### Abstract

- Top of page
- Abstract
- MATERIALS AND METHODS
- RESULTS
- DISCUSSION
- CONCLUSIONS
- Acknowledgements
- APPENDIX
- REFERENCES

The concentric rings two-dimensional (2D) *k*-space trajectory provides an alternative way to sample polar data. By collecting 2D *k*-space data in a series of rings, many unique properties are observed. The concentric rings are inherently centric-ordered, provide a smooth weighting in *k*-space, and enable shorter total scan times. Due to these properties, the concentric rings are well-suited as a readout trajectory for magnetization-prepared studies. When non-Cartesian trajectories are used for MRI, off-resonance effects can cause blurring and degrade the image quality. For the concentric rings, off-resonance blur can be corrected by retracing rings near the center of *k*-space to obtain a field map with no extra excitations, and then employing multifrequency reconstruction. Simulations show that the concentric rings exhibit minimal effects due to *T* modulation, enable shorter scan times for a Nyquist-sampled dataset than projection-reconstruction imaging or Cartesian 2D Fourier transform (2DFT) imaging, and have more spatially distributed flow and motion properties than Cartesian sampling. Experimental results show that off-resonance blurring can be successfully corrected to obtain high-resolution images. Results also show that concentric rings effectively capture the intended contrast in a magnetization-prepared sequence. Magn Reson Med, 2007. © 2007 Wiley-Liss, Inc.

The course of development for MRI has continually seen the need to strike a balance between many goals, including scan time, image resolution, and signal-to-noise ratio (SNR). This is especially true for time-sensitive experiments such as dynamic MRI and magnetization-prepared studies. A concentric rings two-dimensional (2D) *k*-space trajectory can provide new dimensions of flexibility in considering the tradeoff between these goals. Concentric rings are essentially an alternative way to acquire 2D polar data, with many desirable properties that come from its circular geometry and reading out along the angular dimension. Theoretical analysis of the sampling properties and reconstruction effects of polar sampling have been presented by Lauzon et al. (1, 2). Concentric rings as an imaging sequence were first investigated by Matsui and Kohno (3) and used with a fast spin-echo (FSE) sequence by Zhou et al. (4). Liang and Lauterbur (5) also presented the idea of dynamic imaging with concentric rings. Implementations and experimental results were successfully reported, but off-resonance issues and other pertinent properties were not thoroughly investigated. Related imaging trajectories have also been studied, such as spiral-rings by Block et al. (6) and Kerr et al. (7), 3D concentric cylinders by Ruppert et al. (8), and 3D spherical shells by Shu et al. (9). These works all speak about the advantages of using concentric sampling, and it is highly desirable to have more studies that investigate the properties and potential of the concentric rings trajectory.

In this work, we present a study of the concentric rings, including implementation and design procedures, further analysis of its properties and artifacts, and applications of the technique in vivo. We implemented the concentric rings trajectory in a gradient-echo (GRE) sequence. Artifacts due to *T* modulation, off-resonance issues, and flow and motion were characterized by simulations. We found that in addition to being inherently centric-ordered and providing a smooth weighting in *k*-space, this readout trajectory enables shorter scan times and a flexible tradeoff between image resolution and scan time. These properties make the concentric rings well suited as a readout trajectory for magnetization-prepared studies and dynamic MRI. As with other non-Cartesian trajectories, off-resonance blurring in the reconstructed image is a concern. To deal with this issue, we propose a retracing method when acquiring rings near the center of *k*-space to obtain a field map with no extra excitations. This field map can be used in multifrequency reconstruction to correct for the blur. We present experimental results to show in vivo performance.

### DISCUSSION

- Top of page
- Abstract
- MATERIALS AND METHODS
- RESULTS
- DISCUSSION
- CONCLUSIONS
- Acknowledgements
- APPENDIX
- REFERENCES

The concentric rings trajectory provides an alternative way to sample polar data, with many interesting properties that originate from its circular geometry. When acquiring data with the concentric rings, a full-FOV image always exists, and resolution builds up in an isotropic manner with each new ring. Prepared contrast can be captured smoothly and efficiently by starting from the center of *k*-space and expanding outwards.

Concentric rings require fewer excitations for a Nyquist-sampled data set when compared to 2DPR and 2DFT. As a result, the rings can enable shorter total scan times in many cases. Time savings up to two times over 2DPR for the same polar data set can be achieved. A Nyquist-sampled data set was considered in this work as the basis for theoretical comparison; however, in practice, 2DPR acquisitions usually collect a smaller number of spokes. Reducing the number of spokes causes streaking artifacts and results in a smaller aliasing-free FOV, which is actually tolerable to quite an extent. Typically, 256 full-diameter spokes with 256 samples along each spoke may be collected when Nyquist constraints warrant a 403-spoke full acquisition. Further reduction to fewer than 256 spokes is also done in practice, which is often the case for reduced-FOV imaging (27–29). We used a 256-by-256 full-diameter 2DPR trajectory for our IR experiments, but even with a reduced acquisition of 256 2DPR spokes, the concentric rings could still cover the original Nyquist-sampled polar grid within a shorter scan time.

