### Abstract

- Top of page
- Abstract
- METHODS
- RESULTS
- DISCUSSION
- CONCLUSIONS
- Acknowledgements
- REFERENCES

The concentric rings two-dimensional (2D) *k*-space trajectory enables flexible trade-offs between image contrast, signal-to-noise ratio (SNR), spatial resolution, and scan time. However, to realize these benefits for in vivo imaging applications, a robust method is desired to deal with fat signal in the acquired data. Multipoint Dixon techniques have been shown to achieve uniform fat suppression with high SNR-efficiency for Cartesian imaging, but application of these methods for non-Cartesian imaging is complicated by the fact that fat off-resonance creates significant blurring artifacts in the reconstruction. In this work, two fat–water separation algorithms are developed for the concentric rings. A retracing design is used to sample rings near the center of *k*-space through multiple revolutions to characterize the fat–water phase evolution difference at multiple time points. This acquisition design is first used for multipoint Dixon reconstruction, and then extended to a spectroscopic approach to account for the trajectory's full evolution through 3D *k*-*t* space. As the trajectory is resolved in time, off-resonance effects cause shifts in frequency instead of spatial blurring in 2D *k*-space. The spectral information can be used to assess field variation and perform robust fat–water separation. In vivo experimental results demonstrate the effectiveness of both algorithms. Magn Reson Med, 2009. © 2008 Wiley-Liss, Inc.

The concentric rings two-dimensional (2D) *k*-space trajectory samples a polar grid with a set of circular readouts, enabling flexible trade-offs between image contrast, signal-to-noise ratio (SNR), spatial resolution, and scan time (1–5). Balance between spatial resolution and scan time allows the rings to be tailored for efficient dynamic imaging (2). The rings are also inherently centric-ordered in two dimensions, thus being a very effective readout trajectory for magnetization-prepared imaging (5). To fully realize these benefits for in vivo imaging applications, we must have a robust way of dealing with the signal from fat, which can adversely affect image contrast and presents a dominant source of off-resonance artifacts in non-Cartesian imaging.

Popular approaches for suppressing fat signal include applying short-tau inversion-recovery (STIR) prep-pulses, fat-saturation prep-pulses, or spectral–spatial excitation pulses. These methods can suppress fat effectively under ideal conditions, but are sensitive to variations in the *B*_{0} and *B*_{1} fields. Another disadvantage of these methods is the additional scan-time overhead required for the preparation pulses, which reduces the overall SNR time-efficiency. Instead of suppressing fat, it is also possible to resolve its signal, decomposing the reconstruction into a separate fat image and water image. In addition to providing uniform fat suppression, this approach also produces extra information about the relative fat–water composition in each voxel.

Fat–water separation is an important special case of chemical shift imaging (CSI). A general spectroscopic imaging approach is certainly possible, but can become very time-consuming for the desired spatial coverage and resolution. Many methods that take advantage of the prior information have been developed over the past two decades to exclusively deal with fat–water imaging, starting with Dixon's original proposal of a simple 2-point method (6). To improve the robustness of Dixon's method, Glover and Schneider presented a 3-point algorithm (7, 8) to address field inhomogeneity. Recently, formulations based on least-squares estimation have been presented to accommodate an arbitrary number of time points and arbitrary echo times. Reeder et al. (9–12) proposed an iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) algorithm to solve the general nonlinear problem through linearization and iteration. Hernando et al. (13) drew upon the variable projection (VARPRO) algorithm to solve the nonlinear estimation by using a separable formulation and one-dimensional search over field variation. These multi-point fat–water separation techniques are quite effective at separating fat–water signal, but a disadvantage is the doubling or tripling of scan time. Therefore, SNR-efficient acquisition and processing are required to warrant the extra scan time (7–10). There has also been interest in using multi-echo sequences to reduce the total scan time required for acquiring the multiple time points (14–16). Multi-echo acquisitions can also improve the spatial registration of the acquired images.

For non-Cartesian trajectories, fat–water separation is complicated by the fact that off-resonance due to field inhomogeneity and chemical shift both cause blurring artifacts in the reconstruction. Moriguchi et al. (17) presented 2-point and 3-point Dixon techniques based on spiral acquisitions, incorporating multi-frequency reconstruction for off-resonance correction (ORC). However, they discussed but did not support arbitrary echo times. More recently, the least-squares formulation has been applied to fat–water imaging with non-Cartesian trajectories to accommodate an arbitrary number of time points and arbitrary echo times. Gurney (18) proposed an algorithm for 3D cones trajectories that combined off-resonance correction with the least-squares estimation problem, with a 1D search over field variation. Brodsky et al. (19) modified the IDEAL algorithm to demodulate the off-resonant phase caused by chemical shift and perform fat–water separation in *k*-space. They also discussed the possibility of using multi-frequency reconstruction to correct for field-induced blurring. These methods have demonstrated that it is possible to perform robust multipoint fat–water separation with non-Cartesian trajectories, provided the blurring artifacts are properly accounted for.

In this study, we develop two approaches to fat–water imaging with the concentric rings trajectory. Both approaches are based on the same retracing concept we had previously investigated for off-resonance correction (5). After each excitation, a selected set of inner rings may be traced more than once to produce datasets at different effective echo times, which is much in the spirit of a multi-echo acquisition. The first approach follows the multi-point Dixon paradigm, where multiple images acquired at appropriate time points are used to characterize the fat–water phase difference. Using the same retracing design, we present a second approach which follows the concentric rings trajectory through 3D (*k*_{x}, *k*_{y}, *t*)-space. By explicitly reconstructing the rings in 3D space, spatial blurring due to off-resonance becomes a shift along the frequency dimension. This unblurred spectral information allows us to perform robust fat–water separation in the presence of field inhomogeneity. We present in vivo results to show the performance of both approaches.

