1 INTRODUCTION

Three-dimensional spin echo (SE)–based methods are gaining a significant foothold in weighted imaging and can provide increased resolution often with only negligible effects to total imaging time.1-3 In terms of 3D turbo spin echo or fast spin echo (FSE), optimized long echo trains4-11 in combination with short interecho spacings and low refocusing angles has resulted in specialized sequences delivering T1, T2, or proton-density (PD) contrast while minimizing acquisition time (TA) and specific absorption rate. These methods have different names depending on manufacturer, such as SPACE (Sampling Perfection with Application optimized Contrasts using different flip angle Evolution [Siemens]), CUBE (General Electric), and VISTA (Volume Isotropic Turbo spin echo Acquisition [Philips]).

Although increased use of 3D-weighted imaging is emerging, it still lacks the robust, clinical quantification options widely developed for the 2D-FSE analogue. The two prominent 2D methods include acquiring several echoes along the signal decay curve (multi-echo spin-echo [MESE]) or dual-echo (PD-T2) approaches. Although MESE is considered the gold standard for T2 mapping, it is time-consuming and generally not clinically available. As shown in McPhee and Wilman,12 dual-echo FSE T2 mapping from PD and T2-weighted contrasts can be accurate if the spin response and flip angles are properly modeled. With adequate SNR, PD-T2 methods have shown to produce similar results to MESE for a specified range of T2 values, while substantially shortening imaging time due to acquisition of only two effective TEs. Modeling the PD-T2 approximation to the decay curve requires inclusion of the measured flip angles (i.e., the deviation of flip angle from nominal) through map generation13 and detailed knowledge of the pulse sequence. Improving resolution is possible due to decreased TA over MESE, although 2D sequences generally have lower resolution in the slice direction than in-plane, which may result in partial voluming and misclassification of T2s. The 2D PD-T2 methods can also be confounded with incidental magnetization-transfer effects.14 These drawbacks are considerable, although 2D T2 mapping is well established and used in clinical studies.

Building on the 2D approach to T2 fitting, 3D methods have become viable due to sequence modifications, allowing shortening of the TA by using long FSE trains with low flip angles and short interecho spacing, obtaining multiple subresolution images at several TEs, or the addition of gradient-echo (GE) modules to speed data acquisition. Subresolution images, such as those acquired in the stack of stars technique,15, 16 use long echo trains, optimized flip angles, and subspace reconstruction methods to extract T2 information for each echo, thereby decreasing the total TA from a dual-echo or multi-echo scheme, with the drawback of producing a single weighted image for a specific TE. Combination GE/SE techniques speed up the acquisition by additional GE modules following SE trains17 or interleaving of SE and GE acquisitions, such as typically used in myelin-water mapping methods.18 T2-preparation pulses can also be used in standard 3D-SE sequences to produce different magnetization pathways,19 resulting in T2 mapping ability but limited to single image output. Furthermore, the development of specialized MR fingerprinting sequences20-23 has pushed quantification boundaries while seeking to maintain resolution with clinical images within relatively short TAs.

Given the multiple techniques available, T2 quantification from 3D FSE appears promising, although specialized research sequences unavailable in the clinic are often used. Constraining techniques to clinical sequences, the comparison of 3D FSE (often used for high-resolution anatomical images such as fluid-attenuated inversion recovery and T2-weighted and T1-weighted contrast) with established 2D methods is required to prove clinical utility and accuracy. Three-dimensional FSE differs from 2D primarily in the use of extremely low and variable refocusing flip angles and long echo trains, which has not been fully investigated for T2 fitting as compared with gold-standard 2D methods.

In this work, we explore T2 quantification from long echo train 3D-FSE sequences using PD-weighted and T2-weighted acquisitions with optimized echo train parameters, while keeping resulting standard-weighted PD and T2 images. This allows a direct comparison between the established 2D PD-T2 method, as both rely on properly fitting the signal acquired from imaging data at different time points to a set of predicted values (a simulated MR sequence dictionary).24 An easy-to-visualize example—similar to 2D—of a constant flip angle train is used as the initial starting point, and more complicated examples using variable flip angle trains are later examined in simulation, phantom, and healthy volunteer brain experiments.

