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The exact symbolic solution of the Bloch equations is given in the Lagrange form and illustrated with R(2) experiments using a Hahn echo. Two different methods are also applied to approximately solve the Bloch equations, we find that splittings with effective-field interpretations are very substantially better than other approximations by comparing the errors. Estimates of transverse relaxation, R(2), from Hahn echos are effected by frequency offset and field inhomogeneity. We use exact solutions of the Bloch equations and simulations to quantify both effects, and find that even in the presence of expected B(0) inhomogeneity, off-resonance effects can be removed from R(2) measurements, when parallelomega parallel0.5gammaB(1), by fitting the exact solutions of the Bloch equations. Further, the experiments and simulations show that the fitting models with the exact solutions of the Bloch equations do not depend on the sampling density and delay times.
This article was published in the following journal.
Name: Journal of magnetic resonance (San Diego, Calif. : 1997)
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Hypertonic sodium chloride solution. A solution having an osmotic pressure greater than that of physiologic salt solution (0.9 g NaCl in 100 ml purified water).
The application of technology to the solution of medical problems.
The application of mathematical formulas and statistical techniques to the testing and quantifying of economic theories and the solution of economic problems.
The pressure required to prevent the passage of solvent through a semipermeable membrane that separates a pure solvent from a solution of the solvent and solute or that separates different concentrations of a solution. It is proportional to the osmolality of the solution.
Solution that is usually 10 percent glucose but may be higher. An isotonic solution of glucose is 5 percent.