Leo Tam

O-Space Imaging: Highly Efficient Parallel Imaging Using Second-Order Nonlinear Fields as Encoding Gradients with No Phase Encoding

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 sensitivity encoding (SENSE) radial k‐space trajectories, and parallel imaging technique with localized gradients (PatLoc), suggesting that O‐space imaging holds great potential for accelerated scanning. Magn Reson Med, 2010.

Null space imaging: Nonlinear magnetic encoding fields designed complementary to receiver coil sensitivities for improved acceleration in parallel imaging

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 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. The method is compared to conventional Cartesian SENSitivity Encoding as evaluated by mean squared error and robustness to noise. Strategies for developments in the area of nonlinear encoding schemes are discussed. The null space imaging 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. Magn Reson Med, 2012.

In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration.

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. Magn Reson Med, 2013.

Pseudo-random center placement O-space imaging for improved incoherence compressed sensing parallel MRI.

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.

Spin Dephasing Under Nonlinear Gradients: Implications for Imaging and Field Mapping

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. Magn Reson Med, 2011.

Multiecho acquisition of O‐space data

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.

Fast rotary nonlinear spatial acquisition (FRONSAC) imaging.

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.

Accelerate data acquisition using Turbo Spin Echo and O-Space

Turbo Spin Echo (TSE) is a method of acquiring the echoes of a Cartesian readout in a T2-weighted echo train, resulting in a very fast imaging time. On the other hand, recent methods of spatial encoding with nonlinear magnetic fields have been studied by our group and others to reduce data acquisitions time, such as, PatLoc, O-Space, Null Space, 4D-RIO, etc. These efforts have focused on gradient echo imaging. In this paper, a novel method has been proposed to combine the benefits of both TSE acquisition and O-Space to accelerate the data acquisition for T2-weighted imaging. Because O-space acquires DC signal in at least some spatial location within each echo, modifications of the acquisition order and reconstruction method are required. We present simulations and experiments illustrating that the proposed method can further speed up data acquisition of an O-Space imaging sequence using spin echo trains.

Algebraic reconstruction technique for parallel imaging reconstruction of undersampled radial data: application to cardiac cine.

To investigate algebraic reconstruction technique (ART) for parallel imaging reconstruction of radial data, applied to accelerated cardiac cine.

O-space with high resolution readouts outperforms radial imaging

PURPOSE While O-Space imaging is well known to accelerate image acquisition beyond traditional Cartesian sampling, its advantages compared to undersampled radial imaging, the linear trajectory most akin to O-Space imaging, have not been detailed. In addition, previous studies have focused on ultrafast imaging with very high acceleration factors and relatively low resolution. The purpose of this work is to directly compare O-Space and radial imaging in their potential to deliver highly undersampled images of high resolution and minimal artifacts, as needed for diagnostic applications. We report that the greatest advantages to O-Space imaging are observed with extended data acquisition readouts. THEORY AND METHODS A sampling strategy that uses high resolution readouts is presented and applied to compare the potential of radial and O-Space sequences to generate high resolution images at high undersampling factors. Simulations and phantom studies were performed to investigate whether use of extended readout windows in O-Space imaging would increase k-space sampling and improve image quality, compared to radial imaging. RESULTS Experimental O-Space images acquired with high resolution readouts show fewer artifacts and greater sharpness than radial imaging with equivalent scan parameters. Radial images taken with longer readouts show stronger undersampling artifacts, which can cause small or subtle image features to disappear. These features are preserved in a comparable O-Space image. CONCLUSIONS High resolution O-Space imaging yields highly undersampled images of high resolution and minimal artifacts. The additional nonlinear gradient field improves image quality beyond conventional radial imaging.