02Siebers-BasicInteractionsandQuantities.pdf

Basic Radiation Interactions,
Definition of Dosimetric Quantities,
and Data Sources
J.V. Siebers
Virginia Commonwealth University
Richmond, Virginia USA
2009 AAPM Summer School
2009 AAPM Summer School

Learning Objectives
g 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
dosimetry
dosimetry
©JVS: 2009 AAPM SS

Constants Units Conversions
©JVS: 2009 AAPM SS

Scope
Radiation Types
Ionizing
Ionizing
Interactions can remove
atomic orbital electrons Non-Ionizing
Particulate Electromagnetic
Particulate
-electron
-positron
Electromagnetic
-proton
-neutron
- alpha
©JVS: 2009 AAPM SS
p
- etc.

Types of ionizing radiation
yp 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
©JVS: 2009 AAPM SS

Direct Ionization
Coulombic 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)
©JVS: 2009 AAPM SS

Indirectly Ionizing Radiation
y g
 Uncharged particles that must first transfer energy to
a charged particle which can then further ionize
matter
T t
 Two step process
 Examples
El t ti di ti
 Electromagnetic radiations: x- or γ-rays
 Neutrons
©JVS: 2009 AAPM SS

Indirectly Ionizing Radiation
Ph t l t i Eff t
Photoelectric Effect
e-
Ej t d


h
Ejected
electrons
further
ionize
 ionize
matter
©JVS: 2009 AAPM SS

Radiant Energy R
gy
 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
©JVS: 2009 AAPM SS

Energy imparted ε
 ε - Energy imparted
R R Q
    
 ε - Energy imparted
i l i
in out
R R Q
    
Q

 mass to energy conversion resulting
from interactions or radioactive decay
Q

if(m→E), Q>0
in
R  out
R
h

e-
h

e-
©JVS: 2009 AAPM SS
if(E→m), Q<0
       
in in out out
c u c u
R R R R Q
      

Dose
 
Gy
d
D


Energy deposited per unit mass
 
y
dm
 Energy deposited per unit mass
 1 Gy = 1 J/kg
 Knowledge of D is the object of dosimetry
©JVS: 2009 AAPM SS

Equilibrium Part 1:
R di ti E ilib i
Radiation Equilibrium
R R
h

e-
in out
R R

h

e- e-
h

h

e-
R R Q

Q
 d Q
d 
RE
in out
R R Q
    
Q
   d Q
d
D
dm dm

 

RE
RE
©JVS: 2009 AAPM SS

Radiation Sources
S
 Radioactive decay
 Radioactive decay
 Alpha-decay
 Beta-decay
 Electron capture
 Electron capture
 Isomeric transitions
 Accelerated charged particles
 Direct
 Direct
 X-ray generators
 Atomic energy transitions
Characteristic X rays
 Characteristic X-rays
 Auger electrons
 Interaction products
©JVS: 2009 AAPM SS

Radioactive Decay
y
General balance equations
General balance equations
R R
R R
A A A
A
Z Z Z Z
P D R Q


   
P D R
Q M M M
  

©JVS: 2009 AAPM SS

Radioactive Decay
Activity
dN
A N
dt

  
0
t
t
A A e 


1
ln 2
t 
©JVS: 2009 AAPM SS
1
2 

Radioactive Decay
 α
 4 4
2 2
A A
Z Z
P D He Q


   
 α ‘s have short range
  
/  
 
 0
1 1
A A
Z Z
P D Q
 

 
    
 0
1 1
A A
Z Z
P D Q
 


    
 Neutrino ( , ) results in spectrum of  energies
( ) p  g
 max
E and E are tabulated
 ( , ) are non-ionizing
 Electron Capture
0
A A
P D Q

