Justin P. Haldar^{1} and Kawin Setsompop^{2}

We
describe a new approach that enables in vivo whole brain diffusion MRI with
simultaneously high spatial resolution (660 µm isotropic voxels) and high
angular diffusion encoding resolution (64 orientations at b=1500 s/mm^{2}
and 4 b=0 s/mm^{2} images) in only 15 minutes. This is achieved by combining the gSlider-SMS
acquisition strategy with constrained image reconstruction techniques that
enable denoising (exploiting the fact that the diffusion images are smooth with
correlated edge locations) and interlaced data subsampling (achieved by
exploiting the same correlated edge constraints used for denoising, as well as
through the use of q-space smoothness constraints).

Recent
progress has shown that in vivo whole-brain diffusion MRI can be acquired with
simultaneously high spatial resolution (660 µm isotropic voxels) and high
angular diffusion encoding resolution (64 orientations at b=1500 s/mm^{2}
and 7 b=0 s/mm^{2} images) in as short as 25 minutes on the 3T CONNECTOM
system^{1}. This was achieved by
combining the generalized SLIce Dithered Enhanced Resolution Simultaneous
MultiSlice (gSlider-SMS) technique^{2} for SNR-efficient data
acquisition with the SNR-enhancing joint reconstruction (SER)^{3,4} approach.
Other recent work has shown that it possible to accelerate multi-encoding
diffusion techniques like reversed-gradient field inhomogeneity correction^{5},
gSlider-SMS^{6}, and super-resolution reconstruction^{7,8}
using the concept of “interlaced subsampling.” In this approach, each point in
q-space is acquired with only a portion of its nominal set of spatial encodings
to save time in data acquisition. While
this would normally lead to poor image quality, it has been shown
that high-quality image reconstruction is still possible by incorporating
spatial and q-space smoothness constraints into the reconstruction^{5-8}.

In
this work, we show that gSlider-SMS, SER, and interlaced subsampling can all be
combined together to provide substantial additional acceleration, and
demonstrate in vivo human brain images with matching spatial coverage, spatial
resolution, and diffusion encoding resolution to that described previously^{1},
but reducing the acquisition time from 25 minutes to 15 minutes.

The proposed
approach was tested by retrospectively undersampling the same 25 minutes of
gSlider-SMS data described previously^{1}. The conventional gSlider-SMS technique
acquires simultaneous multislice diffusion data with slices that are 5x thicker
than the nominal resolution, and uses 5 different RF encodings (that apply
different phase modulations) to resolve the thinner slices that contribute
signal to the thick slice. To simulate
interlaced subsampling, we randomly discarded 2 out of 5 RF encodings for each
of the 64 diffusion weighted images. We
also discarded 3 out of the 7 images acquired without diffusion weighting (b=0
s/mm^{2}), though retained the full set of encodings for the
remaining unweighted images. This corresponds to keeping only 213 (58%) of the original 369 image volumes.

For simplicity,
thick slices were first reconstructed using standard parallel imaging and
simultaneous multislice reconstruction^{1}. Subsequently, thin slices were estimated by solving the optimization problem:
$$\hat{\mathbf{p}} = \arg\min_{\mathbf{p}} \|\mathbf{b} - \mathbf{E}
\mathbf{p}\|_2^2 + \lambda_1 J(\mathbf{p}) + \lambda_2 R(\mathbf{p}).$$ The first two terms of this equation
correspond to a data consistency constraint ($$$\mathbf{b}$$$ is the vector of
acquired data measurements for all voxels, all diffusion encodings, and all RF
encodings; $$$\mathbf{E}$$$ is the matrix representing the gSlider mapping from
thin slices to subsampled phase modulated thick slices, and also includes the
effects of shot-to-shot phase variations induced by the diffusion encoding; and
$$$\mathbf{p}$$$ is the vector of high-resolution images to be reconstructed)
and a spatial-smoothness regularization constraint for SER^{3,4}
($$$J(\cdot)$$$ is constructed based on a shared compound Markov Random Field
edge model^{3}, that encourages that image edges should be sparse, with
correlation between the edge locations of different images). These two terms are very
similar to what was used in previous work that combined gSlider-SMS with SER^{1}. The third term $$$R(\cdot)$$$ is a
regularization penalty that encourages smoothness of the signal in q-space,
following previous approaches for interlaced subsampling^{5-8}. For simplicity and consistent with some of the
previous interlaced subsampling work^{5}, we choose $$$R(\cdot)$$$ as simply the squared $$$\ell_2$$$-norm of the Laplace-Beltrami smoothness operator
applied to the spherical harmonic representation of the q-space signal
variations of each voxel^{9}. Variables $$$\lambda_1$$$ and $$$\lambda_2$$$ correspond to
regularization parameters that were adjusted manually to achieve the desired
trade-off between spatial resolution and signal-to-noise ratio.

