266
Biomedical Signal and Image Processing
One can argue that since not all tissues absorb the same percentage of the incident
radiation, the exposure X does not give an optimal measure of the radiation absorbed
by the tissue. In other words, in order to obtain an accurate reading of the dose,
the respective tissues irradiated need to be taken into account. This is why another
quantity, the radiation absorbed dose (RAD), is sometimes used an actual indication
of the energy absorbed by the medium (biological tissue) per unit mass. However, in
dosage assessment procedures, it is often observed that the absorption of the x-ray
source is relatively uniform across the entire field of exposure, giving all tissues
relatively the same dosage. This observation means that RAD can be often well
represented by X.
14.3 ATTENUATION-BASED X-RAY IMAGING
With the knowledge of the operating mechanism of x-ray imaging, we can proceed
with the description of the actual image formation. Since almost all commercial
x-ray imaging systems, i.e., conventional x-ray machines as well as CT or computed
axial tomography (CAT) scan systems, are using attenuation as the major physical
quantity to form images, next we focus on the concept using attenuation for image
formation.
As mentioned in Chapter 13, in x-ray attenuation tomography, the difference in
the attenuation between various tissues forms the basis of the formation of an attenuation
contrast image.
The attenuation coefficient, also known as the absorption coefficient, α, plays the
central role in x-ray attenuation imaging. This quantity is defined as the proportionality factor for the change in x-ray radiation intensity. In order to formally define this
quantity, consider the change in intensity, dI, across a differential element of thickness, dx. This intensity change is proportional to the incident intensity, I 0 , and the
distance traversed, i.e.,
dI = −aIdx
(14.7)
Integration of Equation 14.14 gives the following expression of exponential decay as
a function of distance migrated through the biological medium:
−ax
I I e
0
(14.8)
=
or
⎛ I 0 ⎞
ln ⎜ ⎟ = −ax
(14.9)
⎝ I ⎠
where I is the transmitted intensity used for image formation.
As can be seen from the aforementioned formulation, the attenuation coefficient, α,
is the reciprocal distance where the intensity decays to e −1 or 36% of the initial value.
Biomedical Signal and Image Processing
One can argue that since not all tissues absorb the same percentage of the incident
radiation, the exposure X does not give an optimal measure of the radiation absorbed
by the tissue. In other words, in order to obtain an accurate reading of the dose,
the respective tissues irradiated need to be taken into account. This is why another
quantity, the radiation absorbed dose (RAD), is sometimes used an actual indication
of the energy absorbed by the medium (biological tissue) per unit mass. However, in
dosage assessment procedures, it is often observed that the absorption of the x-ray
source is relatively uniform across the entire field of exposure, giving all tissues
relatively the same dosage. This observation means that RAD can be often well
represented by X.
14.3 ATTENUATION-BASED X-RAY IMAGING
With the knowledge of the operating mechanism of x-ray imaging, we can proceed
with the description of the actual image formation. Since almost all commercial
x-ray imaging systems, i.e., conventional x-ray machines as well as CT or computed
axial tomography (CAT) scan systems, are using attenuation as the major physical
quantity to form images, next we focus on the concept using attenuation for image
formation.
As mentioned in Chapter 13, in x-ray attenuation tomography, the difference in
the attenuation between various tissues forms the basis of the formation of an attenuation
contrast image.
The attenuation coefficient, also known as the absorption coefficient, α, plays the
central role in x-ray attenuation imaging. This quantity is defined as the proportionality factor for the change in x-ray radiation intensity. In order to formally define this
quantity, consider the change in intensity, dI, across a differential element of thickness, dx. This intensity change is proportional to the incident intensity, I 0 , and the
distance traversed, i.e.,
dI = −aIdx
(14.7)
Integration of Equation 14.14 gives the following expression of exponential decay as
a function of distance migrated through the biological medium:
−ax
I I e
0
(14.8)
=
or
⎛ I 0 ⎞
ln ⎜ ⎟ = −ax
(14.9)
⎝ I ⎠
where I is the transmitted intensity used for image formation.
As can be seen from the aforementioned formulation, the attenuation coefficient, α,
is the reciprocal distance where the intensity decays to e −1 or 36% of the initial value.