Nonparametric 5D D-R₂ distribution imaging with single-shot EPI at 21.1 T: Initial results for in vivo rat brain

Abstract

In vivo human diffusion MRI is by default performed using single-shot EPI with greater than 50-ms echo times and associated signal loss from transverse relaxation. The individual benefits of the current trends of increasing B₀ to boost SNR and employing more advanced signal preparation schemes to improve the specificity for selected microstructural properties eventually may be cancelled by increased relaxation rates at high B₀ and echo times with advanced encoding. Here, initial attempts to translate state-of-the-art diffusion-relaxation correlation methods from 3 T to 21.1 T are made to identify hurdles that need to be overcome to fulfill the promises of both high SNR and readily interpretable microstructural information.

1. Introduction

NMR diffusion-relaxation correlation methods [1–3] combined with data inversion into nonparametric distributions [4,5] of these MR properties have been applied successfully in low field studies of heterogeneity in materials ranging from porous rocks [6] to dairy products [7] and fruits [8] for decades. The methods more recently have been combined with MRI [9] and demonstrated to have great potential for both ex vivo [10–13] and in vivo [14] clinical applications as summarized in several comprehensive reviews during just the last few years [14–17]. In addition, data challenges aimed to explore sub-sampling strategies has been performed aimed to harness the richness of information in multidimensional data with in feasible clinical scan times [18].

While most previous diffusion-relaxation studies have relied on the simple Stejskal-Tanner sequence [19] for which the effects of multiple aspects of molecular motion including bulk diffusivity, restriction, anisotropy, flow and exchange [20] are merged into apparent diffusion coefficients (ADCs) [21], a few studies [22–26] have incorporated more elaborate encoding strategies deriving from multidimensional solid-state NMR [27] to enable separation and correlation of parameters specific to the various types of motion. These multidimensional diffusion encoding methods build on carefully crafted gradient waveforms to attain selectivity at the expense of requiring higher gradients amplitudes or—when the maximum amplitudes are already reached—longer waveform durations than in conventional diffusion tensor imaging [28,29]. The resulting loss in signal-to-noise ratio (SNR) from transverse relaxation is in practice often compensated by using larger voxel sizes but could in principle be mitigated by ultra-high B₀ [30], the general benefits of which has been demonstrated for MRI and MR spectroscopy (MRS) in several papers [31–39].

So far, in vivo preclinical and human studies employing multidimensional or oscillating gradient diffusion encoding have been performed at 3 T [22–24,26,40–62], 4.7 T [63–65], 7 T [57,66–69], 9.4 T [70] and 11.7 T [71–73] while diffusion-relaxation correlation has been limited to 3 T [14,22–24,26]. All of these studies have relied on echo planar imaging (EPI) signal read-out, which allows for acquisition of a complete 2D image plane after a single excitation, but suffers from B₀-dependent image distortions due to susceptibility inhomogeneity [31,74] and low SNR for materials with high transverse relaxation rate R₂. As ultra-high B₀ systems are being developed also for in vivo human studies [30,75,76], we performed pilot measurements with multidimension diffusion-relaxation correlation and EPI readout at the highest field available for in vivo rodent, 21.1 T [77,78] to investigate the feasibility of translating pulse sequences from moderate to ultra-high B₀ and identify technical issues that need to be addressed to realize the full potential of combining diffusion-relaxation correlation, multidimensional diffusion encoding and ultra-high B₀. Anticipating that transverse relaxation will be one of the main obstacles, we performed measurements yielding nonparametric joint distributions of R₂ and diffusion tensors D [22,23].

2. Methods

2.1. MRI equipment

Experiments were performed using the 21.1-T magnet at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee, FL [77,78]. The magnet was designed and built at the NHMFL, and is equipped with a Bruker Avance III console (Bruker-Biospin, MA, USA) using imaging gradients (Resonance Research Inc., MA, USA) capable of producing a gradient strength up to 600 mT/m. An in-house designed and built radio-frequency (RF) coil was used for all in vitro and in vivo experiments. The RF coil used was a double-saddle quadrature surface coil tuned to 900 MHz, the resonance frequency of ¹H at 21.1 T. The coil was built to accommodate the head of in vivo rodents weighing up to 350 g [34].

