2.1.

Three-Dimensional k-Space Encoding for Optimal Repetition Time

The choice of optimal TR is influenced primarily by the $T_1$ of the object as having a short TR results in signal loss due to incomplete $T_1$ recovery and having a long TR reduces SNR efficiency. Balancing how often data is collected for averaging and the $T_1$ recovery, the optimal TR is $\sim 1.5\text{seconds}$² using a $T_1$ of 1.1 s for white matter at 3 T.¹⁰ In order to maintain whole-brain coverage with such a short TR, multiple slices must be grouped into 3-D slabs. However, for multislab acquisitions the SNR-efficient TR increases to 2 to 3 s when imperfections in RF excitation profiles are considered.¹¹ By switching to a 3-D excitation scheme, which samples data for multiple slices in a 3-D volume, the SNR efficiency can be increased by 50% or more in the same total imaging time compared with a standard two-dimensional (2-D) acquisition when imaging a large number of slices.^2,9,11,12

2.2.

Spiral Readouts for Short Echo Time

The spiral trajectory is a commonly used non-Cartesian trajectory due to its ability to efficiently cover k-space by better leveraging gradient hardware limitations than the EPI trajectory. A spiral trajectory also has the property of being able to sample the center of k-space at the start of the readout, this can allow for significantly shorter TEs to be achieved. This is in contrast to commonly used EPI acquisitions which suffer from expanding echo times when the spatial resolution of the acquisition is increased. The spiral trajectory is also extremely flexible in its design allowing an arbitrary number of shots to be designed to cover k-space in multiple acquisitions. This allows for fine control over the amount of undersampling per shot and the readout duration, to limit susceptibility distortions and $T_2*$-induced blurring. Long readouts are desirable as they will limit the total number of shots required to form an image; however, longer readouts come with increased magnetic susceptibility-induced distortion that must be addressed during image reconstruction. To achieve 3-D encoding with spiral, the stack of spirals k-space trajectory is used in the current work, but other choices are possible.^13,14

2.3.

Navigation for Multishot Diffusion

At high resolutions, a multishot acquisition becomes necessary to limit the duration of the long data readouts to limit the $T_2*$ blurring and image distortions. In DWI, using multiple shots leads to motion-induced phase errors (MPE) due to different shots having differences in small amounts of motion during diffusion encoding.¹⁵ These phase errors lead to artifacts and signal cancellations in the reconstructed image if not corrected. A wide variety of techniques have been developed to handle these errors.^16–24 In addition to subject motion during DWI, these phase errors can be caused by cardiac pulsation or other physiological motions, which may result in nonlinear MPE. The sequence in this work uses a spiral-in readout to acquire a low resolution 2-D navigator image which allows it to be used with most navigator-based motion-correction methods. As long as the resolution of the navigator allows for it to capture the spatial variations of the MPE, the proposed sequence will be scalable to higher imaging resolutions without being limited by the resolution of the navigator. The 2-D navigator for a 3-D slab assumes that the spatial variation of MPE in the slice direction is small, which has been shown to be accurate as long as the slabs are thin.²

2.4.

Proposed Pulse Sequence

The proposed acquisition sequence is designed to achieve a high SNR efficiency. The acquisition uses a standard PGSE⁵ approach for encoding diffusion due to its efficient diffusion encoding and a 3-D multislab approach due to its ability to balance sampling time for a slice with adequate $T_1$ recovery. The use of spiral readouts also enable the short echo time provided by the PGSE scheme to be utilized, enabling higher SNR by shortening the TE. The pulse sequence used to achieve this is shown in Fig. 1. Additionally, a spectrally selective lipid excitation and spoiler gradient is used for lipid suppression (not shown), free induction decay crusher gradients are used for low $b$-values, and gradient spoiling is used after the spiral readout.

Fig. 1

Pulse sequence diagram for the proposed SNR optimized 3-D multislab, multishot navigated DWI sequence.

A short spiral-in navigator is placed immediately after the second diffusion-encoding gradient followed by a kz phase encoding gradient and then a spiral readout for imaging data. For a PGSE sequence, this spiral-in navigator does not add any time to the imaging sequence as long as it is shorter than the slice select rewinder plus one half the excitation pulse duration minus the duration of the kz encode. The placement of the navigator directly before the imaging readout instead of after a second refocusing pulse is beneficial because it does not impact scan time efficiency. A spiral navigator with a $40\times 40$ matrix size acquired with a parallel imaging factor $R=2$ is used for navigation.

