Haifeng Wang^{1}, Yuchou Chang^{2}, and Dong Liang^{1}

Nonlinear spatial encoding magnetic (SEM) fields can accelerate data acquisitions and improve the imaging quality. In this work, the O-Space and FRONSAC imaging are combined into a hybrid nonlinear spatial encoding approach with dynamic nonlinear gradients. The preliminary experiment of phase mapping shows that the proposed method can be implemented in the current O-Space system. Simulations based on the preliminary experiment demonstrate that this approach can accelerate data acquisitions and reduce artefacts caused by highly undersampling acquisitions.

1. Hennig J, Welz AM, Schultz G, Korvink J, Liu Z, Speck O, Zaitsev M. Parallel imaging in non-bijective, curvilinear magnetic field gradients: a concept study. MAGMA. 2008; 21(1-2): 5-14.

2. Stockmann JP, Ciris PA, Galiana G, Tam LK, Constable RT. O-Space images: highly efficient parallel imaging using second-order nonlinear fields as encoding gradients with no phase encoding. Magn Reson Med. 2010; 64(2): 447-56.

3. Tam LK, Stockmann JP, Galiana G, Constable RT. Null Space Imaging: nonlinear magnetic encoding fields designed complementary to receiver coil sensitivities for improved acceleration in parallel imaging. Magn Reson Med. 2012; 68(4): 1166-75.

4. Gallichan D, Cocosco C, Dewdney A, Schultz G, Welz A, Hennig J, Zaotsev M. Simultaneously driven linear and nonlinear spatial encoding fields in MRI. Magn Reson Med. 2011; 65(3): 702-714.

5. Galiana G, Constable RT. Single Echo MRI. PLoS One. 2014;9(1): e86008.

6. Wang H, Tam LK, Constable RT, Galiana G. Fast rotary nonlinear spatial acquisition (FRONSAC) imaging. Magn Reson Med. 2016 Mar;75(3):1154-65.

7. Galiana G., Luedicke N., Improved Parallel Imaging with Resilience to Gradient Errors. Abstrac: 5163, ISMRM 2017.

8. Kaczmarz S. Approximate Solution for Systems of Linear Equations. International Bulletin of Polish Academy of Science and Letters, 1937; 35: 355–57.

9. 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 Magn Reson Part A. 2012; 40A (5): 256-267.

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

11. Wang H, Tam L, Kopanoglu E, Peters DC, Constable RT, Galiana G. O-space with high resolution readouts outperforms radial imaging. Magn Reson Imaging. 2017 Apr;37: 107-115.

12. Seber GAF, Wild CJ. Nonlinear Regression. Hoboken, NJ: Wiley-InterScience, 2003.

13. Setsompop K, Gagoski BA, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g-factor penalty. Magn Reson Med. 2012 May; 67(5):1210-24.

Fig.1 the timing diagram of a single-shot spiral pulse sequence
with the hybrid O-Space and FRONSAC imaging. There is a sinusoidal gradient waveform on the Z2 direction.

Fig.2 the phase gradients for the hybrid O-Space and FRONSAC sequence. The first and second row respectively show the amplitude and phase parts of the spin phase for a timepoint. In every case at different timepoints, the stamp sample a swatch of k-space a point and translates across k-space along the linear trajectory. Meanwhile, the sinusoidal gradients on the nonlinear Z2 channel cause this swatch can change the size.

Fig.3 the phase mapping sequence (a) has a sinusoidal waveform along Z2 and the addition of phase encoding pulses along both X and Y. The results (b) show the amplitudes, and frequencies of each voxel’s phase evolution to calculate the magnitude of the sinusoidal variant nonlinear Z2 field.

Fig.4 the simulation reconstruction results of the conventional linear gradient and hybrid O-Space and FRONSAC methods. Here, a numerical brain phantom is used; SNRs are all 20 dB; image sizes are all 64×64.