Imaging, NMR

4 Chemical Shifts and Spin-Spin Couplings in C-NMR Spectroscopy 

In a space-dependent magnetic field, the Larmor frequency depends on position. A sufficiently weak space dependence of the magnetic field can be expanded into a Taylor series. For example, a variation along the x coordinate is described by 

In most imaging experiments, the second and higher order derivatives in this expansion are small and negligible. However, this is not a necessity for obtaining spatial resolution 

In imaging experiments, the space variation of the external field must be made strong enough to override the spread in chemical shift or linewidth. In this case (1.1.6) can be approximated by 

For a linear space dependence of the Larmor frequency, the spatial resolution 1/Ax is related to the width of the NMR absorption line or the spread Av = Acot/lit in Larmor frequencies col according to (1.1.7) by 

The mapping of the sample is produced by orthogonal gradients of the static magnetic field Bq so that this becomes a function of the Cartesian coordinates of the sample volume. If a linear field gradient is applied in the x direction the Larmor frequency CO, (= 2jrv) at a point / with coordinate jc, is given by 

Some contrast in the NMR image arises from variations in proton density in biotissue, by a factor of 0.2 or so thus grey matter contains 15% more water than white matter in the brain. Much greater is the variation in relaxation times, by a factor of 4 for Ti, and 10 or more for T2, so that particularly high sensitivity may be attained by T2 mapping. At typical field strengths, below 0.5 T or so, the most favorable and T2 values, a few hundred milliseconds (rather more for Ti than for T2) are given by 

Flow imaging has potential for monitoring vascular disease. Commonly blood vessels appear dark as excited nuclei flow out of the slice, and the signal may increase in the presence of thrombosis or atherosclerotic (fatty) plaque. Alternatively, blood flow may be imaged by increased signals from inflowing protons, by appropriate pulse sequences. 

Four characteristics therefore determine the localized signal. This will normally be enhanced by increase in proton density, decrease in Tj, increase in r2, and decrease in flow rate, and images may be needed at several Ti and T2 settings to resolve ambiguities or provide additional information. 

For reasonable resolution and sensitivity spectroscopy needs higher fields and better homogeneity than imaging does, and may be based on a sufficiently wide-bore conventional high resolution NMR spectrometer. The technical problems are far 

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Simple and Complex Organic Molecules. Using modem direct fluorination technology, the synthesis of even the most complex perfluorocarbon stmctures from hydrocarbon precursors is now possible. For example, syntheses of the first perfluoro crown ethers, perfluoro 18-crown-6, perfluoro 15-crown-5, and perfluoro 12-crown-4 (54) have been reported. Perfluoro crown ethers (54,55) are becoming important as the molecules of choice for many F-nmr imaging appHcations (56) in humans and are particularly effective in brain and spinal diagnostics when... 

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Figure 7.21 One-dimensional NMR imaging. When a magnetic field gradient is applied across a sample, it gives a spectrum that is a profile of the sample in the direction of the gradient.

Figure 7.22 The principle of creating a two-dimensional NMR image. A number of profiles of the sample are obtained in different orientations in the presence of magnetic field gradients pointing in different directions (designated by arrows). The x -gradient yields an x -profile, and a /gradient generates a y -profile. A combination of these profiles produces a two-dimensional image.

We attempt to describe NMR Imaging in a simplified manner using only three essential equations that explain why we see a signal and what it looks like. The first equation describes the nuclear spin magnetization, thus the strength of the NMR signal (and indeed much more) ... 

In this section, we will describe three building blocks of NMR imaging phase encoding, frequency encoding and slice selection. All three are related to the signal by the fourth equation ... 

The recipe for the first building block of NMR imaging, the phase encoding, thus goes like this apply a phase gradient of effective area k acquire the signal S(k) repeat for a number of different equidistant values of k perform the inverse... 

Fig.1.6 Left the field of view has been chosen sufficiently large to coverthe whole object a correct image is obtained. Right the field of view is only half as wide the top and bottom portions of the object are folded back into the opposite side of the image. In a real NMR image, the assignment of position becomes ambiguous.

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