Resident Physics Lectures

1. Resident Physics Lectures • Christensen, Chapter 5 Attenuation George David Associate Professor Medical College of Georgia Department of Radiology

2. Beam Characteristics • Quantity • number of photons in beam 1, 2, 3, ... ~ ~ ~ ~ ~

3. ~ ~ ~ ~ ~ ~ ~ Beam Characteristics • Quality • energy distribution of photons in beam 1 @ 27 keV, 2 @ 32 keV, 2 at 39 keV, ... ~

4. 324 mR Beam Characteristics ~ • Intensity • weighted product of # & energy of photons • depends on • quantity • quality ~ ~ ~ ~ ~ ~ ~

5. So what’s a Roentgen? • Unit of measurement for amount of ionizing radiation that produces 2.58 x 10-4 Coulomb/kg of air @ STP • 1 C ~ 6.241509324×1018 electrons

6. Beam Intensity • Can be measured in terms of # of ions created in air by beam • Valid for monochromatic or for polychromatic beam 324 mR

7. MonochromaticRadiation(Mono-energetic) • Radioisotope • Not x-ray beam • all photons in beam have same energy • attenuation results in • Change in beam quantity • no change in beam quality • # of photons & total energy of beam changes by same fraction

8. Attenuation Coefficient • Parameter indicating fraction of radiation attenuated by a given absorber thickness • Attenuation Coefficient is function of • absorber • photon energy Monochromatic radiation beam

9. Linear Attenuation Coef. • Why called linear? • distance expressed in linear dimension “x” • Formula N = No e -mx where No = number of incident photons N = number of transmitted photons e = base of natural logarithm (2.718…) m = linear attenuation coefficient (1/cm); property of energy material x = absorber thickness (cm) • No • N x Monochromatic radiation beam

10. If x=0 (no absorber) • Formula N = No e -mx where No = number of incident photons N = number of transmitted photons e = base of natural logarithm (2.718…) m = linear attenuation coefficient (1/cm); property of energy material x = absorber thickness (cm) • N = No • No • N X=0 Monochromatic radiation beam

11. Linear Attenuation Coef. Larger Coefficient = More Attenuation • Units: 1 / cm ( or 1 / distance) • Note: Same equation as used for radioactive decay • N = No e - m x Monochromatic radiation beam

12. Linear Attenuation Coef. Properties • reciprocal of absorber thickness that reduces beam intensity by e (~2.718…) • 63% reduction • 37% of original intensity remaining • as energy increases • penetration increases / attenuation decreases • Need more distance for same attenuation • linear attenuation coefficient decreases • N = No e - m x Monochromatic radiation beam

13. Linear vsMass Attenuation Coefficient Linear Mass • Units: 1 / cm • absorber thickness: cm • Units: cm 2 / g • {linear atten. coef. / density} • absorber thickness: g / cm2 • {linear distance X density} • N = No e -mx

14. Mass Attenuation Coef. • Mass attenuation coefficient = linear attenuation coefficient divided by density • normalizes for density • expresses attenuation of a material independent of physical state • Notes • references often give mass attenuation coef. • linear more useful in radiology

15. Monochromatic Radiation • Let’s graph the attenuation of a monochromatic x-ray beam vs. attenuator thickness 60% removed 40% remain Monochromatic radiation beam

16. 1 .1 .01 .001 Monochromatic Radiation • Yields straight line on semi-log graph Fraction (also fraction of energy) Remaining or Transmitted 1 2 3 4 5 Attenuator Thickness Monochromatic radiation beam

17. PolychromaticRadiation(Poly-energetic) • X-Ray beam contains spectrum of photon energies • highest energy = peak kilovoltage applied to tube • mean energy 1/3 - 1/2 of peak • depends on filtration

18. Higher Energy Lower Energy X-Ray Beam Attenuation • reduction in beam intensity by • absorption (photoelectric) • deflection (scattering) • Attenuation alters beam • quantity • quality • higher fraction of low energy photons removed • Beam Hardening

19. Half Value Layer (HVL) • absorber thickness that reduces beam intensity by exactly half • Units of thickness • value of “x” which makes N equal to No / 2 • HVL = .693 / m N = No e -mx Monochromatic radiation beam

20. Half Value Layer (HVL) • Indication of beam quality • Valid concept for all beam types • Mono-energetic • Poly-energetic • Higher HVL means • more penetrating beam • lower attenuation coefficient

21. Factors Affecting Attenuation • Energy of radiation / beam quality • higher energy • more penetration • less attenuation • Matter • density • atomic number • electrons per gram • higher density, atomic number, or electrons per gram increases attenuation

22. Polychromatic Attenuation • Yields curved line on semi-log graph • line straightens with increasing attenuation • slope approaches that of monochromatic beam at peak energy • mean energy increases with attenuation • beam hardening 1 .1 Polychromatic Fraction Transmitted .01 Monochromatic .001 Attenuator Thickness

