Impact of pulse sequence, analysis method, and signal to noise ratio on the accuracy of intervertebral disc T2 measurement

Abstract Noninvasive assessments of intervertebral disc health and degeneration are critical for addressing disc degeneration and low back pain. Magnetic resonance imaging (MRI) is exceptionally sensitive to tissue with high water content, and measurement of the MR transverse relaxation time, T 2, has been applied as a quantitative, continuous, and objective measure of disc degeneration that is linked to the water and matrix composition of the disc. However, T 2 measurement is susceptible to inaccuracies due to Rician noise, T 1 contamination, and stimulated echo effects. These error generators can all be controlled for with proper data collection and fitting methods. The objective of this study was to identify sequence parameters to appropriately acquire MR data and to establish curve fitting methods to accurately calculate disc T 2 in the presence of noise by correcting for Rician noise. To do so, we compared T 2 calculated from the typical monoexponential (MONO) fits and noise corrected exponential (NCEXP) fits. We examined how the selected sequence parameters altered the calculated T 2 in silico and in vivo. Typical MONO fits were frequently poor due to Rician noise, and NCEXP fits were more likely to provide accurate T 2 calculations. NCEXP is particularly less biased and less uncertain at low SNR. This study showed that the NCEXP using sequences with data from 20 echoes out to echo times of ~300 ms is the best method for calculating T 2 of discs. By acquiring signal data out to longer echo times and accounting for Rician noise, the curve fitting is more robust in calculating T 2 despite the noise in the data. This is particularly important when considering degenerate discs or AF tissue because the SNR of these regions is lower.

from T 2 -weighted (T 2 w) images. The contrast provided by T 2 w MRI is particularly well-suited for structural evaluation because it provides contrast between a bright nucleus pulposus (NP), a dark annulus fibrosus (AF), and a dark vertebral body at the inferior and superior boundaries of the disc. In the Pfirrmann grading scheme and others, structural features are evaluated and graded based on NP brightness and uniformity, NP-AF distinction, and disc height. 1 Unfortunately, such evaluation is highly subjective and is nonquantitative in terms of degree of pathology. Further, the phenotypes of human disc degeneration are a continuum that are too complex to be categorized by the five Pfirrmann grades. For these reasons, measurement of the MR transverse relaxation time, T 2 , has been proposed and applied as a quantitative, continuous, and objective measure of disc degeneration that is linked to the water and matrix composition of the disc. T 2 is defined as the time constant of the decay, or relaxation, of the transverse signal and is calculated from a series of T 2 w images. 2,3 T 2 is longer in healthy discs, which have higher water content and water mobility, and decreases as the disc degrades and loses proteoglycan and water content.
T 2 measurement is becoming more widely used as a measure of disc degeneration, [4][5][6][7][8][9][10][11][12][13][14][15] however, there are limitations in its application that can make comparisons across studies problematic and, in the Sequence parameters used to acquire data for T 2 calculations shown in Figure 1 Citation Recommended from present study ≥3000 ≥300 Note: There is a large range of sequence parameters used, which lead to wide variations in reported T 2 .
F I G U R E 1 Reported T 2 for healthy discs from volunteers without back pain. Despite sampling a similar population, reported mean T 2 vary by up to a factor of two across studies, ranging from a mean of 76 to 149 ms. Dots and bars represent mean +/− SD worst case, provide inaccurate T 2 values. First, a wide variety of MR sequences and calculation methods have been implemented, leading to a large range of reported average T 2 from 75 to 150 ms for similar populations of young, healthy, nondegenerative discs (Table 1, Figure 1). This is likely due in large part to the variability in the sequence parameters (TR, TE, and number of echoes) which are sometimes outside the recommended range based on disc material parameters (T 1 and T 2 ), as described in the next section. In addition, greater accuracy is often obtained by excluding the first echo in data fits, 16 as seen in some cartilage studies. 17 The first echo is excluded because it is the only data point for which the phenomenon of stimulated echoes does not occur, and therefore it follows a different decay than the subsequent data points 16,18 (Figure 2A). It is assumed that most published work has excluded this first echo, but it is not always explicitly stated and researchers new to the field may not be aware of this limitation, which is ultimately based on the unavoidable inhomogeneity of RF pulse amplitude throughout the sample. Finally, MR imaging is susceptible to noise that can corrupt fits of the T 2 decay curve. Notably, Rician noise results in an altered signal decay curve that decays to a nonzero value called the "noise floor" (Figure 2A) We also evaluated how T 2 is affected by performing fits of intensity data averaged over a region-of-interest (ROI) to suppress noise vs performing fits at each individual voxel. Based on these results, we recommend methods to select sequence parameters and to calculate T 2 for the disc to address the effect of Rician noise and the low signal intensity at long echo times, particularly for the degenerating disc.

