Biomedical Engineering Reference
In-Depth Information
6.1
Chapter 6.1
Fundamentals of magnetic
resonance imaging
Reinaldo Perez
6.1.1 Early history of nuclear
magnetic resonance
approaches the resonance value. The resonance condition
is given by
j
g
jB ¼
u
The root of nuclear magnetic resonance (NMR), or as
it sometimes is called magnetic resonance imaging
(MRI), goes back to World War II. In 1938 I. Rabi
perfected a beam-splitting technique and successfully
achieved NMRda term that Rabi coined. The NMR
experiments made use of the spin-state-dependent
force that inhomogeneous magnetic fields exert on an
atomic beam of silver atoms directed perpendicular to
the gradient fields. For spin-
2
nuclei, the atomic beam
splits, but it reconverges when the polarity of the gra-
dient field reverses. Rabi showed that irradiating the
spins at the transition frequency, which interchanges
the
m ¼
2
states, eliminated the convergence.
The first detection of NMR in bulk matter was
achieved in the mid-1940s by research groups led by
Edward M. Purcell at Harvard University and Felix Bloch
of Stanford University. Purcell used a resonant cavity to
study the absorption of radio-frequency (RF) energy in
paraffin: at resonance, the cavity output was found to be
slightly reduced. By contrast, Bloch and his colleagues
used what they called ''nuclear induction.'' Bloch de-
scribed the experiment as measuring an electromotive
force resulting from the forced precession of the nuclear
magnetization in the applied RF field.
When matter is placed in a magnetic field, the nuclear
magnetic moments orient parallel to the field, leading to
a paramagnetic polarization in the direction of the mag-
netic fielddthe
z
direction. If an oscillating magnetic
field is applied in the
x
or
y
direction, the polarization
vector is deflected from the
z
direction once the field
where
B
is the amplitude of the applied static magnetic
field, u is the nuclear precession frequency, and g is the
gyromagnetic ratio, which is a constant for a given iso-
tope. In NMR, this rotation of the magnetic polarization
vector of the nuclei in a plane perpendicular to the
z
axis
induces an emf in a detector coil; this is the NMR signal.
Nuclear magnetic relaxationdthat is, the return of
the spin system to equilibrium is of great significance to
imaging and was conceptualized by these early in-
vestigators. By repeatedly passing the spin system
through the resonance condition (by varying the ampli-
tude of the polarizing magnetic field) and observing the
reappearance of a signal, Bloch found that for protons
(that is, the hydrogen nuclei) in liquids the time constant
T
1
for the return of the longitudinal magnetization was of
the order of seconds. Further, he concluded from the
sharpness of the resonance that the spins' phase memory
time
is of the order
of hundreds of milliseconds in fluid (and, as shown later,
only slightly shorter in biological tissues). It is clearly
thanks to Mother Nature's good graces, or God, that
NMR in human subjects is possible at all. If it took, in-
stead of seconds, hours for the spin to repolarize, the
technique would be impractical.
The commonly used detection method during the first
two decades of NMR work exploited the principles of
continuous wave excitation, where the field is swept
while the sample is irradiated with RF energy of constant
frequency. An alternative scheme, which is still
d
the transverse relaxation time
T
2
d
in
