Resident Physics Lectures
 Christensen, Chapter 5
Attenuation
George David
Associate Professor
Medical College of Georgia
Department of Radiology
Beam Characteristics
 Quantity
 number of photons in beam
1, 2, 3, ...
~
~
~
~
~
Beam Characteristics
 Quality
 energy distribution of photons in beam
1 @ 27 keV, 2 @ 32
keV, 2 at 39 keV, ...
~
~
~
~
~
~
Energy Spectrum
~
10
20
30
40
50
Energy
~
60
70
80
Beam Characteristics
 Intensity
 weighted product of #
& energy of photons
 depends on
~


quantity
quality
~
~
~
~
~
~
~
324 mR
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
Beam Intensity
 Can be measured in terms of # of ions created in air
by beam
 Valid for monochromatic or for polychromatic beam
324 mR
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
Attenuation Coefficient
 Parameter indicating fraction of
radiation attenuated by a given
absorber thickness
 Attenuation Coefficient is function of
 absorber
 photon energy
Linear Attenuation Coef.
 Why called linear?
 distance expressed in linear dimension “x”
 Formula
N = No e -mx
where
N = number of incident photons
o
N = number of transmitted photons
e = base of natural logarithm (2.718…)
m = linear attenuation coefficient (1/cm); property of
energy
N
N
o
material
x = absorber thickness (cm)
x
If x=0 (no absorber)
 Formula
N = No e -mx
where
N = No
N = number of incident photons
o
N = number of transmitted photons
e = base of natural logarithm (2.718…)
m = linear attenuation coefficient (1/cm); property of
energy
N
N
o
material
x = absorber thickness (cm)
X=0
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
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
Linear vs Mass Attenuation Coefficient
Linear
 Units: 1 / cm
 absorber
thickness: cm
Mass
• Units: cm 2 / g
• {linear atten. coef. / density}
• absorber thickness: g / cm2
• {linear distance X density}
N = No e -mx
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
Monochromatic Radiation
 Let’s graph the attenuation of a
monochromatic x-ray beam vs. attenuator
thickness
Monochromatic Radiation
Yields straight line on
semi-log graph
1
.1
Fraction
(also fraction of
.01
energy)
Remaining or
Transmitted .001
1
2
3
4
5
Attenuator Thickness
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
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
Lower
Energy
Higher
Energy
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
N = No e -mx
HVL = .693 / m
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
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
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 .01
Transmitted
.001
Monochromatic
Attenuator Thickness
Photoelectric vs. Compton
 Fractional contribution of each
determined by
 photon energy
 atomic number of absorber
 Equation
m = mcoherent + mPE + mCompton
Small
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
Photoelectric Effect
 Interaction much more likely for
 low energy photons
 high atomic number elements
1
P.E. ~ ----------energy3
P.E. ~ Z3
Photoelectric vs. Compton
m = mcoherent + mPE + mCompton
 As photon
energy
increases
 Both PE & Compton
decrease
 PE decreases faster


Interaction
Probability
Fraction of m that is
Compton increases
Fraction of m that is
PE decreases
Compton
Photoelectric
Photon Energy
Photoelectric vs. Compton
m = mcoherent + mPE + mCompton
 As atomic # increases
 Fraction of m that is PE increases
 Fraction of m that is Compton decreases
Interaction Probability
Photoelectric
Atomic
Number of
Absorber
Pair
Production
Compton
Photon Energy
• PE dominates for very low
energies
Interaction Probability
Photoelectric
Atomic
Number of
Absorber
Pair
Production
Compton
Photon Energy
• For lower atomic numbers
– Compton dominates for high energies
Interaction Probability
Photoelectric
Atomic
Number of
Absorber
Pair
Production
Compton
Photon Energy
• For high atomic # absorbers
– PE dominates throughout diagnostic energy range
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
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
100
90
80
70
60
50
40
30
20
10
0
Bone
Water
20 keV
100 ke
Applications
Photoelectric
Pair
Production
Compton
 At low x-ray energies
 attenuation differences between bone & soft tissue
primarily caused by photoelectric effect

related to atomic number & density
Applications
Photoelectric
Pair
Production
Compton
 At high x-ray energies
 attenuation differences between bone & soft tissue
primarily because of Compton scatter

related entirely to density
****
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
Photon in
-
Electron out
L to K
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
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
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
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
Abdominal Photons
 ~1% of incident photons on adult abdomen reach film
 fate of the other 99%
 mostly scatter

most do not reach film
 absorption
Scatter Factors
 Factors affecting scatter
 field size
 thickness of body part
 kVp
An increase in any of above increases
scatter.
Scatter & Field Size
 Reducing field size causes significant
reduction in scatter radiation
II
Tube
II
Tube
X-Ray
Tube
X-Ray
Tube
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
Thickness & Scatter
 Increasing patient thickness leads to increased scatter
but
 saturation point reached
 scatter photons produced far from film
 shielded within body
kVp & Scatter
 kVp has less effect on scatter than
than
 field size
 thickness
 Increasing kVp
 increases scatter
 more photons scatter in forward direction
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
Scatter Control Techniques:
Grid
 directional filter for photons
 Increases patient dose
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
Scatter Control Techniques:
Air Gap
 Gap intentionally
left between
patient & image
receptor
 Natural result of
magnification
radiography
 Grid not used
Patient
Air
Gap
Patient
 (covered in detail in
chapter 8)
Grid
Image
Receptor