Resident Physics LecturesChristensen, Chapter 5

AttenuationAttenuation

George DavidAssociate ProfessorMedical College of GeorgiaDepartment of Radiology

Beam CharacteristicsQuantity

number of photons in beam

~

~ ~

~

~1, 2, 3, ...

Beam CharacteristicsQuality

energy distribution of photons in beam

~

~

1 @ 27 keV, 2 @ 32 keV, 2 at 39 keV, ...

~

~

~

~

~

~

10 20 30 40 50 60 70 80

Energy

Energy Spectrum

Beam CharacteristicsIntensity

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 IntensityCan be measured in terms of # of ions created in air

by beamValid for monochromatic or for polychromatic beam

324 mR

Monochromatic Radiation(Mono-energetic)

RadioisotopeNot x-ray beam

all photons in beam have same energy

attenuation results in Change in beam quantityno change in beam quality

# of photons & total energy of beam changes by same fraction

Attenuation CoefficientParameter indicating fraction of

radiation attenuated by a given absorber thickness

Attenuation Coefficient is function ofabsorberphoton energy

Linear Attenuation Coef.Why called linear?

distance expressed in linear dimension “x”Formula

N = No e -x

where

No = number of incident photons

N = number of transmitted photons

e = base of natural logarithm (2.718…)

= linear attenuation coefficient (1/cm); property of

energy

material

x = absorber thickness (cm)

No

N

x

If x=0 (no absorber)Formula

N = No e -x

where

No = number of incident photons

N = number of transmitted photons

e = base of natural logarithm (2.718…)

= linear attenuation coefficient (1/cm); property of

energy

material

x = absorber thickness (cm)

No

N

X=0

N = No

Linear Attenuation Coef.

Units:1 / cm ( or 1 / distance)

Note: Same equation as used for radioactive decay

N = No e - x

Larger Coefficient = More Attenuation

Linear Attenuation Coef. Properties

reciprocal of absorber thickness that reduces beam intensity by e (~2.718…)63% reduction37% of original intensity remaining

as energy increasespenetration increases / attenuation

decreasesNeed more distance for same

attenuationlinear attenuation coefficient decreases

N = No e - x

Linear vs Mass Attenuation Coefficient

Units: 1 / cmabsorber

thickness: cm

N = No e -x

• Units: cm 2 / g

• {linear atten. coef. / density}

• absorber thickness: g / cm2

• {linear distance X density}

Linear Mass

Mass Attenuation Coef.

Mass attenuation coefficient = linear attenuation coefficient divided by densitynormalizes for densityexpresses attenuation of a material

independent of physical stateNotes

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

Attenuator Thickness

Fraction(also fraction of

energy)Remaining or Transmitted

1

.1

.01

.001

1 2 3 4 5

Polychromatic Radiation(Poly-energetic)

X-Ray beam contains spectrum of photon energieshighest energy = peak kilovoltage applied to tubemean energy 1/3 - 1/2 of peak

depends on filtration

X-Ray Beam Attenuation

reduction in beam intensity byabsorption (photoelectric)deflection (scattering)

Attenuation alters beamquantityquality

higher fraction of low energy photons removed

Beam HardeningBeam Hardening

HigherEnergy

LowerEnergy

N = No e -x HVL = .693 /

Half Value Layer (HVL)

absorber thickness that reduces beam intensity by exactly half

Units of thicknessvalue of “x” which makes N equal to No / 2

Half Value Layer (HVL)

Indication of beam qualityValid concept for all beam

typesMono-energeticPoly-energetic

Higher HVL meansmore penetrating beam lower attenuation coefficient

Factors Affecting Attenuation

Energy of radiation / beam qualityhigher energy

more penetration less attenuation

Matterdensityatomic numberelectrons per gramhigher density, atomic number, or electrons

per gram increases attenuation

Polychromatic AttenuationYields curved line on semi-log graph

line straightens with increasing attenuationslope approaches that of monochromatic beam

at peak energymean energy increases with attenuation

beam hardeningbeam hardening

Attenuator Thickness

1

.1

.01

.001

FractionTransmitted

Monochromatic

Polychromatic

Photoelectric vs. Compton

Fractional contribution of each determined byphoton energyatomic number of absorber

