basic radiation interactions, definition of dosimetric ... · basic radiation interactions,...

Basic Radiation Interactions,Definition of Dosimetric Quantities,

and Data Sources

J.V. SiebersVirginia Commonwealth University

Richmond, Virginia USA

2009 AAPM Summer School2009 AAPM Summer School

Learning Objectivesg j

T i d d ib th b i f 1. To review and describe the basics of radiation interactions for understanding radiation dosimetry

2 To review definitions of quantities 2. To review definitions of quantities required for understanding radiation dosimetrydosimetry

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Constants Units Conversions

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©JVS: 2009 AAPM SS

ScopeRadiation Types

IonizingIonizingInteractions can remove atomic orbital electrons Non-Ionizing

Particulate ElectromagneticParticulate-electron-positron

Electromagnetic

-proton-neutron- alpha

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p- etc.

Types of ionizing radiationyp g

Di tl i i i di ti Directly ionizing radiation Direct interactions via the Coulomb force along a

particles track Charged particles

electrons positrons

protons protons heavy charged particles

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Direct IonizationCoulombic Interaction

e-Coulombic Interaction

A charged particle exerts exerts electromagnetic forces on atomic Energy transfer can electrons result in the ejection

of an electron (ionization) (ionization)

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Indirectly Ionizing Radiationy g

Uncharged particles that must first transfer energy to a charged particle which can then further ionize matterT t Two step process

ExamplesEl t ti di ti Electromagnetic radiations: x- or γ-rays

Neutrons

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Indirectly Ionizing RadiationPh t l t i Eff tPhotoelectric Effect

e-

Ej t d

hEjected

electrons further ionize ionize matter

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Radiant Energy Rgy

R Total energy excluding rest mass R – Total energy, excluding rest mass, carried by particles Photons: E = hν = hc/λ Electrons + other CPs: kinetic energy T

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Energy imparted ε

ε - Energy impartedR R Q ε - Energy imparted

i l i

in outR R Q Q mass to energy conversion resulting

from interactions or radioactive decayQ

if(m→E), Q>0

inR outRhe-

he-

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if(E→m), Q<0

in in out outc u c uR R R R Q

Dose

GydD

Energy deposited per unit mass

ydm

Energy deposited per unit mass

1 Gy = 1 J/kg

Knowledge of D is the object of dosimetry

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Equilibrium Part 1: R di ti E ilib iRadiation Equilibrium

R Rh

e-

in outR Rh

e- e-hh

e-

R R QQ d Qd RE

in outR R Q Q d QdDdm dm

RERE

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Radiation SourcesS

Radioactive decay Radioactive decay Alpha-decay Beta-decay Electron capture Electron capture Isomeric transitions

Accelerated charged particles Direct Direct X-ray generators

Atomic energy transitionsCharacteristic X rays Characteristic X-rays

Auger electrons Interaction products

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Radioactive Decayy

General balance equationsGeneral balance equationsR R

R R

A A AAZ Z Z ZP D R Q

P D RQ M M M

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Q

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Radioactive Decay

ActivitydNA Ndt

0t

tA A e

1ln 2t

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12

Radioactive Decay α

4 42 2

A AZ ZP D He Q

α ‘s have short range

/ 0

1 1A AZ ZP D Q

0

1 1A AZ ZP D Q

Neutrino ( , ) results in spectrum of energies( ) p g maxE and E are tabulated ( , ) are non-ionizing

Electron Capture 0A AP D Q 01 1

A AZ ZP e D v Q

Can occur when energetically prohibited Followed by characteristic x-rays or Auger electron

Isomeric Transition so e c a s o * 0

0A AZ ZP P Q

decay from meta-stable state Internal Conversion

* 0 0A AP P Q

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0 01 1

A AZ ZP e P e Q

Competes with isomeric transition Results in ejection of atomic electron

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15 15 0 0 1 732O N M V β+ 15 15 0 08 7 1 0 1.732O N MeV

