Image Processing Reference
In-Depth Information
TABLE 1.1
NMR Properties of Some Selected Nuclei
Nuclear
Spin
Gyromagnetic
Ratio (MHz/T)
Natural
Abundance (%)
Relative
Sensitivity*
Nucleus
1H
1/2
42.58
99.98
1
13C
1/2
10.71
1.11
0.016
19F
1/2
40.05
100
0.870
31P
1/2
17.23
100
0.066
23Na
3/2
11.26
100
0.093
* calculated at constant field for an equal number of nuclei
1.3
NUCLEI IN A MAGNETIC FIELD
In MR experiments we are concerned with the behavior of nuclei placed in an
external magnetic field. According to the
, the presence of a
magnetic moment means that the nucleus behaves like a tiny bar magnet, with a
north and a south pole, and it will therefore interact with a magnetic field.
In the case of a bar magnet, application of an external magnetic field would
cause the magnet simply to align with or against the direction of the field. However,
a nucleus has angular momentum and, consequently, precesses about the direction
of the applied field, just as a spinning top precesses in the Earth's gravitational
field. The interaction between the magnetic moment
classical model
µ
and the field
B
tries to
0
align the two, according to the formula:
L
=
µ
×
B
(1.3)
0
where
L
is the torque or turning force.
This precessional motion is schematized in
Figure 1.2
as a rotation of the
magnetic moment vector
µ
about the direction of the external magnetic field
B
0
in addition to the nuclear spin about its own axis.
The torque force causes the nucleus to precess about
B
, altering the angular
0
momentum
p
; in fact,
d
p
/dt
=
L
=
µ
×
γ
B
(1.4)
0
But
p
=
µ
/
γ
, so that
d
µ
/dt
=
µ
×
γ
B
=
ω
×
µ
(1.5)
0
0
where
ω
=
−γ
B
0
0
is the
frequency of precession
, i.e., the rate at which
µ
rotates about
B
, and is
0
called the
; the minus sign describes the rotation direction.
As said before, this result can be deduced from the laws of classical physics.
However, in order to obtain a complete description of the behavior of nuclei in
a magnetic field, quantum mechanical theory must be considered.
Larmor frequency
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