| THEORY
Determining T 2 requires a longer and more complex imaging sequence than acquisition of the single T 2 w image that is used for grading. However, the advantage of this sequence is that it gives quantitative material property information that is less susceptible than single T 2 w signal intensity to environmental factors, scanner strength, magnetic field inhomogeneities, and subject traits such as body weight. The signal intensity in each voxel in a conventional MR image is often modeled as where the repetition time, TR, is the time between individual spin excitation pulses, and the echo time, TE, is the time of echo occurrence after the initial excitation pulse. TR and TE are user-defined input parameters, while the T 1 and T 2 relaxation times are material The TR selected for the sequence is the dominant determinant of the total scan time. In T 2 w MRI, TR is often selected to minimize T 1 weighting in the acquired signal (i.e., with TR satisfying e −TR = T1 ! 0), so that residual image intensity weighting is primarily dependent on T 2 , or more precisely, on the ratio TE/T 2 . Ideally, TR would be ≥ T 1 *5 in order to achieve <1% T 1 weighting, however since disc T 1 is approximately 1200 ms, 23 this would lead to very lengthy scans. Thus, the selection of TR is a compromise between scan duration and the desired limit e − TR = T1 ! 0.
The echo time in Equation (1), TE, defines the delay between an initial excitation pulse and signal acquisition at the peak of the subsequent echo, with a refocusing pulse applied between these at a time where M is the measured signal intensity, S is the signal intensity without noise, σ is the SD of the Gaussian noise in the real and imaginary components, and I 0 is the modified zeroth order Bessel function of the first kind. 24 A key characteristic of the Rician distribution is that at high SNR it approximates a Gaussian distribution. However, when the SNR is low, the noise associated with the signal is no longer Gaussian because taking the magnitude of real and imaginary components is a nonlinear function. At the extreme of SNR = 0 (no tissue signal, only noise signal) the measured MR signal takes on a nonzero mean value (Rayleigh distribution) that we call the noise floor (dashed line in Figure 2A). 20,24 This phenomenon was previously studied with simulation and articular cartilage samples using a noise corrected exponential (NCEXP) that fit the signal while incorporating the expected value of the Rician noise, thereby more accurately determining T 2. 19 The expected noise corrected signal intensity is given by where α = S = 2σ ð Þ 2 , and I 1 is the modified first order Bessel function of the first kind.

| Simulation of Rician noise and dependence on SNR
We first confirmed that simulated Rician noise recapitulated the noise floor observed in the disc ( Figure 2A) and that we could model the signal intensity of the noise floor as a function of the SNR.
Using MATLAB (MathWorks), an ideal monoexponential decay was generated with an initial signal of 600 (S 0 ) and T 2 of 80 ms.

S TE
Rician noise was simulated by adding Gaussian noise to both the real and imaginary components of the ideal monoexponential decay.
The resulting signal intensity, calculated as the magnitude of the real and imaginary components, was averaged for 100 simulated voxels to mimic the size of an ROI in an in vivo measurement. The σ of the Gaussian noise was given by S 0 /SNR, and this simulation was repeated for SNR ranging from 5 to 60. The resulting signal was plotted over time (every 10 ms out to 1000 ms, that is, TE = 10 ms with 100 echoes) and compared qualitatively to the observed signal intensity decay and noise floor from an in vivo disc ( Figure 2A).
The noise floor of the simulated signal was calculated as the average signal of the last 50 points for each simulated SNR ( Figure 2B).
These values were then plotted as a function of SNR for the 5 SNR values used ( Figure 2C, circles). The expected relationship between noise floor and SNR (mean of Rayleigh distribution) is also plotted ( Figure 2C, curve), based on the following equation where the initial signal, S 0 , was equal to 600.
