Whole-brain quantitative diffusion MRI at 660 µm resolution in 25 minutes using gSlider-SMS and SNR-enhancing joint reconstruction

Justin P Haldar^{1}, Qiuyun Fan^{2}, and Kawin Setsompop^{2}

It is extremely challenging to
acquire whole-brain *in
vivo* diffusion
weighted images (DWIs) with sub-millimeter resolution using
traditional approaches. This work proposes and evaluates a novel
approach to diffusion MRI that can acquire 71 whole-brain DWIs (64
diffusion weightings + 7 *b*=0 images) at (660 µm)^{3}
resolution in 25 minutes. Our approach is based on a novel
generalization [1] of the previous Slider-SMS approach [2], combined
with a regularized reconstruction method that has been demonstrated
to substantially improve the SNR in both healthy [3] and injured [4]
tissues with a minimal loss of spatial resolution.

The previous Slider-SMS acquisition strategy for diffusion MRI [2] combines multiple novel fast imaging technologies to achieve high-resolution whole-brain imaging:

$$$\bullet$$$Blipped CAIPI [5] was used to enable SNR-efficient simultaneous imaging of multiple slices.

$$$\bullet$$$Thick-slice super-resolution techniques [6] were used to increase resolution along the slice dimension. Thick-slice super-resolution techniques acquire overlapping thick slices, and then solve a linear system of equations to estimate the corresponding thin slices of interest. This is advantageous because thin slices can be recovered from an acquisition that exploits the higher SNR-efficiency of 3D volume encoding.

While Slider-SMS was effective at enabling high-resolution whole-brain diffusion MRI [2], it still suffers from blurring due to the inherent ill-conditioning of the thick-slice super-resolution inverse problem, which itself results from the large coherence between the encoding functions of the overlapping thick-slice acquisition. The novel gSlider-SMS acquisition approach [1] uses the same Blipped CAIPI and thick-slice super-resolution approaches as Slider-SMS, except that the excitation RF pulse is modified so that each thick slice has a specially-designed non-uniform phase profile along the slice dimension, which serves as an additional form of RF encoding. This RF phase encoding has the effect of substantially reducing the coherence between the shifted overlapping thick-slice encoding functions, which improves the conditioning of the inverse problem and enables higher-fidelity reconstruction.

While gSlider-SMS is very SNR-efficient, the extremely small isotropic voxel sizes mean that SNR is still a limiting factor for DWIs acquired with high b-values. To address this issue, we employ a variation of a previous regularized reconstruction method [3,4] that uses phase modeling to regain the resolution lost from partial Fourier acquisition, and simultaneously uses the structural similarity between different DWIs to reduce noise perturbation while preserving high-resolution image features.

Whole-brain
gSlider-SMS DWI data was acquired at 660 µm isotropic resolution
over a 220×118×151.8 mm FOV, with 7 *b*=0
images and 64 DWIs with *b*=1,500
s/mm^{2}.
Each average was acquired in 25 minutes, and three averages were
acquired to provide a gold standard reference.
The
acquisition used thick slices (5× larger than each thin slice) with
5 different RF encoding pulses, a multiband factor of 2, and 6/8ths
partial Fourier encoding. The thick slices were first reconstructed
using slice-GRAPPA reconstruction [7]. Subsequently, gSlider
reconstruction, partial Fourier reconstruction, and denoising were
performed simultaneously by solving

$$\{\hat{\mathbf{p}},\hat{\boldsymbol{\phi}}\} = \arg\min_{\mathbf{p},\boldsymbol{\phi}}\|\mathbf{b}- \mathbf{G}( \boldsymbol{\phi}\odot\mathbf{A}\mathbf{p})\|_2^2+\lambda_1 R(\boldsymbol{\phi}) + \lambda_2 J(\mathbf{p}) $$

where $$$\mathbf{b}$$$ is the vector of complex images obtained after slice-GRAPPA reconstruction, $$$\mathbf{p}$$$ is the unknown vector of DWI amplitudes (real-valued and nonnegative), $$$\mathbf{A}$$$ is the matrix modeling the thick-slice and RF encoded gSlider acquisition, $$$\boldsymbol{\phi}$$$ is the unknown phase of each measured thick slice (phase is not consistent in diffusion MRI), and $$$\mathbf{G}$$$ is the matrix modeling the in-plane point-spread function of partial Fourier acquisition. The regularization penalty $$$R(\cdot)$$$ encourages $$$\boldsymbol{\phi}$$$ to be smooth within each slice [8,9], while the $$$J(\cdot)$$$ penalty uses a Huber function to impose that $$$\mathbf{p}$$$ is smooth, but has edge structures that are shared between different DWIs [3,4,10]. Optimization is performed using a majorize-minimize approach that alternates between estimating $$$\mathbf{p}$$$ and $$$\boldsymbol{\phi}$$$.

