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Encyclopedia of Physical Science and Technology EN008M-395 June 29, 2001 15:52

Magnetic Resonance in Medicine 969

It should be realized that the discussion of dephasing located in higher fields will precess more rapidly than
provided here is rather casual. Since we are inferring that those in lower fields. The net result is again a dephasing
the dephasing occurs among individual nuclear spins and of the spins across the sample and an undesirable decrease
that this determines the time course of the relaxation of of the induced voltage in the receiver coil. However, al-
the macroscopic transverse magnetization, the argument though the total magnetization of the sample may have
should include a quantum mechanical justification. Such decrease to a low value, those spins relatively close to
an argument would be too lengthy to provide here. This one another in space will still be nearly in phase one an-
topic is discussed thoroughly in the book by Slichter. For other. Thus, although it is not evident externally, a form
qualitative purposes, the idea of individual nuclear spins of spin order still exists within the sample, even after the
gradually dephasing with one another remains a useful external signal is no longer detectable. In 1950, E. Hahn
one and we will continue to employ it. showed that this remnant order can be detected by apply-
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Two important physical consequences associated with ing a 180 pulse to the precessing spins at a time τ after
dephasing are motional narrowing and spin echoes. It the 90 pulse that created the transverse magnetization.
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might be thought that nuclei that are diffusing rapidly After such a pulse, the spins that had advanced in phase
among their neighbors during an FID would experience beyond the average by an amount of δφ are now behind
more rapid dephasing than nuclei that are relatively fixed the average by the same amount. Because they are still
in position. In fact the opposite is true. The explanation precessing more rapidly, however, these spins will catch
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is that if a spin is relatively fixed in position, it will be up with the average at a time τ after the 180 pulse. At this
forced to respond to whatever its local magnetic environ- time all the spins will be back in phase with one another
ment happens to be for an extended period. Unlike the and the receiver will detect a signal called a spin echo.
externally applied fields, however, there is no reason for Of course, all of the microscopic dephasing mechanisms
the local magnetic fields to be identical from one location are operating continuously so that the amplitude of the
to another because the local environments are not corre- spin echo is reduced by a factor e −2τ/T 2 from the initial
lated. Therefore, if the sample consists of a large number amplitude of the FID.
of localized spins, as in a solid, they will tend to drift In the early days of NMR, spin echos were used to over-
rapidly out of phase with one another. On the other hand, come the relatively high inhomogeneities of the available
if the nuclei are not fixed but move from one location to magnets. In MRI systems today, however, the magnets
another rapidly, as in a liquid, the local fields vary from have sufficient homogeneity that this is not usually nec-
instant to instant, causing the phase of the nuclear pre- essary. In imaging systems, however, special coils that
cession to increase almost as often as it decreases, and produce gradients in B 0 are extensively utilized. Spin
the overall dephasing of the total system proceeds more echoes are often used, as a routine part of the imaging
slowly. Therefore, protons located on fixed sites experi- sequence, to reverse the dephasing produced by the de-
ence a very rapid dephasing, which means a short T 2 , while liberately employed gradient fields. If the gradient field is
thoseonfreelydiffusingwatermoleculeshavemuchlarger constant in time, a 180 rf pulse may be used to produce an
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values for T 2 . After Fourier transformation a larger value echo as just described. On the other hand, if the gradient
for T 2 corresponds to a narrower resonance line. There- field itself is reversed after being applied for at time t,an
fore, this important phenomenon wherein nuclei in highly echo will occur at time 2t without the need for a rf pulse.
mobile molecules manifest long T 2 values is called mo- This is called a gradient recalled echo.
tional narrowing. This remarkable phenomenon was first The physical environment within biological tissues is
explained by N. Bloembergen and coworkers in 1948. It extremely heterogenous. Within a single cell there are
is a very strong effect. The T 2 of protons in ice, for ex- known to be numerous microscopic structures includ-
ample, is shorter than that of protons in water by a factor ing the nucleus, the cell membrane, mitochondria, and
of 100,000. Therefore, signals from solid tissues, such as microtubules. It is likely that the magnetic environment
teeth and dense bone, decay almost instantly after excita- varies somewhat from location to location as a result of
tion and cannot be detected by MRI. As a consequence, this heterogeneity, and consequently, it might be expected
MRI provides images based on the distribution of mobile that the proton relaxation times would vary with intra-
protons only. Because the local feilds are random from one cellular location. Experimentally, however, it is found
nuclear location to another, there is no hope of reversing that, although the relaxation times vary from one organ
this form of spin dephasing and it consequent decrease of to another, there usually does not appear to be a signif-
voltage in the receiver coils. icant deviation from single exponential decay within a
Another source of dephasing of the spins is caused by single histological region. The explanation involves the
macroscopic inhomogeneities in the static applied field rapid self-diffusion of water molecules among one an-
B 0 .If B 0 varies from one location to another, the spins other. At body temperature the self-diffusion coefficient