Our simulation of Rician noise as a function of SNR confirms b the noise floor observed in the disc (Figure 2A,B) and the expected noise floor as derived from MR physics ( Figure 2C). The signal intensity with simulated Rician noise (Gaussian noise applied to the real and imaginary components) demonstrated a nonzero noise floor that depends on the SNR ( Figure 2B) and is consistent with in vivo disc imaging data ( Figure 2A). The signal intensity of the noise floor is greater with a low SNR of 5 and is negligible with a high SNR of 60 ( Figure 2B). Moreover, when the noise floors of the simulated signal intensity values are compared to the curve of the expected noise floor, a perfect overlap is observed that demonstrates the accuracy of our Rician noise simulation ( Figure 2C).

| Simulation of T 2 sensitivity to fitting model and number of echoes
Signal intensity data with simulated noise was used to demonstrate the sensitivity of the calculated T 2 to (a) the degree of noise (low vs high SNR), (b) the model used to calculate T 2 (monoexponential or noise corrected exponential), and (c) the effect of the number of echoes in the dataset (simulating the number of TE chosen for the MR sequence during data acquisition). Data were simulated using physiological T 2 for an unhealthy disc (T 2 = 80 ms) and TE = 13.6 ms with 20 echoes out to 272 ms to reflect typical MR data acquisition. Low and high SNR data were both simulated (SNR = 5 and 30) using the definition SNR = S0 = σ . For each SNR, 100 voxels of signal intensity data were simulated, to represent an ROI, and these signal intensities were averaged and plotted against time to be used for curve fitting to calculate T 2 .
T 2 was then calculated using two different curve fits: typical mono-exponential (MONO) and noise corrected exponential (NCEXP). 19 As described previously, MONO represents the decay to zero which is typically used in the field, and NCEXP represents the TR was selected to minimize the contribution of T 1 in the measured signal (see Section 2 23 ) and 20 echoes were acquired to obtain several data points for evaluating model fits. Scan time was 14:29 minutes.
Image analysis was performed with an in-house code by first creating a circular ROI in the middle of the NP and calculating the average signal intensity in the ROI for each echo, analogous to simulations above. The ROI included 80 to 120 voxels, depending on disc size.
Curve fits were then performed on these average intensities to find T 2 . The first echo was excluded for curve fitting. 16 Signal intensity data were fit using two different models (monoexponential and noise corrected exponential) and two different num- Results were tested for normality using a Jarque-Bera test, and failed to reject the null hypothesis that the data was normally distributed. 25 To test for the effect of curve fit on the calculated T 2 , a 2-way ANOVA was run followed by post-hoc matched pair t-tests between all pairings with a significance level set at alpha = 0.05.
Representative data for a Pfirrmann grade IV disc is plotted vs time with fits for MONO and NCEXP curves with 6 or 20 echoes and their respective T 2 ( Figure 4A). The dashed vertical line represents the last echo in the fit for the MONO6 and NCEXP6 curve fits (the first echo is not shown). As with the simulated data, the MONO20 curve fit overestimates T 2 (124 ms) and the fit is not very strong (MSE = 521). (MSE = 20) meaning it does not accurately describe the full data. This is to be expected as the MONO6 fit only uses the first six echoes and assumes that the signal will decay monoexponentially to zero. The NCEXP6 T 2 is slightly lower than NCEXP20 and MONO6 (58 ms), and while the NCEXP6 fit is good for 6 echoes (MSE = 17), it does not fit the whole data set (MSE = 208) as well as NCEXP20.
When comparing the 4 different calculation methods across all 40 discs ( Figure 4B), the same pattern emerges as with the representative disc ( Figure 4A).  Figure 4B). This finding is the same when the discs are separated into nondegenerate (n = 35, Figure 4C) and degenerate (n = 5, Figure 4D) discs. The error introduced by using the MONO20 fit in healthy discs is approximately 20 ms compared to NCEXP20, while in the degenerate discs the difference is much larger at approximately 40 ms. It should be noted that NCEXP20 predicted an average SNR of 10.07 (min 4.65, max 29.26) across all 40 discs, as calculated from the fitting parameters using SNR = S0 = σ .