2.2. Phantoms

To validate the implementation of the multidimensional sequence on the 21.1-T magnet and for parameter optimization, a “Hex” liquid crystal phantom that provided high anisotropy was created as described by Nilsson et al [79]. In short, the phantom was placed in a 15-mL conical tube consisting of 41.94 wt% water (Milli-Q quality), 13.94 wt% of the hydrocarbon 2,2,4-trimethylpentane (Sigma-Aldrich, Sweden), and 44.12 wt% of the detergent sodium 1,4-bis(2-ethylhexoxy)-1,4-dioxobutane-2-sulfo nate (trade name AOT from Sigma-Aldrich, Sweden). At room temperature, the liquid crystal is in a reverse 2D hexagonal phase wherein water diffuses along cylindrical channels with ~ 5-nm diameters, which span lengths of hundreds of micrometers and gives rise to highly anisotropic diffusion. Around the 15-mL “Hex” phantom, two NMR tubes with 1-octanol (MilliporeSigma, MA, USA) and n-dodecane (TCI America, OR, USA) were placed. The combined tubes were secured and placed in a 50-mL conical tube filled with water. The phantom was secured into the RF coil and placed in the magnet.

2.3. Animals

Two Sprague Dawley rats weighing between 200 and 250 g were used. The animals were housed in cages with a 12-hour night/12-hour daylight cycle, with water and food available ad libitum. The animals were anesthetized with isoflurane (Baxter, IL, USA) and placed prone inside the coil with fore teeth placed on a bite bar. This bite bar also supplied a continuous flow of oxygen mixed with 1–3% of isoflurane. The concentration of isoflurane was set to maintain a steady respiration rate of 25–30 breaths per minute as monitored by a respiratory pillow (SA Instruments Inc., NY, USA) that was placed in between the rat and probe. Temperature was maintained at 37 °C by means of gradient chiller. The coil was tuned and matched for each individual rat for optimal performance. The same acquisition parameters used for the phantom were acquired for animals with the field-of-view (FOV) set to cover the head of the rat (32 × 11 mm). After confirming accurate placement of the rat, shimming was performed using either Bruker’s automatic B₀ shimming sequence or if needed adjusted by localized voxel placed over the parenchyma. All animal procedures were approved by the Florida State University (FSU) Animal Care and Use committee (ACUC).

2.4. MRI measurements

A ParaVision 6.0.1 implementation of a multi-slice 2D spin-echo EPI sequence with pairs of free gradient waveforms bracketing the 180° pulse [80] was kindly provided by Matthew Budde at the Medical College of Wisconsin (https://osf.io/ngu4a). The diffusion encoding tensor b is obtained from the effective gradient g(t) via:

$$q(t)=\gamma {\int }_0^{t}g\left(t^{\prime }\right)\text{d}t\prime ,$$ (1)

and

$$b={\int }_0^{{\tau }_{\text{E}}}q(t)q{(t)}^{\text{T}}\text{d}t,$$ (2)

where the integration is performed from the center of the excitation 90° pulse to the echo time τ_E. The sensitivity of the signal to anisotropy is controlled by the “shape” of b, which is conveniently expressed by the normalized anisotropy b_Δ given by [81]:

$$b_{\Delta }=\frac{1}{b}\left(b_{ZZ}-\frac{b_{YY}+b_{XX}}{2}\right),$$ (3)

where b is the trace of b and b_XX, b_YY, and b_ZZ are the eigenvalues ordered according to (b_ZZ – b/3) > (b_XX – b/3) > (b_YY – b/3). Four 10-ms waveforms of the diffusion encoding gradients were used: linear (b_Δ = 1), planar (b_Δ = −1/2) and spherical (b_Δ = 0) as calculated in Ref. [82], as well as linear (b_Δ = 1) with a 5-ms half-sine pulse on each side of the 180° pulse. Gradient orientations (Θ, Φ) were obtained by the electrostatic repulsion scheme [83], and the number of directions were varied pseudo-randomly between 11 and 15 for the different values of τ_E within the range from 14.1 to 60 ms with an approximate logarithmic distribution. A detailed overview of the acquisition scheme can be found in in Fig. 1. Here gradient amplitude was varied between 10, 25, 45 and 80% (depending on diffusion scan) of peak gradient strength (0.6 T/m) The lowest and highest b-values were chosen to suppress spins undergoing flow, to achieve some attenuation of water spins with the lowest diffusivity, and were distributed logarithmically to improve sampling of the exponential signal decay [26,84]. Data was collected using nine slices of 1-mm thickness and FOV to cover the sample. Matrix was 140 × 48 (0.2 × 0.2 mm in-plane resolution) with a bandwidth of 500 kHz, two dummy scans and partial-FT encoding scheme (1.33 coverage). The repetition time (τ_R) was set to 5 s throughout, and the resultant total acquisition time was 120 min.