15 0 15 08 1 7 0 1.732O e N MeV Electron

Capture

β+

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8 1 7 0Capture

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Accelerated Charged Particlesg

Di t Direct use Electrons, protons, …

Indirect via production of electromagnetic radiationradiation Synchrotron radiation Bremmstrahlung Bremmstrahlung

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Synchrotron Radiation

hRadiation

Magnetic Field

e-

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Synchrotron image courtesy of http://www-project.slac.stanford.edu/ssrltxrf/spear.htm

Bremmstrahlungbremsh

Bremmstrahlungbrems

e-

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Atomic Energy TransitiongyCharacteristic x-ray

xray h

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Atomic Energy TransitionAuger Electron

e-

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Quantifying Radiation FieldsQ y g

Th f Thus far R ε D

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Radiation Fluence

N is number of particles i h

dN particles crossing sphere surrounding P with cross-sectional area da

2

pda m

sectional area da

Integrated over all directions and energies

Single particle type

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Equivalent definition of fluenceq

l = particle track l l = particle track length through a volume

nTracksl

V

l need not be straight

Volume can be irregularU f l f M t Useful for Monte Carlo applications

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Energy Fluencegy Definition

dR J 2

dR Jda m

Poly-energetic Mono-energetic

da m

E

Diff ti l fl

EE E dE E

Differential energy fluence

E E d dE

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E E d dE

Attenuation

td n dl t

l 0el 1n

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l 0tn

m

Attenuation coefficient l 0e

l

Attenuation coefficient

t th i t ti ( l) f µ represents the interaction (removal) of primaries from the beam

No consideration is given to what occurs as a result of the interaction Secondary particles Energy-to-mass conversion …

To remove density dependence, tabulated as µ/ρ[ 2/ ]

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[cm2/g]

TERMA Total Energy Release per unit MAss

Jkg

TERMA

*

Describes loss of radiant energy from uncharged

kg

primaries as they interact in material Energy lost can be absorbed locally or at a distance

©JVS: 2009 AAPM SS J

kgEE

ETERMA E dE

For poly-energetic spectra*

Aside:Photon InteractionsPhoton Interactions

To understand what happens with the radiant energy removed, understand the interactions(e.g. γ interactions)

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Photon interactions contributing to Photon interactions contributing to µ

-1mRayleigh

σ = Rayleigh + Compton scattering σ = Rayleigh + Compton scattering τ = photo-electric κ = pair production κ = pair production η = photo-nuclear

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Rayleigh Scatteringy g S g

Elastic coherent scattering of the photon by an atomy

Important for low energy photonsC t ib t < 20% t t t l tt ti Contributes < 20% to total attenuation coefficient

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Compton ScatteringCompton Scatteringe-

h

e

h

h 2cmAN Z

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ge A

Comptonp

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Photoelectric EffectPhotoelectric Effect

e-

h b AeT h E T beT h E

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Photo-electric

3 4

2 3Zh

Au

τ increases when τ increases when shell can participate in reactionreaction

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Pair ProductionPair Production

e-

h

+

pairh

e+

22 ee eavailT T T h m c ee eavail

2

diom c

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radiano

T

Triplet ProductionTriplet Production

22avail eT h m c

e-

e- tripleth

e+22h

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223

eh m cT

Photo-nuclear interactions

(γ n) (γ Xn) (γ p) (γ,n), (γ,Xn), (γ,p), …

BE (Binding Energies) result in thresholds >~ 10 MeV

Cross-section is small (η<0.1µ) Neutrons are penetrating

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p g

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Pb attenuation coefficient

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Relative importance of interactionsRelative importance of interactions

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Summary photon interactions

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Energy transferred to charged particlesi t ti

