Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 9

31 P in an object resonate at 42.58 MHz and 11.26 MHz, respectively, when the
object is placed in a magnetic field B 0 1 T; this difference in resonance frequency

enables us to selectively image one of them without interacting with the other.
Actually, a specific spin system (i.e., hydrogen protons) may have a range of
resonance frequencies. In this case, each group of nuclear spins that share the
same resonance frequency is called an isochromat .
There are two main reasons for a magnetized spin system to have multiple
isochromats: (1) the presence of inhomogeneities in the B 0 field and (2) the
chemical shift effect, which is exploited for chemical components studies.
When B 0 is not homogeneous, spin with the same

=

value will have different
Larmor frequencies at different spatial locations. Such a condition can be usefully
exploited, as we will see in MR image generation, when the inhomogeneity of
B 0 is known. However, if B 0 inhomogeneities are not known, they are considered
as bringing a negative effect, that is artifacts.
The chemical shift effect is due to the fact that nuclei in a spin system are part
of different molecules in a chemically heterogeneous environment. Because each
nucleus of a molecule is surrounded by orbiting electrons, these orbiting electrons
produce their own weak magnetic fields, which “shield” the nucleus to varying
degrees depending on the position of the nucleus in the molecule. As a result, the
effective magnetic field that a nucleus “sees” is

γ

ˆ

BB
0

=

0 1

( −δ ) (1.9)

is a shielding constant taking on either positive or negative values. Based
on the Larmor relationship, the resonance frequency for the nucleus is

where δ

ˆ

ωω ωω δ
0

=− = − ∆

0 1

( ) (1.10)

0

Equation 1.10 shows that spins in different chemical environments will have
relative shifts in their resonance frequency even when B 0 is homogeneous. The
frequency shift depends on both the strength of the magnetic field B 0 and

the shielding constant

∆ω

is very small, on the order of
a few parts per million (ppm), and it depends on the local chemical environment
in which the nucleus is embedded. Knowledge of these chemical shift frequencies
and the corresponding spin densities is of great importance for determining the
chemical structures of an object, which is the subject of MR spectroscopy.

δ . Usually, the value of δ

1.3.2 B ULK M AGNETIZATION

To describe the collective behavior of a spin system, we introduce a macroscopic
magnetization vector M , which is the vector sum of all the microscopic magnetic
moments in the object:

N s

∑ µ
1

M = (1.11)

i

i =