Biomedical Engineering Reference
In-Depth Information
example is helium. In NMR, it is unpaired nuclear spins
that are of importance.
In NMR and MRI, the quantity y is called the reso-
nance frequency and the Larmor frequency, respectively.
The energy of the two spin states can be represented
by an energy level diagram. We have seen that y
¼
g
B
0
and
E ¼ h
y; therefore the energy of the photon needed to
cause a transition between the two spin states is
Spin properties
When placed in a magnetic field of strength
B
0
, a particle
with a net spin can absorb a photon of frequency y. The
frequency depends on the gyromagnetic ratio g of the
particle:
E ¼ h
g
B
0
(6.1.3)
y
¼
g
B
0
(6.1.1)
When the energy of the photon matches the energy
difference between the two spin states an absorption of
energy occurs. In the NMR, the frequency of the photon
is in the RF range. In NMR spectroscopy, y is between
60 and 800 MHz for hydrogen nuclei. In clinical MRI, y
is typically between 15 and 80 MHz for hydrogen
imaging.
When a group of spins is placed in a magnetic field,
each spin aligns in one of the two possible orientations.
At room temperature, the number of spins in a lower
energy level,
N
þ
, slightly outnumbers the number in the
upper level,
N
.
Boltzmann statistics tells us that
For hydrogen, g
¼
42.58 MHz/T.
Almost every element in the periodic table has an
isotope with a nonzero nuclear spin. NMR can be
performed only on isotopes whose natural abundance is
high enough to be detected. However, some of the nuclei
that are of interest in MRI are listed in
Table 6.1-1.
To understand how particles with spin behave in
a magnetic field, consider a proton. This proton has the
property called spin. Think of the spin of this proton as
a magnetic moment vector, causing the proton to behave
like a tiny magnet with north and south poles. When the
proton is placed in an external magnetic field, the spin
vector of the particle aligns itself with the external field,
just like a magnet would. There is a low-energy configu-
ration of state where the poles are aligned N-S-N-S and
a high-energy state N-N-S-S.
N
N
þ
¼ e
E=kT
(6.1.4)
where
E
is the energy difference between the spin states;
k
is Boltzmann's constant, 1.3805
10
23
J/K; and
T
is
the temperature in kelvin. As the temperature decreases,
so does the ratio
N
/
N
þ
. As the temperature increases,
the ratio approaches one.
The signal in NMR spectroscopy results from the
difference between the energy absorbed by the spins that
make a transition from the lower energy state to the
higher energy and the energy emitted by the spins that
simultaneously make a transition from the higher energy
state to the lower energy state. The signal is therefore
proportional to the difference between the states. NMR
is a rather sensitive spectroscopy since it is capable of
detecting these very small perturbation differences. It is
the resonance, or exchange of energy at a specific fre-
quency between the spins and the spectrometer, that
gives NMR its sensitivity.
It is worth noting two other factors that influence
the MRI signal: the natural abundance of the isotope
and biological abundance. The natural abundance of an
isotope is the fraction of nuclei having a given number
of protons and neutrons, or atomic weight. For exam-
ple, there are three isotopes of hydrogen:
1
H,
2
H, and
3
H. The natural abundance of
1
H is 99.985%.
Table
6.1-2
lists the natural abundance of some nuclei stud-
ied by MRI. The biological abundance is the fraction
of one type of atom in the human body.
Table 6.1-3
lists the biological abundance of some nuclei studied
by MRI.
Transitions
A particle can undergo a transition between the energy
states by the absorption of a photon. A particle in the
lower energy state absorbs a photon and ends up in the
upper energy state. The energy of this photon must
exactly match the energy difference between the two
states. The energy
E
of a photon is related to its fre-
quency y by Planck's constant (
h ¼
6.62
10
34
J s).
E ¼ h
y
(6.1.2)
Table 6.1-1 Net spin of several nuclei of interest for MRI
Nuclei
Unpaired
protons
Unpaired
neutrons
Net spin
g
(MHz/T)
1
H
2
1
0
42.58
2
H
1
1
1
6.54
3
P
1
2
0
1
17.25
23
Na
3
2
2
1
11.27
14
N
1
1
1
3.08
13
C
2
0
1
10.71
19
F
2
0
1
40.08
