Biomedical subjects

Charles L Epstein

Publications and source records attributed to Charles L Epstein.

6 recordsLinked to original sources

PubMed2006

Subelliptic boundary conditions for SpinC-Dirac operators, gluing, relative indices, and tame Fredholm pairs.

Let X be a Spin manifold with boundary, such that the Spin structure is defined near the boundary by an almost complex structure, which is either strictly pseudoconvex or pseudoconcave (and hence contact). Using generalized Szego projectors, we define modified partial differential-Neumann boundary conditions, Reo, for spinors, which lead to subelliptic Fredholm boundary value problems for the Spin-Dirac operator, eth(eo). To study the index of these boundary value problems we introduce a generalization of Fredholm pairs to the "tame" category. In this context, we show that the index of the graph closure of (eth(eo), Reo) equals the tame relative index, on the boundary, between Reo and the Calderon projector. Let X0 and X1 be strictly pseudoconvex, Spin manifolds, as above. Let phi : bX1 --> bX0, be a contact diffeomorphism, S0, S1 denote generalized Szego projectors on bX0, bX1, respectively, and R0(eo), R1(eo), the subelliptic boundary conditions they define. If X1 is the manifold X1 with its orientation reversed, then the glued manifold X = X0 coproduct operator(phi) X1 has a canonical Spin structure and Dirac operator, ethX(eo). Applying these results we obtain a formula for the relative index, R-Ind(S0, phi*S1), [formula: see text]. As a special case, this formula verifies a conjecture of Atiyah and Weinstein [(1997) RIMS Kokyuroku 1014:1-14] for the index of the quantization of a contact transformation between cosphere bundles.

Journal Article↗

PubMed2006

A novel technique for imaging with inhomogeneous fields.

We introduce a simple, efficient, low-SAR method for magnetic resonance imaging in the presence of a static field with a permanent, and possibly large gradient. The technique, which is called slant-slice imaging is essentially a spin-echo imaging sequence except that the imaging slice is oriented such that the static field gradient can be used in conjunction with applied gradients during readout. Data are collected for 2D slices. Unlike single point imaging techniques, entire lines of k-space are acquired with each readout. The slant-slice pulse sequence is used to obtain high quality images, using a clinical scanner to simulate a static field with a large permanent gradient. The effects of the inhomogeneity are quantified by two parameters nu and q, which are useful for assessing the utility of a magnet design for 3D-MR imaging.

Algorithms↗

PubMed2006

Experimental and computational analyses of the effects of slice distortion from a metallic sphere in an MRI phantom.

Susceptibility artifacts due to metallic prostheses are a major problem in clinical magnetic resonance imaging. We theoretically and experimentally analyze slice distortion arising from susceptibility differences in a phantom consisting of a stainless steel ball bearing embedded in agarose gel. To relate the observed image artifacts to slice distortion, we simulate images produced by 2D and 3D spin-echo (SE) and a view angle tilting (VAT) sequence. Two-dimensional SE sequences suffer from extreme slice distortion when a metal prosthesis is present, unlike 3D SE sequences for which--since slices are phase-encoded--distortion of the slice profile is minimized, provided the selected slab is larger than the region of interest. In a VAT sequence, artifacts are reduced by the application of a gradient along the slice direction during readout. However, VAT does not correct for the excitation slice profile, which results in the excitation of spins outside the desired slice location and can lead to incorrect anatomical information in MR images. We propose that the best sequences for imaging in the presence of a metal prosthesis utilize 3D acquisition, with phase encoding replacing slice selection to minimize slice distortion, combined with excitation and readout gradient strengths at their maximum values.

Artifacts↗

PubMed2005

Practical pulse synthesis via the discrete inverse scattering transform.

This paper provides the practical details required to use the inverse scattering (IST) approach to design selective RF-pulses. As in the Shinnar-Le Roux (SLR) approach, we use a hard pulse approximation to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. We explain how to approximate the reflection coefficient to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, we retain direct control on the phase of the magnetization profile throughout the design process. We give explicit recursive algorithms for computing the hard pulse from the inverse scattering data. These algorithms are quite different from the SLR recursion, being essentially discretizations of the Marchenko equations. We call our approach the discrete inverse scattering transform or DIST. Overall, it is as fast as the SLR approach. When bound states are present, we use both the left and right Marchenko equations to improve the numerical stability of the algorithm. We compute a variety of examples and consider the effect of amplitude errors on the magnetization profile.

Algorithms↗

PubMed2004

Minimum energy pulse synthesis via the inverse scattering transform.

This paper considers a variety of problems in the design of selective RF-pulses. We apply a formula of Zakharov and Manakov to directly relate the energy of an RF-envelope to the magnetization profile and certain auxiliary parameters used in the inverse scattering transform (IST) approach to RF-pulse synthesis. This allows a determination of the minimum possible energy for a given magnetization profile. We give an algorithm to construct both the minimum energy RF-envelope as well as any other envelope that produces a given magnetization profile. This includes an algorithm for solving the Gel'fand-Levitan-Marchenko equations with bound states. The SLR method is analyzed in terms of traditional scattering data, and shown to be a special (singular) case of the IST approach. RF-envelopes are computed for a variety of examples.

Journal Article↗

PubMed2004

Exact half pulse synthesis via the inverse scattering transform.

In a paper of Nielson et al. it is shown, using the linear approximation, that it might be possible to create a pair of RF-pulses, which, after summation of the unrephased signals achieve a specified transverse magnetization. Such pulses, designed using the linear approximation, show rather poor slice selectivity. Using the inverse scattering transform formalism we give an algorithm to exactly achieve a specified "summed" transverse magnetization profile. Indeed for a constant phase transverse profile, our algorithm produces infinitely many solutions.

Journal Article↗