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

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

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

4. Beam Characteristics ~ ~ ~ ~ ~ ~ ~ ~ Intensity 324 mR
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 STP
1 C ~ ×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. 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

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. Monochromatic radiation beam
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
N = No e - m x
Units:
1 / cm ( or 1 / distance)
Note: Same equation as used for radioactive decay
Monochromatic radiation beam

12. Linear Attenuation Coef. Properties
N = No e - m x
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
Monochromatic radiation beam

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

17. 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

18. 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
Higher
Energy
Lower

19. Monochromatic radiation beam
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. 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
Photon Energy
Interaction
Probability
Compton
Photoelectric

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

34. Applications At high x-ray energies
Photo-
electric
Compton
Pair
Production
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
****
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 energy SO
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 An increase in any of above increases scatter.
Factors affecting scatter
field size
thickness of body part
kVp
An increase in any of above increases scatter.

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

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 Increasing kVp
field size
thickness
Increasing kVp
increases scatter
more photons scatter in forward direction

46. Scatter Management Reduce scatter by minimizing field size thickness
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. 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 X
Film
Film

49. 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)
Grid
Air Gap
Patient
Patient
Air Gap
Grid
Image Receptor