Biomedical Engineering Reference
In-Depth Information
34
6.626
10
−
[J.s]
×
)
12
(
510
−
1cos45
λ
−×
=
−
f
31
8
9.11
10
−
[kg]
3
10 [m/s]
×
×
×
12
5.71
10
−
m
λ
=
×
f
8
310[m s]
×
15
5
E
4.136
10
−
[eV.s]
2.48
10 eV
0.248 MeV
=
×
×
=
×
=
12
5.712
10
−
[m]
×
Compton scattering occurs in all materials and is dominant with photons of medium
energy (i.e., about 0.5 to 3.5 MeV). It is largely independent from the tissue type, increases
with high energy levels, and causes poor contrast in high energy biomedical images. Since
the scattered X-ray photon has less energy, it has a longer wavelength and is less penetrat-
ing than the incident photon. Together with the photoelectric effect and pair production,
Compton scattering contributes to the attenuation of energy in matter.
8.3.3 Transmission Imaging
With the exception of nuclear medicine, most imaging techniques require that en-
ergy penetrates the body tissues and interacts with those tissues in the form of ab-
sorption and scattering. The resulting medical image reflects the interaction of the
energy with the tissues. A beam of EM wave is passed through the body structure
being examined. The images record how much light passes through the specimen,
such that darker regions indicate more tissue and/or darker tissue. The beam passes
through less dense types of tissue such as watery secretions (Figure 8.3), blood, and
fat, leaving a darkened area on the X-ray film. Attenuation is the rate at which the
signal light decreases in intensity,
ι
, and related by
ι
=
ι
0
·
e
μ
−
x
x
(8.13)
x
μ
x
is the linear attenuation coefficient, which describes the fraction of a beam that
is absorbed or scattered per unit of thickness of the absorber.
where
ι
0
is the intensity of incident X-ray,
ι
x
is the intensity at distance
x
, and
μ
x
accounts for the
number of atoms in a cubic cm volume of material and the probability of a photon
being scattered or absorbed from the nucleus or an electron of one of the atoms.
μ
x
depends on the photon energy and the chemical composition and physical density
of the material. Differences in
μ
x
values among tissues are responsible for image
contrast and identification of different tissues. Another term commonly used is the
mass attenuation coefficient obtained by dividing
μ
x
with density [g/cm
3
] of the
medium.
μ
x
/
ρ
for some tissues are given in Table 8.1, from which one can notice
that
for different tissues are similar at a given incident energy. However, tissue
densities are significantly different. Hence,
μ
x
/
ρ
μ
x
is approximately proportional to the
physical density (kg/m
3
), and
μ
x
tends to increase with an increasing atomic number
at the same photon energy.
EXAMPLE 8.5
A tissue containing bone and air of equal thickness (5 cm) are exposed to a 40-keV X-ray.
If the attenuation coefficients are 0.665 cm
2
/g and 0.095 cm
2
/g, what is the expected
