Quantitative MRI analysis of menisci using biexponential T2* fitting with a variable echo time sequence

The goal of this study was to differentiate between normal, degenerative meniscus, and meniscal tears using monoexponentially and biexponentially calculated T2*. Meniscal disease, characterized by an altered collagen fiber matrix, might be detectable in vivo using quantitative T2* mapping.

With aging and overloading of the knee joint, the prevalence of meniscal degeneration has increased, which is characterized by the macroscopic changes in meniscal tissue. Such affected menisci become weak and substantially thinner (1). The degeneration of the meniscus is usually accompanied by weakness of the meniscal tissue, which can no longer distribute load sufficiently, and may eventually result in a meniscal tear (2). Grades of meniscal degeneration correlate with grades of articular cartilage degeneration. According to statistics, 85% of osteoarthritis (OA) patients who underwent joint replacement surgery suffer from degenerative menisci (3). Conventional morphologic MR imaging is currently the preferred imaging modality for evaluating the menisci (4). The most commonly used sequences include proton density spin echo or fast spin echo (FSE) with or without fat saturation, T 1 -weighted FSE, and gradient echo (GRE) sequences (5). Each of these techniques has a different sensitivity and specificity for the diagnosis of the grade of degeneration in menisci, which are dependent on various factors, such as observer variation or sample size (6)(7)(8). Owing to a high degree of tissue organization, the signal decay in menisci is relatively fast. Therefore, on images with longer echo times (TE), menisci usually appear dark. Ultrashort echo time sequences are useful in acquiring the fast-decaying MR signal from meniscal tissue (9,10). Sequences with radial sampling of k-space often suffer from low resolution or pixel blurring due to their sensitivity to gradient imperfections and clock-shift delays (11). The recently introduced, three-dimensional, spoiled gradient echo (SPGR) sequence with a variable echo time scheme (3D vTE Cartesian SPGR, hereafter referred to as vTE) minimizes the abovementioned issues and was shown to be useful for visualizing MSK structures with a short T 1 , within short and clinically adequate scan times (12). Collagen fibers in the human meniscus are oriented according to the region: randomly in the superficial network; radially in the lamellar layer; and circularly in the main central layer (13). As the relaxation constants, such as T 1 , T 1 *, or T 1r , reflect the collagen structure organization in the meniscus, they are regionally dependent (14)(15)(16). Quantitative analysis of the meniscus has been suggested in a few recent reports. Rauscher et al. demonstrated that T 1 and T 1r can be used in the menisci as markers of different stages of OA (15); both T 1 and T 1r increased in advanced stages of OA. Krishnan et al. studied T 1 in the presence of a gadolinium contrast agent (T 1 (Gd)), and found a relationship between T 1 (Gd) in the menisci and T 1 (Gd) in the cartilage; however, the correlation between T 1 (Gd) in the menisci and the grade of meniscal degeneration was minimal (17). Because of the complexity of the collagen matrix in meniscal tissue, it has been assumed that there are bound and free water pools, as well as a relaxation dependence on collagen fiber orientation that results in multicomponent transverse relaxation of magnetization. When calculating T 1 or T 1 * using a simple monoexponential fitting, the results may be remarkably underestimated, particularly in the areas with clear bi-component decay. To the best of our knowledge, there is no study that has comprehensively discussed the multiple compartment T 1 * mapping of the human menisci in vivo.
Therefore, the aim of this study was to compare the ability of monoexponentially and biexponentially calculated T 2 * to differentiate between normal, degenerative meniscus, and meniscal tears. For this purpose, a novel 3D vTE Cartesian SPGR sequence, with sequentially shifted echo times, was used to optimize T2* sampling in order to offer more accurate quantification of relaxation times. As meniscal disease is characterized by an altered collagen matrix, these alterations might be detectable in vivo using quantitative T 2 * mapping. The regional dependence of monoexponential and biexponential T 2 * decay was studied as well.