Fig. 1.

Acquisition scheme for 5D D-R₂ distribution MRI. Images are recorded as a function of the magnitude b, normalized anisotropy b_Δ (defined in Eq. (3)) and orientation (Θ,Φ) of the b-tensor, as well as the echo time τ_E at constant repetition time τ_R of 5 s. All panels share the same abscissa, where n_acq is the acquisition number sorted in the order of ascending τ_E, b, and b_Δ.

2.5. Data processing

After image reconstruction in ParaVision, data were exported to MatLab (R2018b MathWorks Inc, MA, USA) for denoising using random matrix theory [85]. In-plane motion and eddy correction with the MatLab routine imregister was used for in-plane affine registration, and Monte Carlo inversion [86] generated nonparametric 5D D-R₂ distributions [22] using the dtr2d method in the md-dmri Matlab toolbox [87]. With this method, the signal S(b, τ_E) acquired as a function of b and τ_E at constant τ_R is approximated as originating from multiple sub-populations i, each being characterized by their weight w_i, diffusion tensor D_i, and transverse relaxation rate R_2,i according to:

$$S\left(b,{\tau }_{\text{E}}\right)=\sum _i{w}_i\text{exp}\left(-{\tau }_{\text{E}}{R}_{2,i}\right)\text{exp}\left(-b:D_{\text{i}}\right),$$ (4)

where the sum of w_i gives the non-encoded signal S₀ through:

$$S_0=\sum _i{w}_i,$$ (5)

which is nominally proportional to the spin density.

Assuming diffusion with axial symmetry for each sub-population, the diffusion tensors are parameterized in terms of the axial and radial eigenvalues, D_A,i and D_R,i and orientation (θ_i,ϕ_i). In this work, the Monte Carlo algorithm pseudo-randomly explores the parameter space within the ranges 5·10⁻¹² m²s⁻¹ < D_A,i, D_R,i < 5·10⁻⁹ m²s⁻¹ and 1 s⁻¹ < R_2,i < 80 s⁻¹ and—independently for each voxel—yields 100 solutions consistent with the input data. Each of these solutions comprises up to 20 components i characterized by the parameter set [D_A,i,D_R,i,θ_i,ϕ_i,R_2,i] and the corresponding weights w_i. For visualization of the results, the values of D_A,i and D_R,i are converted to the isotropic diffusivity D_iso,i and squared normalized anisotropy ${D_{\Delta ,i}}^2$ by [81,88]:

$$D_{\text{iso},i}=\frac{D_{\text{A},i}+2D_{\text{R},i}}{3}$$ (6)

and

$${D_{\Delta ,i}}^2={\left(\frac{D_{\text{A},i}-D_{\text{R},i}}{3D_{\text{iso},i}}\right)}^2,$$ (7)

as well as the lab-frame diagonal elements D_xx,i, D_yy,i and D_zz,i according to standard equations. Single-voxel 5D D-R₂ distributions are visualized by projecting the components onto the 2D $D_{\text{iso}}-D_{\Delta }^2$, D_iso-R₂, and $D_{\Delta }^2-R_2$ planes, and parameter maps are generated by extracting means E[x], variances V[x], and covariances C[x,y] according to [89]:

$$\text{E}[x]=\frac{{\sum }_i{w}_i{x}_i}{{\sum }_i{w}_i},$$ (8)

$$\text{V}[x]=\frac{{\sum }_i{w}_i{\left(x_i-\text{E}[x]\right)}^2}{{\sum }_i{w}_i},$$ (9)

and

$$C[x,y]=\frac{{\sum }_i{w}_i\left(x_i-\text{E}[x]\right)\left(y_i-\text{E}[y]\right)}{{\sum }_i{w}_i},$$ (10)

where x and y are various combinations of D_iso, $D_{\Delta }^2$, D_xx, D_yy, D_zz and R₂. For comparison with results from conventional diffusion MRI performed at some finite value of τ_E, the relaxation factor can be included in the calculation of, for instance,

