Recent improvements in parallel imaging have been driven by the use of greater numbers of independent surface coils placed so as to minimize aliasing along the phase encode direction(s). However, gains from increasing the number of coils diminish as coil coupling problems begin to dominate and the ratio of acceleration gain to expense for multiple receiver chains becomes prohibitive. In this work we redesign the spatial encoding strategy in order to gain efficiency, achieving a gradient encoding scheme that is complementary to the spatial encoding provided by the receiver coils. This approach leads to “O-Space” imaging, wherein the gradient shapes are tailored to an existing surface coil array, making more efficient use of the spatial information contained in the coil profiles. In its simplest form, for each acquired echo the Z2 spherical harmonic is used to project the object onto sets of concentric rings, while the X and Y-gradients are used to offset this projection within the imaging plane. The theory is presented, an algorithm is introduced for image reconstruction, and simulations reveal that O-Space encoding achieves high encoding efficiency compared to SENSE, radial projection imaging, and PatLoc imaging, suggesting that O-Space imaging holds great potential for accelerated scanning.

Recently, spatial encoding with nonlinear magnetic fields has drawn attention for its potential to achieve faster gradient switching within safety limits, tailored resolution in regions of interest, and improved parallel imaging using encoding fields that complement the sensitivity profiles of radio frequency receive arrays. Proposed methods can broadly be divided into those that use phase encoding (Cartesian-trajectory PatLoc and COGNAC) and those that acquire nonlinear projections (O-Space, Null space imaging, radial PatLoc, and 4D-RIO). Nonlinear projection data are most often reconstructed with iterative algorithms that backproject data using the full encoding matrix. Just like conventional radial sequences that use linear spatial encoding magnetic fields, nonlinear projection methods are more sensitive than phase encoding methods to imperfect calibration of the encoding fields. In this work, voxel-wise phase evolution is mapped at each acquired point in an O-Space trajectory using a variant of chemical shift imaging, capturing all spin dynamics caused by encoding fields, eddy currents, and pulse timing. Phase map calibration is then applied to data acquired from a high-power, 12 cm, Z2 insert coil with an eight-channel radio frequency transmit-receive array on a 3T human scanner. We show the first experimental proof-of-concept O-Space images on in vivo and phantom samples, paving the way for more in-depth exploration of O-Space and similar imaging methods.

To increase image acquisition efficiency, we develop alternative gradient encoding strategies designed to provide spatial encoding complementary to the spatial encoding provided by the multiple receiver coil elements in parallel image acquisitions. Intuitively, complementary encoding is achieved when the magnetic field encoding gradients are designed to encode spatial information where receiver spatial encoding is ambiguous, for example, along sensitivity isocontours. Specifically, the method generates a basis set for the null space of the coil sensitivities with the singular value decomposition (SVD) and calculates encoding fields from the null space vectors. A set of nonlinear gradients is used as projection imaging readout magnetic fields, replacing the conventional linear readout field and phase encoding. Multiple encoding fields are used as projections to capture the null space information, hence the term Null Space Imaging (NSI). The method is compared to conventional Cartesian SENSitivity Encoding (SENSE) as evaluated by mean squared error and robustness to noise. Strategies for developments in the area of nonlinear encoding schemes are discussed. The NSI approach yields a parallel imaging method that provides high acceleration factors with a limited number of receiver coil array elements through increased time efficiency in spatial encoding.

Purpose Nonlinear spatial encoding magnetic (SEM) field strategies such as O-space imaging have previously reported dispersed artifacts during accelerated scans. Compressed sensing (CS) has shown a sparsity-promoting convex program allows image reconstruction from a reduced data set when using the appropriate sampling. The development of a pseudo-random center placement (CP) O-space CS approach optimizes incoherence through SEM field modulation to reconstruct an image with reduced error. Theory and Methods The incoherence parameter determines the sparsity levels for which CS is valid and the related transform point spread function measures the maximum interference for a single point. The O-space acquisition is optimized for CS by perturbing the Z2 strength within 30% of the nominal value and demonstrated on a human 3T scanner. Results Pseudo-random CP O-space imaging is shown to improve incoherence between the sensing and sparse domains. Images indicate pseudo-random CP O-space has reduced mean squared error compared with a typical linear SEM field acquisition method. Conclusion Pseudo-random CP O-space imaging, with a nonlinear SEM field designed for CS, is shown to reduce mean squared error of images at high acceleration over linear encoding methods for a 2D slice when using an eight channel circumferential receiver array for parallel imaging.