Subjects
The local ethics commission approved this study, and all volunteers and patients gave written, informed consent. Seventeen subjects enrolled in this study (eight males, 34 6 10 years; and nine females, 36 6 14 years), all of who underwent a regular check-up that included an MRI examination. Eight patients underwent Matrix Associated Autologous Chondrocyte Transplantation, one of which after a Microfracture procedure, and nine subjects received MRI because of persistent knee pain. The inclusion criteria for all subjects were no contraindications to MR imaging, such as electronically, magnetically, and mechanically activated implants, insulin pumps, nerve stimulators, pregnancy, claustrophobia, and tattoos. Patients with cartilage repair were included since it is well known that full thickness cartilage defects, particularly in the weight-bearing zone, is a risk factor for the development of meniscal lesions (18,19).

MR Imaging
All MRI examinations were performed on a 3T MR system (Tim Trio, Siemens Healthcare, Erlangen, Germany) with an eight-channel knee coil (In vivo, Gainesville, FL). A custom 3D Cartesian SPGR technique was adapted to enable the use of a vTE approach in combination with an asymmetric readout (12). This sequence enables the use of the minimal effective echo time below 1 ms that is necessary for multicomponent T 1 * analysis. In addition, the sequence was adapted with sequentially shifted echo times in order to achieve better sampling of the signal decay (20).
The vTE sequence was applied with 10 echoes: TE ¼ For morphologic examination, a set of three sequences was used: fat-suppressed proton-density-weighted SPACE in the sagittal plane; PD turbo-spin echo in the coronal plane; and T 2 -weighted turbo-spin echo in the sagittal plane. The sequence parameters are summarized in Table 1.

Image Analysis
Images from the vTE sequence were analyzed using a custom-written script in IDL 6.3 (Interactive Data Language, Research Systems, Inc, Boulder, CO, USA). A monoexponential as well as a biexponential fitting procedure was employed on all MR data sets on a pixel-bypixel basis. For monoexponential fitting, a three-parametric function was used to fit the signal intensity where A 0 is the signal intensity at a TE of $ 0 ms, A 1 corresponds to the actual T 2 * m (monoexponentially calculated T 2 *), and A 2 is the baseline (mostly the noise).
The same dataset was also processed biexponentially, using the function PD-SPACE, fat-suppressed proton-density-weighted SPACE in the sagittal plane; PD-TSE, proton-density turbo-spin echo in the coronal plane; T 2 -TSE, T 2 -weighted turbo-spin echo in the axial plane; TE, echo time; TR, repetition time; FOV, field of view; PAT, parallel acquisition technique; GRAPPA, parallel acquisition techniques generalized autocalibrating partially parallel acquisitions.
where B 1 corresponds to the short component of T 2 * (T 2 * s ), B 3 corresponds to the long component of T 2 * (T 2 * l ), and B 0 and B 2 are the component ratios expressed further as a percentage value of . B 4 is the offset given primarily by noise. During the calculation of T 2 *, only those pixels that satisfied the following condition were considered biexponential: Seven maps for each slice were stored for future use, i.e., the monoexponential T 2 * maps, the short component of biexponential T 2 * maps, the long component of biexponential T 2 * maps, and both short and long T 2 * component ratios. The map of the coefficient of determination (R 2 , goodness of fit) and the binary map based on the biexponential condition (Eq.[3]) (0 ¼ monoexponential decay, 1 ¼ biexponential decay) were saved as well.
On each subject's knee, four different menisci areas were segmented: the anterior and posterior horn of the lateral meniscus, and the anterior and posterior horn of the medial meniscus. Regions of interest were defined on five consecutive slices by an orthopedic surgeon with 10 years of experience (S.A.). Each meniscal part was further subdivided into two regions, a red and a white zone so that 30% of the radial dimension of each horn, from its free edge to its peripheral border, was considered the red zone and 70% the white zone (13,24). An example of the meniscal segmentation is depicted in Figure 1.
Each ROI was represented by a weighted mean value, calculated using an R 2 correction algorithm (25). T 2 * s and T 2 * l were calculated using a mask created from a binary map, and only pixels where the condition 4 Â T 2 * s < T 2 * l was satisfied, were included. From each segment, the ratio of monoexponential and biexponential pixel amounts was calculated (further referred to as M/B).

