Improving the time efficiency of the Fourier synthesis method for slice selection in magnetic resonance imaging.

The design of slice selective pulses for magnetic resonance imaging can be cast as an optimal control problem. The Fourier synthesis method is an existing approach to solve these optimal control problems. In this method the gradient field as well as the excitation field are switched rapidly and their amplitudes are calculated based on a Fourier series expansion. Here, we provide a novel insight into the Fourier synthesis method via representing the Bloch equation in spherical coordinates. Based on the spherical Bloch equation, we propose an alternative sequence of pulses that can be used for slice selection which is more time efficient compared to the original method. Simulation results demonstrate that while the performance of both methods is approximately the same, the required time for the proposed sequence of pulses is half of the original sequence of pulses. Furthermore, the slice selectivity of both sequences of pulses changes with radio frequency field inhomogeneities in a similar way. We also introduce a measure, referred to as gradient complexity, to compare the performance of both sequences of pulses. This measure indicates that for a desired level of uniformity in the excited slice, the gradient complexity for the proposed sequence of pulses is less than the original sequence.

Dipolar recoupling in solid state NMR by phase alternating pulse sequences.

We describe some new developments in the methodology of making heteronuclear and homonuclear recoupling experiments in solid state NMR insensitive to rf-inhomogeneity by phase alternating the irradiation on the spin system every rotor period. By incorporating delays of half rotor periods in the pulse sequences, these phase alternating experiments can be made gamma encoded. The proposed methodology is conceptually different from the standard methods of making recoupling experiments robust by the use of ramps and adiabatic pulses in the recoupling periods. We show how the concept of phase alternation can be incorporated in the design of homonuclear recoupling experiments that are both insensitive to chemical shift dispersion and rf-inhomogeneity.

Fourier synthesis techniques for NMR spectroscopy in inhomogeneous fields.

This paper describes a method for synthesizing spin rotations with arbitrary space dependence on a sample of noninteracting spin 12 by using nonselective radio frequency pulses and pulsed field gradients. This method is used to map out spatial distribution of inhomogeneous B(0) field and to engineer a space dependent evolution of spins that cancels the space dependent phase spins acquire when precessing in an inhomogeneous magnetic field. The technique allows one to record high resolution spectra in inhomogeneous magnetic field by using only time varying linear gradients and rf fields and is expected to find applications in ex situ NMR.

Curve matching on brain surfaces using Frenet distances.

This paper describes methods for diffeomorphic matching of curves on brain surfaces. Distances between curves are defined by Frenet representation via speed, curvature, and torsion. The curvematching algorithm is based on bipartite graph matching, with weights defined by the Frenet distance over diffeomorphic maps of one curve onto the other (Sedgewick [1983]: Algorithms). We follow Khaneja ([1996]: Statistics and Geometry of Cortical Features) and define fundus curves on the brain surfaces as extremal curvature lines generated using dynamic programming. Examples are shown for fundus curve matchings on macaque brain surfaces.

Statistical methods in computational anatomy.

This paper reviews recent developments by the Washington/Brown groups for the study of anatomical shape in the emerging new discipline of computational anatomy. Parametric representations of anatomical variation for computational anatomy are reviewed, restricted to the assumption of small deformations. The generation of covariance operators for probabilistic measures of anatomical variation on coordinatized submanifolds is formulated as an empirical procedure. Populations of brains are mapped to common coordinate systems, from which template coordinate systems are constructed which are closest to the population of anatomies in a minimum distance sense. Variation of several one-, two- and three-dimensional manifolds, i.e. sulci, surfaces and brain volumes are examined via Gaussian measures with mean and covariances estimated directly from maps of templates to targets. Methods are presented for estimating the covariances of vector fields from a family of empirically generated maps, posed as generalized spectrum estimation indexed over the submanifolds. Covariance estimation is made parametric, analogous to autoregressive modelling, by introducing small deformation linear operators for constraining the spectrum of the fields.