| Accuracy of MONO6 and NCEXP20
To determine which fitting method was most accurate, simulations were performed to find the bias and uncertainty from MONO6 and NCEXP20 curve fitting methods. The MONO20 and NCEXP6 fitting methods were omitted from the bias and uncertainty analysis as they were found to be inferior to MONO6 and NCEXP20 fitting methods in the preceding analysis (see Section 3.3). Signal data was simulated F I G U R E 4 A, Representative dataset for a degenerated disc showing all four curve fitting methods. Vertical dashed line represents the last echo used for fitting for MONO6 and NCEXP6 fits (first echo is ignored and not shown) and the rest of the curve is extrapolated. NCEXP fits look better than MONO fits. NCEXP20 and MONO6 give very similar T 2 , but MONO6 is a bad fit. B-D, calculated T 2 for, B, all discs (n = 40), C, healthy discs (n = 35), and D, degenerate discs (n = 5). MONO20 is higher than other measures and likely overestimated because of the noise floor. NCEXP6 is lower than others and likely underestimated because of insufficient data points to predict the noise floor. For all cases MONO6 and NCEXP20 are not different from each other even though the fits for MONO6 are not as strong as those for NCEXP20. Boxes represent median, 25th, and 75th percentiles. Whiskers extend to most extreme data point that is not considered an outlier (+ symbol) to find the bias and uncertainty of the MONO6 and NCEXP20 curve fits over the SNR range from 5 to 40 (steps by 5) and T 2 range from 50 to 200 ms (steps by 10 ms), for 128 combinations of SNR and T 2 .
Each combination of SNR and T 2 was simulated 100 times (representing 100 voxels), and the MONO and NCEXP fits performed to find T 2 for each simulated voxel. The percent error of each calculated T 2 was then found as Calculated T2 − Expected T2 j j Expected T2 × 100 , and the percent errors were averaged across simulations for every combination of SNR and T 2 . The bias was defined as the average percent error of the 100 voxels for each combo of SNR and T 2 . The uncertainty was defined as the SD of the percent error of the 100 voxels. Heatmaps were generated from bias and uncertainty data using MATLAB's contourf function. Zero bias or uncertainty was mapped to white, while 50% error was mapped to red, meaning that areas of white indicated an accurate T 2 calculation while areas of red indicated poor accuracy.
Although true T 2 values are not available in vivo so error cannot be determined, resultant T 2 maps were calculated for each fitting method for the entire disc to compare the heterogeneity of the methods. To do this, the entire disc region was defined in MATLAB using the polygon tool, then signal data across echoes for every voxel inside the ROI was curve fit individually with the MONO6 and NCEXP20 methods. From the resulting T 2 values, maps were made such that each voxel was assigned a color based on a jet colormap with a range of T 2 values from 0 to 250 ms (black/dark blue indicated low T 2 and red indicated high T 2 ). These maps were overlaid on the black and white T 2 w MR images to visualize T 2 and its heterogeneity from MONO6 and NCEXP20 fit methods.
MONO6 has higher bias and uncertainty than NCEXP20, particularly at low SNR ( Figure 5). The two methods are similar when SNR is greater than 40, but NCEXP20 is still superior. Considering typical disc values, SNR of 10 and T 2 of 130 ms, MONO6 has a bias of 125% while NCEXP20 has a bias of 13.4%. NCEXP20 has a maximum bias of 24.8% at T 2 of 50 ms. Further at SNR of 10, MONO6 bias is >50% error for all but three T 2 values and >100% error for most T 2 . Even at SNR of 20, MONO6 exhibits a bias >20% error in half of the T 2 , while NCEXP20 has a maximum of 10.1% error. Uncertainty follows the same pattern where MONO6 has much higher maximum uncertainty at low SNR ( Figure 5). Overall, NCEXP20 is a more precise and accurate method.
F I G U R E 5 Heatmaps of bias (left) and uncertainty (right) in calculated T 2 for MONO6 (top) and NCEXP20 (bottom) using simulated Rician noise. NCEXP20 has lower bias and uncertainty compared to MONO6, making it a more robust calculation method for finding accurate T 2 T 2 maps of full discs allowed visualization of variance of T 2 across the disc ( Figure 6). Fits obtained with NCEXP20 display less random variation than those obtained using MONO6. Fitting each voxel with MONO6 shows areas of overestimated T 2 , likely outliers, as can be seen by dark red voxels near the edges of the disc and in the NP.
These were more frequent in MONO6 fits. MONO6 is much more susceptible to voxels becoming very overestimated or biased, particularly in areas of low signal at the disc edge, but also in the NP. The overall T 2 averaged for all voxels in the disc are impacted by fitting methods. In the healthy disc, where there are larger differences, MONO6 calculates a T 2 of 3547 vs 84 ms for NCEXP20. In the degenerate disc, MONO6 calculates a T 2 of 53 vs 52 ms for NCEXP20. When using the ROI of the NP, the calculated T 2 are more similar. In the healthy disc, MONO6 calculates a T 2 of 155 vs 147 ms with NCEXP20, and in the degenerate disc both curve fits calculate a T 2 of 80 ms. This is likely because the NP has higher SNR compared to the AF and disc edge regions, so there is less bias and fewer outliers. The higher bias in MONO6 at low SNR likely drives the differences between MONO6 and NCEXP20 and results in inaccurate overestimation of T 2 .

