X-ray Attenuation Lecture Notes PDF

X-ray Attenuation Summary Slide 1 fchs.ac.ae Learning Objectives At the conclusion of this lecture, associated tutorial and practical session (if relevant), the student will be able to: 1. Broadly sketch the energy (E) and mass (Z) dependence of  2. Define the mass attenuat...

X-ray Attenuation Summary Slide 1 fchs.ac.ae Learning Objectives At the conclusion of this lecture, associated tutorial and practical session (if relevant), the student will be able to: 1. Broadly sketch the energy (E) and mass (Z) dependence of  2. Define the mass attenuation coefficient, m 3. Broadly sketch the E and Z dependence of m 4. Define the terms ‘monoenergetic’ and ‘polyenergetic’ 5. State the Beer-Lambert law and use it in calculations 6. Explain the absorption edge effect Slide 2 fchs.ac.ae X-ray / Matter Interaction Summary X-rays can behave both in wave-like and particle-like fashion In the photon energy range up to about 10 Mev, the relevant x- ray-matter interactions are: 1. Coherent scattering – elastic (also called Rayleigh, Thompson, or classical scattering) 2. Photoelectric effect (PE) – total absorption 3. Compton effect (CE) or Compton scattering )CS) – inelastic 4. Pair production (PP) – only occurs above 1.022 MeV Attenuation results from both absorption and scattering contributions Slide 3 fchs.ac.ae X-ray / Matter Interaction: Summary Rayleigh scattering occurs only for low Eg and for high Z This scattering also leads to Bragg scattering, a form of diffraction (used for crystal structure determination) Photoelectric effect interaction is proportional to Eg–3 Photoelectric effect interaction is proportional to Z 3 Compton effect interaction is proportional to Eg–1 Pair production has a threshold of 1.022 MeV, then is proportional to energy with increasing Eg These interaction processes are independent of each other Slide 4 fchs.ac.ae Polychromatic and Monochromatic X-rays Conventional x-ray tubes produce polychromatic (many-colored), polyenergetic (many-energies) radiation A monochromatic, monoenergetic source produces x-rays of one ‘colour’ (one wavelength, one frequency) and one energy Sources of monochromatic x-rays: 1. Radioactive decay (nuclear x-ray, g-ray emissions) 2. Fluorescent emission (characteristic atomic lines, Ka) 3. Specialised x-ray optics (synchrotron) poly = ‘many’; mono = ‘one’ Slide 5 fchs.ac.ae Typical X-ray Spectrum Note the poly- energetic nature of the radiation Soft x-rays Hard x-rays Bushberg et al. Figure 6-5, page 176 Slide 6 fchs.ac.ae   X-ray Attenuation I0 x I (x) The fraction of photons removed from an incident mono-energetic x-ray beam per unit thickness of material depends on the linear attenuation coefficient,  The number of photons, DN, removed in thickness Dx is DN = –  N0 Dx Conventionally, we measure intensity, I, or flux (photons per unit area per unit time) as DI = –  I0 Dx Rearranging this and integrating both sides gives us the Beer-Lambert Law: Ix = I0 exp –( x) Slide 7 fchs.ac.ae Linear Attenuation Coefficient for Low Z Materials Carbon (Z=6) Copper (Z=29) Probability of PE increases as Z3 10 10000 Coherent Scatter Coherent Scatter Incoher. Scatter Incoher. Scatter Photoel. Absorb. Photoel. Absorb. CE is largely Pair Production Total Attenuation 1000 Pair Production Total Attenuation Linear attenuation coefficient (cm-1) Linear attenuation coefficient (cm-1) independent of Z 1 100 Note the difference in the 10 vertical scales in 0.1 1 the two examples shown; 0.1 Shapes similar 0.01 0.01 0.1 1 10 0.01 0.01 0.1 1 10 Energy (MeV) Energy (MeV) Slide 8 fchs.ac.ae Linear Attenuation Coefficient for High Z Materials Tungsten (Z=74) Lead (Z=82) Note the overall 10000 10000 very similar Coherent Scatter Incoher. Scatter Coherent Scatter Incoher. Scatter shapes of the Photoel. Absorb. Photoel. Absorb. 1000 Pair Production 1000 Pair Production Total Attenuation Total Attenuation Linear attenuation coefficient (cm-1) Linear attenuation coefficient (cm ) attenuation -1 100 100 curves, for all contributions 10 10 1 1 0.1 0.1 0.01 0.01 0.01 0.1 1 10 0.01 0.1 1 10 Energy (MeV) Energy (MeV) Slide 9 fchs.ac.ae Components of  Let the linear attenuation coefficient for each mechanism be R (Rayleigh), PE (photoelectric effect), C (Compton) and PP (pair production) Ix = I0 exp –(R x) ⨯ exp –(PE x) ⨯ exp –(C x) ⨯ exp –(PP x) = I0 exp –[(R + PE + C + PP)x] Ix = I0 exp –( x) The total linear attenuation coefficient,  = R + PE + C + PP , simply because probabilities multiply. Slide 10 fchs.ac.ae Linear Attenuation Coefficient and E, Z  = R + PE + C + PP is a measure of the probability of a photon interacting in the material per unit length, so it has units of inverse length, as cm-1, m-1, etc. The value of  decreases with increasing Eg except at absorption edges (photoelectric effect = inner shell ionization), until the pair production threshold is reached The probability of an interaction depends on the number of atoms encountered per unit thickness  is dependent on the density,  (g/cm3) of the material and the density of electrons (ne/cm3), and hence depends also on Z Slide 11 fchs.ac.ae Absorption Edges For materials with Z > 30, the K-shell absorption edge increases the contribution of PE to  in