Linear attenuation coefficient

A common contrast agent is barium sulfate [7727-43-7] although iodinated compounds have been used. Owing to the much higher linear attenuation coefficient of the contrast agent, a higher (120 keV) energy x-ray typically is used. 

The value of p, the linear attenuation coefficient, depends on the substance, its density, and on the wavelength of the x-rays [2]. The mass attenuation coefficient, p., is obtained by dividing p, by the density of the substance. Although a powder mixture may be composed of several components, it can be regarded as being composed of just two components component J (which is the unknown), and the sum of the other components (which is designated as the matrix). The intensity of line i of component J in a powder mixture is given as... 

A complete analysis is made by acquiring a number of radiographs (typically about 1000) of the same sample under different viewing angles (one orientation for each radiograph). A final computed reconstruction step is required to produce a 3D map of the linear attenuation coefficients in the material. This 3D map indirectly gives a picture of the structure density. In the X-ray-computed tomography, the X-ray source and detector are placed at the opposite sides of the sample. The spatial resolution of the attenuation map depends on the characteristics of both the detector and number of X-ray projections. 

According to Evans (1995), differentiation of features within the materials is possible because p at each point directly depends on the electron density of the material in that point (pe), the atomic number (Z) of the chemical components of the materials in that point, and the energy of the incoming X-ray beam (/0). In particular, the linear attenuation coefficient can be approximately considered as the sum of the Compton scatter and photoelectric contributions ... 

Spatial distribution of the linear attenuation coefficients within material is based on the average linear attenuation coefficient along the projected line through the sample that can be calculated from the measured X-ray intensities as follows ... 

Thus, the peak efficiency for a sample with linear attenuation coefficient (p p) is represented by the following equation. 

In practice, however, an equation expressing the relationship between the product of shield thickness and linear attenuation coefficient, and the build-up factor is used for calculating the build-up factor at a certain shield thickness. One of the typical approximations is as follows ... 

Attenuation of 7 Radiations. When 7 radiations pass through the absorber medium, they undergo one or a combination of the above three processes (photoelectric, Compton, and pair production) depending on their energy, or they are transmitted out of the absorber without any interaction. The combined effect of the three processes is called the attenuation of the 7 radiations (Fig. 1.9). For a 7 radiation passing through an absorber, the linear attenuation coefficient (fie) of the 7 radiation is given by... 

Figure 1.10. Linear attenuation coefficient of 7 rays of different energies in water (equivalent to body tissue). The relative contributions of photoelectric, Compton scattering, and pair production processes are illustrated.

Another quantity called the mass attenuation coefficient (pg) is given by the linear attenuation coefficient (pe) divided by the density ip) of the absorber and is given in units of cm2/g or cm2/mg. 

The detection efficiency of a detector is another important property in PET technology. Since it is desirable to have shorter scan times and low tracer activity for administration, the detector must detect as many of the emitted photons as possible. The 511-keV photons interact with detector material by either photoelectric absorption or Compton scattering, as discussed in Chap. 1. Thus, the photons are attenuated (absorbed and scattered) by these two processes in the detector, and the fraction of incident 7 rays that are attenuated is determined by the linear attenuation coefficient (/x) given in Chap. 1 and gives the detection efficiency. At 511 keV, /x = 0.92 cm-1 for bismuth germanate (BGO), 0.87 cur1 for lutetium oxyorthosilicate (LSO), and 0.34 cm-1 for Nal(Tl) (Melcher, 2000). Consequently, to have similar detection efficiency, Nal(Tl) detectors must be more than twice as thick as BGO and LSO detectors. 

BGO detectors are used in most of the PET systems because of its highest stopping power (highest density and linear attenuation coefficient). However, it suffers from its longer scintillation decay time 0-300 ns) and poor light output. The longer decay time increases the dead time of the detector and limits... 

The 511-keV annihilation photons originating from different locations in the body are attenuated by the tissue, as they traverse different thicknesses to reach the detector pair in coincidence. If /z is the linear attenuation coefficient of 511-keV photons in the tissue, and a and b are the tissue thicknesses traversed by the two 511-keV photons along the LOR (Fig. 3.7), then the probability P of a coincidence detection is given by... 

If one of the two 511-keV photons arising from annihilation in an organ traverses through a thickness of 2.2 cm of the organ and the other photon traverses 1.8 cm of the organ, what is the attenuation correction factor (Linear attenuation coefficient of 511-keV photons in tissue is 0.5 cm. )... 

In a PET center, a clinical laboratory is situated on the other side of a plaster wall of the PET room. Calculate the amount of lead shielding required to be added to meet the regulatory limit, given the following information number of FDG studies per week = 25 18F-FDG dosage per patient = 10 mCi linear attenuation coefficient of 511 keV photons in lead = 1.26 cm-1 f for 18F = 6.96R-cm2/mCi-h at 1 cm distance between... 

Linear attenuation coefficient (p). The fraction of radiation energy absorbed and scattered per unit thickness of absorber. 

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