In some situations it is more desirable to express the attenuation rate in terms of the mass of the material encountered by the photons rather than in terms of distance. The quantity that affects attenuation rate is not the total mass of an object but rather the area mass. Area mass is the amount of material behind a 1-unit surface area, as shown below. The area mass is the product of material thickness and
density: Show
Area Mass (g/cm2) = Thickness (cm) x Density (g/cm3). The mass attenuation coefficient is the rate of photon interactions per 1-unit (g/cm2) area mass.
The figure compares two pieces of material with different thicknesses and densities but the same area mass. Since both attenuate the same fraction of photons, the mass attenuation coefficient is the same for the two materials. They do not have the same linear attenuation coefficient values. The relationship between the mass and linear attenuation coefficients is Mass Attenuation Coefficient (�/r) = Linear Attenuation Coefficient (�) / Density (r). Notice that the symbol for mass attenuation
coefficient (�/r) is derived from the symbols for the linear attenuation coefficient (�) and the symbol for density (r). We must be careful not to be misled by the relationship stated in this manner. Confusion often arises as to the effect of material density on attenuation coefficient values. Mass attenuation coefficient values are
actually normalized with respect to material density, and therefore do not change with changes in density. Material density does have a direct effect on linear attenuation coefficient values. The total attenuation rate depends on the individual rates associated with photoelectric and Compton interactions. The respective attenuation coefficients are related as follows:
�(total) = �(photoelectric) + �(Compton). Let us now consider the factors that
affect attenuation rates and the competition between photoelectric and Compton interactions. Both types of interactions occur with electrons within the material. The chance that a photon will interact as it travels a 1-unit distance depends on two factors. One factor is the concentration, or density, of electrons in the material. Increasing the concentration of electrons increases the chance of a photon coming close enough to an
electron to interact. In a previous section (Characteristics and Structure of Matter) we observed that electron concentration was determined by the physical density of the material. Therefore, density affects the probability of both photoelectric and Compton interactions. All electrons are not equally attractive to a photon. What makes an electron more or less attractive is its binding energy. The two general rules
are:
In the previous section referred to above we observed that the electrons with binding energies within the energy range of diagnostic x-ray photons were the K-shell electrons of the intermediate- and high-atomic-number materials. Since an atom can have, at the most, two electrons in the K shell, the majority of the electrons are located in the other shells and have relatively low binding energies. Just for you: FREE 60-day trial to the world’s largest digital library.The SlideShare family just got bigger. Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd. Read free for 60 days Cancel anytime. Attenuation of x-rays A beam of x-rays may be:
AttenuationAttenuated x-rays are those that are absorbed, transmitted with a lower energy or scattered. It is an exponential process and, therefore, the beam intensity never reaches zero. There are two main methods through which attenuation occurs:
Attenuation of the beam can be represented numerically by:
Interactions with matterThree processes may occur and contribute to attenuation:
Compton effect
Compton scatter The Compton effect is also called incoherent scatter as the photon energy change is not always orderly and consistent. The change in energy of the x-ray photon depends on the resulting angle of scatter and not on the scattering medium. The larger the energy discharged by the photon to the electron the:
Compton scatter occurs more often with:
Compton attenuating coefficientThis is the probability that an x-ray photon is attenuated via Compton scatter. It is dependent on the number of available electrons; the electron density of the material; and on the physical density but not on the atomic number of the material. This is because, with the exception of hydrogen, all materials have approximately the same number of available electrons per gram of material. Materials with a significant proportion of hydrogen have more electrons per gram and the probability of Compton attenuation is increased. Compton attenuating coefficient = density / energy SummaryThe amount of Compton scatter increases with:
No effect with:
Written by radiologists, for radiologists with plenty of easy-to-follow diagrams to explain complicated concepts. An excellent resource for radiology physics revision.