Purpose Nonlinear spatial encoding magnetic fields (SEMs) have been studied to reconstruct images from a minimum number of echoes. Previous work has also explored single shot trajectories in nonlinear SEMs. However, the search continues for optimal schemes that apply nonlinear SEMs to improve spatial encoding efficiency and image quality. Theory and Methods We enhance the encoding efficiency of standard linear gradient trajectories by adding a rapidly rotating nonlinear SEM of moderate amplitude, the so called FRONSAC (Fast ROtary Nonlinear Spatial ACquisition) imaging. This additional gradient greatly improves the image quality of highly undersampled single-shot trajectories, including EPI, Spiral, and Rosette trajectories. Results Our simulations, including noise and dephasing effects, test the effect of adding FRONSAC gradients, demonstrating the applicability of this approach. Performance is explained by demonstrating the additional k-space sampling the nonlinear gradient provides. Studies of the optimal amplitude and frequency of the additional FRONSAC field are presented, and the role of enhanced sampling during the readout demonstrated. Dynamic field mapping in a second-order gradient system shows the proposed gradient waveforms are feasible. Conclusions Images resulting from highly undersampled existing k-space trajectories, such as EPI, Spiral and Rosette, are greatly enhanced simply by adding a rotating nonlinear SEM field.

Sequences that encode the spatial information of an object using nonlinear gradient fields are a new frontier in MRI, with potential to provide lower peripheral nerve stimulation, windowed fields of view, tailored spatially-varying resolution, curved slices that mirror physiological geometry, and, most importantly, very fast parallel imaging with multichannel coils. The acceleration for multichannel images is generally explained by the fact that curvilinear gradient isocontours better complement the azimuthal spatial encoding provided by typical receiver arrays. However, the details of this complementarity have been more difficult to specify. We present a simple and intuitive framework for describing the mechanics of image formation with nonlinear gradients, and we use this framework to review some the main classes of nonlinear encoding schemes.

This work examines the prototypical MR echo that would be expected for a voxel of spins evolving in a strong nonlinear field, specifically focusing on the quadratic z2-½(x2+y2) field. Dephasing under nonlinear gradients is increasingly relevant given the growing interest in nonlinear imaging, and here we report several notable differences from the linear case. Most notably, in addition to signal loss, intravoxel dephasing under gradients creating a wide and asymmetric frequency distribution across the voxel can cause skewed and nonlinear phase evolution. After presenting the qualitative and analytical origins of this difference, we experimentally demonstrate that neglecting these dynamics can lead to significant errors in sequences that assume phase evolution is proportional to voxel frequency, such as those used for field mapping. Finally, simplifying approximations to the signal equations are presented, which not only provide more intuitive forms of the exact expression, but also result in simple rules to predict key features of the nonlinear evolution.

Purpose Nonlinear gradient encoding methods, such as O-Space imaging, have been shown to provide good images from very few echoes. Acquiring data in a train of spin or gradient echoes is a very flexible way to further speed acquisition time. However, combining these strategies presents significant challenges, both in terms of the contrast and artifacts. We present strategies in both pulse sequence design and image processing to mitigate these effects. Theory and Methods The three strategies include a new echo ordering that takes into account the unique way that O-Space samples the k-space of the image; a new post-processing filter that allows tuning of T2-weighting by emphasizing the contribution of low frequency spatial information at selectable points in space and time; and an offset between linear and nonlinear gradients that makes the central point of each echo unique. Results Simulations indicate that these strategies mitigate artifacts introduced by T2 (or T2*) decay and produce contrast that reflects relaxation at a given TE. Conclusion Turbo spin echo O-Space is theoretically feasible, and the greater undersampling should make it possible to use shorter echo trains for a given scan time.