As transverse magnetization rotates about the Z axis, it will induce a current in a coil of wire located around the X axis.
Plotting current as a function of time gives a sine wave.
This wave will of course decay with time constant
T2*
due to dephasing of the spin packets. This signal is called a free induction decay (FID).
We will see in Chapter 5
how the FID is converted into a frequency domain spectrum.
Transverse magnetization vectors rotating faster than the rotating frame of reference are said to be rotating at a positive frequency relatve to the rotating frame (+
).
Vectors rotating slower than the rotating frame are said to be rotating at a negative frequency relative to the rotating frame
(-).
A set of RF pulses applied to a sample to produce a specific form of NMR signal is called a pulse sequence. In the 90-FID pulse sequence, net magnetization is rotated down into the X'Y' plane with a
90o pulse.
The net magnetization vector begins to precess about the +Z axis.
The magnitude of the vector also decays with time.
A timing diagram is a multiple axis plot of some aspect of a pulse sequence versus time. A timing diagram for a 90-FID pulse sequence has a plot of RF energy versus time and another for signal versus time.
When this sequence is repeated, for example when signal-to-noise improvement is needed, the amplitude of the signal after being Fourier transformed (S) will depend on
T1 and the time between repetitions, called the repetition time (TR), of the sequence. In the signal equation below, k is a proportionality constant and
is the density of spins in the sample.
( 1 - e-TR/T1 )
Another commonly used pulse sequence is the spin-echo pulse sequence.
Here a 90o
pulse is first applied to the spin system.
The 90o
degree pulse rotates the magnetization down into the X'Y' plane. The transverse magnetization begins to dephase.
At some point in time after the 90o pulse, a
180o pulse is applied.
This pulse rotates the magnetization by 180o about the X' axis.
The 180o
pulse causes the magnetization to at least partially rephase and to produce a signal called an echo.
A timing diagram shows the relative positions of the two radio frequency pulses and signal.
The signal equation for a repeated spin echo sequence as a function of the repetition time, TR, and the echo time (TE) defined as the time between the 90o pulse and the maximum amplitude in the echo is
( 1 - e-TR/T1 ) e-TE/T2
An inversion recovery pulse sequence can also be used to record an NMR spectrum. In this sequence, a
180o
pulse is first applied. This rotates the net magnetization down to the -Z axis.
The magnetization undergoes spin-lattice relaxation and returns toward its equilibrium position along the +Z axis.
Before it reaches equilibrium, a 90o pulse is applied which rotates the longitudinal magnetization into the XY plane. In this example, the 90o pulse is applied shortly after the 180o pulse.
Once magnetization is present in the XY plane it rotates about the Z axis and dephases giving a FID.
Once again, the timing diagram shows the relative positions of the two radio frequency pulses and the signal.
The signal as a function of TI when the sequence is not repeated is
( 1 - 2e-TI/T1 )
It should be noted at this time that the zero crossing of this function occurs for TI = T1 ln2.
When an inversion recovery sequence is repeated every TR seconds, for signal averaging or imaging purposes, the signal equation becomes
( 1 - 2e-TI/T1 + e-TR/T1) .
When an atom is placed in a magnetic field, its electrons circulate about the direction of the applied magnetic field. This circulation causes a small magnetic field at the nucleus which opposes the externally applied field.
The magnetic field at the nucleus (the effective field) is therefore generally less than the applied field by a fraction s.
The electron density around each nucleus in a molecule varies according to the types of nuclei and bonds in the molecule. The opposing field and therefore the effective field at each nucleus will vary. This is called the chemical shift phenomenon.
Consider the methanol molecule.
The resonance frequency of two types of nuclei in this example differ. This difference will depend on the strength of the magnetic field, Bo, used to perform the NMR spectroscopy. The greater the value of Bo, the greater the frequency difference. This relationship could make it difficult to compare NMR spectra taken on spectrometers operating at different field strengths. The term chemical shift was developed to avoid this problem.
The chemical shift of a nucleus is the difference between the resonance frequency of the nucleus and a standard, relative to the standard. This quantity is reported in ppm and given the symbol delta, d.
In NMR spectroscopy, this standard is often tetramethylsilane, abbreviated TMS. In the body there is no TMS, but there are are two primary hydrogen containing substances, water and fat. The chemical shift difference between these two types of hydrogens is approximately 3.5 ppm.
| Tissue | T1 (s) | T2 (ms) | r* |
|---|---|---|---|
| CSF | 0.8 - 20 | 110 - 2000 | 70-230 |
| White | 0.76 - 1.08 | 61-100 | 70-90 |
| Gray | 1.09 - 2.15 | 61 - 109 | 85 - 125 |
| Meninges | 0.5 - 2.2 | 50 - 165 | 5 - 44 |
| Muscle | 0.95 - 1.82 | 20 - 67 | 45 - 90 |
| Adipose | 0.2 - 0.75 | 53 - 94 | 50 - 100 |
At what TI value is the signal from fat approximately equal to zero in an inversion recovery sequence?
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