ABSTRACT
Magnetic resonance imaging exploits the existence of induced nuclear magnetism in the patient. Materials with an odd number of protons or neutrons possess a weak but observable nuclear magnetic moment. Most commonly protons (
H) are imaged, although carbon (
C), phosphorus (
P), sodium (
Na), and fluorine (
F) are also of significant interest. The nuclear moments are normally randomly oriented, but they align when placed in a strong magnetic field. Typical field strengths for imaging range between 0.2 and 1.5 T, although spectroscopic and functional imaging work is often performed with higher field strengths. The nuclear magnetization is very weak; the ratio of the induced magnetization to the applied fields is only 4
×
. The collection of nuclear moments is often referred to as magnetization or spins. The static nuclear moment is far too weak to be measured when it is aligned with the strong static
magnetic field. Physicists in the 1940s developed resonance techniques that permit this weak moment to be measured. The key idea is to measure the moment while it oscillates in a plane perpendicular to the static field [3,4]. First one must tip the moment away from the static field. When perpendicular to the static field, the moment feels a torque proportional to the strength of the static magnetic field. The torque always points perpendicular to the magnetization and causes the spins to oscillate or precess in a plane perpendicular to the static field. The frequency of the rotation
ω
is proportional to the field:
where
γ
, the gyromagnetic ratio, is a constant specific to the nucleus, and
B
is the magnetic field strength. The direction of
B
defines the
z
axis. The precession frequency is called the Larmor frequency. The negative sign indicates the direction of the precession.
