Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 22

Equation 1.28 is applicable when the effect of molecular diffusion is negli-
gible. For complete refocusing of isochromats, each nucleus must experience the
same field during period TE. Movement of nuclei in an inhomogeneous field
because of diffusion causes the echo amplitude to be reduced.

1.8 MAGNETIC FIELD GRADIENTS

Magnetic field gradients allow spatial information to be obtained from analysis
of the MR signal. A field gradient is an additional magnetic field in the same
direction as B 0 , whose amplitude varies linearly with position along a chosen
axis. The application of a field gradient G x in the x direction, for example, causes
the magnetic field strength to vary according to:

B z (x) = B 0 + xG x (1.29)

Magnetic field gradients are produced by combining the magnetic fields from
two sources: the main homogeneous B 0 field, plus a smaller magnetic field
directed primarily along the z axis; such a secondary magnetic field is produced
by current-carrying coils (gradient coils). The design of a gradient coil is such
that the strength of the magnetic field produced by it varies linearly along a certain
direction. When such a field is superimposed on the homogeneous field B 0 , it
either reinforces or opposes B 0 to a different degree, depending on the spatial
coordinate. This results in a field that is centered on B 0 .

In Figure 1.10 , the gradient field is added to the uniform B field, obtaining

0

the total magnetic field that varies linearly along the x axis.
It is important to note that the total magnetic field is always along the B 0 axis
(for convention, z axis), while the gradient can be along any axis, x, y, or z:

G x = dB z /dx

G y =

dB z /dy (1.30)

G z = dB z /dz

The units of magnetic field gradient are Tesla per meter (Tm −1 ).
To understand how magnetic field gradients are utilized in MRI, consider
a large sample of water placed in such a field. If the sample is subjected to a
G x gradient, 1 H nuclei at different x coordinates possess different Larmor
frequencies:

ω (x) = γ (B 0 + xG x ) (1.31)

Hence, in the presence of G x , planes of constant field strength also become
planes of constant resonance frequency. Equation 1.31 describes that a relation-
ship between the position and the resonance frequency can be established by
application of a magnetic field gradient. It follows that the 1 H spectrum obtained