Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 8

High energy state

B 0

µ

Energy

∆ E

µ

Low energy state

FIGURE 1.3 Energy level diagram for I = 1/2.

So far, the behavior of a single isolated nucleus has been considered. However,
in practice, the mean result due to a large number of similar nuclei is observed.
When an ensemble of nuclei is subjected to an external magnetic field, nuclei
distribute themselves in the allowed orientations. At equilibrium, the population of
nuclei in the parallel orientation (lower energy state) exceeds that in the antiparallel
orientation (higher energy state) by a small amount, according to Boltzman statis-
tics. The excess population in the lower energy state, , is dependent on the

energy difference between the spin states and the absolute temperature, T:

∆ N

∆
NN

E
kT

∆ ≅ (1.7)

0

2

where N is the total number of nuclei in the sample, and k is the Boltzman

0

) in the lower energy state
is extremely small; for example, for hydrogen nuclei at body temperature (310 K)
in a magnetic field B

constant. The fractional excess of population ( ∆ N / N

0

= 1 T, ∆ N/N = 3.295 × 10

− 6

.

0 0

1.3.1 N L F : C

OTES ON ARMOR REQUENCY HANGES

D D

UE TO ISHOMOGENEITIES

We have seen that the precession frequency of µ experiencing a B 0 field is given

ω 0

by = −γ B 0 and, considering the modulus:

ω 0 = γ B 0 (1.8)

This relation, commonly called the Larmor equation , is important because the
Larmor frequency is the natural resonance frequency of a spin system.
Equation 1.8 shows that the resonance frequency of a spin system is linearly
dependent on both the strength of the external magnetic field B 0 and the value
of the gyromagnetic ratio

γ . This relationship describes the physical basis for

1

achieving nucleus specificity. In fact, as shown in Table 1.1 , the nuclei of H and