Photoelectric effect
Photoelectric linear attenuation coefficient (LAC)The probability of photoelectric interactions depends on a few factors as demonstrated in the equation:
τ = ρZ3 / E3
Key: τ = photoelectric LAC Energy of the x-ray photonThe probability of photoelectric interactions is highest when the x-ray photon energy is slightly above the electron binding energy. If the photon energy is too low it cannot free the electron. If the energy is too high the probability of an interaction significantly decreases due to the inverse relationship with the cube of the energy as demonstrated in the equation for the photoelectric LAC. l-edge and k-edge attenuation graph As the photon energy increases, there are values where there is a sudden jump in attenuation (k-edge and l-edge). For example, at energies just below the k-edge the photons don’t have enough energy to free the k-shell electrons. As the energy increases to just over the required energy, a much larger number of electrons become available for interaction and the probability of the photon being attenuated by a photoelectric reaction significantly increases. This is particularly useful in iodine in which the k-edge is 33 keV, which is in the diagnostic radiation range, and is utilised to massively increase the photoelectric effect and, therefore, give greater tissue contrast. Atomic numberAn increase in the photoelectric interactions occurs with increasing atomic number as the binding energies of electrons becomes closer to the photon energy. SummaryThe photoelectric effect occurs more often with:
The photoelectric effect increases with:
Elastic scatterAka coherent, classical, unmodified or Rayleigh scattering.
Competitive interactionsBoth photoelectric and Compton scatter contribute to the total attenuation of a beam as it passes through material. The relative contribution of photoelectric and Compton interactions depends on a few factors. Graph of photoelectric and compton effects over range of energies As the x-ray photon energy increases:
As the atomic number increases:
As the tissue mass density increases:
Measuring attenuationHalf value layer (HVL)This is the measure of the penetrating power of the x-ray beam and is the amount of matter required to attenuate the beam to half its energy value. The smaller the HVL the more attenuating the material is or the weaker the x-ray beam is. It differs for different materials and strengths of beams. To calculate the factor of reduction use: 2HVL e.g. if the HVL of a beam is 2 mm, by what factor is the beam attenuated if it passes through 8 mm of material? 8 mm = 4 HVLs Linear attenuation coefficient (LAC)This is the probability of the material to attenuate the beam. It can also be expressed as the amount of energy transferred to the material per unit of track length of the particle. The LAC (μ) is calculated by: μ = 0.693 / HVL Mass attenuation coefficientThe MAC is a measure of the rate of energy loss by a photon beam as it travels through an area of material. By dividing LAC by the density of the material the effect of density is removed. The MAC is, therefore, independent of density and depends only on the atomic number of the material and the photon energy. MAC = μ / ρ
Key: μ = LAC, units: cm-1 Effect of beam quality on attenuationThe above only really apply to a monoenergetic (one energy value) beam of x-rays from a point source (infinitely small area) travelling in a vacuum. In reality, the x-ray beam focus is not a fine point and contains photons of different energies that, once they leave the x-ray tube, do not travel in a vacuum. Wider beam Increased width of beam = increased scatter produced and measured = larger measured HVL Heterogeneous beam
Σ Summary
What is xAttenuation is the reduction of the intensity of an x-ray beam as it traverses matter. The reduction may be caused by absorption or by deflection (scatter) of photons from the beam and can be affected by different factors such as beam energy and atomic number of the absorber.
What happens when xThe photoelectric effect occurs when an x-ray interacts with an electron in the matter. The photo is completely absorbed and its energy is transferred to an electron that is removed from the electron cloud.
What happens during xAs an x-ray beam passes through matter, the intensity of the beam decreases as quantity decreases but the mean E of the resultant beam increases.
Which of the following photon interactions contribute to the attenuation of the xWhich of the following photon interactions contribute to the attenuation of the x-ray beam? Coherent scatter, photoelectric absorption, and Compton scatter all contribute to the attenuation of the x-ray beam because these interactions decrease the total number of photons within the x-ray beam.
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