Intraobserver and Interobserver Variation
To calculate the interobserver variability, 10 patients were evaluated by three independent raters (S.A., V.J., P.S.). The variation between raters was expressed as a coefficient of variation (CV, %). Intraobserver variability was calculated from three independent evaluations of 10 patients by one rater (V.J) with a delay of one week between the evaluations and expressed as an intraclass correlation (ICC).

Statistical Analysis
All statistical calculations were performed using SPSS 19.0 and the package pROC version 1.5.4 of R (R Core Team, 2012). Descriptive statistics were performed in order to calculate the mean and standard deviation (SD) of age, T 1 * m , T 1 * s , T 1 * l , component ratios, and M/B values separately for normal, degenerative, and torn menisci. In order to compare average T 1 * m , T 1 * s , T 1 * l , and M/B of different meniscal parts (anterior/posterior, medial/lateral, healthy/degenerated/tear) a hierarchical linear model (HLM) was used in order to consider multiple measures per patient. In addition, ROC analyses were performed to compare healthy with combined degenerated and torn meniscal parts. A p value equal to or below 0.05 was considered to indicate significant results. A binary classification test was performed on the data to obtain the discrimination power using ROC analyses. ROC curves were constructed by plotting the fraction of true positives from the positives (true positive rate) versus the fraction of false-positives from the negatives (false-positive rate), at various threshold settings for each of the parameters (T 1 * m , T 1 * s , T 1 * l , and M/B). The area under the curve (AUC) was calculated by using the trapezoidal rule, which was expressed in percentages and graded in five groups: 0.9-1.0 ¼ excellent; 0.8-0.9 ¼ good; 0.7-0.8 ¼ fair; 0.6-0.7 ¼ poor; and 0.5-0.6 ¼ failed.

RESULTS
The CV for interobserver variation was found to be 9.1%, on average. For different menisci segments, the CV was 9.5% for the red zone of the anterior horn, 7.9% for the white zone of the anterior horn, 10.8% for the white zone of the posterior horn, and 8.2% for the red zone of the posterior horn, separately, and 8.0% for the whole white zone and 10.16% for the whole red zone. Intraobserver variation was expressed using ICC and found to be 0.9, on average. For different segments, the ICC was 0.847 for the red zone of the anterior horn, 0.945 for the white zone of the anterior horn, 0.925 for the white zone of the posterior horn, and 0.874 for the red zone of the posterior horn, separately, and 0.935 for the whole white zone and 0.861 for the whole red zone.
The mean and SD for the pixel count were as follows: in the anterior horn, 17 6 4 (red zone); in the white zone, From a total of 68 evaluated menisci segments, 48 were graded as normal, 12 as degenerated, and eight as torn. Six patients underwent a surgical procedure after the MR examination. One normal meniscus, one degenerated meniscus, and four meniscal tears were confirmed by a surgeon through visual examination to be in agreement with the results of the MRI evaluation. Examples of T 2 * maps for a degenerative meniscus and a meniscal tear are depicted in Figures 2 and 3. The results from descriptive statistics for all relaxation parameters are summarized in Table 2 and in a set of box-plots in Figure 4. When considering the red and white zones of the menisci separately, from 48 cases of normal menisci, the mean and SD of T 2 * m was 7.89 6 1.25 ms in the white zone, and 10.49 6 3.26 ms in the red zone. This difference was statistically significant (P ¼ 0.026, 95% CI À4.25 to À0.27). As for the results of biexponential analysis, the difference between the red and white zones was statistically significant only for the M/B ratio (P ¼ 0.017, 95% CI 0.55-3.49). The results for different segments of menisci with different grades are summarized in Table 3.
Mean values of T 2 * s and T 2 * l were as follows: in normal menisci 0.82 6 0.38 ms and 15.0 6 5.4 ms, respectively; in degenerated menisci 1.29 6 0.53 ms and 19.97 6 5.59 ms, respectively; and in meniscal tears 2.05 6 0.73 ms and 26.83 6 7.72 ms, respectively. Monoexponential fitting provided the following results: 7.61 6 2.49 ms, 9.54 6 2.25 ms, and 14.59 6 5.24 ms, in normal, degenerative, and meniscal tears, respectively. The t-test showed significant differences between both mono and biexponentially calculated T 2 * in various menisci conditions. However, the p-values were much lower for the short and long T 2 * components compared to monoexponential T 2 * results. The p-values of T 2 * m and the M/B ratio were similar. All p-values are summarized in Table 4. When comparing the medial and lateral menisci, no statistical difference was found in either parameter, and, for the anterior versus posterior horns, the only difference in means was found in the M/B ratio (Fig. 5).
The ROC analysis showed mostly fair to good diagnostic value for both the short and long components, as well as for the mono-/bi-ratio value. Table 5 lists the summary of areas under curve for individual parameters. Regarding the differences between the AUC of individual parameters, no statistically significant difference was observed: AUC(M/B) versus AUC(T 2 * s ) p¼0.4192; AUC(M/B) versus AUC(T 2 * l ) p¼0.8053; and AUC(T 2 * s ) versus AUC(T 2 * m ); p¼0.5903.