Equation

= coherent + PE + Compton

Small

Attenuation & Density

Attenuation proportional to densitydifference in tissue densities accounts

for much of optical density difference seen radiographs

# of Compton interactions depends on electrons / unit pathwhich depends on

electrons per gram density

Photoelectric EffectInteraction much more likely for

low energy photonshigh atomic number elements

1P.E. ~ ----------- energy3

P.E. ~ Z3

Photoelectric vs. Compton

As photon energy increasesBoth PE &

Compton decreasePE decreases

faster Fraction of that

is Compton increases

Fraction of that is PE decreases

= coherent + PE + Compton

Photon Energy

InteractionProbability

Compton

Photoelectric

Photoelectric vs. Compton

As atomic # increasesFraction of that is PE increasesFraction of that is Compton decreases

= coherent + PE + Compton

Photoelectric

Compton

PairProduction

Photon Energy

AtomicNumber of Absorber

• PE dominates for very low energies

Photoelectric

Compton

PairProduction

Photon Energy

AtomicNumber of Absorber

• For lower atomic numbers– Compton dominates for high energies

Photoelectric

Compton

PairProduction

Photon Energy

AtomicNumber of Absorber

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

RelationshipsDensity generally increases with atomic

#different states = different density

ice, water, steamno relationship between density and

electrons per gramatomic # vs. electrons / gram

hydrogen ~ 2X electrons / gram as most other substances

as atomic # increases, electrons / gram decreases slightly

ApplicationsAs photon energy increases

subject (and image) contrast decreasesdifferential 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

0102030405060708090

100

20 keV 100 ke

Bone

Water

Applications

At low x-ray energiesattenuation differences between bone & soft

tissue primarily caused by photoelectric effect related to atomic number & density

Photo-electric

Compton

PairProduction

Applications

At high x-ray energiesattenuation differences between bone & soft

tissue primarily because of Compton scatter related entirely to density

Photo-electric

Compton

PairProduction

Photoelectric EffectExiting 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

Electron outPhoton in

M to L

L to K-

****

K-EdgeEach electron shell has threshold for PE

effectPhoton energy must be >= binding energy

of shell For photon energy > K-shell binding energy, k-

shell electrons become candidates for PEPE probability falls off drastically with

energySO

PE interactions generally decrease but increase as photon energy exceeds shell binding energies

1P.E. ~ ----------- energy3

K-Edgestep increase in attenuation at k-edge energy

K-shell electrons become available for interaction

exception to rule of decreasing attenuation with increasing energy

Energy

LinearAttenuationCoefficient

K-Edge SignificanceK-edge energy insignificantly

low for low Z materials k-edge energy in diagnostic

range for high Z materialshigher attenuation above k-

edge useful incontrast agentsrare earth screensMammography beam filters

Scatter RadiationNO Socially Redeeming Qualities

no useful information on imagedetracts from film qualityexposes personnel, public

represents 50-90% of photons exiting patient

Abdominal Photons~1% of incident photons on adult abdomen

reach filmfate of the other 99%

mostly scatter most do not reach film

absorption

Scatter FactorsFactors affecting scatter

field sizethickness of body partkVp

Factors affecting scatterfield sizethickness of body partkVp

An increase in any of above increases scatter.

Scatter & Field SizeReducing field size causes significant

reduction in scatter radiation

IITube

X-RayTube

IITube

X-RayTube

Field Size & ScatterField Size & thickness determine volume

of irradiated tissueScatter 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 reachedscatter photons produced far from filmshielded within body

kVp & Scatter

kVp has less effect on scatter than thanfield sizethickness

Increasing kVp increases scattermore photons scatter in forward direction

Scatter Management

Reduce scatter by minimizingfield size

within limits of examthickness

mammography compressionkVp

but low kVp increases patient dose in practice we maximize kVp

Scatter Control Techniques:Grid

directional filter for photonsIncreases patient dose

Angle of Escapeangle over which scattered radiation

misses primary fieldescape angle larger for

small fields larger distances from film

X

Film

X

Film

Larger Angle of Escape

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)

Patient

Patient

Grid

ImageReceptor

AirGap