Biomedical Engineering Reference
In-Depth Information
−
−
28
23
44.89 10
×
N
−
2
e
1.000001049
=
1.3806505 10
×
*310
=
N
1
The nuclear magnetic moment of spinning charged nucleus of an atom is
ne
Mh
m
(8.27)
=
γ
P
s
4
π
m
where
m
s
is the quantized spin,
n
p
is the number of protons, and
m
is the total mass
of the nucleus. The quantum of energy it carries is given by (8.2). If the nucleus is
immersed in a magnetic field, its spin (and therefore its magnetic moment) gives it
potential energy. Equating
ne
UBMBh
Δ
m
(8.28)
Δ=−Δ =−
γ
P
s
=
V
light
4
π
m
If
m
s
changes from (for instance)
−
1/2 to 1/2, a photon of frequency
f
is emit-
ted. By flipping the spin from 1/2 to
1/2 via radiating the nucleus with photons of
frequency
f
, the radiation can be used to image objects. If the sample is exposed to
a radio frequency (RF) EM wave whose energy would exactly match the difference
between the two energy levels, nuclei in the lower energy level may gain energy by
absorbing photons and those in the higher level may be induced to emit photons
to lose energy. These processes cause nuclei to flip between the two orientations,
modifying the population distribution from Boltzman population. Hence, the mag-
nitude and direction of
M
is changed as long as the RF wave is present to keep the
system.
However, considering the large number of nuclei present in a macroscopic sam-
ple, it is convenient to describe the sample in terms of interactions between the bulk
magnetization (
B
1
) and the magnetic field component of the RF wave. The bulk
magnetization is forced to tilt away from the alignment with
B
0
by the oscillating
RF magnetic field (ignoring the electric component of this field). While the bulk
magnetization is tipped away from alignment, it will precess around
B
0
for the
same reason that a spinning top wobbles around the direction of gravity (replace
the force of gravity with the force due to
B
0
) [Figure 8.9(c)].
If the RF frequency, and hence the frequency at which
B
1
rotates in the
xy
plane, matches the precessional frequency of the magnetic moments,
f
0
. A resonant
condition (resonance describes the maximum transfer of energy when the system is
tuned to a particular frequency, termed
resonance frequency
) is achieved in which
M
tips, (or nutates), from the
z
-axis towards the
xy
plane. The nutation continues
until
B
1
is removed, so the amplitude and duration of
B
1
can be tailored to nutate
M
through specific angles. A special case is that in which
M
is nutated entirely into
the transverse plane, leaving no magnetization along the
z
-axis. An RF wave of
−