The motion and flow properties of the rings are also quite distinct from that of 2DPR or 2DFT. The rings, like 2DPR, have more spatially distributed flow and motion artifacts than 2DFT. Seen from the simulation, 2DPR is more tolerant of pulsatile through-plane flow, while the concentric rings are more robust in the presence of in-plane linear drift. Both 2DPR and the rings have more distributed artifacts than 2DFT for in-plane contraction/dilation. In addition, we observe interesting reconstructions that directly relate to the underlying readout scheme of acquiring a full-FOV bandpass ring each TR. These simulations are by no means exhaustive, but they do provide insight into the type of artifacts to expect when employing the concentric rings trajectory.

From its distinct properties, the concentric rings are well suited for applications in magnetization-prepared studies. The concentric rings are inherently centric-ordered, offer smooth weighting in *k*-space, and have a shorter total scan time. Prepared contrast is thus captured rapidly and smoothly by the rings. As demonstrated, IR preparation can be combined with the concentric rings trajectory for contrast augmentation and species suppression, with better contrast-to-noise ratio and a shorter scan time than centric-ordered 2DFT. It is possible to extend this concept and use the rings with other types of magnetization-prepared studies (30, 31). These same advantages also make the rings well suited for FSE sequences (4, 6).

For dynamic imaging, the same properties considered for magnetization-prepared imaging also make the rings an attractive choice. Furthermore, since each ring represents a specific band in spatial frequency, we can utilize this feature to flexibly update rings that cover the lower spatial frequencies more often than those that represent the higher spatial frequencies during the course of the scan (5, 32–36).

Off-resonance effects pose a limitation to the application of non-Cartesian trajectories. For the concentric rings, this is exacerbated by the fact that the low spatial frequencies are sampled with minimal gradient amplitudes (4). The retracing method proposed in this work addresses the problem in two ways: higher gradient amplitude in the central region of *k*-space and the ability to acquire a field map without any extra excitations. This field map is used in multifrequency reconstruction to effectively correct the off-resonance blurring. The current implementation obtains a field map of limited frequency range, thus high degrees of off-resonance or abrupt changes in the field distribution can be potential problems. It is possible to tweak the retracing design to acquire a field map of greater range that suits the imaging experiment.

To further limit the degree of off-resonance artifacts, preparation such as fat-suppression or saturation can be used with the rings, as is often done in spiral imaging (37). We have seen that the concentric rings are effective at capturing prepared contrast. Therefore, fat suppression methods such as IR can be used in combination with the concentric rings trajectory to reduce the effects of off-resonance (4, 6). Smaller degrees of off-resonance can be corrected using the proposed ORC scheme.

Improvements to the present design are possible. Since we designed gradients for the outermost ring and scaled them down to cover *k*-space, the current design can be readily extended to variable-density *k*-space coverage. Variable-density sampling strategies offer even more flexibility in balancing SNR, scan time, and resolution (2, 19). The proposed retracing design may also be extended to more than two revolutions for other potential applications, such as retracing the inner rings three or more times to enable multiple-point Dixon reconstruction techniques (38, 39). It is also natural to consider a variable number of rings per excitation, such as spiral-rings (6, 7), or using separately optimized gradient designs for different rings. Asymmetric FOVs can be obtained by incorporating additional constraints in the gradient design procedure. The rings can also be combined with partial *k*-space approaches and multiple-echo acquisitions. Data can be sampled during the dephaser and rephaser gradients for purposes such as motion correction.

The implementation and analysis of the concentric rings *k*-space trajectory presented in this work focused on 2D imaging. Extension to concentric 3D coverage is possible by using 2D multislice acquisition schemes or related 3D concentric trajectories such as “stack-of-rings,” “rings-PR-hybrid” (40), concentric cylinders (8), and concentric spheres (9). A 2D multislice acquisition could allow interleaved ordering of slices to accommodate long recovery times and maximize tissue contrast, while a 3D readout trajectory would allow improvements in SNR. Characteristics of a 2D multislice acquisition should follow directly from what we have analyzed in this work, while the behavior of 3D concentric trajectories is a closely related but distinct subject of their own. Many properties of concentric sampling discussed in the context of this work would carry over to the case of 3D concentric imaging, including the advantages for magnetization-prepared imaging, dynamic imaging, and scan-time efficiency.