 0
1 1
A A
Z Z
P 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
0
A A
Z Z
P P Q

   
 decay from meta-stable state
 Internal Conversion
* 0 0
A A
P P Q

©JVS: 2009 AAPM SS
 0 0
1 1
A A
Z Z
P e P e Q
 
    
 Competes with isomeric transition
 Results in ejection of atomic electron

15 15 0 0
1 732
O N M V
 
  
β+ 15 15 0 0
8 7 1 0 1.732
O N MeV
 


   
15 0 15 0
8 1 7 0 1.732
O e N MeV


   
Electron
Capture
β+
©JVS: 2009 AAPM SS
8 1 7 0
Capture

Accelerated Charged Particles
g
Di t
 Direct use
 Electrons, protons, …
 Indirect via production of electromagnetic
radiation
radiation
 Synchrotron radiation
 Bremmstrahlung
 Bremmstrahlung
©JVS: 2009 AAPM SS

Synchrotron
Radiation
h
Radiation
Magnetic Field
e-
©JVS: 2009 AAPM SS
Synchrotron image courtesy of http://www-project.slac.stanford.edu/ssrltxrf/spear.htm

Bremmstrahlung
brems
h
Bremmstrahlung
brems
e-
©JVS: 2009 AAPM SS

Atomic Energy Transition
gy
Characteristic x-ray
xray h
©JVS: 2009 AAPM SS

Atomic Energy Transition
Auger Electron
e-
©JVS: 2009 AAPM SS

Quantifying Radiation Fields
Q y g
Th f
 Thus far
 R
 ε
 D
©JVS: 2009 AAPM SS

Radiation Fluence
 N is number of particles
i h
dN particles
 
 crossing sphere
surrounding P with cross-
sectional area da
2
p
da m
 
   
 
sectional area da
 Integrated over all
directions and energies
 Single particle type
©JVS: 2009 AAPM SS

Equivalent definition of fluence
q
 l = particle track
l
  l = particle track
length through a
volume
nTracks
l
V
 

 l need not be
straight
 Volume can be
irregular
U f l f M t
 Useful for Monte
Carlo applications
©JVS: 2009 AAPM SS

Energy Fluence
gy
 Definition
dR J
 
2
dR J
da m
 
   
 
 Poly-energetic Mono-energetic
da m
 
 
 E
 
Diff ti l fl
 
E
E E dE
  
 E
  
 Differential energy fluence
 
E E d dE
  
©JVS: 2009 AAPM SS
 
E E d dE
 

Attenuation
t
d n dl
   
t
l
 0
el
1
n

 
  
©JVS: 2009 AAPM SS
l 0
t
n
m
    
 

Attenuation coefficient
l
 0
el
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/ ]
©JVS: 2009 AAPM SS
[cm2/g]

TERMA
 Total Energy Release per unit MAss
J
kg
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
kg
E
E
E
TERMA E dE


   
     
 
 

For poly-energetic spectra
*

Aside:
Photon Interactions
Photon Interactions
 To understand what happens with the
radiant energy removed, understand the
interactions
(e.g. γ interactions)
©JVS: 2009 AAPM SS

Photon interactions contributing to
Photon interactions contributing to µ
-1
m
Rayleigh
       
      
 σ = Rayleigh + Compton scattering
 σ = Rayleigh + Compton scattering
 τ = photo-electric
 κ = pair production
 κ = pair production
 η = photo-nuclear
©JVS: 2009 AAPM SS

Rayleigh Scattering
y g S g
 Elastic coherent scattering of the photon
by an atom
y
 Important for low energy photons
C t ib t < 20% t t t l tt ti
 Contributes < 20% to total attenuation
coefficient
©JVS: 2009 AAPM SS

Compton Scattering
Compton Scattering
e-
h
e
h



h
2
cm
A
N Z


 
 

©JVS: 2009 AAPM SS
g
e
A

  
 

e-


h b A
e
T h E T

   
b
e
T h E

  

©JVS: 2009 AAPM SS

Photo-electric
 
3 4
2 3
Z
h

 