diagnostic radiography Contrast agents take advantage of the rise in  at the K-edge located in the middle of the diagnostic x-ray energy range: Iodine Z = 53 with K edge at 33 keV Barium Z = 56 with K edge at 37 keV The primary characteristic x-ray emission lines from W and Mo: Element Ka1 Ka2 Kb1 Tungsten (W) Z = 74 59.32 keV 57.98 keV 67.24 keV Molybdenum (Mo) Z = 42 17.48 keV 17.37 keV 19.61 keV (These are relevant for target material in diagnostic x-ray tubes) Slide 12 fchs.ac.ae DEFINITIONs Linear attenuation co efficient- is a quantitative measurement of attenuation per centimeter of absorber Half value layer- is the absorber thickness required to reduce the intensity of the original beam by one half. Mass attenuation co efficient- is used to quantitate the attenuation of materials independent of their physical state. It is obtained by dividing linear attenuation co efficient by density. Slide 13 fchs.ac.ae Slide 14 fchs.ac.ae Mass Attenuation Coefficients We can remove the density dependence of the total linear attenuation coefficient, , by dividing it by the material density to give the mass attenuation coefficient m = / The mass attenuation unit is then area/mass, usually cm2/g. In x-ray imaging, it is this density difference that gives rise to overall attenuation (Z and Eg are the important factors) Slide 15 fchs.ac.ae Half Value Layer (HVL) One HVL is defined as the thickness of a given absorber that reduces the intensity of the exiting x-ray beam to half that of the primary incident beam x-ray attenuation depends strongly on x-ray energy After one HVL, the spectrum of the exiting x-rays is not necessarily the same as the incident spectrum High energy x-rays are more penetrating than low energy x-rays A larger (thicker) HVL value is associated with an x-ray beam that has, on average, a higher energy For polychromatic beams, HVL gives a rough but convenient measure of the beam quality Slide 16 fchs.ac.ae HVL: Why Do We Need It? If you place aluminium, one HVL thick, in the beam before the patient, then the intensity falling on the film/detector behind the patient should halve. We could achieve the ‘same’ intensity result by simply using less beam quantity The point of knowing the HVL of an x-ray beam is not to manage the flux, but to give you a feel for the relative penetrating ability of a polychromatic x-ray beam If we could measure directly the x-ray spectrum, then we could cite the mean photon x-ray energy to the same effect. It is possible to measure in-beam spectra. The thickness of aluminium for one HVL provides an easy method to have a rough measure for the mean photon energy Slide 17 fchs.ac.ae HVL, TVL and  For a monochromatic beam, at x = HVL, IHVL = I0/2 = I0 exp –( HVL) which yields HVL = ln(2)/ = 0.693/ Similarly, the tenth value layer (TVL) thickness x is that which reduces the incident beam intensity to 1/10 of I0 ITVL = I0/10 = I0 exp –( TVL) which yields TVL = ln(10)/ = 2.303/ Slide 18 fchs.ac.ae HVL, TVL and  – Example Calculations The HVL in a given situation is 3.0 cm Calculate  Calculate the TVL Slide 19 fchs.ac.ae HVL and Geometry HVL measures beam quality for narrow beam geometry For broad beam geometry, scattering events result in extra primary beam attenuation and a reduced HVL Bushberg, et al. Figure 3-15, page 48 Slide 20 fchs.ac.ae Effective Energy and Penetrability HVL is a complex function of the number of photons at each energy, the measuring geometry and the attenuating material HVL is a measure of the ‘hardness’ of a polychromatic beam; A ‘hard’ beam has a predominance of high energy photons A ‘soft’ beam has a predominance of low energy photons It is convenient to convert the HVL to an effective energy, as if the incident spectrum were monochromatic. This is a measure of the penetrating power of the beam; (E) = 0.693/HVL Slide 21 fchs.ac.ae  Image details? Beam Hardening Recall that low energy photons are much more likely to be absorbed than high energy photons (due to the PE effect) The transmitted beam for a polychromatic source will thus be harder than the X-ray spectra with increasing amounts of Al incident beam; the spectrum filtering: after 30 mm of Al, the mean photon will be shifted energy is about 70 keV. At 0 mm Al, the mean photon energy is about 40 keV. Slide 22 fchs.ac.ae  Image details? Beam Conditioning Low energy photons contribute a large dose to the patient, but do not contribute to the image All diagnostic x-ray systems are required to be filtered (minimum of 1.5 mm Al) to remove non-diagnostic low energy photons Higher Z filters cause more A ‘well-conditioned’ beam has little spectral beam hardening due to change as more filtration is added (the HVL increased density and more becomes nearly constant as the beam is more monochromatic) interactions  Z3/E3 Slide 23 fchs.ac.ae Summary Check you can satisfy the learning outcomes for this lecture Go over calculations/exercises undertaken during the lecture Make sure you can define/describe the following terms: the two interactions of x-ray that affect the image the Z dependence of these interactions the E dependence of these interactions linear attenuation coefficient mass attenuation coefficient HVL and TVL, and how these are measured Slide 24 fchs.ac.ae