Tuesday, September 5, 2017

Gradients for removing artifacts

The previous post gave an introduction to gradient pulses, describing what they are. In this post, and the next few, I will describe a few applications of gradients. This post will describe how they can be used to reduce artifacts from imperfect pulses, allowing phase cycles to be reduced and experiments to be run more quickly.

The figure below shows an NMR sample tube at various stages of a sequence of radio frequency and gradient pulses. The top row of the figure shows the NMR tube viewed from the side, while the lower row is the view from the top, down the center of the tube. The arrows in the tube represent the orientation of the magnetic vector of nuclei at different positions in the tube. The shade of the arrows indicates the position of the nucleus in the tube. The darker the arrow the closer it is to the top of the sample.

The first tube shows the nuclei at equilibrium aligned with the static magnetic field. In the top view, the magnetic vectors of the nuclei are pointing directly up along the z-axis through the center of the tube.

The second tube shows the magnetic vectors immediately after a 90o pulse along the x-axis. The vectors of all the nuclei are now pointing along the y-axis. Looking from the top, we see all the vectors aligned, creating a coherent signal.

In the third tube a gradient has been applied along the z-axis (Gz) creating a stronger magnetic field at the top of the tube and a weaker one at the bottom. After a time Δ this difference in magnetic field strength will cause the magnetic vectors to spread out and lose coherence. As the vectors rotate in a clockwise direction, those at the top of the tube, in the stronger magnetic field, will move faster than those in the middle. Those at the bottom, in the weaker magnetic field, will move more slowly and get left behind. If we were to try and record a spectrum at this stage the signal would be so spread out that we could not detect anything.

In the fourth tube, immediately after a 180o pulse along the x-axis, the orientation of all the magnetic vectors in the xy-plane has been inverted. Again, recording a spectrum at this point would not detect any signal.

In the fifth tube, an identical gradient to the first one is applied. After the same delay Δ used previously, the vectors rotate back into alignment. The gradient creates a stronger magnetic field at the top of the tube and a weaker one at the bottom. As the vectors continue to rotate clockwise the fast moving vectors at the top of the tube will catch up to those at the center of the tube and these will in turn catch up with the slow moving vectors at the bottom of the tube. The final result is a coherent signal along the -y-axis.

The usefulness of this sequence arises from the fact that only nuclei experiencing a perfect 180o pulse will be refocused after the second gradient. By adding gradients on either side of a 180o pulse we can eliminate artifacts created by imperfect pulses. Before gradients became standard on NMR probes these artifacts were removed by phase cycling. In its simplest form phase cycling involves changing the phase of a pulse on alternate scans and adding and subtracting the scans so that signals accumulate and artifacts cancel. With gradients the artifacts can be removed in a single scan allowing the number of scans to be reduced and experiments to be quicker.

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