DISCUSSION
Here, we propose a technique for in vivo, quantitative, bi-component T 1 * analysis of the human meniscus based on a 3D vTE Cartesian SPGR sequence with sequentially shifted echo times. The results of this study showed that biexponential analysis of the human meniscus in vivo may better distinguish between normal and degenerative menisci, as well as meniscal tears, compared to uncorrected, monoexponential decay. These differences most likely reflect the compositional alteration of the collagen matrix, which is most pronounced in meniscal tears, but is also present in degenerative menisci. Three layers have been described in the meniscus by electron microscopy imaging: the superficial layer; the lamellar layer; and the central main layer (26). However, with the current set-up, we were unable to distinguish between these zones. Meniscal tissue tears occur along the circular main course of the collagen fibrils in the majority of meniscus lesions (horizontal tear, longitudinal tear, bucket-handle tear) (26). It is important to distinguish between degenerative and traumatic tears (1). There is a strong relationship between meniscal damage, degenerative tears, and cartilage loss (27). However, in this study, we did not look at the relationship between cartilage state and meniscus impairment.
Transversal relaxation time (T 2 ), as well as T 2 that includes magnetic field inhomogeneities (T 2 *), are sensitive to the macromolecular content in tissue, especially glycosaminoglycans and collagen fibers, as has been shown in cartilage studies (14,28). Collagen orientation and anisotropy primarily define the absolute values of T 2 in meniscus (29) and cartilage (30). Higher collagen content and the greater organization of the collagen fiber network in menisci result in substantially shorter transversal relaxation times compared to articular hyaline cartilage.
To the best of our knowledge, meniscal degeneration was previously studied using quantitative MR imaging by only a few groups. Williams and colleagues studied monoexponential T 2 *, measured by UTE, as a potential marker for degenerative menisci (31). They observed significantly lower T 2 * values in asymptomatic volunteers (9.8 ms) than in patients with meniscal degeneration (18.3 ms). T 2 * also correlated strongly with the degree of joint pathology. Rauscher and colleagues successfully used T 2 as a marker for detecting early OA stages through meniscal matrix analysis, and also showed that T 2 relaxation times in menisci correlate with the morphologic score of cartilage in OA (15). In the same study, it was shown that T 1 relaxation time in a rotating frame (T 1r ) also has the potential to be used as a marker for distinguishing between healthy and degenerated menisci. The differences in T 2 relaxation times between young male and female volunteers were studied by Tsai et al. (32). They found a statistically significant difference in T 2 values between males and females in the red and white zones; the T 2 values were significantly lower in men than in women (mean difference, 1.320 and 0.865 ms; P ¼ 0.002 and P < 0.001, respectively). They attributed these differences to the sex differences in the occurrence of knee OA. Recently, an initial attempt to analyze the menisci using a biexponential fitting procedure was performed in an in vitro porcine model (33). In contrast to the current study, high-resolution MR images were used because of the microimaging capabilities (resolution of 0.27 mm per pixel), which enabled visualization of the laminar structure of meniscal tissue. It was postulated that the transfer to in vivo conditions might be limited, to some extent. However, the SPGR-based vTE sequence used in this study allowed the acquisition of images with relatively high resolution (0.47 Â 1.02 mm/px), and in reasonable scan times. The selection of TE range is critical for biexponential fitting. Acquired TEs should be, at best, more dense in the first quarter of the fitting curve to allow the fitting algorithm to calculate the short T 2 * component precisely enough, and to distinguish T 2 * s from T 2 * l .
