Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 24

Gradient

y

Object

0 x

MR spectrum

0 Frequency

FIGURE 1.11 Relationship between the spatial extent of the sample of water and the MR
spectrum, in the presence of a linear gradient: the MR spectrum corresponds to the projec-
tion of the object in the gradient direction.

is to make the resonance frequency a function of position along the z direction:

ω (z) = γ B z (z) = γ (B 0 + zG z ) (1.32)

As seen before, the RF pulse is not just an on - off pulse of radio waves, but
it is shaped (i.e., amplitude modulated) so that it contains a narrow spread of
frequencies close to the fundamental resonance frequency of the magnet

ω 0 .

Then, the width of the slice, ∆ z, is given by:

∆ z = ∆ω / γ G z (1.33)

as shown in Figure 1.12 , where ∆ω is the bandwidth of frequencies contained

within the selective RF pulse.