 Au
τ increases when
τ increases when
shell can
participate in
reaction
reaction
©JVS: 2009 AAPM SS

Pair Production
Pair Production
e-
h
+
pair
h
e+
2
2 e
e e
avail
T T T h m c

 

   e
e e
avail
 
2
di
o
m c

©JVS: 2009 AAPM SS
 
radian
o
T
 


Triplet Production
Triplet Production
2
2
avail e
T h m c

 
e-
e- triplet
h
e+
2
2
h
©JVS: 2009 AAPM SS
2
2
3
e
h m c
T
 


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
©JVS: 2009 AAPM SS
p g

Pb attenuation coefficient
©JVS: 2009 AAPM SS

Relative importance of interactions
Relative importance of interactions
©JVS: 2009 AAPM SS

Summary photon interactions
©JVS: 2009 AAPM SS

Energy transferred to charged particles
i t ti
Energy transferred to charged particles
 per-interaction
 general
   
nonr
tr in out
u u
R R Q
    
 photo
u u
=
 compton
 pair
=
=
 Average
i
tr
n



©JVS: 2009 AAPM SS
i
tr
i
n
 

Recall
l
 0
el
 represents the interaction (removal) of
 µ represents the interaction (removal) of
primaries from the beam
result of the interaction
 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 l
particles

 
tr tr
h
  
  
 
  
 
©JVS: 2009 AAPM SS

KERMA
 Kinetic Energy Release per unit MAss
d tr
d
KERMA K
dm

 
*
J
kg
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
   
nonr
net r r
tr tr u in out u
u u
R R R R Q
 
      
       
r nonr r
net
tr tr out in out out
u u u u
R R R R Q
 
      
Te-
T’
h
 Accounts for portion of kerma is radiated away
brems
hv
Compton example
h Te-
net
tr brems
e
T hv
 
 
©JVS: 2009 AAPM SS
h

Mass energy absorption coefficient
Mass-energy absorption coefficient
R di ti l f ti
 Radiative loss fraction g
1
net
tr
g

 
M b ti ffi i t
1
tr
g


 Mass-energy absorption coefficient
 
1
en tr
g
 
 
 
1 g
 

©JVS: 2009 AAPM SS

Kerma Components
C lli i K
c r
K K K
 
 Collision Kerma
net
tr
d
K


en
K

 
*
 Portion of kerma that remains collisional energy losses
c
K
dm
 c
K

 
(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
C
kg
dQ
X
dm
 
  
 
 Related to air collision kerma by mean energy
required to produce an ion pair
required to produce an ion pair
 
C
kg
c air
e
X K
W
 
 
    
   
kg
air
W
   
19
19
1.602 10 ( ) 1
33.97 33.97
1 602 10 ( )
W ev J eV ip J
e ip C electron electron C


   
      
   
   
     
    
   
 
©JVS: 2009 AAPM SS
1.602 10 ( )
air
e ip C electron electron C
    
   
 

Aside
Indirectly ionizing radiation
Indirectly ionizing radiation
 How many ionization events can be initiated by a
10 keV photo-electron?
   
3 1
? 10 10 294
ip
ip eV ip
 
   
   
? 10 10 294
33.97
p
ip eV ip
eV
   
 
 
©JVS: 2009 AAPM SS

Equilibrium Part 2:
Charged Particle Equilibrium
Charged Particle Equilibrium
h

e-
   
R R
e-
e- e-
   
in out c
c
R R

h

e-


       
in in out out
c u c u
R R R R Q
      
    net
R R Q

CPE CPE
CPE


    ... net
in out tr
u u
R R Q
 
    

net
tr
d
d
D K


CPE CPE
CPE
CPE
©JVS: 2009 AAPM SS
tr
c
D K
dm dm
  

Charge particles
g 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
©JVS: 2009 AAPM SS

undisturbed incident trajectory
CP interactions
b = impact parameter
t i di
b
a = atomic radius
n = nuclear radius
 b>>a
Soft, atomic interaction
 b~a
Hard, knock-on interaction
a
 b<<a
Nuclear interactions
possible
©JVS: 2009 AAPM SS

