Christine Law^{1}, Gary Glover^{1}, and Sean Mackey^{1}

^{1}Stanford University, Stanford, CA, United States

### Synopsis

**We
present a novel idea for quickly detecting the optimal half k-space for use in
partial Fourier acquisition. With EPI acquisition, the center of k-space can be offset from the
origin by local magnetic field inhomogeneity.
This offset can occur in both positive and negative phase encode directions. For partial Fourier acquisition, it is
important to sample the portion of k-space containing the center peak. Before data collection using partial Fourier
acquisition, a reference scan that collects two time frames (each with
different halves of k-space coverage) can be used to determine the proper half
of k-space to collect for each slice.**### Purpose

We
present a novel idea for quickly detecting the optimal half k-space for use in
partial Fourier acquisition. When using echo
planar imaging (EPI) acquisition, the center of k-space can be offset from the
origin by local magnetic field inhomogeneity.
This offset can occur in both positive and negative phase encode (PE) directions. For partial Fourier acquisition, it is
important to sample the portion of k-space containing the center peak. Before data collection using partial Fourier
acquisition, a reference scan that collects two time frames (each with
different halves of k-space coverage) can be used to determine the proper half
of k-space to collect for each slice.

### Methods

One
technique, to speed up fMRI acquisition, is partial Fourier acquisition that
samples slightly over half of k-space instead of full k-space. Ideally, if objects are real, k-space samples
have Hermitian symmetry. Sampling half
of k-space should provide enough information to fill in missing k-space samples. Due to off-resonance, motion, and flow, k-space
data is not purely real. So, a few extra
k-space lines are acquired in order to calculate a low frequency phase map to correct
for incidental phase variation as in homodyne reconstruction

^{1}.
For
objects with minimal off-resonance, the center of k-space contains the peak
energy since most energy is contained at low spatial frequency. In objects where local field inhomogeneity is
severe, k-space peak energy is no longer centered at the origin. For EPI, the phase encode direction has very
low bandwidth when compared to the frequency encode direction. Thus, local field inhomogeneity will cause a
shift mainly in the PE direction

^{2}. When
shift is greater than coverage of the extra k-space lines acquired, low
resolution k-space data will not be captured which results in suboptimal
reconstruction (Fig.1).
Since
the direction of k-space center-shift is related to sign of the local
off-resonance magnetic field gradient, it is possible to have the center of k-space
shift in the positive phase encode direction for one slice then shift in the
negative phase encode direction in another. (If isocenter is placed between
superior frontal and lateral parietal lobes, for instance, k-space for slices
containing each lobe may shift in opposite directions.) The best option in acquiring partial Fourier
data is to collect data only in respective halves of k-space containing the
peaks. We propose a reference scan,
consisting of two time frames, in order to locate the center of k-space for
each and every slice. See flowchart in
Figure 2.
Assume
that the first time frame, of the proposed reference scan, covers the top
portion of k-space while the second time frame covers the lower (Fig.1a,b). Since
data from k-space center should contain the highest energy, choosing the half
of k-space having higher energy should indicate that the k-space center has shifted
to that particular half. After knowing
which half of k-space should be sampled for each slice, an acquisition table in
the pulse sequence is then automatically filled by either top or bottom partial
Fourier acquisition trajectories for that slice in the actual fMRI scan (Fig. 3).
To prove this concept, a full
set of k-space data was acquired (3T GE Discovery MR750) using a single-channel
head coil and EPI trajectory (matrix size/slices/TE/thickness/FOV=64x64, 16, 50ms,
4mm, 220mm). We used top and bottom 5/8
portion of k-space to reconstruct two images by homodyne technique from the
same slice for comparison. We also
calculated total energy for each half of k-space data.

### Results

As
shown in Fig.1, there is a shift of k-space center from the slice near frontal
sinus caused by magnetic susceptibility difference and off-resonance in local
magnetic field. Reconstruction from the top
half of k-space, that contains center peak, retains most of the image
information. Using the lower half of
k-space instead leads to signal loss and image distortion.

### Discussion

Partial
Fourier acquisition is an efficient way to improve imaging speed by undersampling
k-space. In the presence of local field inhomogeneity,
k-space center can experience a shift in the PE direction under EPI
acquisition. Before using partial
Fourier acquisition in fMRI, a reference scan can be used to quickly calculate the
proper k-space half. The center of
k-space can be determined from the half of k-space containing highest energy;
even without reconstructing the two half Fourier images. This can help streamline an automatic
pipeline for choosing the proper k-space trajectory for each slice in actual
fMRI scans.

### Acknowledgements

General Electric Healthcare. NIH Grant: P41 EB0015891, R01 NS053961, K24 DA029262. Ambhir-RSL Innovation Challenge Grant### References

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DC, Nishimura DG, Macovski A. Homodyne Detection in Magnetic Resonance Imaging. IEEE Trans Med Imaging. 1991; 10(2):154-163.
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R, Howseman A, Rees GE, Josephs O, Friston K. Functional Magnetic Resonance
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