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Physics Board Review X-Ray Attenuation Interactions of x-rays with matter

Physics Board Review X-Ray Attenuation Interactions of x-rays with matter. Norbert Pelc. Department of Radiology Stanford University School of Medicine. Department of Radiology. Attenuation. X-Rays can be: absorbed – incident photon energy is absorbed

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Physics Board Review X-Ray Attenuation Interactions of x-rays with matter

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  1. Physics Board ReviewX-Ray Attenuation Interactions of x-rays with matter Norbert Pelc Department of Radiology Stanford University School of Medicine

  2. Department of Radiology Attenuation • X-Rays can be: • absorbed – incident photon energy is absorbed • scattered – photon changes direction and may lose some energy • Attenuation • “removal” of a photon from the incident (primary) beam. • scattered photons are “attenuated” although they are still around.

  3. I Io Department of Radiology Attenuation For monoenergetic photons, I=Ioe-μt I = intensity transmitted (not attenuated) Io = incident intensity t = absorber thickness μ = linear attenuation coefficient of the material t Attenuation coefficient μ depends photon energy depend on material (chemical composition and density) units of (1/distance), e.g. cm-1 if x is in cm probability of attenuation per unit path traveled multiple interaction mechanisms – components add slope = -  μ = μpe + μc + μr + …

  4. Department of Radiology Photoelectric effect • photon of energy E is absorbed • bound electron (Eb) is emitted (photoelectron) • E must be ≥ Eb • photoelectron kinetic energy is E - Eb • photoelectron slows by ionizing other atoms (delivering dose) • electronic vacancy results in: • Auger (pronounced like OJ) electron • emission (most likely at Z < 33), or • characteristic x-rays (might escape for very high Z) • most of the photon energy produces local dose (1) incident photon is absorbed (2) electron is ejected (photoelectron) (3) higher shell electron fills the vacancy Excess energy shows up as (4) characteristic x-ray, or (5) Auger electron

  5. Photoelectric effect probability: μpe Department of Radiology • increases rapidly at each electron binding energy (absorption edge, e.g. K-edge) • proportional to 1/E3 (between edges) • proportional to Z3 (for same electron shell) • an element is relatively transparent to its own characteristic x-rays

  6. E Esc = 1 + {E (keV)/511}{1 - cos()} Department of Radiology Compton scattering • elastic collision between incident photon and free (or loosely bound) electron • photon changes direction and loses some energy • lost energy carried away by Compton electron => dose • least for “forward” scatter • most in “backward” scatter • Probability (μc): • proportional to electron density (electrons/cc) • since Z/A~1/2 for most elements, • ~proportional to density • exception is Hydrogen • decreases with increasing energy energy E energy Esc (1) incident photon (2) interacts with loosely bound electron (3) scattered photon loses energy (4) electron is ionized and receives kinetic energy

  7. Coherent (Raleigh) scattering Department of Radiology • photon changes direction slightly but loses no energy • probability (μr): • decreases as 1/E2 • increases with Z2 • never dominant (<10%) in the diagnostic energy range (same energy)

  8. Department of Radiology Other Interactions • Pair production • Photon is absorbed • 1.02 MeV used to create electron-positron pair • electron-positron pair split remaining energy (E-1.02 MeV) • E must be ≥ 1.02 MeV • Photodisintegration • photo-nuclear interactions • photon is absorbed • nuclear particles are released • very high energy photons

  9. Department of Radiology Relative importance of interaction mechanisms μ = μpe + μc + μr + … Photoelectric absorption dominates E ≤ 25 keV (mammography), all tissues Z ≥ 20, all energies in the diagnostic range Compton effect dominates when photoelectric effect doesn’t soft tissue, E>25 keV lots of scattered photons

  10. Department of Radiology More on attenuation • Mass Attenuation Coefficient: μ/ρ • I = Ioe-μt = Ioe-(μ/ρ)(tρ) • ρ is density, g/cm3 • μ/ρ usually in units of cm2/g • tρ (g/cm2) is the mass of material traversed per unit area • characterizes attenuation behavior independent of density • Molecules and mixtures • constituent elements contribute α fraction by weight • high Z constituents dominate

  11. Attenuation vs. absorption Department of Radiology Attenuation absorption or scattering μμρ Absorption μenμenρ fraction of beam energy absorbed per unit distance (or mass) μen <μ

  12. Department of Radiology More on attenuation • HVL and TVL • Half Value Layer (HVL), typically in cm • Attenuates half the protons • HVL = 0.693/μ • Two HVLs transmit ¼, three transmit 1/8, etc. • Tenth Value Layer (TVL), typically in cm • Attenuates 90% (transmits 10%) of the photons • HVL = 2.3/μ • two TVLs transmit 1%, three transmit 0.1%, etc. • e.g. at 50 keV, μwater~0.2 cm-1, HVL~3 cm, TVL~10 cm • transmission through 10 cm (lung) ~10% • transmission through >20 cm (abdomen) <1% • lots of scattered photons

  13. More on attenuation Department of Radiology • Polychromatic (polyenergetic) beams • beam becomes progressively more penetrating (harder) in the material • generally, average energy increases with increasing depth • HVL and TVL increase with increasing depth

