Concepts in Magnetic Resonance Part A最新文献

The Clebsch–Gordan coefficients are extremely useful in magnetic resonance theory, yet have an infamous perceived level of complexity by many students. The Clebsch–Gordan coefficients are used to determine both the matrix elements of the spherical tensor operators and the total angular momentum states of a system of component angular momenta. Full derivations of these coefficients are rarely worked through step by step. Instead, students are provided with tables accompanied by little or no explanation of where the values in it originated from. This lack of direction is often a source of confusion for students. For this reason, we work through two common examples of the application of the Clebsch–Gordan coefficients to magnetic resonance experiments. In the first, we determine the components of the magnetic resonance Hamiltonian of ranks 0, 1, and 2 and use these to identify the secular portion of the static, heteronuclear dipolar Hamiltonian. In the second, we derive the singlet and triplet states that arise from the interaction of two identical spin-1/2 particles.

In this paper, we want to consider what would be involved in calculating the R₂ relaxation of amide protons in a protein caused by dipolar interactions with nearby protons, for which there are many. NMR textbooks give analytical equations and sometimes derivations for solution NMR relaxation due to dipolar interactions between two spins. There are also closed equations for dipolar interactions between three spins, which include relaxation interference, also known as cross-correlated cross-relaxation. We here derive an expression for interference between four spins. For larger systems, such as amide protons in a protein, we develop a local-field methodology, from which solution relaxation interference can be computed for a basically limitless number of interacting spins.

Vertical electrical sounding and magnetic methods were carried out to assess groundwater potential in Adilo catchment, Kembata Tembaro Zone, South Nations, Nationalities and Peoples Regional Government, Main Ethiopian Rift. The data were acquired from eight VES points using Schlumberger electrode arrays with maximum half current electrode spacing (AB/2 = 500) and 253 magnetic data points were analyzed. The qualitative analysis of VES data was accomplished by using curves, apparent resistivity, and pseudodepths, and the quantitative interpretations of the VES data were constructed by the VES data using IPI-Res3, IPI2Win, and surfer software and constructing geoelectric section along with profiles and lithological information from the borehole and Geosoft interpretation was used for magnetic data. The VES results of the data revealed five geoelectric layers which differ in degree of fracturing, weathering, and formation. The upward continued magnetic field map anomaly to 560 m illustrated northwestern to the southwest; areas have a low magnetic anomaly. Examining the potential aquifer of profile one’s geoelectric section, the horizons of layer four were better potential aquifers as the highly fractured and weathered ignimbrite zone of layer five of VES13 was 219 m deeper than the depths of the other VES points, and along with profile two geoelectric sections, the horizon of layer four VES23 layer five has the lowest resistivity with large thickness at a depth of 253 m. Thus, the low resistivity and the large thickness of these formations are an indication of the high yield of groundwater potential in the study area.

Stretched hydrogels make uniformly anisotropic environments for quadrupolar nuclei such as ²H, ²³Na, and ¹³³Cs. Such surroundings cause the partial alignment of nuclear spin bearing ions and molecules that is sufficiently pronounced to alter the nuclear magnetic resonance spectra of the guest species. In most cases, resonance splittings are directly related to the spin quantum number I. The relative intensities of the components of the resonance multiplets can be inferred from basic quantum mechanics.

In MRI, at ultrahigh field, the use of parallel transmit radiofrequency (RF) arrays is very beneficial to better control spin excitation spatially. In that framework, the so-called “universal pulse” technique, proposed recently for head imaging at 7 tesla, gives access to “plug-and-play” nonadiabatic solutions exhibiting good robustness against intersubject variations in the resonant transmit fields. This new type of solution has been defined so far as the result of numerical pulse optimizations performed across a collection of RF field maps acquired on a small population sample (pulse design database). In this work, we investigate an alternative universal pulse design approach in the linear small tip angle regime whereby the database of RF field maps is first transformed into a second-order statistical model and which then exploits a statistical robust design formalism for the optimization of the RF and magnetic field gradient waveforms. Experimental validation with an eightfold transmit RF coil for 7 tesla brain imaging shows that this new approach brings some benefit in terms of computational efficiency. Hence, for a design database composed of 35 maps, the computation time initially of 50 min could be reduced down to 3 min. The proposed statistical approach thus enables integration of large databases, presumably necessary to ensure robust solutions. Finally, it provides means to compute flip angle statistics and, along with it, simple performance metrics for quality assurance (RF pulse performance) or guidance in the optimization of TX array architectures.

