Nonlinear gradient fields (NLGFs) offer many benefits including accelerated-imaging^1-3, reduced SAR⁴, improved excitation fidelity⁵, curved-slice imaging⁶, reduced peripheral nerve stimulation⁷, motion navigation⁸ peripheral resolution enhancement⁹ and region-specific imaging¹⁰. O-Space imaging uses a second-order NLGF (x^2/2+y^2/2-z^2) during readout for improved accelerated imaging, to yield a fairly uniform encoding throughout the field-of-view (FoV)¹¹. Previously, we proposed an adaptation of O-Space imaging for region-of-interest (ROI) imaging¹². Here, we compare the method to radial and O-Space imaging techniques via simulations and experiments in terms of resolution, noise-performance and image-quality.

In O-Space imaging, a trapezoidal Z2-gradient waveform with constant amplitude is applied simultaneously with a radial-sequence to yield center-placements (CPs) of the Z2-gradient at uniformly distributed points on a circle enclosing the FoV. In rOi-Space, the center is shifted to points on a boundary with a non-trivial shape, such that the ratio between the two LGF amplitudes may vary significantly, hampering encoding along one direction (Figure 1). We fixed the NLGF to 200mT/m/m so that the maximum field amplitude and field slew-rate generated inside a (20 cm)³ FoV are smaller than those generated by the 40 mT/m, 140 mT/m/msec gradient coils of the scanner available at the research center. Note that, the designed LGF amplitudes may exceed those in radial, as discussed below.

Simulations were performed in Matlab (Mathworks Inc., Natick, MA, USA). Images were reconstructed using Kaczmarz with 5 iterations, λ=0.75, and random-ordering. In noisy simulations, the standard variation of the noise was adjusted to be 1.7% and 7% of the maximum intensity of the brain data. Center-placements were performed as outlined in ¹².

Experiments were performed on a 3T scanner with an 8-channel head coil (Siemens Healthcare, Erlangen, Germany), using a nonlinear gradient insert (Resonance Research Inc., Billerica, MA, USA) and a cylindrical contrast phantom (J7239, JM Specialty Parts, San Diego, CA, length: 172 mm, diameter: 203 mm). Parameters were; FoV, (256mm)², projections/CPs, 256; samples during full-echo readouts, 256; bandwidth, 80Hz/px; Kaczmarz reconstruction with 5 iterations and λ=0.02. The NLGF amplitude was gradually increased such that center-placement radii ranged between 9.6 cm and 51.2 cm, with the center of the FoV being the center of the circular region-of-interest. The Z2-field was characterized using a slice-selective sequence with phase-encodes in both in-plane directions (Figure 2). B0-inhomogeneity was measured to be 0.7% as strong as the Z2-harmonic for CP radius of 12.8cm. In both simulations and experiments, experimentally obtained sensitivity maps¹³ of the 8-channel coil were used (Figure 2) in image reconstruction. Because of the additional winding caused by the NLGF in rOi-Space, local encoding frequencies may exceed the Nyquist rate, and lead to intra-voxel dephasing. To account for this, the spatial encoding functions generated by the magnetic fields were averaged on a 7x7 higher resolution grid.

Radial and rOi-Space acquisitions were compared using simulations for various acceleration factors (Figure 3), demonstrating the efficiency of the proposed method in focusing the encoding effort into the ROI. For 3.9x acceleration, the root-mean-squared error calculated inside the ROI was reduced by more than 70%, compared to the radial acquisition.

When the linear gradient fields can be adjusted freely by the algorithm, the local k-space coverage is enhanced in the target region with a more homogeneous coverage in all directions (Figure 1). Intra-voxel dephasing however leads to a degradation in signal-to-noise ratio as expected (Figure 4).

Experiments (Figure 5) show that at 4x acceleration, radial images show a loss-of-detail due to blurring (1-2,5-6), incorrect reconstruction of straight lines (3-4) and artificial reconstruction of grid in homogeneous regions (7-8). As the nonlinear gradient field is introduced (Figure 5c) visibility of fine details is improved (2-4,6) while some features are worsened (5). Increasing the field strength improves all details (2-8) and finally at the maximum field strength, the inner detail (1) is recovered.

The proposed method locally improves resolution by focusing the encoding effort to within the ROI. Excessive encoding leads to intra-voxel dephasing, which degrades noise performance, however, using lower NLGF amplitudes could minimize SNR-loss.

In rOi-Space, the LGF amplitudes are re-designed, and may exceed those in radial. Hence, an rOi-Space implementation may require a longer readout than a radial counterpart using LGFs at the limits. However, this would degrade SNR performance of radial due to the prolonged readout. Here we used longer readouts for all methods such that noise-performances could be compared.

The proposed method creates a trade-off between resolution and SNR/readout duration, and hence, can be used to improve resolution in applications with adequate SNR or that can tolerate increased readout durations.