  14. Department of Radiology More on Attenuation Linear Attenuation Coefficient (μ in cm-1), Half Value Layer (HVL in cm), Tenth Value Layer (TVL in cm) for muscle, bone and lead

  15. ln(I) c a b t Q1: In the figure, which plot is intensity of a 100 keV beam as a function of depth Q2: In the figure, which plot is intensity of a 100 kVp beam as a function of depth Q3: Which doesn’t contribute to patient dose? a. Coherent scattering b. Compton scattering c. Characteristic radiation adapted from recalls

  16. Q4: A 100 keV photon interacts via Compton scattering. The energy of the scattered photon: a. is 100 keV b. is 50 keV c. decreases with increasing scattering angle Q5: A 100 keV photon interacts via Compton scattering. The energy of the Compton electron a. is 100 keV b. is 50 keV c. decreases with increasing scattering angle d. is 100 keV minus the energy of the scattered photon adapted from 2004 recalls

  17. Q6: At 100 keV, what is the dominant interaction mechanism in tissue? a. photoelectric absorption b. Compton scattering c. Coherent scattering Q7: When 100 keV x-rays interact in tissue, what particles produce most of the ionizations: a. photoelectrons b. Compton scattered photons c. Compton recoil electrons Q8: When 40 keV x-rays interact in tissue, what particles produce most of the ionizations: a. photoelectrons b. Compton scattered photons c. Compton recoil electrons adapted from 2008 recalls

  18. Q9: A 20 cm thick patient is imaged with 50 keV x-rays. The fraction of the primary beam remaining midway through the patient is a. 50%, b. 10%, c. 1% Q10: A 20 cm thick patient is imaged with 50 keV x-rays. The fraction of the primary beam transmitted through the patient is a. 50%, b. 10%, c. 1% adapted from 2008 recalls

  19. Q11: In CT, the reconstructed image values (HU) are proportional to: a. effective atomic number b. electron density c. linear attenuation coefficient d. half value layer Q12: In a non-contrast CT, image contrast among soft tissues depends most strongly on: a. effective atomic number b. electron density c. mAs adapted from 2008 recalls

  20. Q13: The kinetic energy of a 100 keV electron is: a. <0.1 MeV between 0.1 and 0.255 MeV between 0.255 and 0.511 MeV > 0.511 MeV Q14: The linear attenuation coefficient can be best described as a. the probability of x-ray absorption b. the fractional attenuation per unit thickness traveled c. the average distance a photon travels before interacting d. the probability the beam will scatter in 1 cm of material e. 1/HVL adapted from 2004 recalls

  21. Q15: In a photoelectric absorption event: a. all of the incident energy is transferred to an electron b. characteristic x-rays can be produced c. Auger electrons can be produced d. the energy of the electron is related to its angle e. a, b, and c f. b and c Q16: In a Compton scattering event: a. all of the incident energy is transferred to an electron b. characteristic x-rays can be produced c. Auger electrons can be produced d. the energy of the electron is related to its angle e. a, b, and c f. b and c adapted from old recalls

  22. Q17: In a typical x-ray beam the second HVL ___ than the first HVL a. is always greater than b. is always less than c. is equal to d. may be greater than or less than Q18: Contrast between bone and soft tissue in a diagnostic radiograph is primarily due to a. Compton scattering b. pair production c. photoelectric absorption d. Coherent scattering Q19: Carbon (Z=6, A=12) is __ times more likely than hydrogen (Z=1, A=1) to undergo photoelectric absorption a. 216, b. 144, c. 36, d. 1/6, e. 1/36 2004 Raphex

  23. Q20: A photoelectric interaction occurs involving a 9 keV photon and the K shell of an atom. A 4 keV electron is observed. The binding energy of the K shell a. is 4 keV b. is 5 keV c. is 9 keV d. is 13 keV e. cannot be estimated from the data given Q21: Pair production can occur at which photon energy? 0.1 MeV, b. 0.5 MeV, c. 1 MeV, d. 1.5 MeV Q22: A 3 MeV photon interacts by pair production. The combined kinetic energies of the electron-positron pair is: a. 1.02 MeV, b. 1.98 MeV, c. 2.04 MeV, d. 3 MeV 2004 Raphex

  24. Q23: At what angle does Compton scattered photon retain more of initial energy? a. 10 degrees b. 30 degrees c. 90 degrees d. 180 degrees Q24: A photon of energy E interacts via photoelectric absorption and releases a K-shell electron. An M-shell electron fills the vacancy. Then an Auger electron is released from the M-shell. The binding energies of the K, L, and M shells are EK, EL, and EM. What is the kinetic energy of the Auger electron? a. E-EM b. EK-EM c. EK-2EM d. 2EK-EM adapted from recalls

  25. Answers Q1: b Q2: a Q3: a Q4: c Q5: d Q6: b Q7: c Q8: a Q9: b Q10: c Q11: c Q12: b Q13: a Q14: b Q15: f Q16: d Q17: a Q18: c Q19: a Q20: b Q21: d Q22: b Q23: a Q24: c

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