In order to minimize artifacts associated with imperfections in 3-D slab excitation, several considerations were made. First, we used relatively long (10 ms) RF pulses that were designed using the Shinnar–Le Roux procedure²⁵ to result in sharp transition widths. Additionally, the number of slices in a slab was kept low in order to decrease the amount of signal loss that can sometimes be observed at edge slices. The slabs were also excited in an interleaved manner to reduce interactions between adjacent slabs. Finally, a TR is used that is slightly longer than the $T_1$-optimal TR to enable further relaxation between adjacent slabs.

2.5.

Image Reconstruction

An iterative, model-based image reconstruction scheme is used to allow modeling of non-Cartesian spiral readouts, nonlinear MPE,²² parallel imaging using sensitivity encoding,²⁶ and correction for magnetic susceptibility-induced image distortions.²⁷ The magnetic field inhomogeneity correction enables the use of longer readouts, reducing the total number of shots, with their diffusion encoding overhead, leading to a higher SNR efficiency.²⁸

2.6.

In Vivo Data

In vivo data were collected on Siemens 3 T Trio scanner using a 32-channel head coil. Scanning was done under local institutional review board approval with all subjects giving written consent before participating. To compare the SNR achievable with the optimized, 3-D multislab sequence, several data sets using EPI and spiral with a variety of imaging parameters were obtained, see Table 1 for a description of the parameters of these acquisitions. First, a standard spatial resolution of 2 mm isotropic was targeted, collecting DWI data with a 2-D acquisition with both single-shot EPI (referred to as “2-D_EPI”) and spiral readouts (referred to as “2-D_spiral”). The 2-D_EPI acquisition was chosen as a basis of comparison as it is the most commonly used acquisition on clinical MRI scanners at 2 mm spatial resolution. The proposed 3-D multislab acquisition with 2 mm isotropic resolution (referred to as “3-D_spiral”) was acquired with a single in-plane shot for each kz encoding in order to match readout duration for single shot imaging with the 2-D_spiral protocol. For all of these acquisitions, the same FOV and slice coverage were used with the minimum TE and TR possible for each technique. Notably, these acquisitions all require the exact same number of excitations to do the imaging as all are single-shot in a kz plane or single-shot within a 2-D slice. A high resolution $T_1$-weighted MPRAGE (TE: 2.3 ms, TR: 1900 ms, TI: 900 ms, FOV: $230\times 172\times 230\mathrm{mm}$, matrix $256\times 192\times 256$) was acquired. Additionally, reference images with different echo times were acquired for field map estimation²⁹ to enable field inhomogeneity correction²⁷ and to estimate the coil sensitivity map.²⁶ This scan utilized an asymmetric spin echo, spin echo TE of 17 ms, gradient echo TE was 1 ms delayed, matrix size: $120\times 120$, FOV: $240\times 240\mathrm{mm}$, slices: 40, slice thickness: 3 mm, TR: 1800 ms.

Table 1

Sequence protocols.

SNR measurements were derived by taking the temporal mean divided by the temporal standard deviation from 25 repeats of each measurement for a single diffusion encoding direction. A white matter mask was obtained in the subject’s diffusion tensor imaging (DTI) space by segmenting the MPRAGE image using FMRIB’s automatic segmentation tool³⁰ in FSL³¹ and then registering the segmentations to the diffusion weighted images using FLIRT.^32,33 The pixel-wise SNR was then averaged across the mask to create a single image SNR value for each of the acquisitions: 2-D_EPI, 2-D_spiral, and 3-D_spiral. SNR efficiency was calculated by taking the SNR in the image and dividing it by the square root of scan time required to acquire the image.

To demonstrate that the proposed sequence can be used at higher resolutions, a 1.25 mm isotropic (3-D_spiral_HR1) and 0.8 mm isotropic DWI data sets (3-D_spiral_HR2) were acquired with the proposed sequence. A matched coverage 2 mm resolution data set (2-D_epi_DTI) was acquired to compare 0.8 mm to 2 mm resolution. Fractional anisotropy (FA) images were created using DTIFit³⁴ in FSL. These data acquired 30 different diffusion directions for estimating a diffusion tensor in order to match what is most commonly done at lower resolutions. However, depending on the diffusion model being used it may be possible that other diffusion schemes may be better for estimating a tensor.³⁵

3.1.

