Michael A. Ohliger

Ultimate intrinsic signal-to-noise ratio for parallel MRI: electromagnetic field considerations.

A method is described for establishing an upper bound on the spatial encoding capabilities of coil arrays in parallel MRI. Ultimate intrinsic signal‐to‐noise ratio (SNR), independent of any particular conductor arrangement, is calculated by expressing arbitrary coil sensitivities in terms of a complete set of basis functions that satisfy Maxwells equations within the sample and performing parallel imaging reconstructions using these basis functions. The dependence of the ultimate intrinsic SNR on a variety of experimental conditions is explored and a physically intuitive explanation for the observed behavior is provided based on a comparison between the electromagnetic wavelength and the distance between aliasing points. Imaging at high field strength, with correspondingly short wavelength, is shown to offer advantages for parallel imaging beyond those already expected due to the larger available spin polarization. One‐dimensional undersampling of k‐space yields a steep drop in attainable SNR for more than a 5‐fold reduction of scan time, while 2D undersampling permits access to much higher degrees of acceleration. Increased tissue conductivity decreases baseline SNR, but improves parallel imaging performance. A procedure is also provided for generating the optimal coil sensitivity pattern for a given acceleration, which will serve as a useful guide for future coil designs. Magn Reson Med 50:1018–1030, 2003.

Self-calibrating parallel imaging with automatic coil sensitivity extraction.

Calibration of the spatial sensitivity functions of coil arrays is a crucial element in parallel magnetic resonance imaging (PMRI). The most common approach has been to measure coil sensitivities directly using one or more low‐resolution images acquired before or after accelerated data acquisition. However, since it is difficult to ensure that the patient and coil array will be in exactly the same positions during both calibration scans and accelerated imaging, this approach can introduce sensitivity miscalibration errors into PMRI reconstructions. This work shows that it is possible to extract sensitivity calibration images directly from a fully sampled central region of a variable‐density k‐space acquisition. These images have all the features of traditional PMRI sensitivity calibrations and therefore may be used for any PMRI reconstruction technique without modification. Because these calibration data are acquired simultaneously with the data to be reconstructed, errors due to sensitivity miscalibration are eliminated. In vivo implementations of self‐calibrating parallel imaging using a flexible coil array are demonstrated in abdominal imaging and in real‐time cardiac imaging studies. Magn Reson Med 47:529–538, 2002.

Highly parallel volumetric imaging with a 32-element RF coil array.

The improvement of MRI speed with parallel acquisition is ultimately an SNR‐limited process. To offset acquisition‐ and reconstruction‐related SNR losses, practical parallel imaging at high accelerations should include the use of a many‐element array with a high intrinsic signal‐to‐noise ratio (SNR) and spatial‐encoding capability, and an advantageous imaging paradigm. We present a 32‐element receive‐coil array and a volumetric paradigm that address the SNR challenge at high accelerations by maximally exploiting multidimensional acceleration in conjunction with noise averaging. Geometric details beyond an initial design concept for the array were determined with the guidance of simulations. Imaging with the support of 32‐channel data acquisition systems produced in vivo results with up to 16‐fold acceleration, including images from rapid abdominal and MRA studies. Magn Reson Med 52:869–877, 2004.

3Parallel magnetic resonance imaging with adaptive radius in k‐space (PARS): Constrained image reconstruction using k‐space locality in radiofrequency coil encoded data

A parallel image reconstruction algorithm is presented that exploits the k‐space locality in radiofrequency (RF) coil encoded data. In RF coil encoding, information relevant to reconstructing an omitted datum rapidly diminishes as a function of k‐space separation between the omitted datum and the acquired signal data. The proposed method, parallel magnetic resonance imaging with adaptive radius in k‐space (PARS), harnesses this physical property of RF coil encoding via a sliding‐kernel approach. Unlike generalized parallel imaging approaches that might typically involve inverting a prohibitively large matrix for arbitrary sampling trajectories, the PARS sliding‐kernel approach creates manageable and distributable independent matrices to be inverted, achieving both computational efficiency and numerical stability. An empirical method designed to measure total error power is described, and the total error power of PARS reconstructions is studied over a range of k‐space radii and accelerations, revealing “minimal‐error” conditions at comparatively modest k‐space radii. PARS reconstructions of undersampled in vivo Cartesian and non‐Cartesian data sets are shown and are compared selectively with traditional SENSE reconstructions. Various characteristics of the PARS k‐space locality constraint (such as the tradeoff between signal‐to‐noise ratio and artifact power and the relationship with iterative parallel conjugate gradient approaches or nonparallel gridding approaches) are discussed. Magn Reson Med 53:1383–1392, 2005.

Calibrationless parallel imaging reconstruction based on structured low‐rank matrix completion

A calibrationless parallel imaging reconstruction method, termed simultaneous autocalibrating and k‐space estimation (SAKE), is presented. It is a data‐driven, coil‐by‐coil reconstruction method that does not require a separate calibration step for estimating coil sensitivity information.