Energy transferred to charged particles per-interaction

general nonrtr in outu u

R R Q photo

u u

= compton pair

==

Averagei

trn

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itr

in

RecallAttenuation coefficient

l 0el

Attenuation coefficient represents the interaction (removal) of µ represents the interaction (removal) of

primaries from the beam No consideration is given to what occurs as a No consideration is given to what occurs as a

result of the interaction Secondary particles Secondary particles Energy-to-mass conversion …

To remove density dependence, tabulated as µ/ρ[cm2/g]

©JVS: 2009 AAPM SS

Mass-energy transfer coefficient

Describes the transfer of energy to charged ti lparticles

tr tr

h

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KERMA Kinetic Energy Release per unit MAss

d trdKERMA Kdm

*Jkg

tr

The transfer of radiant energy from uncharged primaries

to charged particles as they interact in a material

kg

to charged particles as they interact in a material Energy transferred can be absorbed locally or at a distance

©JVS: 2009 AAPM SS *Mono-energetic, integrate for poly-energetic

Net energy transfer

Accounts for portion of kerma is radiated away

nonrnet r rtr tr u in out uu u

R R R R Q r nonr rnettr tr out in out outu u u u

R R R R Q

Te-T’

h

Accounts for portion of kerma is radiated away

bremshvCompton example

h Te-nettr bremse

T hv

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h

Mass energy absorption coefficientMass-energy absorption coefficient

R di ti l f ti Radiative loss fraction g

1nettrg

M b ti ffi i t

1tr

g

Mass-energy absorption coefficient 1en trg

1 g

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Kerma Components

C lli i Kc rK K K

Collision Kermanet

trdK enK

*

Portion of kerma that remains collisional energy losses

cKdm

cK

(non-radiative)

Radiative Kerma Portion of kerma (transported elsewhere) by radiative losses

©JVS: 2009 AAPM SS

Exposure and W Exposure

Hi t i l di ti it Historical radiation unit Ionization density in air

Ckg

dQXdm

Related to air collision kerma by mean energy required to produce an ion pairrequired to produce an ion pair

Ckgc air

eX KW

kgairW 19

19

1.602 10 ( ) 133.97 33.971 602 10 ( )

W ev J eV ip Je ip C electron electron C

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1.602 10 ( )air

e ip C electron electron C

AsideIndirectly ionizing radiationIndirectly ionizing radiation

How many ionization events can be initiated by a 10 keV photo-electron?

3 1? 10 10 294ipip eV ip ? 10 10 29433.97

pip eV ipeV

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Equilibrium Part 2:Charged Particle EquilibriumCharged Particle Equilibrium

he-

R Re-e- e-

in out ccR Rh

e-

in in out outc u c uR R R R Q netR R QCPE CPECPE

... netin out tru u

R R Q net

trddD K

CPE CPE

CPE

CPE

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trcD K

dm dm

Charge particlesg p e-, e+, p, α, … Sources Sources

Accelerated beams Radioactive decay Reaction products Reaction products

(e,γ) , … (n,p), … (e,e), …( )

Coulomb force interaction Inverse square dependence Semi-continuous rather than discrete interactions Semi continuous rather than discrete interactions Results in energy loss and directional change Interaction can be classified by impact parameter

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undisturbed incident trajectoryCP interactionsb = impact parameter

t i di

b

a = atomic radiusn = nuclear radius

b>>aSoft, atomic interaction

b~aHard, knock-on interaction

a b<<a

Nuclear interactions possible

©JVS: 2009 AAPM SS

Stopping powerS pp g p

E l it th l th Energy loss per unit path-lengthMeVdES 2MeV cmS dE

S t t b i t ti

MeVcm

dESdx

MeV cm

gS dE

dx

Separate components by interactioncol radS SS

©JVS: 2009 AAPM SS

Stopping power formulationsS pp g p

B d B th Bl h H itl Based on Bethe-Bloch, Heitler, … Electrons: ICRU 37

2

2 222 2

212 ln2

e e ACollisional

S Zr m c N FA I m c

2Collisional eI m c 2

eT m c vc

2

2 2

13rad e A

reS r N Z E m c B

A

137 eA

221 1 2 1 ln 2

8F

Material dependent terms

©JVS: 2009 AAPM SS

Material dependent terms

Stopping power formulationsS pp g p

Protons/ Heavy charged particles: ICRU 49 Protons/ Heavy charged particles: ICRU 49