Our proposed
new approach was compared against traditional gSlider-SMS from 25 minutes of
data acquisition (without SER and without interlaced subsampling) and
gSlider-SMS from 25 minutes of data acquisition with SER (without interlaced
subsampling). After images were
reconstructed, we computed orientation distribution functions (ODFs) using the
Funk-Radon and Cosine Transform^{10} (using BrainSuite software, http://brainsuite.org/) and also estimated diffusion tensors.

1.
Haldar
JP, Fan Q, Setsompop K. “Whole-brain
quantitative diffusion MRI at 660 µm resolution in 25 minutes using gSlider-SMS
and SNR-enhancing joint reconstruction.”
*Proc. ISMRM* 2016, p. 102.

2.
Setsompop
K, Stockmann J, Fan Q, Witzel T, Wald LL.
“Generalized SLIce Dithered Enhanced Resolution Simultaneous MultiSlice
(gSlider-SMS) to increase volume encoding, SNR and partition profile fidelity
in high-resolution diffusion imaging.” *Proc. ISMRM* 2016, p. 607.

3.
Haldar
JP, Wedeen VJ, Nezamzadeh M, Dai G, Weiner MW, Schuff N, Liang Z-P. “Improved diffusion imaging through
SNR-enhancing joint reconstruction.” *Magn Reson Med* 69:277-289, 2013.

4.
Kim
JH, Song S-K, Haldar JP.
“Signal-to-noise ratio-enhancing joint reconstruction for improved
diffusion imaging of mouse spinal cord white matter injury.” *Magn
Reson Med* 75:1499-1514, 2016.

5.
Bhushan
C, Joshi AA, Leahy RM, Haldar JP.
“Improved B0-distortion correction in diffusion MRI using interlaced
q-space sampling and constrained reconstruction.” *Magn
Reson Med* 72:128-1232, 2014.

6.
Ning
L, Setsompop K, Rathi Y. “A combined
compressed sensing super-resolution diffusion and gSlider-SMS
acquisition/reconstruction for rapid sub-millimeter whole-brain diffusion
imaging.” *Proc ISMRM* 2016, p. 4212.

7.
Ning
L, Setsompop K, Michailovich O, Makris N, Shenton ME, Westin C-F, Rathi Y. “A joint compressed-sensing and
super-resolution approach for very high-resolution diffusion imaging.” *NeuroImage*
125:386-400, 2016.

8.
Van
Steenkiste G, Jeurissen B, Veraart J, den Dekker AJ, Parizel PM, Poot DH,
Sijbers J. “Super-resolution
reconstruction of diffusion parameters from diffusion-weighted images with
different slice orientations.” *Magn Reson Med* 75:181-195, 2016.

9.
Descoteaux
M, Angelino E, Fitzgibbons S, Deriche R.
“Regularized, fast, and robust analytical Q-ball imaging. *Magn
Reson Med* 58:497-510, 2007.

10. Haldar JP, Leahy RM. “Linear transforms for Fourier data on the
sphere: Application to high angular resolution diffusion MRI of the
brain.” *NeuroImage* 71:233-247, 2013.

11. Shattuck DW, Chiang MC, Barysheva M,
McMahon KL, de Zubicaray GI, Meredith M, Wright MJ, Toga AW, Thompson PM. “Visualization tools for high angular
resolution diffusion imaging.” *Proc MICCAI* 2008, pp. 298-305.