| Comparison of average intensity of ROI vs voxel calculation methods
We also determined if there is a difference between calculated T 2 when first averaging the signal in the ROI and performing a single curve fit to obtain disc T 2 vs performing the curve fit to the signal in each voxel individually and then averaging the T 2 of each within an ROI to obtain disc T 2 . ROI results using NCEXP20 curve fitting were taken from section 3.3 and voxel-wise maps were generated as described in section 3.4. The same circular ROI used in the ROI method in the NP was applied to the disc map from the previous section, and the average T 2 of all voxels inside the ROI was calculated.
The resulting distributions of T 2 from all 40 discs were compared with a paired t test, and a histogram of the differences between ROI calculation methods was generated as ROI T 2 -voxel-wise T 2 .
The two methods give very similar results with an average absolute difference of 3.54 ms and average percent difference of 2.77% (p > .05, Figure 7A). Of the 40 discs investigated, only two discs exhibited a difference between methods of more than 10 ms (11.19 and 30.23, both Grade I, Figure 7B). The average absolute differences are within the range of standard deviations of reported T 2 . Although voxel methods require much more computation time and single voxels may create outliers (Figure 6), both methods should be assumed to be accurate when SNR is reasonable. However, care may need to be taken when the ROI has a small number of voxels or contains very low SNR regions that may create outliers that may skew the data. Of note, the fit for the voxel method required 60 to 300 seconds depending on ROI size, while a single fit for the ROI method takes less than 5 seconds.

| DISCUSSION
This study showed that using the noise corrected exponential (NCEXP) to fit data from 20 echoes out to $300 ms is the best method for calculating T 2 of discs because it is the least likely to be biased by low SNR. By acquiring data out to longer echo times and accounting for Rician noise, the curve fitting is more robust in calculating T 2 despite the noise in the data. This is particularly important when considering degenerate discs or AF tissue because the SNR of these regions will be lower. Additionally, there is little difference between the calculated T 2 from either averaged intensity fitting or voxel-wise T 2 calculation, so either method is viable.
NCEXP20 was more accurate at fitting simulated and in vivo data than other fitting methods and had smaller bias and uncertainty compared to MONO6 across all T 2 and SNR combinations. Collecting data out to longer echo times and taking the Rician noise into account during curve fitting resulted in better fitting of signal decay data and more accurate calculation of T 2 . In simulated data, at high SNR, either MONO or NCEXP fitting worked reasonably well, as the signal decays to zero and not into the noise floor. But with low SNR, F I G U R E 6 T 2 maps of a healthy L34 disc and degenerate L51 disc with A, MONO6 and B, NCEXP20 fits. NCEXP20 maps are more homogenous with less variation or outlier pixels. MONO6 is more susceptible to error due to noise in signal decay the signal decay is altered by noise and does not decay to zero, so MONO fitting overestimates the T 2 . As a result, the difference in fit quality is most noticeable in degenerate discs that have lost water content in the NP and therefore lost signal in T 2 w images and have a lowered SNR. Attempting to fit only the first several echoes (representing some studies that do not have sufficient number of echoes in their protocols) with NCEXP was also inaccurate because the data give little information about the eventual noise floor that the NCEXP curve is trying to fit. Thus, using a short TE with an acquisition time out to 2× the expected T 2 of the tissue (producing a high number of TE and $85% signal decay) and a NCEXP curve fit is optimal for disc T 2 measurement.
The T 2 values calculated were consistent with previous literature for both healthy and degenerate discs. The healthiest of discs feature NP T 2 in the 150 to 200 ms range, while degenerate grade IV discs were closer to 80 ms. Most literature reports T 2 for healthy discs near 150 ms, while very degenerate discs can be as low as 50 ms. 11,13,14 Specifically, our data matches closest with literature that has sequence parameters with echoes out to 288 ms and TR of 3000 ms. 13 Based on MR physics and this observation, we recommend sequence parameters of TR = 3000 ms (3× the expected T 1 of the tissue) and TE out to at least 300 ms (2× the expected T 2 of the tissue). A short TE should be utilized to maximize the number of echoes that can be curve fit and to capture quick decaying signal. Some published data report healthy disc T 2 in the 75 to 100 ms range. This is surprisingly low for healthy discs and contrary to our data. These T 2 can be used as a marker for disc health because of its relation to water content and matrix integrity. As the disc begins to degenerate, the NP loses proteoglycan content and water content. T 2 measurement quantifies the biochemical state because T 2 decreases as water content and water mobility decrease, and thus T 2 serves as a marker for disc degeneration. Further, changes in quantitative T 2 are more robust than simple changes in T 2 weighted signal intensity.