$${\text{E}}^{\left({\tau }_{\text{E}}\right)}\left[D_{\text{iso}}\right]=\frac{{\sum }_i{w}_i\text{exp}\left(-{\tau }_{\text{E}}{R}_{2,i}\right)D_{\text{iso},i}}{{\sum }_i{w}_i\text{exp}\left(-{\tau }_{\text{E}}{R}_{2,i}\right)},$$ (11)

which is closely related to the conventional a ADC [21] and mean diffusivity (MD) [28], and where “τ_E” serves as a reminder that the mean value includes weighting by R₂ relaxation during τ_E. An even more direct comparison with conventional ADC measured with a single b-value is obtained by:

$$\text{ADC}\left(b,{\tau }_{\text{E}}\right)=\frac{\text{ln}S\left(b,{\tau }_{\text{E}}\right)-\text{ln}S\left(0,{\tau }_{\text{E}}\right)}{b},$$ (12)

where S(b,τ_E) is given by Eq. (4).

The extraction of quantitative metrics according to Eqs. (8–10) are performed for each of the 100 individual solutions per voxel, and the values finally displayed in parameter maps are obtained by taking the medians of the results for the individual solutions.

3. Results

Fig. 2 shows signals and corresponding 5D D-R₂ distributions for individual white matter (WM), gray matter (GM) and cerebral spinal fluid (CSF) voxels for a single representative rat brain. The S₀ maps are calculated according to Eq. (5), hence corresponding to signal at TE = 0 and b = 0. Consistent with previous in vivo mouse [90], in vivo human [22–24,26] and ex vivo rat results [25], the main distribution components of WM, GM and CSF are located in distinct corners of the 2D $D_{\text{iso}}-D_{\Delta }^2$ projection (WM: low D_iso and high $D_{\Delta }^2$, GM: low D_iso and low $D_{\Delta }^2$, CSF: high D_iso and low $D_{\Delta }^2$), thereby enabling “binning” for calculation of signal fractions f_bin1, f_bin2 and f_bin3 and associated diffusion-relaxation metrics nominally specific for WM, GM and CSF [22] ss seen in Fig. 3a The challenges of EPI readout at 21.1 T are readily apparent as distortions of the S₀ image stemming from susceptibility artifacts and Nyquist ghosting in the phase encoding direction [31,35]. Nevertheless, the bin-resolved fractions map captures the known spatial distributions of WM, GM and CSF. In addition to the binning, Fig. 3 also displays quantitative parameter maps obtained by extracting means E[x], variances V[x], and covariances C[x,y] by applying Eqs. (8)–(10) over selected dimensions and sub-divisions of the per-voxel 5D D-R₂ distributions [22–26,61,89,91]. The bin-resolved maps in Fig. 3b reveal E[R₂]-values of 70 and 60 s⁻¹ for WM and GM, respectively, which can be contrasted with the values 20 and 15 s⁻¹ observed for in vivo human at 3 T [22]. The per-voxel E[D_iso], $\text{E}\left[D_{\Delta }^2\right]$ and E[R₂] metrics in Fig. 3c are closely related to the more traditional parameters ADC [21] and MD [28], microscopic fractional anisotropy (μFA) [80,91], and quantitative T₂ = 1/R₂. Similar to μFA, the $\text{E}\left[D_{\Delta }^2\right]$ metric provides information on diffusion anisotropy independently from the underlying degree of orientational order, which is in contrast to the traditional FA [80,91]. Intravoxel heterogeneity are described with the variance and covariance measures V[x] and C[x,y] for which x and y imply various combinations of D_iso, $D_{\Delta }^2$ and R₂. Out of all these measures, V[D_iso] is most familiar from the literature under the names and symbols isotropic 2nd moment ${\mu }_2^{\text{iso}}$ [80], size variance V_MD [47] and isotropic mean kurtosis MK_I [46], and has been shown to be related to intra-voxel variance of cell density in brain tumors [46]. A more detailed discussion about the biological meanings of the remaining heterogeneity metrics can be found in [25,26]. Low GW/WM contrast can be seen in certain structures, in particular the corpus callosum (cc), cerebellum and edges of white matter areas. This decrease is due to partial volume effects from the relatively large slice thickness but also from the chosen human brain-based boundary values for the various bins [90].

