A dual method for discrete Chebychev curve fitting

This paper presents a special purpose dual algorithm for obtaining a Chebychev approximation to an overdetermined system of linear equations. The method is founded on the principles of linear programming and is designed to take advantage of the problem's special structure. It is shown that, while maintaining a reduced basis, certain iterations of the standard dual algorithm may be combined into one. Two computer code implementations of the method are discussed and a computational comparison with another algorithm for Chebychev approximation is given.     

B(1)(+)/actual flip angle and reception sensitivity mapping methods: simulation and comparison

Knowledge of the spatial distribution of transmission field B₁⁺ and reception sensitivity maps is important in high-field (≥3 T) human magnetic resonance (MR) imaging for several reasons: these include post-acquisition correction of intensity inhomogeneities, which may affect the quality of images; modeling and design of radiofrequency (RF) coils and pulses; validating theoretical models for electromagnetic field calculations; testing the compatibility with MR environment of biomedical implants. Moreover, inhomogeneities in the RF field are an essential source of error for quantitative MR spectroscopy. Recent studies have also shown that B₁⁺ and reception sensitivity maps can be used for direct calculation of tissue electrical parameters and for estimating the local specific absorption rate (SAR) in vivo.Several B₁⁺ mapping techniques have been introduced in the past few years based on actual flip angle (FA) mapping, but, to date, none has emerged as a standard. For reception sensitivity calculation, the signal intensity equation can be used where the nominal FA distribution must be replaced with the actual FA distribution calculated by one of the B₁⁺ mapping techniques.This study introduces a quantitative comparison between two known methods for B₁⁺/actual FA and reception sensitivity mapping: the double-angle method (DAM) and the fitting (FIT) method. Experimental data obtained using DAM and FIT methods are also compared with numerical simulation results.     

Exact solution of the CPMG pulse sequence with phase variation down the echo train: application to R₂ measurements

An implicit exact algebraic solution of CPMG experiments is presented and applied to fit experiments. Approximate solutions are also employed to explore oscillations and effective decay rates of CPMG experiments. The simplest algebraic approximate solution has illustrated that measured intensities will oscillate in the conventional CPMG experiments and that using even echoes can suppress errors of measurements of R? due to the imperfection of high-power pulses. To deal with low-power pulses with finite width, we adapt the effective field to calculate oscillations. An optimization model with the effective field approximation and dimensionless variables is proposed to quantify oscillations of measured intensities of CPMG experiments of different phases of the π pulses. We show, as was known using other methods, that repeating one group of four pulses with different phases in CPMG experiments, which we call phase variation, but others call phase alternation or phase cycling, can significantly smooth the dependence of measured intensities on frequency offset in the range of ±?γB?. In this paper, a second-order expression with respect to the ratio of frequency offset to π-pulse amplitude is developed to describe the effective R? of CPMG experiments when using a group phase variation scheme. Experiments demonstrate that (1) the exact calculation of CPMG experiments can remarkably eliminate systematic errors in measured R?s due to the effects of frequency offset, even in the absence of phase variation; (2) CPMG experiments with group phase variation can substantially remove oscillations and effects of the field inhomogeneity; (3) the second-order expression of the effective decay rate with phase variation is able to provide reliable estimates of R? when offsets are roughly within ±?γB?; and, most significantly, (4) the more sophisticated optimization model using an exact solution of the discretized CPMG experiment extends, to ±γB?, the range of offsets for which reliable estimates of R? can be obtained when using the preferred phase variation scheme.     

Schonland ambiguity in the electron nuclear double resonance analysis of hyperfine interactions: principles and practice

For the analysis of the angular dependence of electron paramagnetic resonance (EPR) spectra of low-symmetry centres with S=1/2 in three independent planes, it is well-established-but often overlooked-that an ambiguity may arise in the best-fit g<--> tensor result. We investigate here whether a corresponding ambiguity also arises when determining the hyperfine coupling (HFC) A<--> tensor for nuclei with I=1/2 from angular dependent electron nuclear double resonance (ENDOR) measurements. It is shown via a perturbation treatment that for each set of M(S) ENDOR branches two best-fit A<--> tensors can be derived, but in general only one unique solution simultaneously fits both. The ambiguity thus only arises when experimental data of only one M(S) multiplet are used in analysis or in certain limiting cases. It is important to realise that the ambiguity occurs in the ENDOR frequencies and therefore the other best-fit result for an ENDOR determined A<--> tensor depends on various details of the ENDOR experiment: the M(S) state of the fitted transitions, the microwave frequency (or static magnetic field) in the ENDOR measurements and the rotation planes in which data have been collected. The results are of particular importance in the identification of radicals based on comparison of theoretical predictions of HFCs with published literature data. A procedure for obtaining the other best-fit result for an ENDOR determined A<--> tensor is outlined.     

Fitting of EPR spectra: the importance of a flexible bandwidth

Utilizing a standard spin Hamiltonian for an S=32 spin system, we fit complete X-band powder EPR spectra of the Cr(oxalate)(3)(3-) anion diluted into K(3)[Co(oxalate)(3)]·3H(2)O. By using models for the bandshape and bandwidths of varying degree of flexibility, we show that the successful outcome of such a fitting endeavour very much depends on the used bandshape-bandwidth model. The best results are obtained when the bandwidth model incorporates anisotropic intrinsic bandwidths in addition to being able to account for inhomogeneous line broadening caused by distributions of the spin Hamiltonian parameters.