Basic Radiation Interactions, Definition of Dosimetric ... · Basic Radiation Interactions,...
Transcript of 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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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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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
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
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
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 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
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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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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
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]
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Equilibrium Part 4:Transient Charged Particle Transient Charged Particle
F t l For external beams
( ) ( )cD x K xTCPE
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