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The Z1 Profile

 

Shimming, Part IV

The Z1 Profile

One tool which can be used to help the NMR operator in the shimming process is the “Z1 Profile”. This can be thought of as an axial image of the sample in the probe. To take a Z1 profile, the NMR operator applies a large Z1 gradient and examines the resulting lineshape. If the probe had no magnetic susceptibility and the magnet’s field were perfect, then when a large Z1 gradient is applied the resulting lineshape is a rectangle as shown in the figure below:

While this may seem a very uninteresting and undesired lineshape it contains a lot of useful information. Imagine the NMR sample being composed of many discrete finite samples placed along the axis of the NMR tube. When a Z1 gradient is applied to the sample, each of these finite samples would have a slightly different frequency based on the slightly different Z1 gradient value at each position along the Z axis. Under these conditions the left side of the lineshape spectrum above is one end of the NMR sample, the middle of the spectrum is the middle of the sample and the right end of the spectrum is the other end of the sample. There is no standard for NMR instruments as to which direction of Z1 gradient is generated with a positive current in the Z1 coil. For this reason, whether the left end is the top or the bottom of the sample depends on the polarity of the Z1 gradient applied in the NMR system when the Z1 gradient is adjusted in one specific direction. On some instruments the adjustment of the Z1 gradient in one direction (positive) creates the Z1 profile with the bottom of the sample to the low frequency side. The same adjustment on a different instrument could produce the opposite effect. No matter which direction is the top in this profile, the application of the Z1 gradient produces an “image” of the sample in the coil. This means that we now have some positional information to work with. Let’s explore what we can do with this information.

While we have our Z1 profile image, let’s apply a Z2 gradient to the shims. Depending on the direction, we get something like one of the two lineshape images below:

+ Z2

– Z2

It is easy to note that the shape is asymmetrical. It can also be noted that the top of the Z1 profile is a curve with the order Z2. With practice and when comparing to later examples, the reader will see that as the gradient order increases, the outside edges of the Z1 profile are affected more than the center. In fact, with the higher order gradients the center of the Z1 profile is relatively unaffected.

Starting from the basic Z1 profile again and applying a Z3 gradient would give one of the two pictures below:

+ Z3

– Z3

Here it is easy to note that the Z1 profile changed shape symmetrically. For now the reader should note the drooping edges when Z3 is changed in one direction and the peaked edges when Z3 is changed in the opposite direction. Also note how far from the center the effects start taking place. As we move to higher order gradients, it will be easy to note that the effect takes place farther to the outside edges.

Starting once again from the basic Z1 profile and applying a Z4 gradient would give one of the two pictures below:

+ Z4

 

– Z4

It can be seen that the change in the Z1 profile is again asymmetrical, but now there is a flat region near the center that is relatively unaffected compared to the ends of the Z1 profile.

Starting again from the basic Z1 profile and applying a Z5 gradient would give one of the two pictures below:

+ Z5

– Z5

It can be seen that the change in the Z1 profile is symmetrical. Again there is a flat region near the center that is relatively unaffected compared to the sides of the Z1 profile.

Starting from the basic Z1 profile and applying a Z6, Z7, and a Z8 gradient would give following set of pictures:

 

+ Z6

 

– Z6

 

+ Z7

 

– Z7

 

+ Z8

 

 

– Z8

 

A pattern emerges from the complete set of Z1 profiles:

  1. Even order gradients ( Z2, Z4, Z6, and Z8 ) produce asymmetrical changes in the Z1 profile. The plus and minus Z1 profiles have about the same width at half height.
  2. Odd order gradients ( Z1, Z3, Z5, and Z7 ) produce symmetrical changes in the Z1 profile. The plus and minus Z1 profiles have different width at half height.
  3. The higher the order of shim gradient applied, the farther from the center the significant effects are observed in the Z1 profile.
  4. Odd order gradients, particularly Z3, give different widths with opposite polarity Z1 profiles, while even order gradients are unchanged. Z3 should be adjusted to give the same width at half height in the presence of positive and negative Z1 gradients.

There are similar effects that can be observed when shimming while looking at normal lineshapes instead of the Z1 profile:

  1. An asymmetrical change in lineshape is seen when even order Z shims are adjusted.
  2. A symmetrical change in lineshape is seen when odd order Z shims are adjusted.
  3. The higher the order of shim gradient adjusted, the lower down the peak the lineshape distortion is noticed.

From this study of Z1 profiles, a very different procedure of shim optimization emerges as a new shim tool. Normally the lowest order gradients ( Z1, Z2 and Z3 ) are adjusted first, then based on lineshape criteria, the higher order gradients are adjusted. The low order gradients are re-adjusted as necessary in this process. However, if the NMR operator applies a Z1 gradient to get a “Z1 profile” of the sample, the highest order gradients are adjusted first to get the most square and symmetrical ends on the Z1 profile, then the center region is flattened with the lower order gradients. During the entire process odd order gradients are adjusted when a symmetrical change is desired. Even order gradients are adjusted when an asymmetrical change is desired.

In general, when trying to shim using this technique the goal is to make the squarest and flattest Z1 profile possible. This applies even when the NMR probe has magnetic susceptibility problems. When you shim for the squarest and flattest Z1 profile, you will get the best lineshape when the Z1 gradient is removed. If the NMR probe has very severe magnetic susceptibility problems, the Z1 profile will not be very flat at all. With probe magnetic susceptibility problems localized to specific regions of the probe’s coil, the Z1 profile may have many peaks and valleys where it should be flat. Probes that have several regions of deep peaks and valleys will be very difficult to shim and probably not produce a good lineshape when done shimming.

This technique is not the “one and only, best way” to shim. It should be considered a tool and used when necessary. It does seem to offer some advantages when trying to adjust the higher order gradients. Use this technique as one of your many tools for shimming logically.

The Z1 profile can also be used to visualize the probe’s B1 homogeneity. After shimming is complete, apply a Z1 gradient. Take a spectrum with a 90 o pulse and plot out the rectangular lineshape. This represents the probes coil’s excitation picture. Now take another spectrum with a 180 o pulse and plot it out with the same scale and position as above. This plot will have a region near the center of the initial rectangular region which is near zero intensity. This shows the area of the sample which is experiencing the 180o degree tip angle. The ends of the initial rectangular region represent the ends of the probe’s coil. These regions will not be near zero because the ends of the coil receive less than a 180 o tip angle. In probes with a good B1 homogeneity the region near zero will be a significant portion of the initial rectangular region. In probes with poor B1 homogeneity, the center region will dip slightly below zero intensity with little or no flat region near zero. This is a picture of the sample receiving a 180o tip angle versus position in the probe’s coil.

 

The Quickie Z1 Profile Approach to Shimming.

  1. Start with a first pass optimized shimmed instrument with at least Z1 and Z2 optimized using a sample with a single strong resonance.
  2. Put on a Z1 gradient by the amount (MagZ1) to get a Z1 profile with a width at half height of at least 200 Hz.
  3. Note the width at half height with both positive Z1 gradient (+MagZ1) and negative Z1 gradient (-MagZ1). If they are different, change Z3 by an incremental amount and re-measure. Continue adjusting Z3 until the width at half height of the positive and negative Z1 profiles are the same.
  4. Adjust Z4 for the flattest top with the same symmetry with both the positive and negative Z1 profiles.
  5. take off the Z1 gradient and optimize Z1 and Z2.

 

Return to Part I, Introduction

Return to Part II, Basics

Return to Part III, Symptoms of Inhomogeneity

Proceed to Part V, Effect of Sample and Coil


Last updated: 01/22/03