Fig. 2.

Experimental results for representative WM (red), GM (green) and CSF (blue) voxels of an in vivo rat brain at 21.1 T. The signal S is shown as a function of the acquisition number n_acq according to the scheme in Fig. 1 (color-coded circles: experimental, black dots: fit). Nonparametric 5D D-R₂ distributions obtained by Monte Carlo data inversion of Eq. (4) are visualized as projections onto the 2D $D_{\text{iso}}-D_{\Delta }^2$, D_iso-R₂, and $D_{\Delta }^2-R_2$ planes, where D_iso is the isotropic diffusivity, $D_{\Delta }^2$ the squared normalized anisotropy defined in Eqs. (6)–(7), and R₂ is the transverse relaxation rate.

Fig. 3.

Quantitative parameter maps derived from the per-voxel 5D D-R₂ distributions. (a) S₀ image obtained by Eq. (5). Image segmentation is performed by dividing the 2D $D_{\text{iso}}-D_{\Delta }^2$ plane into three “bins” and calculating signal fractions [f_bin1,f_bin2,f_bin3] mainly reporting on the spatial distributions of WM, GM and CSF. Here, blue refers to CSF, red to WM and green to GM. (b) Bin-resolved signal fractions and means E[x] over the D_iso, $D_{\Delta }^2$, and R₂ dimensions according to Eq. (8). The bin fractions and means are coded into brightness intensity, and the properties of interest are represented by the color scales, which are each combined by two orthogonal scales in the image. Direction-encoded colors derive from the lab-frame diagonal values [D_xx,D_yy,D_zz] and maximum eigenvalue D₃₃. (c) Per-voxel means E[x], variances V[x] and covariances C[x,y] of various combinations of D_iso, $D_{\Delta }^2$, and R₂ are as defined in Eqs. (8–10).

In Fig. 4, data from the phantom are presented. Here, the liquid crystal (red tube in Fig. 4a phantom cartoon), hydrocarbons (yellow and green tubes in Fig. 4a phantom cartoon) and water are used to emulate the diffusion properties of WM, GM and CSF, respectively [79]. Even though the images are heavily distorted from chemical shift artifacts of the hydrocarbons and ghosting in the phase direction, the 21.1-T implementation of the 5D D-R₂ method yield parameter maps consistent with the known diffusion and relaxation properties of the constituents of the phantom. Notably, the binning in the $D_{\text{iso}}-D_{\Delta }^2$ plane designed for the calculation of tissue-specific signal fractions in the in vivo data also separates the liquid crystal, hydrocarbons and water fractions in the phantom data cleanly. For the liquid crystal, the directionally color-coded map E[D_xx,D_yy,D_zz] clearly shows the structure of the anisotropic domains [82]. The magnetic susceptibility anisotropy results in an orientational dependence on T₂ and ${T_2}^{*}$ as shown in Fig. 4c. These magnetic field dependent distortions are amplified at ultra-high fields as described by ΔB = χ_mB₀, where ΔB is the field imposed by the tissue/material interface and perturbing B₀ by the magnetic susceptibility, χ_m, of the material [92]. Susceptibility differences in the phantom consequently exacerbate the warping artifact of the phantom that is not seen in vivo. Likewise, the low bandwidth in the phase encoding dimension together with the resonance frequency difference between the water and hydrocarbons leads to pronounced chemical shift displacements of the latter from the top to the lower part of the image.

Fig. 4.

Parameter maps for the composite phantom comprising an assembly of tubes with liquid crystal (red tube in 4a phantom cartoon), hydrocarbons (1-octanol and n-dodecane, shown as yellow and green tubes respectively in 4a phantom cartoon) and water having diffusion properties similar WM, GM and CSF, respectively. See caption of Fig. 3 for detailed explanation of the panels and legends. Image distortions are exacerbated by susceptibility artifacts and chemical shift displacement of the two hydrocarbons not seen in vivo.

4. Discussion

Reassuringly, the straightforward 21.1-T implementation of a standard EPI sequence broadly reproduces previous results from 3 T [22], however with noticeably lower signal on account of the nearly four-fold increase in R₂ and field gradients induced by differences in magnetic susceptibility.

