Nuclear magnetic resonance Bloch equations

Reeves L W and Shaw K N 1970 Nuclear magnetic resonance studies of multi-site chemical exchange. I. Matrix formulation of the Bloch equations Can. J. Chem. 48 3641-53... 

For a given sequence, Bloch equations give the relationship between the explanatory variables, x, and the true response, i]. The / -dimensional vector, 0, corresponds to the unknown parameters that have to be estimated x stands for the m-dimensional vector of experimental factors, i.e., the sequence parameters, that have an effect on the response. These factors may be scalar (m — 1), as previously described in the TVmapping protocol, or vector (m > 1) e.g., the direction of diffusion gradients in a diffusion tensor experiment.2 The model >](x 0) is generally non-linear and depends on the considered sequence. Non-linearity is due to the dependence of at least one first derivative 5 (x 0)/50, on the value of at least one parameter, 6t. The model integrates intrinsic parameters of the tissue (e.g., relaxation times, apparent diffusion coefficient), and also experimental nuclear magnetic resonance (NMR) factors which are not sufficiently controlled and so are unknown. 

The AlP nuclear magnetic resonance spectrum of a corundum or a-AlgOg single crystal is an orientation-dependent quintet arising from the quadrupole moment = - - 0.149 (136-139). O Reilly (140) obtained the Al dispersion mode envelope (141) powder pattern spectrum which results when y-alumina is heated to 1400°, and thereby eonverted to a-AlaOs. He interpreted the line shape in terms of the Redfield modification (142,143) of the Bloch equations. 

The equations that Bloch constructed using these definitions are solved in many texts (cf also p. 19ff.). Their most important prediction is that the nuclear magnetic resonance measured under the usual absorption-mode conditions in the presence of a radiofrequency field 2Bj cos cot will be proportional to... 

The relaxation times Ti and T2 provide only an empirical treatment of the effects of the internal magnetic fields. In practice, they must be found by experiment rather than by calculation. Once Ti and T2 have been determined, experimental results indicate that the Bloch equations provide a completely satisfactory description of all nuclear magnetic resonance phenom-... 

The Bloch Equations for Magnetic Resonance. At thermal equilibrium, the magnetization Mo, due to individual electron or nuclear magnetizations hi, is assumed to be proportional to the static field Ho along the z axis ... 

The n-site Bloch-McConnell equations describe the evolution of nuclear spin magnetization in the laboratory or rotating frames of reference for molecules subject to chemical or conformational interconversions between n species with distinct NMR chemical shifts. Trott and Palmer used perturbation theory to approximate the largest eigenvalue of the Bloch-McConnell equations and obtain analytical expressions for the rotating-frame relaxation rate constant and for the laboratory frame resonance frequency and transverse relaxation rate constant. The perturbation treatment is valid whenever the population of one site is dominant. The new results are generally applicable to investigations of kinetic processes by NMR spectroscopy. 

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