Partial Fourier fMRI acquisition pipeline for optimal half k-space coverage
Christine Law1, Gary Glover1, and Sean Mackey1

1Stanford 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 reconstruction1. 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 direction2. 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

1. Noll DC, Nishimura DG, Macovski A. Homodyne Detection in Magnetic Resonance Imaging. IEEE Trans Med Imaging. 1991; 10(2):154-163. 2. Turner R, Howseman A, Rees GE, Josephs O, Friston K. Functional Magnetic Resonance Imaging of the Human Brain: Data Acquisition and Analysis. Exp Brain Res. 1998 Nov; 123(1-2): 5-12.

Figures

Figure 1. (a) If partial Fourier sampling covers that portion of k-space data containing the center peak (marked by red dot), the resulting reconstructed image (c) is more desirable than (d) which results from sampling the (lower) portion of k-space that misses the center peak (b).

Figure 2. Flowchart for optimal partial Fourier acquisition for fMRI by automated selection of upper/lower k-space.

Figure 3. From the reference scan, k-space center-shift direction can be determined for each slice; e.g, slice 1 and 2 have their k-space centers shifted in opposite directions (b,c). The pulse sequence acquisition table can be automatically updated by the proper partial k-space trajectories (d and e respectively).



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