Concepts in Magnetic Resonance Part A最新文献

Determination of the distribution of magnetic resonance (MR) transverse relaxation times is emerging as an important method for materials characterization, including assessment of tissue pathology in biomedicine. These distributions are obtained from the inverse Laplace transform (ILT) of multiexponential decay data. Stabilization of this classically ill-posed problem is most commonly attempted using Tikhonov regularization with an L₂ penalty term. However, with the availability of convex optimization algorithms and recognition of the importance of sparsity in model reconstruction, there has been increasing interest in alternative penalties. The L₁ penalty enforces a greater degree of sparsity than L₂, and so may be suitable for highly localized relaxation time distributions. In addition, L_p penalties, 1 < p < 2, and the elastic net (EN) penalty, defined as a linear combination of L₁ and L₂ penalties, may be appropriate for distributions consisting of both narrow and broad components. We evaluate the L₁, L₂, L_p, and EN penalties for model relaxation time distributions consisting of two Gaussian peaks. For distributions with narrow Gaussian peaks, the L₁ penalty works well to maintain sparsity and promote resolution, while the conventional L₂ penalty performs best for distributions with broader peaks. Finally, the L_p and EN penalties do in fact outperform the L₁ and L₂ penalties for distributions with components of unequal widths. These findings serve as indicators of appropriate regularization in the typical situation in which the experimentalist has a priori knowledge of the general characteristics of the underlying relaxation time distribution. Our findings can be applied to both the recovery of T₂ distributions from spin echo decay data as well as distributions of other MR parameters, such as apparent diffusion constant, from their multiexponential decay signals.

Nonuniform sampling (NUS) offers NMR spectroscopists a means of accelerating data collection and increasing spectral quality in multidimensional (nD) experiments. The data from NUS experiments are incomplete by design, and must be reconstructed prior to use. While most existing reconstruction techniques compute point estimates of the true signal, Bayesian statistics offers a means of estimating posterior distributions over the signal, which enable more rigorous quantitation and uncertainty estimation. In this article, we describe the variational approach to approximating Bayesian posterior distributions, and illustrate how it can be applied to extend existing results from Bayesian spectrum analysis and compressed sensing. The new NUS reconstruction algorithms resulting from variational Bayes are computationally efficient, and offer new insights into the concepts of spectral sparsity and optimal sampling in NMR experiments.

The starting point of all NMR experiments is a spin polarization which develops when we place the sample in static magnetic field B₀. There are excess of spins aligned along B₀ (spin up with lower energy) than spins aligned opposite (spin down with higher energy) to the field B₀. A natural question is what is the source of this excess spin polarization because relaxation mechanisms can flip a up spin to a down spin and vice-versa. The answer lies in the density of states. When a molecule with spin down flips to spin up it loses energy. This energy goes into increasing the kinetic energy of the molecule in the gas/solution phase. At this increased kinetic energy, there are more rotational-translational states accessible to the molecule than at lower energy. This increases the probability the molecule will spend in spin up state (higher kinetic energy state). This is the source of excess polarization. In this article, we use an argument based on equipartition of energy to explicitly count the excess states that become accessible to the molecule when its spin is flipped from down to up. Using this counting, we derive the familiar Boltzmann distribution of the ratio of up vs down spins. Although prima facie, there is nothing new in this article, we find the mode counting argument for excess states interesting. Furthermore, the article stresses the fact that spin polarization arises from higher density of states at increased kinetic energy of molecules.

A simple approach how to calculate analytical expressions for unbalanced steady-state free precession (ubSSFP) signals of arbitrary dephasing order is presented. Dephasing order is the number of effective gradient dephasing cycles that magnetization immediately after an RF-pulse has experienced during the ubSSFP sequence. Based on the obtained equations, which are in accordance with existing literature, the sensitivity of ubSSFP signals to T₂^∗ is derived under the assumption of a Lorentzian frequency distribution resulting from static field inhomogeneities. Further, the phases of all ubSSFP signals are calculated and a general expression of how to use them for B₀-fieldmapping is given. The derivation is supported by the extended phase graph (EPG) model, and as such the work also acts as a comprehensive introduction to the formal description of SSFP. In addition, the balanced SSFP (bSSFP) sequence is explored. The connection of bSSFP to ubSSFP is shown, and potential T₂^∗-sensitivity of bSSFP is examined based on numerical simulations. It is shown that ubSSFP signals with negative dephasing order have a refocusing character and behave similar to spin-echo signals. Conversely, ubSSFP signals with zero or positive dephasing order can be regarded as T₂^∗-weighted. The behavior of bSSFP depends largely on the exact distribution of frequencies. For instance, for a narrow spherical distribution, bSSFP acts like a spin-echo sequence, while for a Lorentzian distribution a refocusing behavior does not occur.

Nitroxide biradicals have been prepared with electron-electron spin-spin exchange interaction, J, ranging from weak to very strong. EPR spectra of these biradicals in fluid solution depend on the ratio of J to the nitrogen hyperfine coupling, A_N, and the rates of interconversion between conformations with different values of J. For relatively rigid biradicals EPR spectra can be simulated as the superposition of AB splitting patterns arising from different combinations of nitrogen nuclear spin states. For more flexible biradicals spectra can be simulated with a Liouville representation of the dynamics that interconvert conformations with different values of J on the EPR timescale. Analysis of spectra, factors that impact J, and examples of applications to chemical and biophysical problems are discussed.

In this tribute to our friend, mentor and colleague Alexander Davidson Bain we have collectively recapitulated the milestones of his career at McMaster university. We start from Alex's scientific and educational achievements and continue with his accomplishments as a community and infrastructure builder. We attempt to provide a sense of the breadth and depth of his seemingly endless scientific contributions while at McMaster by briefly summarizing selected representative examples from his body of work. Following Alex's lead, the scientific account is mixed with anecdotes and “bits of wisdom” we fondly remember from our interactions and collaborations with him. We also touch upon his brilliant and nurturing educational style and his “aggregator” role within the McMaster and wider NMR communities. We conclude with a more personal picture of Alex D. Bain, in which his scientific excellence and profound intellect are inextricably tied to his kind, nurturing and optimistic character and to his uniquely wry humor. He was not just a “good guy,” he was the epitome of the “good guy.”