2 2

2 2 2 21 22 2 2

21 14 lncol e me e A

S m c WZ Cr m c N z B B

1 22 2 22 21e e A A ZI

With Wm, the maximum energy that can be

22 2

22 11 2e e e

mm c m mW

m, gytransferred to an electron in a single collision

Material dependent terms2 21 1

m M M

©JVS: 2009 AAPM SS

Recall KERMA

Transfer of radiant energy from uncharged Transfer of radiant energy from uncharged primaries to charged particles as they interact in a materiala material

max ( )E

trE

EK E dE

trdK

0

EE

Kdm

c rK K K

max ( )E

enc E

EK E dE

nettr

cdKd

c r

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0E

c dm

CEMA Converted Energy per unit MAss

D ib f f i h d i l Describes energy transfer from primary charged particlesto secondary charged particles (δ-rays)

Energy transferred can be absorbed locally or at a distancegy y Defined in ICRU 60 Charged particle analog to KERMA

C=dEc/dm Jkg

cdECdm

C = integral(). max

0

E colE

S EC E dE

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CEMA examplep Thin slab

CP Φ

constant S/ρ straight particle paths

Fluence Φ of incident

t

mono-energetic charged particles

t

cSdE t

Energy loss JcSC

CEMA

dE t

kgC

δCPE

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When δ-ray equilibrium exists, CEMA = doseδCPE

Restricted CEMA Restricted CEMA E l d l t ti (E Δ) δ Excludes energy losses to energetic (E>Δ) δ-rays (aka knock-on electrons)

Such δ-rays are added to the fluence Φ’

E

L EC E dE

colE E E

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E E EE E E

Restricted Stopping Power Restricted Stopping Power

l kS dEL col keS dELdx

Includes energy transfers only up to energy Δ Includes energy transfers only up to energy Δ Excludes energy losses from to energetic

(E>Δ) δ-rays Δ is chosen with respect to the distance the δ-rays

can travel in the material of interest

©JVS: 2009 AAPM SS

Restricted CEMA est cted C maxE col

E E

L E S EC E dE E dE

0E E

Track end term & electronsEnergy loss for E > ∆ Track end term & electrons generated outside volume

Energy loss for Ee > ∆

lim max

limE

C C

limlim colSL

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maxE

Path Length and Range

Variations in energy loss and scattering result in different paths through a material ( & different different paths through a material ( & different maximum penetration distances) p = total distance traveled by a particle w/o relation to p y p

direction R = average path length CSDA Range CSDA Range

20

1 g( ) cm

oT

CSDAR dES E

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( ) cmS E

RangeRange

Rt = average depth of penetration in the original Rt average depth of penetration in the original particle direction

R50 = range at 50% max dose50 g Rp = practical or extrapolated range, intersection of

tangent @R50 with brems tail50

©JVS: 2009 AAPM SS

Range-Energy Relationships

Incident energy Incident energy

0 502.33E R

Average energy at depth (Harder’s Formula)

1op

depthE E R

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Equilibrium Part 3:CPE RevisitedCPE Revisited

For an external beam if For an external beam, if no attenuation, CPE exists beyond Dmax

But, e- production due to attenuation T CPE t i t True CPE cannot exist for external beam

©JVS: 2009 AAPM SS

Equilibrium Part 4:Transient Charged Particle Transient Charged Particle

F t l For external beams

( ) ( )cD x K xTCPE

©JVS: 2009 AAPM SS

basic radiation interactions, definition of dosimetric ... · basic radiation interactions,...

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