What is larmor frequency
Larmor frequency is defined as precession frequency at which a magnetic moment, such as that of a proton, precesses around an external magnetic field. Larmor frequency depends upon external magnetic field strength and material properties called gyromagnetic ratio refer Table 1, Figure 1, 2.
NMR Principle
Nuclear Magnetic Resonance (NMR) is based on the principle that any object can be subdivided into atoms. Each atom is composed of two types of
charged particles: protons and electrons. Subatomic particles such as electrons and protons have a property known
as spin. Although a proper explanation of subatomic particle behavior requires quantum mechanics, NMR principles can
be accurately described using classical models because NMR involves collections of particles. Spin is often associated
with the angular momentum of the atom and may be visualized as a top spinning about its vertical axis.Spin values
come in integer multiples of 0.5 and may be positive or negative. The spin for an unpaired
subatomic particle is 0.5. The net spin of a collection of particles is the sum of the individual spins. Techniques
based on NMR, including MRI, are dependent on collections of particles with net spin. According to Ampere's law,
a time-varying electric charge distribution induces a magnetic field. As a consequence, the nucleus of an atom with
net spin will produce a small magnetic field. This magnetic field is represented by the vector quantity \( \mu \) and known
as the nuclear magnetic dipole moment or the magnetic moment. The magnetic moment is related to the spin angular
momentum by the following relationship: \[\vec{\mu} = \gamma \, \vec{L}
\]
The constant of proportionality, \( \gamma \), known as the gyromagnetic ratio, is dependent on
the nucleus type. The \( \gamma \) values for select nuclei are listed in Table 1. Most clinical applications of MRI
require an abundance of hydrogen inside the object to be imaged because its relatively high gyromagnetic ratio eases the
imaging process. The human body is primarily fat and water, both of which have many hydrogen atoms. The magnitude of the
magnetic moment can be calculated by
\[\mu = \gamma \hbar \sqrt{I(I+1)} \]
where h is Planck's constant (approximately ) divided by 2 , and I, the nuclear spin quantum number, is the magnitude
of the spin value mentioned earlier and must take on a value that is a positive integer multiple of 0.5, such as
I = 0, 0.5, 1, 1.5, 2.0, 2.5, 3.0
Although the magnitude of \( \mu \) is known, its direction is random unless an external magnetic field is applied. When
placed in an external magnetic field, the magnetic moment vector \( \mu \) of a subatomic particle will align with the external
field in two possible energy states. The low energy state requires that the magnetic moment align itself parallel to the
direction of the magnetic field, as shown in Figure 2.2. The higher energy state, shown in Figure 2.3, occurs when the
magnetic moment is aligned in the opposite direction as the main magnetic field.
