Biomedical Engineering Reference
In-Depth Information
6.6
magNetic properties of NaNoparticles
an MRI system consists of a wide variety of components working together to form
the desired images [4]. These components include the magnet, shim coils, gradient
coils, radio-frequency (Rf) coils, amplifier systems, Rf transmission and receiving
electronics, and computer systems that synchronize the components, control the
electronics, and process the imaging data. The MRI magnet produces a large uniform
magnetic field, denoted as B
0
. The maximum field strength currently used in clinical
imaging is 3.0 T, whereas experimental scanners may exceed 7 T. Inside the bore of
the magnet, gradient coils produce spatially variable magnetic fields that perturb B
0
along the x-, y-, and z-directions. The Rf coil is also positioned within the magnet
bore to generate an oscillating magnetic field perpendicular to B
0
, denoted as B
1
. as
a basic analogy, the Rf coil acts like an antenna that generates and receives the sig-
nals that will be used to construct the image. When exposed to the large B
0
magnetic
field, protons in the body act like little bar magnets and line up parallel to B
0
. The B
1
field rotates the proton magnetization, typically by 90° or 180°, and then detects the
proton signals as they relax back to equilibrium. By convention, the B
0
field is aligned
along the
z
-axis, and the B
1
field rotates the proton signal into the
x-y
plane. The
z
-axis is often called the longitudinal axis, while the
x-y
plane is called the transverse
plane. Relaxation of the protons is governed by two mechanisms, longitudinal and
transverse relaxations, which are commonly utilized to generate MRI contrast both
in clinical applications and research studies.
6.6.1
relaxation
following rotation of the proton magnetization into the
x-y
plane, the mechanism by
which protons relax back to equilibrium along the
z
-axis is called longitudinal relax-
ation or spin-lattice relaxation. longitudinal relaxation is an exponential process
given by
(
)
0
−
tT
/
MM
z
=
1
−
e
1
z
where
M
z
0
is the equilibrium proton magnetization,
M
z
is the magnetization along
the
z
-axis at time
t
, and
T
1
is the time constant for longitudinal relaxation. another
relaxation process is called transverse relaxation or spin-spin relaxation. This pro-
cess occurs when protons exchange energy but do not loose energy to their surround-
ings. This results in loss of proton magnetization in the transverse plane, but does not
necessary generate magnetization along the
z
-axis. Transverse relaxation is an
exponential process given by
0
−
tT
/
MMe
xy
=
*
2
xy
where
M
x
0
is the initial transverse magnetization,
M
xy
is the transverse magnetiza-
tion at time
t
, and
T
2
is the time constant for transverse relaxation. In addition to
T
2
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