2 METHODS

To quantify the performance of 3D-FSE sequences for T2 mapping, simulations are necessary to provide dictionary values for both decay curve matching and improved fitting via parameter optimization. Although the optimization and evaluation approach is presented for the generic case, the solution space is systematically constrained to two types of sequences, specifically the constant flip angle train mimicking 2D acquisitions and a common T2-weighted variable flip angle train. Once the sequence has been analyzed, phantom and volunteer experiments were conducted to verify the numerical outcomes.

2.1 Choosing a 3D-FSE sequence

The first step is to choose a desired 3D-FSE sequence to determine T2 mapping performance. Common sequences include constant flip angle trains or scanner-defined variable flip angle trains targeting specific image weightings (PD-weighted, T2-weighted, or T1-weighted). Knowledge of the echo train length (ETL), echo spacing, TR, and flip angle array is required for sequence evaluation.

2.2 Pulse sequence simulations

The a priori information required for quantification, the decay curve dictionary, can be as simple as assuming a mono-exponential decay and fitting the acquired image points, although studies have shown that this approach results in heavily biased T2 values. Accurate T2 quantification requires true sequence simulation using extended phase graph (EPG25 for 3D) or Bloch equation techniques (2D and 3D) to account for indirect and stimulated echoes when flip angles deviate from 180°.26, 27 Furthermore, in 2D experiments, slice selection and crusher gradient application requires simulation of spins in space.26, 28, 29 Additionally, while simulations can predict the response at each echo for a fully relaxed system, steady-state solutions should be explored when using TRs shorter than complete relaxation described by typical in vivo longitudinal relaxation rates.

Fortunately, 3D FSE often uses nonselective refocusing; therefore, slice modeling is not required, resulting in significant overhead time savings. Instead, single voxels can be modeled as receiving a constant rather than a slice profile distribution. The simplest and most intuitive FSE sequence uses a reduced (from 180°) constant refocusing flip angle throughout the echo train, with a series of intermediate pulses following the 90° excitation pulse to move the response into the pseudo-steady state (PSS).30, 31 More generic sequences manipulate the flip angle evolution in terms of plateaus and ramps to provide increased signal sustainability at a certain level, reduction of point-spread function artifact, or selection of specific mixed contrasts through traversal of the k-space center at a specific TE with optimized signal.10 As discussed in Weigel and Hennig,5 the flip angle evolution for FSE can be described by several sections, consisting of a transition from excitation to the PSS, a flip angle ramp, and a plateau followed by a transition to a second PSS. During the ramp, flip angles are increased for succeeding echoes to generate a relatively high signal plateau for k-space center acquisition (for examples, see Mugler10).

For each echo train investigated, simulations of decay curves were produced using in-house MATLAB code, modeling steady-state nonselective EPG and Bloch equation solutions for various combinations of T1, T2, and , with other sequence parameters fixed (ETL, echo spacing, TR, and flip angle array). The decay curve dictionary is therefore a 4D matrix with dimensions of T1, , T2, and echo number (or TE). After the dictionary is constructed, fitting involves matching image points (PD, T2, and ) to simulated decay curves, with the assumption that T1 does not vary significantly (see Section 3).

2.3 Echo-time selection The fitting approach requires selection of TEs for two images, to model the simulated decay curve and provide T2 quantification. Curve fitting will be successful if there is (1) sufficient SNR for both echoes to alleviate T2 errors from noise,12 and (2) adequate variance in relative signal intensity between PD and T2 across the T2 range of interest. Although actual image weighting may differ based on TE selection, S1 and S2 will refer to the signal of the PD and T2 images, respectively. These two requirements can be explored using calculated signal parameters. First, the difference between the two echo signals, Sd = S1 − S2, can be used as a measure of available contrast. A large range of Sd values across the T2 range of interest is desirable to allow maximum distinction between T2 isochromats. In other words, Sd should be as large as possible for each investigated T2 value, and Sd should also be different for each T2 value in the range of interest to prevent multiple fitting solutions. As Sd will depend on sequence parameters, parameter maps provide insight into the variation of Sd and performance across the T2 range (e.g., Sd as a function of T1 and T2). To aid TE selection for the two images for an individual sequence, a normalized difference parameter, Snd, can be defined as (1)ensuring that each difference is weighted by the signal of the first echo. For a typical decay, S2 is less than S1 (e.g., during a near-exponential decay) and therefore 0 ≤ Snd ≤ 1. In the case when a later echo (S2) has greater amplitude than S1, a negative value for Snd occurs (signal ramp). During a perfect plateau in the signal, S1 = S2 and Snd = 0. Snd is a means for measuring the difference produced by the sequence for individual T2s to be mapped, and due to the normalization, this parameter can be compared between different sequences. To include both parameters (Sd and Snd) in measuring the T2 mapping performance of a sequence, a third measure can be constructed as follows: (2)

