E. H. Bhuiyan^{1}, Nadine L. Dispenza^{1}, R. Todd Constable^{1}, and Gigi Galiana^{1}

This work reports the performance of various gradient waveforms
for Fast Rotary Nonlinear Spatial Acquisition (FRONSAC) encoding, varying the amplitude,
frequency and phase of the oscillation on different channels. Waveforms using
three NLG channels were used to image an American College of Radiology (ACR) phantom,
and root-mean-square error (RMSE) relative to a fully sampled reference was
used to evaluate performance. Experimentally observed trends support those
reported in previous work, which was based on theory and simulations. For the given hardware, the results suggest
that the best combination for C3, S3 and Z2 are 64, 64 and 32 cycles per
readout and 1.74×10^{6}mTm^{-3}, 1.74×10^{6}mTm^{-3}
and 3.05×10^{6}mTm^{-2} respectively.

Parallel imaging can significantly accelerate acquisition and consequently reduce the cost of MR imaging.^{1-8 }While many non-Cartesian sequences show excellent potential for parallel imaging, they generally do so at the cost of complicated contrast and enhanced sensitivity to off-resonance spins and timing errors. However, previous work has suggested that FRONSAC can maintain the contrast and reliability of standard Cartesian acquisitions while improving artifacts due to undersampling.^{9-17}

With FRONSAC encoding, as the sampling function moves across k-space on the trajectory defined by the linear gradients, a rapidly changing nonlinear gradient changes the shape and orientation of the sampling function. These broader and more diverse sampling functions, modulated by coils and aided by oversampling, provide more measurements in the gaps of the linear trajectory in k-space, which subsequently reduces undersampling artifacts. However, the optimal gradient waveform to fill gaps in k-space is an open question with a staggering number of degrees of freedom.^{16-19 }Here we undertake an experimental optimization using three nonlinear gradients available at our site and restricted to sinusoidal waveforms.

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9. Stockmann JP, Ciris PA, Galiana G, Tam L, Constable RT. O‐Space imaging: Highly efficient parallel imaging using second-order nonlinear fields as encoding gradients with no phase encoding. Magnetic Resonance in Medicine. 2010:64(2):447-56.

10. Stockmann JP, Galiana G, Tam LK, Nixon TW, Constable RT. First O‐Space images using a high‐power, actively shielded 12cm Z2 gradient insert on a human 3T scanner. Proceedings of the ISMRM 19th Annual meeting. 2011:717.

11. Stockmann JP, Galiana G, Tam L, Juchem C, Nixon TW, Constable RT. In vivo O‐Space imaging with a dedicated 12 cm Z2 inserted coil on a human 3T scanner using phase map calibration. Mgn Reson Med. 2013;69(2): 444-55.

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16. Wang H, Tam L, Kopanoglu E, Peters D, Galiana G, Constable RT. Improving O‐Space Imaging Using High‐Resolution Oversampled Data Acquisitions. Proceedings of the ISMRM 22nd Annual Meeting. 2015: talk.

17. Wang H, Tam L, Constable RT, Galiana G. Fast Rotary Nonlinear Spatial Acquisition (FRONSAC) Imaging. Magn Reson Med. 2017 (March); 75(3) 1154-1165.

18. Galiana G, Stockmann JP, Tam L, Peters D, Tagare H, Constable RT. The role of nonlinear gradients in parallel imaging: A k-space based analysis. Concepts in Magnetic Resonance Part A.40A (5):253‐67.

19. Luedicke N, Tagare H, Galiana G, Constable RT, editors. Trajectory design of optimized repeating linear and nonlinear gradient encoding using a k-space point spread function metric. ISMRM Annual Meeting; 2016; Singapore.

20. Nadine L. Dispenza, Sebastian Littin, Maxim Zaitsev, R. Todd Constable, Gigi Galiana, Clinical Potential of a New Approach to MRI Acceleration, Scientific Report, Nature Publishing (submitted).

21. Nadine L. Dispenza, Maxim Zaitsev, R. Todd Constable, Gigi Galiana, ``Clinical Imaging Potential of FRONSAC”, invited talk for ISMRM Annual Meeting and Exhibition, Paris, France June 18, 2018.

Cartesian images for
R=1 (A) and R=4 (B), and a corresponding R=4 image with FRONSAC (C). All images
are reconstructed by GPU-accelerated conjugate gradients (CG) instead of
Fourier transform. Though imperfect coil profiles leave some undersampling
artifacts at R=4 for this 8-channel data, the improvements gained from FRONSAC
encoding are significant.

A representative set
of nine FRONSAC images acquired in a Siemens 3T Trio B by using different
combinations of NLG gradients C3, S3 and Z2. In each case, the acceleration
factor R=4. The FRONSAC gradient parameters used for each
acquisition are noted above each panel where F (f_C3, f_S3, f_Z2) denotes cycles
per readout and A (A_C3, A_S3, A_Z2) denotes gradient amplitude on the C3, S3,
and Z2 channels, respectively.

The residual images
are obtained by comparing the R=4 images with each FRONSAC gradient to the
normalised Cartesian R=1 images.

Summary of parameters used for each image
acquisition whose results are shown in Figures 2 and 3. RMSE, shown in the last column, is calculated
for each image relative to a fully sampled Cartesian reference.