advanced knee coil provides an excellent B.sub.1 homogeneity, with less than 5% variations in flip angle reported across the cartilage regions of interest in the sagittal plane. Therefore, ARCADE could be reasonably considered to be insensitive to both B.sub.0 and B.sub.1 inhomogeneities. In short, an isotropic high-resolution 3D morphological and more relevant and sensitive R().sub.2.sup.a relaxation metric imaging could be fore-seen with a single scan in a clinical setting for both knee and other joints

    [0076] With reference to FIG. 9, an exemplary system for implementing the blocks of the method and apparatus includes a general-purpose computing device in the form of a computer 12. Components of computer 12 may include, but are not limited to, a processing unit 14 and a system memory 16. The computer 12 may operate in a networked environment using logical connections to one or more remote computers, such as remote computers 70-1, 70-2, . . . 70-n, via a local area network (LAN) 72 and/or a wide area network (WAN) 73 via a modem or other network interface 75. These remote computers 70 may include other computers like computer 12, but in some examples, these remote computers 70 include one or more of (i) a medical imaging system, such as magnetic resonance imaging (MRI) device, (ii) a signal records database systems, (iii) a scanner, and/or (v) a signal filtering system.

    [0077] In the illustrated example, the computer 12 is connected to a medical imaging system 70-1. The medical imaging system 70-1 may be a stand-alone system capable of performing imaging of molecules, such as water, in biological tissue for in vivo examination. The system 70-1 may have resolution of such biological features as fibers, membranes, micromolecules, etc., wherein the image data can reveal microscopic details about biological tissue architecture, in a normal state or diseased state.

    [0078] Computer 12 typically includes a variety of computer readable media that may be any available media that may be accessed by computer 12 and includes both volatile and nonvolatile media, removable and non-removable media. The system memory 16 includes computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM) and random access memory (RAM). The ROM may include a basic input/output system (BIOS). RAM typically contains data and/or program modules that include operating system 20, application programs 22, other program modules 24, and program data 26. The computer 12 may also include other removable/non-removable, volatile/nonvolatile computer storage media such as a hard disk drive, a magnetic disk drive that reads from or writes to a magnetic disk, and an optical disk drive that reads from or writes to an optical disk.

    [0079] A user may enter commands and information into the computer 12 through input devices such as a keyboard 30 and pointing device 32, commonly referred to as a mouse, trackball or touch pad. Other input devices (not illustrated) may include a microphone, joystick, game pad, satellite dish, scanner, or the like. These and other input devices are often connected to the processing unit 14 through a user input interface 35 that is coupled to a system bus, but may be connected by other interface and bus structures, such as a parallel port, game port or a universal serial bus (USB). A monitor 40 or other type of display device may also be connected to the processor 14 via an interface, such as a video interface 42. In addition to the monitor, computers may also include other peripheral output devices such as speakers 50 and printer 52, which may be connected through an output peripheral interface 55.

    [0080] Referring now to FIG. 10, a flow diagram of an exemplary method for measuring clinically relevant Magnetic Resonance (MR) anisotropic water proton transverse relaxation rates of cartilage in human knee and other joints is illustrated, in accordance with an embodiment. A single sagittal T2-weighted magnetic resonance image of cartilage associated with a human joint may be acquired (block 102). For example, the cartilage may be associated with a human knee joint (e.g., femoral cartilage, tibial cartilage, patellar cartilage, etc.), a human hip joint, a human elbow joint, etc. An internal reference signal in the acquired sagittal image may be measured (block 104). Generally speaking, the internal reference signal is a signal intensity (S()) from the deep femoral cartilage with its collagen fiber orientated approximately 54.7 to the main magnetic field. An anisotropic R.sub.2 relaxation rate (R().sub.2.sup.a) may be calculated (block 106) for the human knee cartilage using the following equation:


    R().sub.2.sup.a={log(S(=54.7))log(S())}/TE.

    [0081] An indication of a degeneration of the cartilage may be determined (block 108) using the calculated anisotropic R.sub.2 relaxation rates.

    [0082] While the present invention has been described with reference to specific examples, which are intended to be illustrative only and not to be limiting of the invention, it will be apparent to those of ordinary skill in the art that changes, additions and/or deletions may be made to the disclosed embodiments without departing from the spirit and scope of the invention.

    [0083] Thus, although certain apparatus constructed in accordance with the teachings of the invention have been described herein, the scope of coverage of this patent is not limited thereto. On the contrary, this patent covers all embodiments of the teachings of the invention fairly falling within the scope of the appended claims either literally or under the doctrine of equivalents.