Dong-Hoon Lee^{1}, Do-Wan Lee^{2}, Jae-Im kwon^{3}, Chul-Woong Woo^{3}, Sang-Tae Kim^{3}, Jin Seong Lee^{4}, Choong Gon Choi^{4}, Kyung Won Kim^{4}, Jeong Kon Kim^{4}, and Dong-Cheol Woo^{3,5}

GluCEST is a novel molecular MR imaging technique to detect glutamate in the brain parenchyma by measuring the exchange of glutamate amine protons with bulk water. However, a disadvantage of CEST imaging is the relatively long scan time required to collect the data while varying the resonance frequency around the water. In this abstract, we describe the application of a retrospective motion correction approach using a gradient-based motion correction (GradMC) algorithm to CEST data for investigating the feasibility of motion correction, using an epileptic seizure rat model with head motion. Our results clearly show that the GradMC can be used in CEST imaging to efficiently correct for motion.

*CEST experiment: *Epileptic seizure was
induced in six male Wistar rats by 15 mg/kg intraperitoneal injection of kainic
acid (KA).^{5} CEST data were
obtained using a 7T Bruker MRI scanner before and 3 hours after KA injection.
CEST data were acquired using a turbo-RARE pulse sequence with the following
parameters: S_{0} image
and -3.67~+3.67ppm at 0.33ppm intervals, TR/TE=4200/36.4ms, RARE factor=16, and
a continuous-wave RF saturation pulse (power/time=5.6μT/1s). A B_{0} map with double
echo-times (1.9 and 2.6ms) and a B_{1} map with double flip-angles (30° and 60°) were
acquired to correct field inhomogeneities.^{1} The
GluCEST signal was calculated at 3.0ppm using the following equation: [S_{sat}(-3.0ppm) - S_{sat}(+3.0ppm)]/S_{sat}(-3.0ppm)^{1,2} based on the manually drawn
ROI in the hippocampus region.

*Motion correction procedures*: The cost function based
on the image gradient entropy metric was constructed as follows: Φ(*u*)=H(D_{x}*u*)+H(D_{y}*u*),
H(*u*)=-*v*^{T}ln *v*, *v*=√(*u○ū*/*u*^{H}*u*), where D_{x} and D_{y} are horizontal and vertical finite difference
matrices, H(∙) is a pixel entropy, *u* is an unknown image, and a○b is the
pointwise (Hadamard) product of two vectors. We estimated the motion parameters θ, which best
describe the motion in the corrupted volume, and then corrected for motion. By
empirical inversion we mean the application of A_{θ} directly to
a motion-corrupted observation *y* as follows: *u*_{θ}=F^{H}A_{θ}*y*, where *u*_{θ} is
a result image in the spatial domain, A_{θ} is a rigid
motion transformation matrix, and F is an orthonormal Fourier matrix. We regularized the trajectory of the recovered
motion parameters by putting a quadratic penalty on the differences of
consecutive motion parameters as follows: θ=argminΦ(F^{H}A_{θ}*y*)+λ|Dθ|^{2},
where D is a finite difference matrix, T is the number of k-space lines,
and λ is a regularization parameter controlling the smoothness. The translation correction amounts to a
multiplication of each k-space line with a linear phase ramp, exp(-2πik_{x}θ_{t}),
where θ_{t} is a translation function, and k_{x} is
the Fourier coefficient of the affected view. To compute the rotation effect, we
constructed a deformed grid by rotating the points of each k-space line by
their time-respective angles, and then we performed the interpolation in an
oversampled k-space to estimate the values on the points of the rotated grid.
We performed a minimizing cost function using a multi-scale coarse-to-fine
approach. In the first scale iteration, GradMC finds only the lowest frequency
segments of the motion trajectory. These segments are surrounded by gaps
corresponding to yet unknown motion parameters of higher-frequency views. In
each scale iteration, the gaps shrink until finally the whole trajectory is
recovered. More details of GradMC are available (see Ref. 3,4).

1. Cai K, Haris M, Singh A, Kogan F, Greenberg JH, Hariharan H, Detre JA, Reddy R. Magnetic resonance imaging of glutamate. Nat Med. 2012;18(2):302-306.

2. Davis KA, Nanga RP, Das S, Chen SH, Hadar PN, Pollard JR, Lucas TH, Shinohara RT, Litt B, Hariharan H, Elliott MA, Detre JA, Reddy R. Glutamate imaging (GluCEST) lateralizes epileptic foci in nonlesional temporal lobe epilepsy. Sci Transl Med. 2015;7(309):309ra161.

3. Loktyushin A, Nickisch H, Pohmann R, Schölkopf B. Blind retrospective motion correction of MR images. Magn Reson Med. 2013;70(6):1608-1618.

4. Loktyushin A, Nickisch H, Pohmann R, Schölkopf B. Blind multirigid retrospective motion correction of MR images. Magn Reson Med. 2015;73(4):1457-1468.

5. Lee DH, Lee
DW, Kwon
JI, Woo
CW, Kim
ST, Lee
JS, Choi
CG, Kim
KW, Kim
JK, Woo
DC. In vivo mapping and quantification
of creatine using chemical exchange saturation transfer imaging in rat models
of epileptic seizure. Mol Imaging Biol.
2018. In press.