Biomedical Engineering Reference
In-Depth Information
I
=
I
0
e
−μ
x
I
I
0
Fig. 2
Representation of the interaction that a monoenergetic beam of photons suffer when passes
through an object of thickness
x
.
I
0
is the intensity of the incident beam.
I
represents the intensity
of the emerging beam. The intensity of the incident beam is reduced by a fraction equal to e
x
where
is the linear attenuation coefficient of the medium
From (
5
) it can be concluded that there is a symmetry plane (front/rear) and, as a
corollary, that the cross section has the same value for
˛ D 0
ı
and
˛ D 180
ı
,which
is the maximum.
Note that for low energies, the Klein-Nishina formula (
2
) reduces to the Rayleigh
formulation (
5
). For this circumstance,
P
E;˛
can be considered equal to the unity and
after replacing this condition in (
2
) the conclusion is direct. When a high energy
photon (
>
1,022 keV) produces an electron-positron pair by interacting with the
nucleus, the process is known by pair production. Since it only takes place for very
high energies, this process is not likely to occur in the range of energies used in
nuclear medicine.
The probability of occurrence of photoelectric effect is higher than for Compton
effect for low energy photons. On the contrary, for average energies, such as those
used in nuclear medicine, the likelihood of Compton effect occurring is higher than
for the photoelectric effect. For higher energies, pair production is the dominant
process (Fig.
3
).
As a result of the interaction of radiation with matter, when a photon beam with
intensity
I
(energy per unit area) is incident on an object of thickness
x
, it suffers
attenuation. That is, the beam intensity is reduced by a factor that depends on the
material and on the thickness of the object and, also, on the energy of the photons.
The relation between the intensities of the incident beam
.I
0
/
and emerging beam
.I /
, is described by the exponential equation:
D I
0
e
x
I
(6)
The attenuation is often due to a multiple process where several and successive
interactions occur until the photon energy is completely transformed (Fig.
2
).
Figure
3
shows the variation of the attenuation coefficient for each of the
interaction mechanisms as a function of the energy of the incident photons. The at-
tenuation coefficient is presented normalized to the total attenuation. The attenuation
coefficient shown is relative to the water, which is the main constituent of the human
body and, therefore, generally considered as the biological equivalent.