The Sp parameter essentially weights the differences in T2 mapping values (Snd) by the available contrast (Sd) based on the difference of the two points.

As Sp depends on specific selections of TEs for evaluation, a method is needed to determine optimal TEs for the PD and T2 images. An iterative scheme can be used by looping through all echoes in the train and computing Snd for each pair of echoes. By fixing T1 and and constraining T2 to in vivo values, a matrix of modified Snd values (oT2) can be computed with dimensions ETL × ETL, and each element described by (3)where S is the signal for the ith or jth echo, and T2 max and T2 min represent the maximum and minimum T2s to be investigated. Consequently, each oT2 value describes the signal variation between extreme values in the T2 range (i.e., the spread between T2 min and T2 max), with the largest oT2 value corresponding to the echo combination producing the maximum signal variation between T2s.

As an example to visualize the signal parameters, consider the plot in Figure 1E illustrating Snd for a range of T1 and T2 values for the constant 32-echo case, with echo selections of 1 and 16. In healthy brain samples in vivo at 3 T, expected values of T2 and T1 fall in the range of 40–90 ms and 800–1400 ms,32 respectively. A single point in the oT2 matrix (i.e., the available mapping space for T2 values at echoes 1 and 16) can be estimated using Snd and taking the difference of Snd (, T1, 0.1 s) and Snd (, T1, 0.03 s), where and T1 are the constant values used for subtraction in Equation (3) and the T2 range has been broadened to allow for uncertainty. Note that in sequences with strong T1 dependence, this approximation will not hold, as different T1s will produce different results. To complete oT2 generation, the difference calculation is repeated for each combination of echo pairs ranging from 1 to ETL. Optimal TEs are then chosen based on the maximum value of oT2. After TE selection is determined for a given sequence, it is important to consider the signal parameters: the total signal difference between echoes reflecting SNR (Sd) and the normalized difference showing T2 decay spread and T1 dependence (Snd), which are reflected in Sp. Additionally, images should be visually inspected to ensure that the desired contrast is produced for the PD-weighted and T2-weighted images to maintain clinical usability. Once Sp has been computed, different sequences can be compared at optimal TEs.

Echo signal, signal difference (Sd), and normalized difference (Snd) as a function of T1 and T2 with = 1.0 for a 32-echo constant flip angle train. (A) Comparison of flip angles and responses (S120 and S180) between the constant 120° (circles) and 180° (squares) trains for T2 = 100 ms and T1 = 1 s (flip angles are normalized to 180°). Signal amplitudes are shown for echo 1 (TEeff = 6 ms) (B) and echo 16 (TEeff = 96 ms) (C). The signal has been normalized to the maximum achievable value of 1.0 at TE = 0. (D) Sd parameter, and (E) Normalized differences (Snd). Note that the nearly horizontal contours in Snd reflect the T1 invariance (TR = 1.4 s). 2.4 Steps for sequence evaluation In summary, optimization of the sequence includes the following steps: Choose a flip angle evolution either manually or based on clinical implementations of 3D FSE sequences with a specified flip angle array, ETL, TR, and echo spacing. Simulate the sequence (in T1, T2, and space) using Bloch equation or EPG simulations to produce a dictionary of signal-decay values. Compute oT2 and determine the optimal TEs (using oT2 and visually inspecting contrast) for the PD (S1) and T2 (S2) images. Calculate Sd, Snd, and the combined parameter, Sp, using the optimal TEs from oT2 and validate the constant T1 approximation (using 3D plots of Snd in T2 and T1 space). Determine Sp response across T2s of interest (using 3D plots of Sp in T2 and T1 space). Repeat steps 1–5 for different sequences to evaluate different flip angle evolutions on T2 mapping and compare Sp.

