Image Processing Reference
In-Depth Information
the initial amplitude of the FID or, more exactly, it is equal to the area under
the FID envelope.
1.6
MR SIGNAL CHARACTERISTICS
1.6.1
R
ELAXATION
Following the perturbation by the RF pulse, the spin system returns to the
equilibrium population distribution between the energy levels by releasing excess
energy into the surroundings. In the classical vector model, this corresponds to
the return of the magnetization
M
to the equilibrium position along the z axis.
Thus, during the relaxation period, any transverse magnetization component M
xy
created by the RF pulse decays to zero, and, at the same time, the longitudinal
magnetization component M
z
returns to the equilibrium value of
M
0
. The decay
of M
xy
and the recovery of M
z
are two distinct processes, and they are referred
to as
spin-spin
and
spin-lattice relaxation
, respectively.
1.6.1.1
The Decay of Transverse Magnetization: T2
The decay of transverse magnetization following an
α
-degree pulse, due to spin-
spin relaxation can be described with the equation:
Mt M
()
=
sin
α
e
i
(
ωϕ
t
+−
)
e
t T
/
2
(1.18)
0
xy
0
where the parameter T 2 is called the
transverse relaxation time
or
spin-spin
relaxation time
; it represents the time interval required for the transverse mag-
netization to decay to 36.7% of its initial value M
0
.
1.6.1.2
The Recovery of Longitudinal Magnetization: T1
After the application of an
-degree RF pulse, the longitudinal magnetization M
z
recovers back to equilibrium at a rate that is linearly proportional to the difference
between its current value and the equilibrium value; this rate is also characteristic
of the sample. It can be derived that:
α
Mt
()
=
M
(
11
− −
(
cos )
α
e
−
tT
/
1
)
(1.19)
z
0
where the parameter T 1 is called the
longitudinal relaxation time
or
spin-
lattice relaxation time
, and it represents the time interval needed for the
longitudinal magnetization to recover to a value of 63.2% of the equilibrium
value
M
0
.
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