Page 249 - Biomedical Engineering and Design Handbook Volume 2, Applications

228 DIAGNOSTIC EQUIPMENT DESIGN
where K is Boltzmann’s constant. The fraction of nuclei aligned with B 0 may be expressed as

/
2mB 0 K T 2mB 0
1
η= − e ≈ (8.3)
K T
For protons at 1.5 T at body temperature (37 C), about one proton in 100,000 is aligned with the
static magnetic field. Aligned protons provide the MR signal. So, assuming all other parameters
equal, higher static magnetic fields provide higher signal levels.
Nuclei with magnetic moments precess in static magnetic fields at frequencies proportional to the
local static magnetic field strength. Let B 0 represent the static magnetic field strength, let γ represent
a proportionality constant called the magnetogyric ratio, and let the radian precession frequency be
ω (= 2πf, where f is the linear frequency of precession). Then the relationships between these quan-
3
tities may be expressed mathematically as the Larmor equation:
(8.4)
ω=γB 0
Properly designed coils may receive signals induced by the time-varying magnetic flux. Ideally,
magnetic resonance scanners would produce perfectly homogeneous magnetic fields. In magnetic
resonance spectroscopy (MRS), nearby nuclei with magnetic moments may alter the local static
magnetic field and the precession frequency so that various chemical components may be identified
by the received spectrum.
If small, linear “gradient” magnetic fields are added to the static magnetic field, then received fre-
quency would correlate to physical location. Magnetic resonance imaging uses magnetic field gra-
dients to spatially encode all three dimensions. Note that the most widely used nucleus in MR is the
hydrogen nucleus or proton.
For diagnostic purposes, signals from various tissues should differ sufficiently to provide con-
4
trast to distinguish them. There are two relaxation processes in magnetic resonance. One mecha-
nism is called spin-lattice or T relaxation. In the absence of a static magnetic field, a collection of
1
nuclei with magnetic moments are randomly oriented and the net macroscopic magnetic moment
vector is zero. In the presence of a static magnetic field, the collection of nuclei with magnetic
moments has a net macroscopic magnetic moment vector aligned with the static magnetic field.
Consider a static magnetic field in which there are nuclei with magnetic moments. When resonant
RF pulses excite the nuclei, the macroscopic magnetic moment vector tips by some angle related to
the RF waveform. Gradually, the nuclei lose energy to the lattice and the macroscopic magnetic
moment vector relaxes back to alignment with the static magnetic field. This type of relaxation is
called spin-lattice or longitudinal or T relaxation. Biologically relevant T values are typically in
1
1
the 100- to 2000-ms range. 5
The other relaxation mechanism is called spin-spin or T relaxation. The presence of other
2
nuclei with magnetic moments causes changes in the local magnetic field. These changes lead to
slightly different precession frequencies for the spins. As the spins get out of phase, signal is lost.
This type of relaxation is called spin-spin or transverse or T relaxation. Note that T ≤ T , because
2 2 1
T depends on T loss mechanisms as well as others. Typical T values of biological interest are in
1 2 2
the 20- to 300-ms range. 5
Fortunately, various tissues differ in their T and T properties. Different imaging sequences
1 2
and pulse parameters can be used to optimize contrast between tissues. So, MR pulse sequences
are analogous to histological stains; different sequences and parameters can be used to highlight
(or obscure) differences.
Magnetic resonance scanners use static magnetic fields to produce conditions for magnetic reso-
nance (see Fig. 8.1). In addition, three coil sets (along with amplifiers and eddy-current correction
devices) are needed to spatially encode the patient by producing time-varying gradient magnetic
fields. Radio frequency (RF) transmit and receive coils, amplifiers, and receivers are used to excite
the nuclei and to receive signals. Computers are useful to control the scanner and to process and dis-
play results (i.e., images, spectra, or flow velocities). Other equipment includes patient tables,
patient-gating systems, patient-monitoring equipment, and safety systems.