Selection optimization will be discussed in examples given in the following sections.

2.5 Constant echo train

Simulations were conducted to model echo trains with ETLs of 16 (the 3D analogue of the 2D PD-T2 FSE sequence) and 32. Contrast is typically reflective of PD-weighted and T2-weighted images, with degree dependent on the selected echoes, similarly to 2D PD-T2 methods. Therefore, the first echo in the train was chosen for S1, and a middle echo was used for S2. Constant cases used flip angle trains with PSS initialization through a one-ahead approach described in Hennig et al.4 The signal difference, Sd, was calculated across T1, T2 and , and while Snd can still be used to help understand the constant case, its utility is greater in more complex trains.

2.6 Generic echo trains

A 96 ETL with variable refocusing angles using the PSS-ramp-plateau-ramp flip angle approach described earlier was investigated. Generally, this shape is used for T2-weighted contrast in 3D-FSE images and sustains relatively high signal at later TEs. (For example, the T2-weighted variable flip angle train for our Siemens Prisma produces a plateau for the T2 ~ 100 ms species.) The signal plateau was varied between responses for T2 = 50 (P50), 100 (P100), and 200 (P200) ms species to investigate the T2 spread based on Sp. Echo-time selection was performed through oT2 optimization.

2.7 analysis

As is also a variable used in the fitting, Snd can be computed for expected ranges (Snd []), given the optimized TEs for each sequence to evaluate the variation of T2 fitting response in terms of and ensure that a large signal difference is present to provide unique mapping solutions. For T2 values of 20–100 ms, ranging from 0.7 to 1.25, and a constant T1 = 1 s, signal parameters Sd, Snd, and Sp were computed. Additionally, experiments were performed on a doped spherical phantom to measure P200 T2 mapping performance in varying environments, detailed in the next section.

2.8 Phantom and healthy brain experiments

All data were acquired using a Siemens Prisma (Erlangen, Germany) 3 T scanner with an 80 mT/m gradient set. A Siemens 64-channel head and neck array was used for signal reception. The phantom consisted of six 50 mL tubes filled with water and doped with magnesium chloride to simulate different T2 environments ranging from 40 to 82 ms (with T1 ranging from 720 to 1950 ms). Sequences tested included 2D MESE, 2D PD-T2, C32 (constant flip angle 32-echo train), C16, P200, P100, and P50 (acquisition parameters detailed subsequently). Experiments using an additional spherical phantom (20 cm diameter, doped with 1.25 g NiSO4/L) were conducted to measure the T2 mapping performance of P200 in an environment mimicking the variation in the human head.

The volunteer study consisted of 3 healthy subjects giving informed consent with ages of 23, 30, and 42 years. Parameters for 3D-FSE quantification included two independent experiments with optimized TEs (P200: 54 and 294 ms; P100: 78 and 318 ms; P50: 60 and 198 ms; C32: 6 and 96 ms), TR = 1.4 s, an isotropic resolution of 1 mm3 (matrix size of 256 × 256 × 208), parallel imaging (GRAPPA) with an acceleration factor of 2 in the phase-encode dimension, echo spacing of 6 ms, and a TA depending on ETL (96 for P200, P100 and P50; and 32 for C32). A -mapping sequence using the Bloch-Siegert33 method was included to supply flip angles to the quantification, with parameters of TE = 2.24 ms, TR = 4.6 ms, flip angle = 5°, voxel size = 1.1 × 1.1 × 3.0 mm3, matrix size = 192 × 192 × 36, and TA = 33 s. Furthermore, an MP-RAGE sequence (1 mm3 isotropic, TE = 2.27 ms, TI = 1800 ms) was used as reference for registering all images using FSL FLIRT.34-36 Finally, compared with previous 2D methods, standard 2D PD-T2 (16 ETL, TE1 = 10 ms, TE2 = 90 ms, 10-ms echo spacing, TR = 7000 ms, flip angle [constant] = 165°, 1.0 × 1.0 mm2 in-plane resolution with 3-mm slices [35 total], TA = 3:58 min) and 2D MESE images (32 ETL, 10-ms echo spacing, TR = 3000 ms, flip angle = 180°, 1.0 × 1.0 mm2 in-plane resolution, 5-mm slice thickness [6 total slices], TA = 6:09 min) were acquired.

