Kelvin J. Layton

Single shot trajectory design for region-specific imaging using linear and nonlinear magnetic encoding fields.

It has recently been demonstrated that nonlinear encoding fields result in a spatially varying resolution. This work develops an automated procedure to design single‐shot trajectories that create a local resolution improvement in a region of interest. The technique is based on the design of optimized local k‐space trajectories and can be applied to arbitrary hardware configurations that employ any number of linear and nonlinear encoding fields. The trajectories designed in this work are tested with the currently available hardware setup consisting of three standard linear gradients and two quadrupolar encoding fields generated from a custom‐built gradient insert. A field camera is used to measure the actual encoding trajectories up to third‐order terms, enabling accurate reconstructions of these demanding single‐shot trajectories, although the eddy current and concomitant field terms of the gradient insert have not been completely characterized. The local resolution improvement is demonstrated in phantom and in vivo experiments. Magn Reson Med 70:684–696, 2013.

Modelling and Estimation of Multicomponent

Estimation of multiple T2 components within single imaging voxels typically proceeds in one of two ways; a nonparametric grid approximation to a continuous distribution is made and a regularized nonnegative least squares algorithm is employed to perform the parameter estimation, or a parametric multicomponent model is assumed with a maximum likelihood estimator for the component estimation. In this work, we present a Bayesian algorithm based on the principle of progressive correction for the latter choice of a discrete multicomponent model. We demonstrate in application to simulated data and two experimental datasets that our Bayesian approach provides robust and accurate estimates of both the T2 model parameters and nonideal flip angles. The second contribution of the paper is to present a Cramér-Rao analysis of T2 component width estimators. To this end, we introduce a parsimonious parametric and continuous model based on a mixture of inverse-gamma distributions. This analysis supports the notion that T2 spread is difficult, if not infeasible, to estimate from relaxometry data acquired with a typical clinical paradigm. These results justify the use of the discrete distribution model.

T_{2}

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches by, for example, enabling reduced imaging times. Imaging schemes that employ general nonlinear encoding fields are difficult to analyze using traditional measures. In particular, the resolution is spatially varying, characterized by a position-dependent point spread function (PSF). Likewise, the use of nonlinear encoding fields creates an additional spatial dependence on the signal-to-noise ratio (SNR). Although the two properties of resolution and SNR are linked, in this work we focus on the latter. To this end, we examine the pixel variance, which requires a computation that is often not feasible for nonlinear encoding schemes. This paper presents a general formulation for the performance analysis of imaging schemes using arbitrary encoding fields. The analysis leads to the derivation of a practical and computationally efficient performance metric, which is demonstrated through simulation examples.

Distributions

PatLoc (Parallel Imaging Technique using Localized Gradients) accelerates imaging and introduces a resolution variation across the field‐of‐view. Higher‐dimensional encoding employs more spatial encoding magnetic fields (SEMs) than the corresponding image dimensionality requires, e.g. by applying two quadratic and two linear spatial encoding magnetic fields to reconstruct a 2D image. Images acquired with higher‐dimensional single‐shot trajectories can exhibit strong artifacts and geometric distortions. In this work, the source of these artifacts is analyzed and a reliable correction strategy is derived.

Performance Analysis for Magnetic Resonance Imaging With Nonlinear Encoding Fields

The response of a magnetic resonance spin system is predicted and experimentally verified for the particular case of a continuous wave amplitude modulated radiofrequency excitation. The experimental results demonstrate phenomena not previously observed in magnetic resonance systems, including a secondary resonance condition when the amplitude of the excitation equals the modulation frequency. This secondary resonance produces a relatively large steady state magnetisation with Fourier components at harmonics of the modulation frequency. Experiments are in excellent agreement with the theoretical prediction derived from the Bloch equations, which provides a sound theoretical framework for future developments in NMR spectroscopy and imaging.

Single-shot imaging with higher-dimensional encoding using magnetic field monitoring and concomitant field correction

Multiple nonlinear gradient fields offer many potential benefits for spatial encoding including reduced acquisition time, fewer artefacts and region‐specific imaging, although designing a suitable trajectory for such a setup is difficult. This work aims to optimize encoding trajectories for multiple nonlinear gradient fields based on the image signal‐to‐noise ratio.

Rabi resonance in spin systems: Theory and experiment

Implementing new magnetic resonance experiments, or sequences, often involves extensive programming on vendor‐specific platforms, which can be time consuming and costly. This situation is exacerbated when research sequences need to be implemented on several platforms simultaneously, for example, at different field strengths. This work presents an alternative programming environment that is hardware‐independent, open‐source, and promotes rapid sequence prototyping.

Trajectory optimization based on the signal‐to‐noise ratio for spatial encoding with nonlinear encoding fields

Abstract The “Leave-out Sign-dominant Correlation Regions” (LSCR) algorithm is extended to deliver a guaranteed confidence set for the parameters of a time-varying system at any given time. The algorithm is derived by assuming that an upper bound on the parameter variation is available, and the delivered confidence set is valid without any prior knowledge of the noise. Simulation examples are provided to illustrate the performance of the algorithm.

Pulseq: A rapid and hardware‐independent pulse sequence prototyping framework

In waveform design for magnetic resonance applications, periodic continuous-wave excitation offers potential advantages that remain largely unexplored because of a lack of understanding of the Bloch equation with periodic continuous-wave excitations. Using harmonic balancing techniques the steady state solutions of the Bloch equation with periodic excitation can be effectively solved. Moreover, the convergence speed of the proposed series approximation is such that a few terms in the series expansion suffice to obtain a very accurate description of the steady state solution. The accuracy of the proposed analytic approximate series solution is verified using both a simulation study as well as experimental data derived from a spherical phantom with doped water under continuous-wave excitation. Typically a five term series suffices to achieve a relative error of less than one percent, allowing for a very effective and efficient analytical design process. The opportunities for Rabi frequency modulated continuous-wave form excitation are then explored, based on a comparison with steady state free precession pulse sequences.

Online Algorithms for the Construction of Guaranteed Confidence Sets for the Parameters of Time-varying Systems

Recently there has been increasing interest in estimating the distribution of relaxation times contributing to a magnetic resonance signal. This paper shows that it is impractical to estimate the spread of such a distribution from typical measurements. Instead, a Bayesian estimator is developed for a discrete distribution, which is very robust to noise. Although the distribution spread is not modelled, the estimates capture the main features of the distribution such as the mode locations and often provide improved myelin water fraction estimates in simulation examples.