The magnetization differential equations of Bloch are integrated using a matrix diagonalization method. The solution describes several limiting cases and leads to compact expressions of wide validity for a spin ensemble initially at equilibrium.

Magnetic resonance imaging based on steady-state free precision (SSFP) sequences is a fast method to acquire T₁, T₂, and $$-weighted images. In inhomogeneous tissues such as lung tissue or blood vessel networks, however, microscopic field inhomogeneities cause a nonexponential free induction decay and a non-Lorentzian lineshape. In this work, the SSFP signal is analyzed for different prominent tissue models. Neglecting the effect of non-Lorentzian lineshapes can easily result in large errors of the determined relaxation times. Moreover, sequence parameters of SSFP measurements can be optimized for the nonexponential signal decay in many tissue structures.

Cerebral malaria causes several deaths every year. Global metabolic alteration, specifically hypoglycemia and lactic acidosis are hallmarks of severe malaria. Glucose being the major fuel source for the brain, it is important to understand cerebral glucose utilization in the host during cerebral complications of the disease that may have a significant role in cerebral pathogenesis. We have used ¹³C NMR spectroscopy to understand glucose utilization in the brain and liver of mice with cerebral malaria (CM), noncerebral malaria (NCM), and in control mice. Animals were challenged with intravenous glucose bolus followed by metabolic profiling of brain and liver extracts. Our result suggests a differential glucose utilization in the malaria group with respect to that of controls, while no difference between CM and NCM.

In order to thoroughly comprehend and adequtely interpret NMR data, it is necessary to perceive the complex structure of spin Hamiltonian. Although NMR principles have been extensively discussed in a number of distinguished introductory publications, it still remains difficult to find illustrative graphical models revealing the tensorial nature of spin interaction. Exposure of the structure standing behind mathematical formulas can clarify intangible concepts and provide a coherent image of basic phenomena. This approach is essential when it comes to hard to manage, time-dependent processes such as Magic Angle Spinning (MAS), where the anisotropic character of the spin system interactions couple with experimentally introduced time evolution processes. The presented work concerns fundamental aspects of solid state NMR namely: the uniqueness of the tetrahedral angle and evolution of both dipolar D and chemical shield σ coupling tensors under MAS conditions.

We modeled the magnetic field up to the quadrupole term to investigate not only the average susceptibility (dipole), but also the susceptibility distribution (quadrupole) contribution. Expanding the magnetic field up to the 2^nd order provides the quadrupole (0^th: monopole, 1^st: dipole). Numerical simulations were performed to investigate the quadrupole contribution with subvoxel nonuniformity. Conventional dipole and our dipole + quadrupole models were compared in the simulation, the phantom and human brain. Furthermore, the quadrupole field was compared with the anisotropic susceptibility field in the dipole tensor model. In a nonuniformity case, numerical simulations showed a nonnegligible quadrupole field contribution. Our study showed a difference between the two methods in the susceptibility map at the edges; both the phantom and human studies showed sharper structural edges with the dipole + quadrupole model. Quadrupole moments showed contrast mainly at the structural boundaries. The quadrupole moment field contribution was smaller but nonnegligible compared to the anisotropic susceptibility contribution. Nonuniform and uniform source distributions can be separately considered by quadrupole expansion, which were mixed together in the dipole model. In the presence of nonuniformity, the susceptibility maps may be different between the two models. For a comprehensive field model, the quadrupole might need to be considered along with susceptibility anisotropy and microstructure effects.