Li Feng^{1}, Hersh Chandarana^{1}, Tiejun Zhao^{2}, Mary Bruno^{1}, Daniel K Sodickson^{1}, and Ricardo Otazo^{1}

^{1}Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, United States, ^{2}Siemens Healthineers, New York, USA

### Synopsis

This work compares golden-angle stack-of-stars
sampling and golden-angle Cartesian sampling for free-breathing liver MRI with
eXtra-Dimensional (XD) compressed sensing reconstruction. For Cartesian
sampling, the phase-encoding steps in the *k*_{y}-k_{z}
plane are segmented into multiple interleaves that rotate at a golden angle. Each
interleave starts from the center (*k*_{y}=k_{z}=0)
of k-space and follows a pseudo-radial pattern on a Cartesian grid. Results
from this initial study suggest that golden-angle Cartesian sampling achieves higher
effective spatial resolution than radial sampling, but it still suffers from residual
ghosting artifacts due to respiratory motion for free-breathing liver imaging.

**INTRODUCTION**

Golden-angle radial sampling^{1}
has several attractive benefits for abdominopelvic imaging. It enables continuous
data acquisitions and provides a high level of incoherence for the application
of compressed sensing techniques^{2,3}. The repeated sampling of the k-space
center reduces sensitivity to motion^{4,5} and provides self-navigation^{6,7}.
However, compared to conventional Cartesian imaging, radial sampling requires
longer reconstruction time and poses several challenges, including sensitivity
to off-resonances, gradient delays, and non-ideal gradient-amplifier responses.
These system imperfections may result in image distortion or blurring if not
corrected properly. In recent years, several studies have incorporated the
golden-angle rotation scheme into 3D Cartesian sampling^{8-12}. Here,
phase-encoding steps in *k*_{y}-k_{z}
plane are segmented into multiple radial- or spiral-like interleaves, and each
interleave is rotated by the golden angle from previous one. Such a sampling
strategy is expected to overcome the challenges presented in radial imaging
while offering the benefits of golden-angle radial sampling. Moreover, it provides
higher flexibility in the design of the sampling trajectory, allowing either
isotropic or anisotropic data acquisitions along different spatial dimensions. In
this work, golden-angle radial and golden-angle Cartesian sampling schemes were
compared for e**X**tra-**D**imensional (XD) sparse reconstruction of liver MRI. **METHODS**

**Sampling Trajectory Design:** Our sampling trajectories were designed for axial acquisitions,
which is the major imaging orientation employed in routine clinical liver MR
exams. Golden-angle radial sampling was implemented using a star-of-stars
trajectory, where radial encoding was employed in the *k*_{x}-k_{y} plane and fully-sampled Cartesian
encoding was employed along the *k*_{z}
dimension (the head-to-foot direction in our study) (Figure1a). Respiratory
motion signal was detected from the centers of k-space in each *k*_{x}-k_{y} plane (red
dots), as described in (7). Golden-angle Cartesian sampling was implemented in
the *k*_{y}-k_{z} plane,
which are the anterior-posterior direction (*k*_{y})
and the head-to-foot direction (*k*_{z}),
respectively (Figure1b). In addition, an extra k-space measurement orientated
along *k*_{z} (red lines in
Figure1b) was consistently acquired in the end of each interleave for
respiratory motion detection. The motion detection procedure was the same as
that performed in radial imaging.

**Imaging Studies: **IRB-approved liver imaging
was performed in 3 patients after contrast injection and also in one volunteer
without intravenous contrast. For each subject, both golden-angle radial sampling
and golden-angle Cartesian sampling were performed, and each dataset was continuously
acquired for 90 seconds in a transverse orientation. Each dataset was sorted
into four respiratory states using extracted motion signals, and motion-resolved
sparse reconstruction (XD-Sparse) was performed as previously described in (7).
For each pair of results (one radial and one Cartesian), a radiologist blinded
to the acquisition schemes was asked to select a preferred result.

**RESULTS**

Figure2a shows non-contrast results from the volunteer
comparing radial sampling (left) and Cartesian sampling (right) for two slices.
These results suggest that radial sampling suffers from slight blurring, which is
likely due to a combination of residual motion and off-resonance effects. Cartesian
sampling, on the other hand, achieved increased image sharpness, but suffered
from residual ghosting artifacts (green arrow) due to motion. For the first patient
study in Figure3, radial sampling and Cartesian sampling achieved comparable image
sharpness, but the latter suffered from residual ghosting artifacts (green
arrows) as in the non-contrast case in the volunteer. The results from the
second patient study (Figure4) were similar to those for the first patient, with
residual ghosting artifacts clearly visible in the Cartesian approach. In the
last patient study (Figure5), radial sampling and Cartesian sampling achieved comparable
image sharpness, and motion artifacts were not noted in any of them, which is
likely due to lighter breathing of the subject during data acquisition. For all
the five pairs of images, a radiologist blinded to the acquisition scheme
preferred the radial result.**DISCUSSION**

In this initial
study, golden-angle Cartesian sampling produced slightly higher image sharpness,
which is likely due to its immunity to system imperfections such as
off-resonance and gradient-nonlinearity. However, the performance of radial
sampling was more consistent and more reliable for free-breathing liver imaging
due to its higher robustness to motion. Although the center of k-space is
oversampled in both golden-angle radial and Cartesian trajectories, leading to
reduced sensitivity to respiratory motion, the interpolation process in the gridding
operation results in increased averaging effects in radial image reconstruction,
which explains the appearance of residual ghosting artifacts in Cartesian
sampling. However, although our study suggested that golden-angle radial
sampling is more reliable for liver imaging, golden-angle Cartesian sampling
could be a better choice for applications where motion is less of a challenge,
such as DCE-MRI of the brain^{11} or pediatric imaging with sedation^{8,13}### Acknowledgements

This work was supported in part by the NIH, and was performed under the rubric of the Center for Advanced
Imaging Innovation and Research (CAI^{2}R), a NIBIB Biomedical Technology
Resource Center (NIH P41 EB017183).### References

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