23. Photoelectric vs. Compton • Fractional contribution of each determined by • photon energy • atomic number of absorber • Equation m = mcoherent + mPE + mCompton Small

24. Attenuation & Density • Attenuation proportional to density • difference in tissue densities accounts for much of optical density difference seen radiographs • # of Compton interactions depends on electrons / unit path • which depends on • electrons per gram • density

25. Photoelectric Effect • Interaction much more likely for • low energy photons • high atomic number elements 1 P.E. ~ ----------- energy3 P.E. ~ Z3

26. Interaction Probability Compton Photoelectric Photon Energy Photoelectric vs. Compton m = mcoherent + mPE + mCompton • As photon energy increases • Both PE & Compton decrease • PE decreases faster • Fraction of m that is Compton increases • Fraction of m that is PE decreases

27. Photoelectric vs. Compton m = mcoherent + mPE + mCompton • As atomic # increases • Fraction of m that is PE increases • Fraction of m that is Compton decreases

28. Interaction Probability Photoelectric Atomic Number of Absorber Pair Production Compton Photon Energy • PE dominates for very low energies

29. Interaction Probability Photoelectric Atomic Number of Absorber Pair Production Compton Photon Energy • For lower atomic numbers • Compton dominates for high energies

30. Photoelectric Pair Production Compton Interaction Probability Atomic Number of Absorber Photon Energy • For high atomic # absorbers • PE dominates throughout diagnostic energy range

31. Relationships • Density generally increases with atomic # • different states = different density • ice, water, steam • no relationship between density and electrons per gram • atomic # vs. electrons / gram • hydrogen ~ 2X electrons / gram as most other substances • as atomic # increases, electrons / gram decreases slightly

32. Applications • As photon energy increases • subject (and image) contrast decreases • differential absorption decreases • at 20 keV bone’s linear attenuation coefficient 6 X water’s • at 100 keV bone’s linear attenuation coefficient 1.4 X water’s

33. Photo- electric Pair Production Compton Applications • At low x-ray energies • attenuation differences between bone & soft tissue primarily caused by photoelectric effect • related to atomic number & density

34. Photo- electric Pair Production Compton Applications • At high x-ray energies • attenuation differences between bone & soft tissue primarily because of Compton scatter • related entirely to density

35. **** Photoelectric Effect • Exiting electron kinetic energy • incident energy - electron’s binding energy • electrons in higher energy shells cascade down to fill energy void of inner shell • characteristic radiation M to L Electron out Photon in - L to K

36. K-Edge • Each electron shell has threshold for PE effect • Photon energy must be >= binding energy of shell • For photon energy > K-shell binding energy, k-shell electrons become candidates for PE • PE probability falls off drastically with energySO • PE interactions generally decrease but increase as photon energy exceeds shell binding energies 1 P.E. ~ ----------- energy3

37. K-Edge • step increase in attenuation at k-edge energy • K-shell electrons become available for interaction • exception to rule of decreasing attenuation with increasing energy Linear Attenuation Coefficient Energy

38. K-Edge Significance • K-edge energy insignificantly low for low Z materials • k-edge energy in diagnostic range for high Z materials • higher attenuation above k-edge useful in • contrast agents • rare earth screens • Mammography beam filters

39. Scatter Radiation • NO Socially Redeeming Qualities • no useful information on image • detracts from film quality • exposes personnel, public • represents 50-90% of photons exiting patient

40. Abdominal Photons • ~1% of incident photons on adult abdomen reach film • fate of the other 99% • mostly scatter • most do not reach film • absorption

41. Scatter Factors • Factors affecting scatter • field size • thickness of body part • kVp An increase in any of above increases scatter.

42. II Tube II Tube X-Ray Tube X-Ray Tube Scatter & Field Size • Reducing field size causes significant reduction in scatter radiation

43. Field Size & Scatter • Field Size & thickness determine volume of irradiated tissue • Scatter increase with increasing field size • initially large increase in scatter with increasing field size • saturation reached (at ~ 12 X 12 inch field) • further field size increase does not increase scatter reaching film • scatter shielded within patient

44. Thickness & Scatter • Increasing patient thickness leads to increased scatter but • saturation point reached • scatter photons produced far from film • shielded within body

45. kVp & Scatter • kVp has less effect on scatter than than • field size • thickness • Increasing kVp • increases scatter • more photons scatter in forward direction

46. Scatter Management • Reduce scatter by minimizing • field size • within limits of exam • thickness • mammography compression • kVp • but low kVp increases patient dose • in practice we maximize kVp

47. Scatter Control Techniques:Grid • directional filter for photons • Increases patient dose

48. X Angle of Escape • angle over which scattered radiation misses primary field • escape angle larger for • small fields • larger distances from film Larger Angle of Escape X Film Film

49. Scatter Control Techniques:Air Gap Grid Air Gap • Gap intentionally left between patient & image receptor • Natural result of magnification radiography • Grid not used • (covered in detail in chapter 8) Patient AirGap Patient Grid ImageReceptor