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1. Resident Physics Lectures Christensen, Chapter 5
Attenuation
2. Beam Characteristics Quantity
number of photons in beam
3. Beam Characteristics Quality
energy distribution of photons in beam
4. Beam Characteristics Intensity
weighted product of number and energy of photons
depends on
quantity
quality
5. Beam Intensity Can be measured in terms of # of ions created in air by beam
Valid for monochromatic or for polychromatic beam
6. Monochromatic Radiation (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
7. Attenuation Coefficient Parameter indicating fraction of radiation attenuated by a given absorber thickness
Attenuation Coefficient is function of
absorber
photon energy
8. 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)
9. Linear Attenuation Coef. Units:
1 / cm ( or 1 / distance)
Properties
reciprocal of absorber thickness that reduces beam intensity by e (~2.718…)
~63% reduction
37% of original intensity remaining
as photon beam energy increases
penetration increases / attenuation decreases
attenuating distance increases
linear attenuation coefficient decreases
Note: Same equation as used for radioactive decay
10. Linear & Mass Attenuation Coefficient coefficient (m)
Linear atten. Coef.
1 / cm
absorber thickness(x)
linear
cm
11. 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 may be more useful in radiology
12. Monochromatic Radiation Let’s graph the attenuation of a monochromatic x-ray beam vs. attenuator thickness
13. Monochromatic Radiation Yields straight line on semi-log graph
14. Polychromatic Radiation (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
15. 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
16. 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
17. 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
18. 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
19. Polychromatic Attenuation Yields curved line on semi-log graph
line straightens with increasing attenuation
slope approaches that of monochromatic beam at the peak energy
mean energy increases with attenuation
beam hardening
20. Photoelectric vs. Compton Fractional contribution of each determined by
photon energy
atomic number of absorber
Equation
m = mcoherent + mPE + mCompton
21. 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
22. Photoelectric Effect Interaction much more likely for
low energy photons
high atomic number elements
23. Photoelectric vs. Compton 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
24. Photoelectric vs. Compton As atomic # increases
Fraction of m that is PE increases
Fraction of m that is Compton decreases
25. Interaction Probability
26. Interaction Probability
27. Interaction Probability
28. 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
29. 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
30. Applications At low x-ray energies
attenuation differences between bone & soft tissue primarily caused by photoelectric effect
related to atomic number & density
31. Applications At high x-ray energies
attenuation differences between bone & soft tissue primarily because of Compton scatter
related entirely to density
32. Applications Difference between water & fat only visible at low energies
effective atomic # of water slightly higher
yields photoelectric difference
electrons / cm almost equal
No Compton difference
Photoelectric dominates at low energy
33. 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
34. 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 energy SO
PE interactions generally decrease but increase as photon energy exceeds shell binding energies
35. 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
36. 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
37. 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
38. Abdominal Photons ~1% of incident photons on adult abdomen reach film
fate of the other 99%
mostly scatter
most do not reach film
absorption
39. Scatter Factors Factors affecting scatter
field size
thickness of body part
kVp
40. Scatter & Field Size Reducing field size causes significant reduction in scatter radiation One of the most effective ways of minimizing operator exposure is to reduce field size through collimation. Even a relatively small reduction in field size can often result in a substantial reduction in operator exposure. This occurs for two reasons. The first is that a smaller beam irradiates a less volume of tissue so that there is less tissue to act as a scatter radiation source. Secondly reducing beam size means that scatter radiation must travel further through the patient before exiting. The increased travel distance means a less intense scatter field for the operator. A fluoroscopist should always collimate the x-ray beam to a size no larger than is required clinically.One of the most effective ways of minimizing operator exposure is to reduce field size through collimation. Even a relatively small reduction in field size can often result in a substantial reduction in operator exposure. This occurs for two reasons. The first is that a smaller beam irradiates a less volume of tissue so that there is less tissue to act as a scatter radiation source. Secondly reducing beam size means that scatter radiation must travel further through the patient before exiting. The increased travel distance means a less intense scatter field for the operator. A fluoroscopist should always collimate the x-ray beam to a size no larger than is required clinically.
41. 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
42. Thickness & Scatter Increasing patient thickness leads to increased scatter but
saturation point reached
scatter photons produced far from film
shielded within body
43. kVp & Scatter kVp has less effect on scatter than than
field size
thickness
Increasing kVp
increases scatter
more photons scatter in forward direction
44. 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
45. Scatter Control Techniques: Grid directional filter for photons
Increases patient dose
46. Angle of Escape angle over which scattered radiation misses primary field
escape angle larger for
small fields
larger distances from film
47. Scatter Control Techniques: Air Gap Gap intentionally left between patient & image receptor
Natural result of magnification radiography
Grid not used
(covered in detail in chapter 8)