### DISCUSSION

- Top of page
- Abstract
- METHODS
- RESULTS
- DISCUSSION
- CONCLUSIONS
- Acknowledgements
- REFERENCES

The concentric rings trajectory has a unique circular symmetry in 2D *k*-space that easily enables retracing of the inner rings to obtain fat–water phase information at multiple time points without extra excitations. Previously, this retracing acquisition format was used for off-resonance correction (5), and in this work the processing has been extended to enable fat–water separation. In this design, only the inner rings are retraced to provide the multiple time points. However, the “lower” spatial frequencies covered by the inner rings achieve a relatively high 1.2-mm isotropic in-plane resolution and because most of the fat–water contrast is contained in the low spatial frequencies, we are able to achieve effective fat separation. No misclassification of high-frequency features in either the fat or water images due to this limited retracing was observed in our experimental results. We did not correct for the remaining off-resonance blurring in the Dixon reconstructions due to field variation, as it did not result in visible artifacts. The remaining field variation is typically on the order of a few tens of Hz and results in sub-pixel blurring (Fig. 2b). It is certainly possible to combine multifrequency reconstruction with iterative Dixon reconstruction (18).

The same retracing design was also used to develop a spectroscopic approach, which accounted for the rings' full evolution through 3D (*k*_{x}, *k*_{y}, *t*)-space. Because the concentric rings do not have a strictly-defined echo time (as 2DFT does), this 3D perspective provides the key to fully appreciating the concentric rings trajectory. When the rings trajectory is reconstructed as a 2D *k*-space acquisition, the time axis is collapsed and off-resonance effects (field inhomogeneity, chemical shift) manifest as blurring in image space (PSF in Fig. 2). By reconstructing the same dataset explicitly in 3D space, these off-resonance effects become shifts along the frequency dimension and we can obtain images free of spatial blurring. We would like to note that such a spectroscopic approach could also be applied to many other readout trajectories, because it is just Fourier-transform analysis. In the case of bipolar multi-echo Cartesian trajectories, appropriate density compensation is needed to account for variation in the temporal sampling of each spatial frequency component. By using a spectroscopic reconstruction for bipolar multi-echo Cartesian readouts, it may be possible to account for even/odd echo phase discrepancies and chemical-shift misregistration in one step. Further investigation of this topic is required to analyze the benefits.

The water and fat-referencing algorithm proposed in this work is one way to use the spectral information for fat–water separation. Because the spectrum at each voxel is simply shifted in frequency to correct for the offset caused by field inhomogeneity, this algorithm does not cause partial volume effects. However, the current algorithm does assume that the off-resonance due to field inhomogeneity is less than the chemical shift. This may become invalid at tissue boundaries and air–tissue interfaces. In that case, we could modify the algorithm (and even the acquisition) to consider a more complete model of the spectrum. For example, the acquisition could be extended to characterize the multiple peaks of the fat spectrum (21) and use this full set of peaks as a more robust signature for classifying fat-dominant voxels.

Experimental results demonstrate that the Dixon-based approach and the spectroscopic approach can both achieve effective and uniform fat suppression. The Dixon-based approach is more computationally efficient, while the spectroscopic approach provides a more general reconstruction framework for the retracing design. By using all of the information in 3D *k-t* space, the spectroscopic approach is able to provide effective fat suppression even in cases of limited spectral coverage (i.e., two-revolutions, Fig. 8e). With our implementation in MATLAB (The MathWorks, Inc., Natick, MA), the Dixon-based approach took approximately 4 s for each image slice, while the spectroscopic approach took around one minute for each slice due to 3D gridding and 3D Fourier-transform operations. The computational time required for the spectroscopic approach is longer but still quite reasonable, and these computing times will definitely improve as the implementation is optimized and computing power increases. However, this does indicate that it may be favorable to use the Dixon-based approach for applications that demand near-real-time reconstruction. With these respective advantages in mind, both techniques should be able to handle a wide variety of imaging applications, as they can both be extended to accommodate modifications of the acquisition design itself.

There are many possible improvements to the proposed algorithms. For example, when performing signal averaging, we can shift the TE for each repeated acquisition to provide more time points for the Dixon technique and better coverage of (*k*_{x}, *k*_{y}, *t*)-space for full 3D reconstruction. More sophisticated field map processing schemes such as region-growing and probability constraints in image space can be incorporated into the iterative Dixon-based reconstruction, and also into the fat–water classification step for the spectroscopic reconstruction. Processing used for MR spectroscopic imaging, such as parametric model fitting of the spectrum (22), can be used for the spectroscopic approach to incorporate other prior information and improve robustness. In addition, the retracing design can be extended to more than three revolutions to provide higher SNR and more points for Dixon-based parametric reconstructions (16), and support higher spectral bandwidth and resolution for the spectroscopic perspective.

The concentric rings trajectory can be applied to many in vivo applications that benefit from magnetization-prepared imaging and robust fat–water separation, such as musculoskeletal imaging, structural brain imaging, and contrast-enhanced breast imaging. The ability for concentric rings to simultaneously offer spatial and spectral coverage also indicates its potential for imaging applications that require information in both space and time (23–25).