Recent advances in image reconstruction, coil sensitivity calibration, and coil array design for SMASH and generalized parallel MRI

Parallel magnetic resonance imaging (MRI) techniques use spatial information from arrays of radiofrequency (RF) detector coils to accelerate imaging. A number of parallel MRI techniques have been described in recent years, and numerous clinical applications are currently being explored. The advent of practical parallel imaging presents various challenges for image reconstruction and RF system design. Recent advances in tailored SiMultaneous Acquisition of Spatial Harmonics (SMASH) image reconstructions are summarized. These advances enable robust SMASH imaging in arbitrary image planes with a wide range of coil array geometries. A generalized formalism is described which may be used to understand the relations between SMASH and SENSE, to derive typical implementations of each as special cases, and to form hybrid techniques combining some of the advantages of both. Accurate knowledge of coil sensitivities is crucial for parallel MRI, and errors in calibration represent one of the most common and the most pernicious sources of error in parallel image reconstructions. As one example, motion of the patient and or the coil array between the sensitivity reference scan and the accelerated acquisition can lead to calibration errors and reconstruction artifacts. Self-calibrating parallel MRI approaches that address this problem by eliminating the need for external sensitivity references are reviewed. The ultimate achievable signal-to-noise ratio (SNR) for parallel MRI studies is closely tied to the geometry and sensitivity patterns of the coil arrays used for spatial encoding. Several parallel imaging array designs that depart from the traditional model of overlapped adjacent loop elements are described.

Inherently self-calibrating non-Cartesian parallel imaging.

The use of self‐calibrating techniques in parallel magnetic resonance imaging eliminates the need for coil sensitivity calibration scans and avoids potential mismatches between calibration scans and subsequent accelerated acquisitions (e.g., as a result of patient motion). Most examples of self‐calibrating Cartesian parallel imaging techniques have required the use of modified k‐space trajectories that are densely sampled at the center and more sparsely sampled in the periphery. However, spiral and radial trajectories offer inherent self‐calibrating characteristics because of their densely sampled center. At no additional cost in acquisition time and with no modification in scanning protocols, in vivo coil sensitivity maps may be extracted from the densely sampled central region of k‐space. This work demonstrates the feasibility of self‐calibrated spiral and radial parallel imaging using a previously described iterative non‐Cartesian sensitivity encoding algorithm. Magn Reson Med 54:1–8, 2005.

Effects of inductive coupling on parallel MR image reconstructions.

Theoretical arguments and experimental results are presented that characterize the impact of inductive coupling on the performance of parallel MRI reconstructions. A simple model of MR signal and noise reception suggests that the intrinsic amount of spatial information available from a given coil array is unchanged in the presence of inductive coupling, as long as the sample remains the dominant source of noise for the coupled array. Any loss of distinctness in the measured coil sensitivities is compensated by information stored in the measured noise correlations. Adjustments to the theory are described to account for preamplifier noise contributions. Results are presented from an experimental system in which preamplifier input impedances are systematically adjusted in order to vary the level of coupling between array elements. Parallel image reconstructions using an array with four different levels of coupling and an acceleration factor up to six show average SNR changes of −7.6% to +7.5%. The modest changes in overall SNR are accompanied by similarly small changes in g‐factor. These initial results suggest that moderate amounts of inductive coupling should not have a prohibitive effect on the use of a given coil array for parallel MRI. Magn Reson Med 52:628–639, 2004.

MOLECULAR AND STRUCTURAL ANALYSIS OF NUCLEAR LOCALIZING ANTI-DNA LUPUS ANTIBODIES

To determine the structure of three nuclear localizing lupus anti-DNA immunoglobulins (Igs) and to search for clues to mechanisms of cellular and/or nuclear access, their H- and L-chain variable region sequences were determined and subjected to three-dimensional modeling. Although the results indicate heterogeneity in their primary structures, the H chains are encoded by 3 members of the J558 VH gene family with a common tertiary conformation that is not shared by a J558-encoded nonnuclear localizing anti-DNA control Ig. Furthermore, at least two of the Igs share a conformational motif in the H-chain CDR3, and all three Igs contain multiple positively charged amino acids in their CDRs, resembling nuclear localization signals that direct protein nuclear import. Notably, each VH and VK gene is also found recurrently among previously described autoantibodies. Molecular analysis further indicates that both germline-encoded and significantly mutated V genes can generate nuclear localizing anti-DNA Ig.

Performance evaluation of a 32-element head array with respect to the ultimate intrinsic SNR.

The quality of an RF detector coil design is commonly judged on how it compares with other coil configurations. The aim of this article is to develop a tool for evaluating the absolute performance of RF coil arrays. An algorithm to calculate the ultimate intrinsic signal‐to‐noise ratio (SNR) was implemented for a spherical geometry. The same imaging tasks modeled in the calculations were reproduced experimentally using a 32‐element head array. Coil performance maps were then generated based on the ratio of experimentally measured SNR to the ultimate intrinsic SNR, for different acceleration factors associated with different degrees of parallel imaging. The relative performance in all cases was highest near the center of the samples (where the absolute SNR was lowest). The highest performance was found in the unaccelerated case and a maximum of 85% was observed with a phantom whose electrical properties are consistent with values in the human brain. The performance remained almost constant for 2‐fold acceleration, but deteriorated at higher acceleration factors, suggesting that larger arrays are needed for effective highly‐accelerated parallel imaging. The method proposed here can serve as a tool for the evaluation of coil designs, as well as a tool to guide the development of original designs which may begin to approach the optimal performance. Copyright