Optimization of a 3-channel gradient waveform for FRONSAC encoding
E. H. Bhuiyan1, Nadine L. Dispenza1, R. Todd Constable1, and Gigi Galiana1

1Radiology and Biomedical Imaging, Yale University, New Haven, CT, United States


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 1.74×106mTm-3, 1.74×106mTm-3 and 3.05×106mTm-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.


Gradient waveforms were tested at 96, 64 and 32 cycles per readout and two phases (sin and cos). For these high frequency waveforms, maximum amplitude is limited by slew limits over one period of the waveform. To test various amplitudes, waveforms were tested at the maximum achievable amplitude for that frequency and half the maximum amplitude. These tests were performed applying the existing 380mm ID gradient coil which delivers 10.1mT/m3/A, 9.8mT/m3/A and 1.5mT/m2/A, for C3, S3, and Z2, respectively. After collecting field maps and 8-channel coil profiles as previous described, an ACR phantom was imaged. A 3mm slice in the transverse plane was imaged with 250mm FOV, 128 phase encodings, 4x oversampling in the readout (512 points), TE/TR/BW= 16ms/50ms/130Hz/pixel.20-21 Images are reconstructed as previously described with a GPU accelerated CG algorithm.


Figure 1 shows a fully sampled Cartesian reference image of the phantom, along with an R=4 undersampled Cartesian image and an R=4 FRONSAC image. While the low number of channels and possible imperfections in the coil profiles limit the image quality in the undersampled images, these results demonstrate that FRONSAC encoding does significantly improve undersampling artifacts. Figure 2 shows a representative set of reconstructions achievable for various FRONSAC gradients, showing dramatic variations in image quality for different candidate waveforms. Difference images and RMSE, compared to a fully sampled Cartesian reference, are shown in Figure 3, and this data is summarized in the table of Figure 4, which tabulates these results ordered by RMSE. These experiments show that dephasing becomes an issue at large moments that are reached when lower frequency waveforms are applied on the strong and steep C3 and S3 gradients, as seen by comparing panels (A)-(C) to (E) and (F). Dephasing is further appreciated in the difference images, which show significant darkening across the image as well as the periphery. However, running these gradients at very high frequency does not allow for sufficient moment to maximally improve image quality, as seen in a comparison of panel (A) with panels (B)-(D). A similar trend is seen in variations of the Z2 gradient field, as shown in panels (G)-(I), for data taken on a different slice of this phantom. In the case of Z2, the gradient is less strong and steep, so a lower frequency and higher moment are favoured.

Discussion and Conclusion

Previous simulation studies on the effect of frequency in the FRONSAC waveform suggested higher frequency always improves image quality, but that work assumed a fixed gradient moment in each lobe of the sinusoid. Experimentally, there is a tradeoff between achievable moment and rapid oscillation in the sampling function.17 In agreement with previous simulations, these experiments did verify that very high gradient moments, especially in higher order gradient shapes, cause dephasing which inhibits image quality. This work tested a large set of possible waveforms to identify one well suited to the gradient capabilities, coil configuration, and noise characteristics of the scanner. The results are in agreement with previous generalizations deduced from theory and simulations. Furthermore, the results provide a waveform suitable for future studies of clinical sequences and contrasts in human brain imaging. A general strength of FRONSAC encoding is that this waveform, optimized for a particular protocol, will provide significant improvements to scans with different contrasts, resolutions, and geometries.


We would like to thank Andrew Dewdney (Siemens) and Terry Nixon for supporting the nonlinear gradient hardware.


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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.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)