2.9 In vivo T2 analysis

Several regions were segmented manually on matching axial slices of the T2 maps for each method (2D PD-T2, MESE, and 3D FSE). Included regions of interest were the frontal white matter (64 total pixels), inferior longitudinal fasciculus (20), cortical gray matter (21), corticospinal tract/internal capsule (16), putamen (56), globus pallidus (48), thalamus (48), and red nucleus (25). Comparison of methods was made using Bland-Altman analysis.37, 38 Differences of each method compared with MESE for all regions and subjects were computed and tested for normality using a one-sided Kolmogorov-Smirnov test. An acceptable range of tolerance between two measurements was defined as the T2 mean SD of each tissue measurement for all MESE regions in all subjects. As measured in Section 3, the mean MESE SD was equal to 4 ms; consequently, by this definition, two methods agree within limits if the confidence interval (CI) range is less than or equal to 8 ms.

3 RESULTS 3.1 Constant echo train simulations

Simulations for the constant 32 echo train with flip angle of 120°, echo selections of 1 (S1, effective TE [TEeff] of 6 ms) and 16 (S2, [TEeff] = 96 ms), and nominal of 1.0 are shown in Figure 1B,C, with signal as a function of T1 and T2. The signal response at T2 = 100 ms and T1 = 1 s is illustrated in Figure 1A (as compared with a constant 180° train). These echoes were chosen to mimic the 2D PD-T2 contrasts (typically using echoes 1 and 9 in a 16-echo sequence, corresponding to TEeff of 10 ms and 90 ms, respectively). Maximum echo signal variance (Snd) across in vivo T2s was calculated to be 0.58 with an average of 0.51 (measured between 30 and 100 ms at a constant T1 of 1 s). The nearly constant T1 variation illustrated by Snd (Figure 1E) indicates mapping using the constant 32-echo sequence with 120° flip angle is practically T1 invariant. Consequently, the assumption of a constant T1 in T2 quantification to reduce the number of variables is valid. Due to the T1 invariance, further reduced TR cases (32 echoes with TR of 0.5 s and 16 echoes with minimal TR of 0.2 s) were explored but did not provide sufficient SNR in phantom and in vivo experiments.

3.2 Generic train simulations

The response and flip angles for a 3D-FSE sequence commonly used for T2-weighted images with signal plateau at T2 = 100 ms (P100) are shown in Figure 2. Figure 2A illustrates the signal response of three T2 isochromats (50, 100, and 200 ms) to the P100 sequence and shows the flip angle evolution used to produce the signal. Further analysis of the spread of different T2 decays for a T2 range of 20 to 200 ms is shown in Figure 2B (constant T1), and T1 decays (range of 0.6 to 1.6 s, constant T2) in Figure 2C. Because the spread of response based on individual T2 isochromats in Figure 2B is greatest following the plateau (echo number 53, TEeff = 318 ms), it follows intuitively that this point would make an ideal second echo candidate for mapping T2s in combination with an earlier echo in the train. Compared with the diverse variation of T2 decays in Figure 2B, the amount of T1 variation is noticeably constrained (Figure 2C), indicating a small variation in signal due to differences in T1.

