Biomedical Engineering Reference
In-Depth Information
90 flip into the x-y-plane and partial dephasing a 180 flip about the r-axis of the
rotating reference frame with rephasing of magnetization follows.
The MR-signal depends on the density of tissue protons, the magnetic field
strength of the static field B
0
(which determines the time T
1
of longitudinal
magnetization), the longitudinal relaxation time T
1
(time period until 63.3 % of
tissue may experience full re-excitation) and the transverse relaxation time T
2
(time duration of the MR-signal). To obtain the MR-image, the protons of each
slice of imaged tissue must be excited multiple times. The contrast of the obtained
image is determined by the time period between different rf-excitations (repetition
time:TR) and the time between excitation and signal detection (echo time: TE).
Depending on the variation of these time periods, the image contrast is either
referred to as T
1
-weighted or T
2
-weighted.
A further crucial point is to correlate the measured MR-signals with the par-
ticular spatial body location (spatial encoding). This leads to a revision of (
3.9
)by
augmenting dependency of the magnetic gradient field strength (
3.35
). The total
magnetic field B
¼
B
ð
x
;
y
;
z
;
t
Þ;
and correspondingly the precessional frequency
x
¼
x
ð
x
;
y
;
z
;
t
Þ;
depends on the particular spatial position
x
ð
x
;
y
;
z
;
t
Þ¼
cB
ð
x
;
y
;
z
;
t
Þ
with
B
ð
x
;
y
;
z
;
t
Þ¼
B
0
þ
xG
x
ð
t
Þþ
yG
y
ð
t
Þþ
zG
z
ð
t
Þ
thus
x
ð
x
;
y
;
z
;
t
Þ¼
x
0
þ
cxG
x
ð
t
Þþ
cyG
y
ð
t
Þþ
czG
z
ð
t
Þ
ð
3
:
35
Þ
where G
h
ð
t
Þ
with h
¼ð
x
;
y
;
z
Þ
denotes a transiently applied (and spatially constant)
magnetic field gradient in the h-direction whose z-component linearly varies along
the h-direction and is augmented in the static field B
0
G
x
ð
t
Þ¼
o
B
z
ð
t
Þ
ox
G
y
ð
t
Þ¼
o
B
z
ð
t
Þ
oy
G
z
ð
t
Þ¼
o
B
z
ð
t
Þ
oz
;
and
:
ð
3
:
36
Þ
Practically, the superposition of the static field with gradient fields is achieved
by employing gradient coils which (most usefully linearly) vary the static
magnetic field in spatial directions. Specifically, the static external field B
0
is
superposed by a linearly varying magnetic field in the z-direction, which makes the
precessional frequency also (linearly) vary in that direction. In a single slice-plane
and slice-volume (perpendicular to z) the precessional frequency of the protons'
magnetic moments in the direction of the homogenous field is thus equal. Each rf-
signal (which is equivalent to a particular frequency) thus excites only the protons
processing with that particular frequency (cf. resonance condition (
3.31
) according
to (
3.35
), i.e. only those protons contained in the particular slice (slice selection).
Only those magnetic dipole moments are being rotated into the transverse plane
that satisfy the resonance conditions. Since neighboring protons exhibit different
resonance frequencies, they are not affected.
To obtain spatial information, additionally, x- and y-gradient fields are super-
posed. The x-gradient field most often serves to encode the frequency, whereas the
y-gradient field is used for phase-encoding of the precessions of the magnetic
moment vectors. In this process, each slice is divided into a matrix where each
