Gigi Galiana^{1} and Nadine Luedicke^{2}

FRONSAC encoding, which adds a rapidly oscillating low-amplitude nonlinear gradient to a standard undersampled trajectory based on linear gradients, has been shown to significantly improve k-space coverage and parallel imaging reconstructions. This abstract further shows that a fixed FRONSAC waveform improves image quality for Cartesian trajectories of various FOV and resolution, while avoiding many of the pitfalls of other highly efficient gradient trajectories. Results show that FRONSAC provides better reconstruction than Cartesian encoding alone, while offering better resilience to delays and off-resonance effects than non-Cartesian trajectories, such as spiral.

One of the attractive features of Cartesian imaging is that
experimental imperfections, e.g. gradient delays, trajectory errors, or
off-resonance spins, lead to relatively simple errors in the reconstructed
image. But Cartesian encoding is not
optimal for undersampled parallel imaging.^{1} Non-Cartesian trajectories, such
as spiral, permit higher undersampling factors, but these methods are generally
intolerant of experimental imperfections and require rigorous field
mapping. Since each new FOV, matrix
resolution or slice orientation requires a different gradient trajectory,
measuring or predicting these trajectories is a significant challenge.^{2}

With FRONSAC encoding, the readout is accompanied by two
oscillating nonlinear gradients, which produce a rotating nonlinear field. (Figure
1) Cartesian imaging with FRONSAC encoding is a recent method which enhances
the k-space coverage of parallel imaging and results in better undersampled
images, while avoiding many pitfalls of other highly efficient gradient
trajectories.^{3,4} This work considers adding a fixed FRONSAC encoding field
to Cartesian acquisitions where the linear gradients are adjusted to image different
FOVs and matrix sizes, and various experimental imperfections are introduced. Results show that FRONSAC provides markedly
better images than Cartesian encoding alone, while offering better resilience
to delays and off-resonance than non-Cartesian trajectories, such as
spiral.

Figure1: FRONSAC Pulse Sequence

Cartesian FRONSAC encoding adds an additional oscillating gradient to a standard spin warp sequence. This amounts to adding a rotating nonlinear field to the readout, which spreads k-space sampling and improves images from undersampled scans.

Figure 2: Undersampled Images

FRONSAC improves images from undersampled trajectories. Rows compare Cartesian with 12 or 24 readouts, spiral trajectories with 12 or 24 rotations in k-space, and FRONSAC with 12 or 24 readouts. FRONSAC encoding is identical to the Cartesian case, except that an additional rapidly rotating nonlinear gradient is played with each readout.

Figure 3: A Fixed FRONSAC Waveform Can Enhance Many Scans

These images show that the FRONSAC gradients do not need to be tailored to the scan prescription to improve parallel imaging performance. A single well-characterized FRONSAC waveform can dramatically improve images despite changes to the linear sampling pattern, such as those needed to change FOV or resolution.

Figure 4: Sensitivity to Off-Resonance Spins

FRONSAC is insensitive to off-resonance imperfections. R=8 imaging was simulated with various linear off-resonance for three sequences: Cartesian with 12 phase encode steps, spiral with 12 cycles, and FRONSAC with 12 phase encode steps. Cartesian images show strong undersampling artifacts at this high acceleration, but linear off-resonance generates simple distortions that further degrade the parallel imaging only slightly. In a perfectly shimmed field, the spiral and FRONSAC images are of comparable quality and quite good, but FRONSAC reconstructions do much better in the presence of off-resonance.

Figure 5: Sensitivity to Gradient Delays

FRONSAC is insensitive to gradient delays. Since FRONSAC is based on a Cartesian trajectory along the linear gradients, it shows similar insensitivity to delays in those channels. As in a Cartesian image, the error in the encoding matrix is equivalent to adding a fixed phase roll to the reconstructed object, which does not affect the magnitude image.