(A) Response at T2 = 200 ms (blue), T2 = 100 ms (orange), and T2 = 50 ms (black) to the 96-echo flip angle evolution optimized for 100 ms (P100) prescribed in purple (secondary y-axis). and T1 were held constant for this illustration with values of 1.0 and 1.0 s, respectively. Note the long ramp with sustained T2 = 100 ms signal. The variation of the response is shown with respect to T2 (B) and T1 (C), where each line shows a different T2 (in the range of 20–200 ms) or T1 (with range of 0.6 to 1.6 s) species. Echo spacing is 6 ms; therefore, 60 ms denotes 10 echoes

To investigate effects of adjusting the plateau, three variable flip angle sequences with plateaus occurring at 50 (P50), 100 (P100), and 200 ms (P200) were designed and simulated, and the decay curves are shown in Figure 3. As mentioned, P100 was used as the starting point, as it mimics the common T2-weighted variable flip angle train used for clinical routine, while preliminary simulations showed an improved result in T2 mapping when the plateau was optimized at a higher T2 (P200). The P50 case was used to illustrate effects of using a lower T2 plateau. The response of T2 species in the in vivo range of 30–100 ms is illustrated for each variable flip angle train (P200, 3A; P100, 3B; P50, 3C) and compared with the constant flip angle, 32-echo case (Figure 3D). The required flip angle arrays are shown in each as the dotted line on the secondary y-axis. In the case of P50, larger flip angles are needed earlier in the evolution to maintain the plateau due to the more rapid transverse decay of the T2 = 50 ms isochromat in comparison to species with slower relaxation rates. There is substantial T2 variation in all sequences, indicating that T2 mapping utility is possible with variable trains, with the most spreading occurring for the P50 case.

Spread of decay curves (multiple lines) for different T2 values ranging from 20 to 200 ms for variable flip angle sequences. Sequences have been optimized to produce sustained signal at plateaus of T2 = 200 ms (P200) (A), T2 = 100 ms (P100) (B), and T2 = 50 ms (P50) (C). The decay of the constant case is shown in (D). Vertical bars indicate the location of the chosen, optimized echoes for the T2 mapping experiment. The flip angle train is shown as a dashed line at the top, corresponding to the secondary y-axis. All experiments used an echo spacing of 6 ms, with a total of 96 echoes (A-C) and 32 echoes (D)

Sequence evaluation and calculation of optimal TEs through Sp and oT2 was performed (Figure 4), and Sd, Snd, and Sp for the optimal TEs are shown in Figure 4A–C. Although there is some T1 variation at higher T2 values (curvature of the plane in the T1 direction in Snd), there remains a very small variance of signal due to T1 contributions in the in vivo range (<3% for P200). The largest signal difference occurs for P200 (4A), with a gradual decline in difference toward higher T2 values. Although P50 shows some ability to distinguish T2 values < 40 ms, Sp is close to zero around the T2 values of interest (T2 = 60 ms), and therefore should not perform as well as P100 or P200. P100 varies similarly to P200, with a reduced T2 mapping capacity due to lower available contrast.

Signal difference (Sd) (A), normalized difference (Snd) (B), and T2 mapping performance (Sp) (C) for the three investigated variable trains. The greatest signal difference occurs in the P200 case (highest plane in [A]) showing the greatest available SNR after signal difference. The T2 variation shown in Snd is greatest for P50 (largest curvature in T2 direction in [B]). C, Sp shows the best potential for accurate mapping occurs for the P200 sequence (a combination of T2 variation and SNR). D-F, Optimized TEs using the ETL × ETL matrix approach for P50, P100, and P200. The coordinates of the peak of the optimization (oT2) are shown in brackets (proton density [PD] echo, T2 echo). All sequences used an echo spacing of 6 ms. Note that the oT2 parameter is in arbitrary units

Analysis of oT2 (echo selection) resulted in optimized echoes in each case occurring near the beginning and before the end of the plateau (Figure 4D–F). Consequently, an earlier echo is prescribed for S2 (33, TEeff = 198 ms) in P50 versus S2 for the P200 case (echo 49, TEeff = 294). Optimal TEeffs are shown as coordinates in the format (TEeffPD, TEeffT2). There is a considerable amount of variation in the P50 plot (Figure 4D) and a relative singular peak for optimal TEs, while more flexibility in TE selection is afforded with P100 and P200 (i.e., similar results can be achieved at several combinations due to the elongated maximum). Note that the optimal TEs in Figure 4D–F were used to produce the signal parameter maps in Figure 4A–C.