The CV between observers was quite low in this study (7.5%); this is probably due to the excellent contrast between menisci and surrounding tissues. For the same reason, the intraobserver variation (ICC ¼ 0.92) was also very low. The high reproducibility can be attributed to the SPGR-vTE sequence, which allows subtracting very short TE images (0.75 ms) from those measured with conventional TEs, resulting in an optimal contrast created by short T 2 tissues (34,35).
Compared to conventional radial 3D-UTE sequences, the vTE sequence has the advantage of the intrinsic robustness of Cartesian sampling methods, and allows high-resolution imaging within reasonable scan times (20). This sequence also enables the use of common acceleration methods, such as partial Fourier or parallel imaging techniques. It also allows measurements in offcenter conditions or with nonisotropic voxel sizes.
The receiver operating characteristic analysis in this study suggested a relatively high specificity and sensitivity for this method. The area under curve for T 2 * s was similar to that of T 2 * m ; however, the sensitivity and specificity was higher for T 2 * s compared to T 2 * m (93 and 77% versus 80 and 79%, respectively). Regarding the threshold for distinguishing between normal and degenerative menisci, or tears, neither of the investigated  FIG. 5. The difference between the T 2 * s , T 2 * l , T 2 * m , and M/B ratio in the medial versus lateral menisci and the anterior versus posterior horns in all subjects. The asterisk represents statistical significance (P < 0.05).
parameters was able to accomplish this. However, when degenerative menisci and meniscal tears were pooled, it was possible to determine the thresholds.
The higher variability of all parameters (T 2 * m , T 2 * l , T 2 * m and M/B) in normal menisci compared to degenerative menisci and meniscal tears can be attributed to the higher number of cases of normal menisci (48) compared to 12 degenerative menisci and eight tears; thus, the likelihood of outliers is much higher. However, all data had a normal distribution.
Our study has several limitations. First, there was a small number of patients and, in addition, the group of patients was not distributed equally. Second, the 'magic angle effect' can influence T 2 * values due to the minimization of the dipolar interactions of fiber orientation with respect to B 0 (36)(37)(38). To minimize the 'magic angle effect,' the ROIs in this study were defined through five consecutive slices in the anterior and posterior horn separately. We believe that the menisci segmentation used in this study was sufficient for evaluating meniscal degeneration and meniscal tears without significant influence from the 'magic angle effect. ' Third, no histologic assessment was performed in order to confirm the MRI findings. The diagnosis relied fully on the evaluation of morphologic MRI. Only six subjects underwent a surgical procedure in which the problematic menisci were visually confirmed. Histologic evaluations would improve the validity of lesion confirmation, but, MRI is already a fully established modality for the diagnosis of meniscal problems (39-41) even with the known limitations, such as the fact that not every intrameniscal signal seen on MRI represents meniscal degeneration. Also, the pathology at the body of the meniscus was not covered in this study.
Some bias may have also been introduced by choosing the biexponential condition to 4 Â T 2 * s < T 2 * l , which was based on empiric findings. This choice seemed to best fit the mathematical model of biexponential fitting at the noise level observed in this study; however, no thorough simulations were performed to validate this.
Another complication may have been introduced by local B 0 inhomogeneities, which might have affected T 2 * estimation. Although several methods for static magnetic field have been developed (42)(43)(44), we did not perform B 0 mapping in this study. However, we know from our previous experience with our MR scanner that there are no substantial B 0 fluctuations other than those caused by anisotropy of the tissue.

CONCLUSION
In conclusion, the results of this study suggest that a biexponential analysis of meniscal tissue is more robust than a monoexponential approach. The short component of T 1 * better reflects the anisotropy of collagen fibers and the change in degeneration processes that may result in meniscal tear.