Signal-to-Noise Ratio Analysis

Table 2 provides the parameters for each acquisition protocol along with the theoretical relative SNR efficiency from those protocols, compared with the parameters used in the 2-D EPI acquisition. The “SNR efficiency from TR” is the theoretical change in signal due to changing TR using a standard spin echo recovery equation, assuming the sequences have the same readout and TE. The “SNR ratio from TE” is the amount of signal gained by reducing the TE due to a spiral trajectory assuming the TR and readout are the same between sequences. These equations use white matter values of 1.1 ms for $T_1$ and 69 ms for ${\mathrm{T}}_2$.¹⁰ The SNR ratio for a single image is the theoretical gain in SNR taking into account the TE, TR, and readout durations, which includes the gains in SNR due to a 3-D acquisition. The SNR efficiency additionally takes into account the time it takes to acquire an image, normalizing the image SNR by the square root of the acquisition time.

Table 2

Theoretical differences in SNR and SNR efficiency.

Table 3 summarizes the SNR measurements from 5 subjects across the 2-D_EPI, 2-D_spiral, and 3-D_spiral acquisitions that all had 2 mm isotropic resolution. Table 3 also gives the estimated SNR efficiency increase of 53% from the shorter TE and TR associated with spiral by comparing the 2-D_EPI with the 2-D_spiral acquisitions. It also gives the estimated SNR efficiency increase of 71% for the 3-D encoding and spiral acquisition over the 2-D EPI. Figure 2 shows a comparison of the reconstruction of a single slice for the three different acquisitions used for the SNR analysis.

Table 3

Comparison of SNR and SNR efficiency across 5 subjects (S1 to S5) at b=1000. The percentage increase in SNR and SNR efficiency over the equivalent 2-D EPI acquisition is given at the bottom of the table.

Fig. 2

Comparison of resulting images for $b=0$, $b=1000$, and estimated ADC from the 2-D_EPI, 2-D_spiral, and 3-D_spiral acquisitions for a single slice. A line plot through the image is shown in the right column to more closely look at the differences in the images.

3.2.

In-Vivo DTI Images

The ability of the proposed method to acquire multiple direction diffusion data at higher spatial resolution (1.25 mm isotropic) in a reasonable time (19.8 min for 30 direction DTI data) is demonstrated in Fig. 3 using the 3-D_spiral_HR1 data set.

Fig. 3

1.25 isotropic FA images from spiral_3-D_HR1 data set. Color-coded FA image, with red left–right, blue inferior–superior, green anterior–posterior. Note the resolved fine white matter structures, such as the hippocampal layers as indicated by the arrow.

To demonstrate the scalability to higher resolutions, the 3-D multislab sequence was used to acquire a 30-direction data set at a 0.8 mm isotropic resolution (3-D_spiral_HR2). Figure 4 shows the color-coded FA from the 0.8 mm isotropic acquisition. At this increased resolution, partial volume effects of fine white matter structures are greatly reduced.

Fig. 4

Color-coded FA images: (a) 2 mm isotropic and (b) 0.8 mm isotropic. Several commonly studied white matter regions are labeled, including the corpus callosum (CC), corona radiata (CR), and the superior longitudinal fasciculus (SLF). An axial view is shown on top with a coronal view on bottom.

In order to achieve a short total acquisition time and maintain a high acquisition efficiency, the collection of longer data readouts per diffusion encoding is desired. As previously stated, this results in a tradeoff with magnetic field inhomogeneity induced image distortion. Figure 5 shows the image reconstruction results for a single slice in a 3-D slab with and without field correction from the 3-D_spiral_HR2 acquisition along with type of distortion observed when no motion correction is used. The spiral readout for this imaging data had a relatively long duration of 52 ms. The long data readout results in significant susceptibility-induced distortions in the image, which are radial blurs for spiral acquisitions. Using the magnetic field inhomogeneity corrected image reconstruction, a high-quality image was recovered from the data.

Fig. 5

3-D_spiral_HR2 images (0.8 mm isotropic resolution): (a) without MPE correction and without field inhomogeneity correction, (b) with MPE correction and without field inhomogeneity correction, and (c) with MPE correction and with field inhomogeneity correction. The frontal region (indicated by arrows) are the areas that are most impacted by field inhomogeneity in this slice.