Huajun She^{1}, Bian Li^{1}, Joshua S. Greer^{1,2}, Jochen Keupp^{3}, Ivan E. Dimitrov^{1,4}, Ananth Madhuranthakam^{1,5}, Robert Lenkinski^{1,5}, and Elena Vinogradov^{1,5}

^{1}Radiology, UT Southwestern Medical Center, Dallas, TX, United States, ^{2}Bioengineering, UT Dallas, Dallas, TX, United States, ^{3}Philips Research, Hamburg, Germany, ^{4}Philips Healthcare, Gainesville, FL, United States, ^{5}Advanced Imaging Research Center, UT Southwestern Medical Center, Dallas, TX, United States

### Synopsis

Chemical
exchange saturation transfer (CEST) is a new contrast mechanism in MRI. However,
a successful application of CEST is hampered by its slow acquisition and fast acquisition
is desired. Compressed sensing (CS) is powerful for perfect reconstruction of highly
undersampled data. Existing works mostly focus on the retrospectively downsampled
studies, but few implementation and analysis of truly undersampled scheme with
CEST has been reported. This work experimentally implements the random Cartesian
undersampled scheme and the golden angle radial sampling sequence for CEST. The
results demonstrate influence of experimental conditions that are not accounted
for in the retrospectively undersampled studies.

### Purpose

Chemical
exchange saturation transfer (CEST) imaging is a new MRI contrast approach and
many promising applications have been proposed, such as cancer and stroke [1]. CEST
imaging is time-consuming and fast acquisition is highly desired. As the new emergency of compressed sensing
(CS) theory [2-4], several
works have been developed to accelerate CEST with CS [5-8]. However, to the best of
our knowledge, no experimental implementation of a Cartesian undersampled CS
scheme with CEST had been reported. In this study, we design random Cartesian sampling
[4] sequence and golden angle radial (GAR) [9] sampling sequence
and use the low rank plus sparse matrix decomposition (L+S) method [10] to
reconstruct the truly undersampled phantom and in vivo human brain data.### Acquisition Method

Experiments
were performed on a Philips 3T Ingenia system using a 32-channel
head coil. Cartesian random sampling scheme uses the variable
density undersampling pattern [4]. After the saturation pulses, the k-space
lines are acquired with a low-high order as shown in Fig. 1. The low frequency k-space is fully sampled first and then high
frequency k-space is randomly sampled. Compared to the linear order, which samples
from the bottom of k-space
to the top, low-high order acquires the most important low frequency
information before T_{1} recovery diminishes the CEST effects. Radial sampling follows
an angular increment of 111.25°, which is designed to make the x and y gradients performs as: $$$Gy/Gx=tan^{-1}(n*111.25)$$$, where n is the number of spokes. The CEST images for human brain were acquired
with a TSE sequence, TR/TE=4200/6.4ms, slice thickness=4.4mm, FOV=240x240mm, 21
points swept between ±1000Hz in steps of 100Hz with one additional image
without saturation for normalization. Phantom consists of iopamidol solution
with pH values of 6.0 and 7.5. The CEST for phantom used similar parameters for
brain, only FOV=224x224mm. In all experiments, saturation RF consisted 10 hyper-secant pulses, each
of 49.5ms duration with 0.5ms intervals, and saturation power is 1.6μT
for human brain and 1.2μT for phantom. CEST processing used WASSR [11] for B_{0}
inhomogeneity correction. For fully sampled acquisitions, Cartesian and GAR samplings
were used in phantom and Cartesian sampling in human. In the CS
acquisitions, the Cartesian undersampling pattern was used with the reduction factor
R=5 for phantom and R=4 for brain. The GAR spokes were 224 and 56.### Reconstruction Method

In CEST imaging, voxels in the same compartment
have similar z-spectra [6]. The high spatiotemporal correlation is suitable
for the low rank matrix model. L+S decompose the CEST images matrix as a
summation of a low-rank matrix (few non-zero singular values) and a sparse
matrix (few non-zero elements). Specifically, the reconstruction algorithm tries
to solve this problem: $$$\min_{L,S}\parallel F(L+S)-d\parallel_2^2+\alpha\parallel L\parallel_*+\beta\parallel S\parallel_1$$$, where $$$F$$$ is the undersampling Fourier operator, $$$d$$$ is the undersampled k-space data, $$$\parallel \cdot\parallel_*$$$ is the nuclear norm to regularize the sparsity of the low-rank matrix $$$L$$$, $$$\parallel \cdot \parallel_1$$$ is the *l*_{1}-norm to regularize
the sparsity of the sparse matrix $$$S$$$, $$$\alpha$$$ and $$$\beta$$$ are regularization parameters.### Results and Discussion

Fig. 2 compares MTR_{asym} map and z-spectra between the reconstruction
of Cartesian fully sampled and undersampled phantom for different pHs. The CEST
effects are measured at 4.2ppm. The reconstruction is very close to the fully
sampled case. Fig. 3 demonstrates the APT maps for brain data, and the undersampled
result is similar to the fully sampled one but there is some difference at the
center part, which might be due to the volunteer’s motion between the
acquisitions or the B_{0} inhomogeneity. Fig. 4 compares the
reconstruction of fully sampled Cartesian and GAR of phantom. The
reconstruction of 224 spokes has a smaller CEST effects than 56 spokes, and
both of them are smaller and more inhomogeneous than Cartesian
one. The possible explanation is presented in Fig. 5: the linear radial sampling is implemented,
which means every radial k-space line goes through the k-space center. Thus, the
total CEST effect in the image is an average along the T_{1} recovery curve, and
the CEST effect should be smaller than the low-high order Cartesian
acquisition. Less spokes acquires data only at the beginning of T_{1} recovery, so
the CEST effect is larger in the heavier undersampled radial scheme. ### Conclusion

We experimentally designed the undersampled Cartesian and GAR CEST sequence,
and tested in the phantom and in vivo data. Phantom results demonstrate the undersampled
Cartesian scheme performs similar to the fully sampled case. The radial sampling
leads to decreased CEST effects compared to the Cartesian one. Work is underway
to conduct additional in vivo experimental
tests and to analyze different undersampling schemes.### Acknowledgements

The authors thank Dr. Ricardo Otazo (New
York University) for making the low rank plus
sparse matrix decomposition (L+S) code
available online. The authors thank Dr. Asghar Hajibeigi (University of Texas
Southwestern Medical Center) for phantom preparation. This work is supported in
part by the NIH grant R21.

### References

[1] van Zijl P, et
al. MRM 2011;65:927–948.

[2] Candes EJ, et
al. IEEE TIT 2006;52:489–509.

[3] Donoho DL. IEEE
TIT 2006;52:1289–1306.

[4] Lustig M, et
al. MRM 2007;58:1182–1195.

[5] Heo HY, et al.
MRM 2016 epub.

[6] Zhang Y, et al.
JMR 2013;237:125–138.

[7] She H, et al.
ISMRM 2016;2904.

[8] Kim J, et al.
ISMRM 2014;3621.

[9] Feng L, et al.
MRM 2013;69:1768-76.

[10] Otazo R, et
al. MRM 2015;73:1125-36.

[11] Kim M, et al.
MRM 2009;61:1441–1450.