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 _at_ 27 keV, 2 _at_ 32 keV, 2 at 39 keV, ...

4
Beam Characteristics

• Intensity
• weighted product of number and energy of photons
• depends on
• quantity
• quality

324 mR








5
Beam Intensity

• Can be measured in terms of of ions created in
  air by beam
• Valid for monochromatic or for polychromatic beam

324 mR
-


6
Monochromatic Radiation

• 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

Monochromatic radiation beam
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)

No
N
x
Monochromatic radiation beam
9
Linear Attenuation Coef.
Larger Coefficient More Attenuation

• 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

N No e - m x
Monochromatic radiation beam
10
Linear Mass Attenuation Coefficient

• coefficient (m)
• Linear atten. Coef.
• 1 / cm
• absorber thickness(x)
• linear
• cm

• coefficient (m)
• Mass atten. Coef.
• cm 2 / g linear atten. coef. / density
• absorber thickness(x)
• mass
• g / cm2 linear distance X density

N No e -mx
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

• Lets graph the attenuation of a monochromatic
  x-ray beam vs. attenuator thickness

60 removed 40 remain
Monochromatic radiation beam
13
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
14
Polychromatic Radiation

• 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)
N No e -mx

• 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
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

1
.1
Fraction Transmitted
Polychromatic
.01
Monochromatic
.001
Attenuator Thickness
20
Photoelectric vs. Compton

• Fractional contribution of each determined by
• photon energy
• atomic number of absorber
• Equation
• m mcoherent mPE mCompton

Small
21
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

22
Photoelectric vs. Compton
m mcoherent mPE mCompton

• As atomic increases
• Fraction of m that is PE increases
• Fraction of m that is Compton decreases

23
Interaction Probability
Photoelectric
Atomic Number of Absorber
Pair Production
Compton
Photon Energy

• PE dominates for very low energies

24
Interaction Probability
Photoelectric
Atomic Number of Absorber
Pair Production
Compton
Photon Energy

• For lower atomic numbers
• Compton dominates for high energies

25
Interaction Probability
Atomic Number of Absorber
Photon Energy

• For high atomic absorbers
• PE dominates throughout diagnostic energy range

26
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

27
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

28
Applications

• As photon energy increases
• subject (and image) contrast decreases
• differential absorption decreases
• at 20 keV bones linear attenuation coefficient 6
  X waters
• at 100 keV bones linear attenuation coefficient
  1.4 X waters

29
Applications

• At low x-ray energies
• attenuation differences between bone soft
  tissue primarily caused by photoelectric effect
• related to atomic number density

30
Applications

• At high x-ray energies
• attenuation differences between bone soft
  tissue primarily because of Compton scatter
• related entirely to density

31
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

32
K-Edge

• Each electron shell has threshold for PE effect
• Photon energy must be gt binding energy of
  electron shell
• For photon energy gt K-shell binding energy
• k-shell electrons are candidates for PE
• PE interactions increase as photon energy exceeds
  k-shell binding energy

33
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
34
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

35
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

36
Abdominal Photons

• 1 of incident photons on adult abdomen reach
  film
• fate of the other 99
• mostly scatter
• most do not reach film
• absorption

37
Scatter Factors

• Factors affecting scatter
• field size
• thickness of body part
• kVp

An increase in any of above increases scatter.
38
Scatter Field Size

• Reducing field size causes significant reduction
  in scatter radiation

39
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

40
Thickness Scatter

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

41
kVp Scatter

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

42
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

43
Scatter Control TechniquesGrid

• directional filter for photons
• Increases patient dose

44
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
45
Scatter Control TechniquesAir 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
AirGap
Patient
Grid
FilmCassette