Filip Szczepankiewicz^{1}, Jens Sjölund^{2,3,4}, Freddy Ståhlberg^{1,5,6}, Jimmy Lätt^{7}, and Markus Nilsson^{5,6}

Diffusion weighting along more than one direction at a time (tensor-valued encoding) can be used to probe features of the microstructure that are not accessible by conventional encoding. For example, it enables diffusional variance decomposition (DIVIDE) which can separate the effects of microscopic anisotropy, orientation dispersion, and heterogeneous isotropic diffusivity. Tensor-valued encoding is usually demanding with respect to gradient performance, limiting its applicability to high-performance MRI systems. However, a recent method for optimized encoding significantly reduced the demand on gradient performance, which warrants an investigation of the applicability of such encoding on a wider range of MRI hardware configurations. In this study, we demonstrate whole-brain diffusional variance decomposition (DIVIDE) in less than 8 minutes at a wide range of clinical MRI systems with different hardware configurations.

Diffusional variance decomposition (DIVIDE) is a method that
enables estimation of the microscopic diffusion anisotropy independent of
orientation coherence^{1,2}, and
it can distinguish between disordered eccentric cells and variable cell density^{3}—features which are conflated by methods
that use only conventional (linear) diffusion encoding^{4}, such as DTI^{5} or DKI^{6}. The DIVIDE method is based on b-tensors with multiple
eigenvalue configurations, or shapes
(rank 1–3). Rank 2 encoding is enabled
by double diffusion encoding, but arbitrary shapes can be rendered by q-space trajectory encoding (QTE)^{2,7}. However, QTE usually requires strong
gradients to render feasible echo times, which has previously restricted its
implementation to high-performance systems.

Recent
development of optimized QTE^{8} has motivated its implementation at a wider range of MRI systems. The
purpose of this study was therefore to investigate the feasibility of
whole-brain DIVIDE based on QTE at a wide range of clinical MRI systems.

We performed QTE at three MRI systems (A-C, Table 1) in a single
healthy volunteer (male, 35 y). Hardware specifications and the 8-minute imaging
protocols are shown in Table 1. Asymmetric waveforms^{8} that
yield linear and spherical b-tensors (LTE and STE) were tailored for each
system independently. Images
were corrected for motion and eddy-currents^{9,10}.
Smoothing was avoided to retain the effect of noise.The signal model was based on the gamma distribution
function, which was fitted to the powder averaged signal to estimate the mean
diffusivity (MD) and the isotropic and anisotropic diffusional variance (V_{I} and V_{A})^{2,3}. The diffusional variance components (or mean kurtosis^{6} components) were scaled and normalized,
according to

$$\text{MK}_x=3\frac{{V_x}}{\text{MD}^2}$$

where ‘x’ denotes the specific
component (MK_{T}=MK_{I}+MK_{A})^{3}. The µFA was defined as^{2,3,7}

$$\text{µFA}=\sqrt{\frac{3}{2}}\left( 1+ \frac{ \text{MD}^2+V_I}{5/2 \cdot V_A} \right)^{-1/2}$$

We note that MK_{I}
reflects the heterogeneity of isotropic diffusivities, whereas MK_{A}
and µFA reflect the diffusion anisotropy on the microscopic level (µFA can be
interpreted as the FA that would be observed if all structures were ordered in
parallel)^{2,3,7}.
The SNR=E[S(b)]/σ[S(b)] was calculated from
multiple repetitions of the STE. A metric of quality (*Q*_{3}) was computed from the fractional volume of the brain
parenchyma where SNR>3 (cf. ref. 11) at *b*=2000
s/mm^{2}, excluding regions where MD<1.5 µm^{2}/ms. We
consider the quality of data to be sufficient if *Q*_{3}≥95%.
We also investigated if the high performance of system B
afforded 2 mm isotropic voxels. A whole-brain volume was acquired at a
resolution of 2×2×2 mm^{3} in 9 min by using only *b*=100, 1000, and 2000 s/mm^{2} in 6, 10, and 16 directions at
TR=8400 ms.

We have demonstrated that whole-brain DIVIDE based on QTE is
feasible at a wide range of MRI systems, and shown examples of the
parameter maps that can be expected at acquisition times of 8 minutes. The feasibility hinges on optimized asymmetric waveforms; these reduce the echo times by ≈ 40% vs. previous implementation^{1,3}, which increases SNR
by a factor 2–3 (T_{2} times from ref. 12). Furthermore, we achieved 2 mm isotropic voxels at system B, which is an unprecedented spatial resolution in
the context of b-tensor encoding.

Notably, this study cannot account for different RF systems, reconstruction, post-processing etc. This is most relevant at 7 T where improved RF homogeneity and fat suppression will likely improve the results. Furthermore, the proposed protocols are adapted to the brain, and may require modifications if applied to other tissues.

In conclusion, whole-brain DIVIDE is technically feasible in 8 minutes at main magnetic fields between 1.5 and 7 T, and gradient amplitudes as low as 43 mT/m. This demonstration may incite the investigation of relatively unexplored features, such as the microscopic diffusion anisotropy and the components of diffusional variance, on a wider range of systems.

Fig. 1 | Parameter maps in
transversal and coronal slices at three MRI systems (A-C, see Table 1) in one healthy volunteer. Parentheses show *B*_{0} and *G*_{max} in units of T and mT/m. Generally, the image
quality improves with field strength and gradient amplitude. At system C, two
notable artifacts appeared (red arrows); the anterior region exhibited negative
MK_{I} possibly due to poor RF homogeneity, and in the posterior region we
observed a prominent fat artifact. Furthermore, system E generally exhibited
higher values of MK_{A} and µFA compared to the other systems.

Fig. 2 | SNR maps at *b*=2000 s/mm^{2} in five
transversal slices, calculated from data acquired MRI systems A-C in one
healthy volunteer. Red outlines show regions where SNR<3; white outlines
show the outer bound where SNR>3. On systems A and B the SNR was only low in
regions that contain cerebrospinal fluid. Generally, the SNR was lower in the
central and inferior parts of the brain. The
irregular brain outline at system C was likely caused by poor RF homogeneity;
as indicated by the white outline, some of these regions were not included in
the quality metric (*Q*_{3}).

Fig. 3 | Parameter and SNR maps in
transversal and coronal planes in a healthy brain at a resolution of 2×2×2 mm^{3}.
The high spatial resolution lowered the SNR compared to the default resolution
of 2×2×4 mm^{3}, however, the SNR remained sufficient at *Q*_{3}=98%.

Table 1 | Hardware specification
and imaging protocols. All systems used matrix 256×256×30, resolution 2×2×4 mm^{3}, partial Fourier 0.75, acceleration factor 2, bandwidth
1400 Hz/voxel, min/max b-values 100/2000 s/mm^{2}. The echo and repetition time determined the number of samples b-shells^{13}. Equal
number of linear and spherical b-tensors were used. Systems A and B used 20-channel
receive head coils. System C used a 32 channel transmit/receive
head-coil. Systems A and C used b ≈ 100, 700, 1400, and 2000 s/mm^{2}; system B used b ≈ 100, 500, 1000, 1500, and 2000 s/mm^{2}.