Biomedical Engineering Reference
In-Depth Information
Solution: The frequency encoding equation is
Δ
f
=
γ
G
, where
Δ
f
is the frequency offset
from isocenter
γ
is the gyromagnetic ratio, 42.58 MHz/T, and
G
is the frequency encoding
gradient
=
0.0001 T/cm
x
=
0 cm,
Δ
f
=
0
x
=
2.0 cm,
Δ
f
=
8.516 kHz
Figure 8.10
Spatial encoding. (a) Effect of constant magnetic fi eld and output frequency. (b) Effect
of a gradient magnetic fi eld and the output frequency. (c) Use of the magnetic fi eld gradient for
selective excitation of a slice. (d) Slice image formation using both frequency encoding and phase
encoding.
Slice Selection
If the gradient is applied along the
z
-direction [Figure 8.10(c)] simultaneously with
the initial RF pulse, and the pulse is modified to contain a narrow band of frequen-
cies (
x
) of spins can be selectively
excited. Using this approach, a 2D tomographic imaging is obtained. The band-
width of the RF excitation pulse is obtained by substituting
δ
f
) rather than a single frequency, a thin slice (
δ
in (8.32)
and then the slice thickness is selected. There are two ways to select different slices:
change the position of the zero point of the slice selection gradient with respect to
the isocenter, or change the center frequency of the RF to correspond to a resonance
frequency at the desired slice. The second option is usually used as it is not easy to
change the isocenter of a given gradient coil.
Δ
f
=
Δω
/2
π
Frequency Encoding
From (8.29), the resonance frequency is a linear function of the magnetic field
strength. If a gradient field is applied during image acquisition (i.e., after activat-
ing the RF excitation pulse), then the position of a nucleus along that gradient can