It should be noted that it is usually accepted that T 2 does not change very much, if at all, with magnetic field strengths of 3.0T or lower, 26 though the signal intensity of a disc can vary depending on the scanner, magnetic field strength, coils used, sequence used, temperature of the subject, and many other factors. T 2 is more robust to these factors because it is a signal decay time constant.
Last, unlike Pfirrmann grading, T 2 is quantitative, continuous, and objective, all of which are important for a measurement scheme that is intended to be used across studies. Pfirrmann grading has been shown to correlate with T 2 across grades, but T 2 avoids the problem of subjective binning of discs into five grades. 6,11 Even more importantly, T 2 is easy to calculate, with sequences readily available on clinical scanners, so T 2 measurements can be easily added to existing imaging protocols as a diagnostic tool or for evaluation of treatments.
Our application of NCEXP in disc follows application of this approach in articular cartilage, which generally has a higher water content and higher SNR. The NCEXP fitting with long echo trains is more robust to noise and more accurate in finding T 2 in phantoms and articular cartilage. 19,20 We applied these methods to the disc in order to improve T 2 calculation in the spine. This approach can be applied to F I G U R E 7 A, Comparison of NCEXP20 for average ROI intensity (left) and Voxel (right) calculation methods for a circular ROI in the NP. Distributions are very similar between methods. B, histogram of the differences between the two ROI methods. Differences are centered around 0 with one outlier that has much higher voxel T 2 . Only two discs have T 2 differences greater than 10 ms. Boxes represent median, 25th, and 75th percentiles. Whiskers extend to most extreme data point that is not considered an outlier (+ symbol) other quantitative MRI methods that are based on fitting monoexponential signal decay (e.g., T 1ρ ) and to other fibrous tissues with low SNR (e.g., meniscus or tendon). T 1ρ also follows a monoexponential signal decay over time and is also susceptible to Rician noise and the presence of a noise floor. 27 Our pilot studies with agarose phantoms show that NCEXP curve fitting can be applied to T 1ρ data for better T 1ρ time calculation at low SNR. Meniscus has very low MR signal because the tightly packed collagen matrix leads to low water mobility and low water content (compared to disc or cartilage), leading to low SNR in the tissue. NCEXP fitting may be an appropriate method to get accurate T 2 or T 1ρ for this tissue.
Many previous reports calculated T 2 on a voxel basis, but T 2 is often reported for a specific ROI, for example, the NP in the disc, and calculation of an ROI by averaging the signal intensity and only fitting the averaged data once is computationally faster and suppresses effects of noise. On the other hand, voxel-wise maps are useful for observing inhomogeneities in a region but require a curve fit for every voxel of interest. There appears to be no prior comparison of these two methods in the literature. Depending on the goal of the research, a voxel-wise method can be used to look at the heterogeneity of a region or for looking at the T 2 of the disc across its width in either the anterior-posterior or lateral directions. There should be clear lower T 2 regions at the edges of the disc while the NP region will have higher T 2 . The differences between the AF and NP may be smaller in less healthy discs. For simply calculating the T 2 of a whole region, the average intensity of the ROI method measures T 2 as robustly as traditional voxel-wise measures and takes less computation time.
In conclusion, NCEXP curve fitting of long echo trains with short TE should be adopted as the primary method for calculating T 2 in the disc. Researchers should use TR times that are at least 3000 ms so that nearly full recovery of magnetization is achieved and signal is not contaminated by T 1 weighting. The first echo should be ignored in multi-echo sequences because of the stimulated echo effect. Either the average ROI intensity method or voxel-wise method can be used to calculate T 2 depending on the goal of the research, but the average intensity ROI method will be computationally quicker. Moving forward, sequence parameters and calculation methods need to be clearly defined in reports of T 2 in disc and other tissues. If similar methods are adopted by the field, results can be compared more usefully, promoting faster scientific discovery.