Biomedical Engineering Reference
In-Depth Information
be recorded by shifting its resonance frequency. This is called frequency encoding.
The signal can be decomposed using Fourier transform methods to determine the
amount of signal at each frequency and hence at each position, resulting in a pro-
jection through the sample. The acquired signal originates from the entire object
under study, and spatial information is obtained only by breaking that signal down.
Phase Encoding
If the gradient field is turned on for a short term after activating the RF excitation
pulse and turned off before image acquisition, then the effect of the gradient field
is no longer time-varying. However, the phase of a nucleus's signal is dependent
on its position and the gradient field is a fixed phase accumulation determined by
the amplitude and duration of the phase-encoding gradient. This method is called
phase encoding. By repeating the experiment a number of times with different gra-
dient amplitudes, it is possible to generate a set of data in the third dimension and
have the data Fourier transformed to yield spatial information along the direction
perpendicular to the frequency encoding axis [Figure 8.10(d)]. During signal acqui-
sition, the phase of the
xy
-magnetization vector in different columns will systemati-
cally differ. When the
x
- or
y
-component of the signal is plotted as a function of the
phase-encoding step number
n
, it varies sinusoidally. As each signal component has
experienced a different phase encoding gradient pulse, its exact spatial reconstruc-
tion is located by the Fourier transformation analysis. Spatial resolution is directly
related to the number of phase-encoding levels (gradients) used.
All three methods are applied to generate multiple 2D slices through the pa-
tient. To allow time for this process, acquisition of the NMR signal is delayed for
up to a few hundred milliseconds after excitation by using magnetic field gradients
and RF pulses to produce an echo at the desired time. Unlike X-ray CT, MRI can
image slices in any desired plane by appropriate use of gradients. Alternatively,
the technique is modified to produce 3D volumes of data that can be viewed using
various software or postprocessed to generate arbitrary slices. Spatial resolution is
determined by the number of frequency encoded projections and phase-encoded
projections for a given field of view.
As described thus far, an MRI of the body is essentially a map of water distri-
bution. Such an image would be of limited clinical value, since water density varies
relatively little between tissues. One of the major strengths of MRI is the ability to
manipulate image contrast by tissue relaxation times. Once the RF exposure is dis-
continued, the high-energy state protons in the material would continue to dump
their transition energy (or relax) at the same frequency as was previously absorbed
until the Boltzmann equilibrium is reestablished. Nuclei return to their initial popu-
lation distribution via a variety of relaxation processes, categorized according to
whether they cause loss of energy from the spin system or just the exchange of en-
ergy between spins. These two phenomena are known as spin-lattice and spin-spin
relaxation, and are characterized by the relaxation times
τ
1
and
τ
2
, respectively.
τ
1
relaxation results in exponential recovery of
z
-magnetization,
M
z
, while
τ
2
proc-
esses cause exponential decay of the precessing transverse magnetization,
M
xy
:
(8.31)
z
MM e
τ
−
=−
t
/
(1
)
1