Evaluation of signal parameters in terms of T2 and space using an expected range of 0.7 to 1.25 (where nominal = 1.0) and a constant T1 of 1 s (Supporting Information Figure S1) resulted in significant variation in both T2 and directions. This is contrasted to measured signal parameters in T2 and T1 space (Figure 4), where variation was constrained primarily to T2, indicating a need to take both T2 and into account when performing fitting using an acquired map. P200 showed a signal variation of 0.1 (T2 = 100 ms, B1 = 0.7) to 0.95 (T2 = 30 ms, = 1.25), with a similar shape to Snd (Figure 4B) in the T2 direction. P100 showed less variation (0 to 0.8) in T2, while the P50 case produced similarly shaped Snd () maps to the P50 case in Figure 4B, with the least amount of total variation of 0 to 0.6 in T2. The Sp analysis indicated best performance should be expected for the P200 case, with the greatest available contrast and most variation in T2 and directions.

3.3 Phantom experiments

Results of experiments using the six-cylinder phantom are shown in Figure 5, with T2 values recorded in Table 1. The SNR measurements quoted were measured using the first vial image (MESE T2 = 82 ms), and contrast-to-noise ratio (CNR) used an average for all vials (corrected to voxel size). The constant train with 32 echoes (C32, 5C) and P200 (5F) compared the most favorably with the MESE T2 maps, having percent differences of 2.2 and 1.3, respectively. As the TR for C32 was equivalent to the variable trains (1.4 s), the time for acquisition was three times longer due to a shorter ETL, making the C32 case less feasible for clinical studies. All phantom T2 maps show more variation and noise compared with MESE. C16 (constant flip angle train with 16 echoes and TR = 0.2 s, not shown) and P50 (5D)—as predicted from the simulations—were the worst performers, with large deviations from MESE, and therefore were not included in the in vivo study. The SNR decreases of the variable echo trains from MESE and 2D PD-T2 are due to increased resolution in the slice direction and longer ETL. Note that C32 maintains SNR near the 2D cases using an ETL one third the length of the P200/P100/P50 cases. Individual vial CNR measurements showed a small decrease with increasing T2, as expected (Supporting Information Figure S2 and Supporting Information Table S1), although a strong relationship between CNR and accuracy of estimated T2 values was not present between the different T2 vials. However, the overall average CNR did correlate with increased accuracy of T2 value estimation, indicating that a threshold of about 200 is required for accurate T2 prediction. All sequences with CNRs below 200 performed poorly (P100, 79; P50, 88; C16, 140).

Phantom T2 maps for 2D multi-echo spin-echo (MESE) (A) and 2D PD-T2 (B) experiments compared with the constant 32-echo train (C32) (C) and variable trains P50 (D), P100 (E), and P200 (F). The expected circular axial cuts are slightly elongated vertically in the MESE and PD-T2 cases due to thicker slices—illustrating the slight off-axis alignment of the phantom. Nominal phantom T2 values that mimic in vivo brain tissues from the top left, clockwise, as measured from MESE, were 82.2, 73.9, 57.9, 40.0, 64.1, and 46.0 ms. The color bars are in seconds

TABLE 1. Phantom T2 measurements for constant and variable flip angle trains Train Time (s) SNR (PD-weighted) SNR (T2-weighted) 1b 2 3 4 5 6 Average CNRc Diff from MESE (%)d MESE 285 343 57a 82.2 ± 0.6 73.9 ± 0.5 57.9 ± 0.3 40.0 ± 0.0 64.1 ± 0.7 46.0 ± 0.1 418 – PD-T2 182 328 178 82.8 ± 3.2 73.7 ± 2.9 57.5 ± 1.7 39.5 ± 1.1 63.8 ± 2.2 45.5 ± 1.2 336 0.7 C32 528 281 196 84.7 ± 1.4 75.1 ± 1.1 58.9 ± 0.8 41.0 ± 0.7 65.2 ± 0.1 47.1 ± 0.6 818 2.6 C16 150 71 58