292
Biomedical Signal and Image Processing
H
H 0
X
Z
Y
FIGURE 15.9 Magnetic field gradient diagram. (Courtesy of Siemens AG, Medical
Solutions, Magnetic resonance; brochure: Magnets, flows and artifacts.)
The Larmor frequency will now be a function of position as expressed by combining
Equations 15.5 and 15.6:
f
= f + k . x
(15.5)
Larmor
0
2
where k 2 is a constant.
When an RF pulse with frequency f R is sent through the patient, only the protons
in the locations that obey the following restriction will come into resonance at any
given time:
f R − f 0
f
x =
=
(15.6)
k 2
k 2
where f = f R − f 0 .
It has to be emphasized that only the hydrogen nuclei that obey the condition stated
in Equation 15.9 will emit the FID signal after the external RF pulse is removed.
This will select a slice of the patient’s body for imaging based on the frequency f R ,
as illustrated in Figure 15.10.
Immediately after the FID signal has been collected, the gradient of the magnetic
field is rotated over a 90° angle. A common way of applying the magnetic field is by
rotation of the field gradient over 90° and, after a delay time T D , rotating the field
gradient back to the original direction and acquiring the FID signal. This process
produces an external magnetic field with the gradient in the direction of the y-axis
formulated by Equation 15.11:
H = H 0 + G y
(15.7)
Biomedical Signal and Image Processing
H
H 0
X
Z
Y
FIGURE 15.9 Magnetic field gradient diagram. (Courtesy of Siemens AG, Medical
Solutions, Magnetic resonance; brochure: Magnets, flows and artifacts.)
The Larmor frequency will now be a function of position as expressed by combining
Equations 15.5 and 15.6:
f
= f + k . x
(15.5)
Larmor
0
2
where k 2 is a constant.
When an RF pulse with frequency f R is sent through the patient, only the protons
in the locations that obey the following restriction will come into resonance at any
given time:
f R − f 0
f
x =
=
(15.6)
k 2
k 2
where f = f R − f 0 .
It has to be emphasized that only the hydrogen nuclei that obey the condition stated
in Equation 15.9 will emit the FID signal after the external RF pulse is removed.
This will select a slice of the patient’s body for imaging based on the frequency f R ,
as illustrated in Figure 15.10.
Immediately after the FID signal has been collected, the gradient of the magnetic
field is rotated over a 90° angle. A common way of applying the magnetic field is by
rotation of the field gradient over 90° and, after a delay time T D , rotating the field
gradient back to the original direction and acquiring the FID signal. This process
produces an external magnetic field with the gradient in the direction of the y-axis
formulated by Equation 15.11:
H = H 0 + G y
(15.7)