The trend towards higher fields is expanding with 7 T becoming more applicable in the clinic [93–95] and now with extension to 11 T for animals as well as humans [30]. Discussions and a feasibility study for a 20-T human magnet further predicts future high field trends [75], showing the importance of translating these sequences to higher fields and identifying needs for improvements to overcome challenges introduced at these field strengths. Increased B₀ has many benefits such as SNR, spectral dispersion and higher spatial resolution, but also some impairments such as susceptibility and warping artifacts in EPI-based encoding due to susceptibility gradients and other artifacts that are amplified by low bandwidths [74]. Depending on the application, relaxation can benefit image contrast but also complicate quantitative assessment. Spin-lattice relaxation of tissues is generally increased with some convergence in values for different tissues, leading to a decreased contrast for T₁-weighted scans. On the other hand, tissue signals are more readily saturated, benefiting contrast agent and time-of-flight applications. Transverse relaxation (T₂) times are generally shortened at increased field strength leading to improved blood oxygen saturation (BOLD) scans and susceptibility imaging, while also increasing the need for short TE scans to compensate for the decreased signal from shortened T₂.

Published values of the ADC for the striatum of in vivo rat at 21.1 T cover the range from 0.7 to 0.8·10^–9 m²s⁻¹ for image readout using simple spin echo, EPI, and spatio-temporal encoding (SPEN) at b-values up to 1·10⁹ sm⁻² and values of τ_E in the range from 25 to 40 ms [31]. For comparison with literature data, ADC values were calculated from S(b,τ_E) images synthesized from the 5D D-R₂ distributions according to Eq. (12), yielding ADC = (0.78 ± 0.04) 10⁻⁹ m²s⁻¹ (mean ± standard deviation) at b = 1·10⁹ sm⁻² and τ_E = 30 ms, which can be contrasted with E[D_iso] = (0.99 ± 0.09) 10⁻⁹ m²s⁻¹ corresponding to ADC in the limit b = 0 and τ_E = 0.

To capitalize on the potential SNR gains by ultra-high field, advanced diffusion sequences may require correspondingly ultra-strong gradients [38,39,60,96–98] to minimize the duration of typically lengthy gradient waveforms and, image read-out approaches. SPEN [31,35,90,99] or gradient and spin echo (GRASE) [100] are examples of such approaches that are less susceptible to B₀ inhomogeneity and relaxation than single-shot EPI. SPEN has been used at 21.1-T and has shown that B₀ artifacts can be overcome despite the minimum τ_E being longer than that of traditional spin-echo EPI [31,35]. With SPEN, τ_E increases linearly with the spatial coordinate in the low-bandwidth dimension, producing a gradient in T₂-weighting that potentially can produce a bias in diffusion metrics. Yon et al. has expanded on SPEN readout and incorporated the multidimensional diffusion approach at 15.2 T (79, 90). In doing so, Yon et al. employed SPEN in its fully refocusing mode and increased bandwidth to reduce B₀ inhomogeneity artifacts without compromising diffusion tensor distribution metrics from the incorporated multidimensional diffusion acquisition scheme [90]. In addition, Yon et al [101] showed that the SPEN technique alleviated artifacts in distortion prone regions of mouse brains for diffusion tensor imaging (DTI). Interleaved multi-segmented EPI acquisitions at 21.1 T also have been shown to reduce echo times and alleviate geometric distortions; however, this approach did not provide reliable ADC values, potentially due to motion or sampling impacts on signal [31]. Notably, the current study, as with other single-shot EPI readouts acquisitions [31,35], did provide expected and reliable diffusion measures. Persistent geometric distortions and artifacts are particularly prevalent in the composite phantom for which susceptibility mismatches together with chemical shift significantly reduce image quality. Nevertheless, as shown not only in this report but also others, in vivo and phantom diffusion data are accurate quantitively [31,35,79]. There are other strategies that can be implemented for future work that are commonly used in clinical settings to correct for EPI or field inhomogeneities, such as acquiring B₀ maps or inverted EPI blips. Other corrections such as brain/skull extraction, signal drift correction, denoising, etc [102] to improve data visualization should be considered for future work but may not be relevant in a preclinical setting.

5. Conclusion

In this study, it has been shown that an advanced diffusion scheme such as the multidimensional diffusion can be implemented at 21.1 T to provide results consistent with previous lower field studies. To realize the full potential of ultra-high field, efforts need to be directed to both sequence design and gradient hardware improvements to minimize warping artifacts and reach even shorter values of τ_E.