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X ray attenuation & law of exponential attenuation
- 1. X-ray Attenuation &law of exponential attenuation RAVI CHRISTIAN M.SC MRIT DMIMS(DU)
- 3. Introduction In aclinical environment, all X-ray beams (although not all X-ray photons) will interact with the medium through which they pass and therefore, to a greater or lesser extent, the beam will be attenuated Attenuation is the reduction in the intensity of an x-ray beam as it traverses matter, by either the absorption or deflection of photons from the beam Attenuation = absorption + scatter. Primarily affected by the atomic number of the medium and the energy of the X-rays photons
- 5. ATTENUATION COEFFICIENTS Anattenuation coefficient is a measure of the quantity of radiation attenuated by a given thickness of an absorber. The name of the coefficient is determined by the units used to measure the thickness of the absorber.
- 6. ATTENUATION COEFFICIENTS Thelinear attenuation coefficients (cm-1) The mass attenuation coefficients (cm2/g) The electronic attenuation coefficients(cm2/electron) The atomic attenuation coefficients(cm2/atom)
- 7. Linear Attenuation Coefficient The linear attenuation coefficient (µ) describes the fraction of a beam of x-rays or gamma rays that is absorbed or scattered per unit thickness of the absorber. The linear attenuation coefficient is the most important coefficient for diagnostic radiology. In Simple word It is a quantitative measurement of attenuation per centimeter of absorber, so it tells us how much attenuation we can expect from a certain thickness of tissue.
- 8. Because wemeasure our patients in centimeters, it is a practical and useful attenuation coefficient. The unit of the linear attenuation coefficient is per centimeter, and thus the name linear attenuation coefficient, because a centimeter is a linear measurement. The expression per Cm is the same as 1/cm, and is usually written cm-1. Its symbol is the Greek letter µ.
- 10. Water, fat,bone, and air all have different linear attenuation coefficients, Linear Attenuation Coefficient is for monochromatic radiation The size of the coefficient changes as the energy of the x-ray beam changes. When the energy of the radiation is increased, the number of x rays that are attenuated decreases, and so does the linear attenuation coefficient. exponential equation for x-ray attenuation
- 11. Linear attenuation coefficient-problem The main problem with using linear attenuation coefficient as the guide to how much attenuation will occur in a given thickness of material is that as the physical conditions of the material change (a material could be a solid, a liquid or a gas), then the accuracy of that coefficient can change. If, for example, a material was heated and expanded, it is extremely likely that its thickness would change (i.e. its volume would increase, its density would decrease and the number of atoms per unit volume would decrease proportionately). This would mean that the linear attenuation coefficient would also change
- 12. Mass attenuation coefficient However, if the linear attenuation coefficient were divided by the density of the medium, the numerical value would remain proportionally consistent. In this context, density is represented by ρ (the Greek letter rho): (total) mass attenuation coefficient (μ/ρ). The mass attenuation coefficient is, therefore, the linear attenuation coefficient (represented by μ) divided by the density of the medium (represented by ρ) and this ratio removes the anomalies caused by any physical changes which may occur as a result of environmental conditions
- 13. Mass attenuation coefficient The mass attenuation coefficient is independent of density.
- 15. Attenuation Coefficient andBeam Energy The attenuation coefficient varies with photon energy. The linear attenuation coefficient is defined for monochromatic beams. There is difficulty in the application of this coefficient to polychromatic beam. Basically X-rays are polychromatic radiation beams. The low energy components are removed, while it is passing through the matter. Hence, the effective energy of the beam increases, resulting beam hardening effect. In addition, X-ray tube and filter also hardens the beam. Hence, diagnostic X-rays are heavily filtered beam that can be approximated to monochromatic X-rays.
- 16. Law of exponentialattenuation If a beam passes through an absorber of thickness x, both absorption and scattering takes place. As a result, the transmitted beam will have less number of photons and it is given by the relation where I is the number of transmitted photons, I0 is the number of incident photons, e is the base of natural logarithm and µ is the linear attenuation coefficient of the absorber material.
- 17. FACTORS AFFECTING ATTENUATION Increasingthe radiation energy increases the number of transmitted photons (and decreases attenuation), while increasing the density, atomic number, or electrons per gram of the absorber decreases the number of transmitted photons
- 18. Thickness ofattenuator: The greater the thickness of attenuating material, the greater is the attenuation. X-rays are attenuated exponentially Density and attenuator: As the density of the material increases, the attenuation produced by a given thickness increases Thus different material such as water, fat, bone and air have different linear attenuation coefficient, as do the different physical state or densities of a material such as water vapor, ice and water
- 19. Atomic numberof attenuator: Materials with higher atomic number (Z) have higher attenuation values for a given thickness , The higher atomic number indicates there are more atomic particles for interaction with the x-ray photons
- 20. Attenuation of Monochromaticradiation A beam of 1000 photons is directed at a water phantom. With each succeeding centimeter of water, 20% of the remaining photons are removed from the beam. The quality of monochromatic radiation does not change as it passes through an absorber. (Change in the number, or quantity, of photons in the beam.)
- 21. Attenuation of polychromaticx-rays Polychromatic beam contain a spectrum of photon energies Because of the spectrum of photon energies, the transmission of a polychromatic beam through an absorber does not strictly follow exponential law Photons of low energy are attenuated more rapidly than the high energy photons The number of transmitted photon and quality of beam changes with increasing absorber thickness
- 22. Half-value layer(HVL): The half value layer (HVL) is defined as the thickness of material required to reduced the intensity of x or gamma ray beam to one half of its initial value Tenth-Value Layer (TVL): The tenth-value layer (TVL) is the thickness of the material necessary to reduce the intensity of the beam to a tenth of its initial value
- 23. The half-valuelayer is always stated together with the value of the applied voltage and the filtration. Aluminum and copper are the materials commonly used to specify HVL. HVL is measured by thickness of aluminium in diagnostic X-rays and it is given for its effective energy. For diagnostic X-ray beam energies, the HVL for soft tissue ranges from 2.5 to 3.0 cm. The half value layer (HVL) of the mammographic beam is about 0.3–0.4 mm Al. This depends upon the kVp range and type of target/filter used in the tube.
- 24.