[1]
K. Setsompop, J. Stockmann, Q. Fan, T. Witzel, L. L. Wald.
“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.

[2]
K. Setsompop, B. Bilgic, A. Nummenmaa, Q. Fan, S. F. Cauley, S.
Huang, I. Chatnuntawech, Y. Rathi, T. Witzel, L. L. Wald. “SLIce
Dithered Enhanced Resolution Simultaneous MultiSlice (SLIDER-SMS) for
high resolution (700 um) diffusion imaging of the human brain.” *
Proc ISMRM*
2015, p. 339.

[3]
J. P. Haldar, V. J. Wedeen, M. Nezamzadeh, G. Dai, M. W. Weiner, N.
Schuff, Z.-P. Liang. “Improved Diffusion Imaging through
SNR-Enhancing Joint Reconstruction.” *Magn
Reson Med* 69:277-289,
2013.

[4]
J. H. Kim, S.-K. Song, J. P. Haldar. “Signal-to-Noise
Ratio-Enhancing Joint Reconstruction for Improved Diffusion Imaging of Mouse
Spinal Cord White Matter Injury.” *Magn
Reson Med*, Early
View. DOI: 10.1002/mrm.25691

[5]
K. Setsompop, B. A. Gagoski, J. R. Polimeni, T. Witzel, V. J. Wedeen,
L. L. Wald. “Blipped-controlled aliasing in parallel imaging for
simultaneous multislice echo planar imaging with reduced g-factor
penalty.” *Magn
Reson Med* 67:1210-1224,
2012.

[6]
H. Greenspan. “Super-resolution in medical imaging.” *Comput
J* 52:43-63, 2009.

[7]
S. F. Cauley, J. R. Polimeni, H. Bhat, L. L. Wald, K. Setsompop.
“Interslice leakage artifact reduction technique for simultaneous
multislice acquisitions.” *Magn
Reson Med* 72:93-102,
2014.

[8]
J. P. Haldar, Z. Wang, G. Popescu, Z.-P. Liang. “Deconvolved
spatial light interference microscopy for live cell imaging.” *IEEE
Trans Biomed Eng*
58:2489-2497, 2011.

[9]
F. Zhao, D. C. Noll, J. F. Nielsen, J. A. Fessler. “Separate
magnitude and phase regularization via compressed sensing.” *IEEE
Trans Med Imaging*
32:1713-1723, 2012.

[10]
J. P. Haldar, Z.-P. Liang. “Joint reconstruction of noisy
high-resolution MR image sequences.” *IEEE
Int Symp Biomed Imaging* 2008,
pp. 752-755.

Single-average
gSlider reconstruction of a (660 µm)^{3} resolution *b*=1,500 s/mm^{2} DWI (a) without joint regularization (λ_{2}=0) and (b) with joint regularization.
The use of regularized joint reconstruction leads to substantial gains
in image SNR without substantially reducing the image resolution.

Fractional
anisotropy (FA) maps derived from (a) single-average gSlider without
joint regularization, (b) single-average gSlider with
SNR-enhancing joint regularization, and (c) three-average gSlider without
joint regularization.
Single-average gSlider yields biased noisy FA maps without
regularization, which leads to a
loss of contrast between white and gray matter in inferior portions of the brain. In contrast,
the regularized results match quite well with the
three-average results.

Whisker
plots showing the primary orientations of diffusion tensors estimated from (a)
single-average gSlider without joint regularization, (b)
single-average gSlider with SNR-enhancing joint regularization, and (c)
three-average gSlider without joint regularization. Orientations derived from single-average
data without regularization are noisy, while the regularized results match closely with the
three-average results, and are sensitive enough to detect coherent
anisotropy in gray matter.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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