Biomedical Engineering Reference
In-Depth Information
gradient
G
x
is applied for a duration
t
x
, during which the
free-induction decay signal is collected. During the de-
tection period the spins precess at a frequency u
x ΒΌ
g
G
x
x
. One thus encodes spatial information into both the
phase and the frequency of the NMR signal, whose
magnitude is proportional to r(
x
,
y
). Of course, in the
case of imaging a real object, the signal has a multitude of
frequency and phase components.
An obvious drawback of stepping the duration of the
gradient
G
y
is the decrease in signal amplitude due to
the irreversible decay (with relaxation time
T
2
) of the
transverse magnetization. Because the phase shift
imparted to the signal by the gradient
G
y
is a function of
the gradient's duration as well as its amplitude, one can
achieve the same effect by stepping the amplitude of the
gradient while keeping its duration constant. This im-
portant modification of the technique gave rise to what
is called spin-warp imaging. The term refers to the
''warping'' of the phase caused by the gradient. Raising
the amplitude of the first gradient incrementally during
each excitation and read cycle yields an
N
1
N
2
array of
raw data, from which one can reconstruct an image by
double Fourier transformation of the signal. The resulting
digital image consists of
N
1
N
2
picture elements, or
pixels, whose values are proportional to the amplitudes
of the detected transverse magnetizations. The process
of incrementally increasing a gradient in amplitude to
encode spatial information into phases of processing
spins is called phase encoding.
The basis of the signal and contrast in NMR is the
transient nature of the signal. Spins, following excitation,
return to their equilibrium state with characteristic time
constants, the spin relaxation times
T
1
and
T
2
, which for
water in biological tissues are of the order of hundreds of
milliseconds or even seconds. This process can be de-
scribed by the phenomenological Block equations, which
predict the evolution of the spin system in terms of the
longitudinal and transverse components of the complex
spin magnetization.
Consider a typical imaging experiment in which RF
pulses are applied repeatedly at time intervals s
< T
1
for
the purpose of spatial encoding. Then the magnetization
available for detection is attenuated by a factor
1
e
s
=T
1
:
This, in itself, would not be a sufficient
mechanism for modulating the image signal were it not
for the large range of relaxation times found for the water
protons in mammalian tissues
levels, and thus the greater the relaxation rates. A case
in point is the brain, the majority of which consists of
gray and white matter adjacent to fluid-filled cavities,
the ventricles. Because water is more tightly bound in
white matter than in gray matter, the water molecules in
white matter reorient more slowly than those in gray
matter, thus more closely matching the Larmor fre-
quency; hence
T
1
wm (wm is for white matter) is less
than
T
1
gm (gm is for gray matter). By contrast, spinal
fluid, which from the point of view of molecular motion
closely parallels neat water, has much faster molecular
motion, and thus
T
1
sf is much greater than both
T
1
wm
and
T
1
gm.
The equilibrium magnetization is proportional to the
proton concentration in the tissues, hence the different
plateau values. For short pulse-recycle times (s
T
1
) the
signal amplitudes follow the reciprocal of
t
1
, whereas at
long recycle times (s [
T
1
) they are governed by their
equilibrium magnetization
that is, they follow the
proton concentrations. Contrast in MRI is therefore
a continuum, and unlike in x-ray imaging, there is no
universal gray scale. Further, it was recognized early on
that in most diseased tissues, such as tumors, the re-
laxation times are prolonged. This difference provides
the basis for image contrast between normal and patho-
logical tissues.
d
6.1.2 General review of MRI
Protons (hydrogen nuclei) precess when placed in
a magnetic field. This phenomenon is the basis for NMR.
Nuclear precession occurs with a frequency directly
proportional to the strength of the magnetic field, with
a proportionality constant called the gyromagnetic ratio,
of about 42.6 MHz/T. Typical frequencies range from
300 to 800 MHz (see
Figure 6.1-2
).
The precessional axis lies along the direction of
the magnetic field. If an oscillating magnetic field at the
precessional frequency is applied perpendicular to the
static field, the protons will now precess about the axis of
the oscillating field, as well as that of the static field. The
condition is known as nutation. The oscillating field is
generated by a tuned RF resonator, or RF coil, which
usually surrounds the sample. The magnetic field of the
precessing protons induces, in turn, an oscillating voltage
in the RF coil, which is detected when the RF field is
gated off. This voltage is then amplified and demodulated
to baseband, as in a normal superheterodyne receiver,
and digitized using an analog-to-digital converter (see
Figure 6.1-3
).
Little information of practical use would attach
to the demodulated signal if all the protons exhibit
identical precessional frequencies. In fact, very minor
perturbations arise in the proton precessional frequency
d
from about 100 ms to
several seconds.
Though the process of tissue water relaxation is not
completely understood, its rate is related to the extent
of binding of water to the surface of biological macro-
molecules. Increased binding slows molecular motion.
The more closely the reorientation motion of the mag-
netic dipoles matches the Larmor frequency, the greater
the transition probabilities between the nuclear energy