Stopping power
S pp g p
E l it th l th
 Energy loss per unit path-length
MeV
dE
S
  2
MeVcm
S dE  
S t t b i t ti
MeV
cm
dE
S
dx
 
  
 
MeVcm
g
S dE
dx
 
 
  
 
 Separate components by interaction
col rad
S S
S
 
  
 
©JVS: 2009 AAPM SS

Stopping power formulations
S pp g p
B d B th Bl h H itl
 Based on Bethe-Bloch, Heitler, …
 Electrons: ICRU 37
 
 
 
2
2 2
2
2 2
2
1
2 ln
2
e e A
Collisional
S Z
r m c N F
A I m c
 
  
 

 
 

   
 
  
   
 
   
 
 
 
2
Collisional e
I m c
 
   
 
 
2
e
T m c
 
v
c
 
 
2
2 2
13
rad e A
r
e
S r N
Z E m c B
A
 
 
 
137
e
A
      
2
2
1 1 2 1 ln 2
8
F

  
  
    
 
 
Material dependent terms
©JVS: 2009 AAPM SS

Stopping power formulations
S pp g p
 Protons/ Heavy charged particles: ICRU 49
 Protons/ Heavy charged particles: ICRU 49
 
2 2
2 2 2 2
1 2
2 2 2
2
1 1
4 ln
col e m
e e A
S m c W
Z C
r m c N z B B
 
 

 
 
 
 
     
 
 
  1 2
2 2 2
2 2
1
e e A
A Z
I

  
 
 

 
 
With Wm, the maximum energy that can be
2
2 2
2
2 1
1 2
e e e
m
m c m m
W
  
   
  
 
   
 
m, gy
transferred to an electron in a single collision
2 2
1 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 material
a material
 
max
( )
E
tr
E
E
K E dE

 
   
 

tr
d
K

  
0
E
E


 
 

K
dm
c r
K K K
 
 
max
( )
E
en
c E
E
K E dE


 
   
 

net
tr
c
d
K
d


c r
©JVS: 2009 AAPM SS
 
0
E


 
 

c
dm

CEMA
 Converted Energy per unit MAss
D ib f f i h d i l
 Describes energy transfer from primary charged particles
to secondary charged particles (δ-rays)
 Energy transferred can be absorbed locally or at a distance
gy y
 Defined in ICRU 60
 Charged particle analog to KERMA
 C=dEc/dm
J
kg
c
dE
C
dm
 
  
 
 C = integral(). 
 
max
0
E
col
E
S E
C E dE

 

©JVS: 2009 AAPM SS

CEMA example
p
 Thin slab
CP Φ
 constant S/ρ
 straight particle paths
 Fluence Φ of incident
t
mono-energetic charged
particles
t
c
S
dE t

 
Energy loss
J
c
S
C
 
   
CEMA
dE t


 
kg
C

   
 
δCPE
©JVS: 2009 AAPM SS
 When δ-ray equilibrium exists, CEMA = dose
δCPE

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 E
C E dE




 
 
     
col
E E E

    
©JVS: 2009 AAPM SS
     
E E E
E E E

    

Restricted Stopping Power
Restricted Stopping Power
l k
S dE
L 
col ke
S dE
L
dx
  


 
 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
 
 
 
 
max
E
col
E E
L E S E
C E dE E dE



 
   
 
   
0
E E
 
 
 
Track end term & electrons
Energy loss for E > ∆ Track end term & electrons
generated outside volume
Energy loss for Ee > ∆
 lim
max
lim
E
C C



 lim
lim col
S
L

©JVS: 2009 AAPM SS
max
E  


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
2
0
1 g
( ) cm
o
T
CSDA
R dE
S E 
 
  
 

©JVS: 2009 AAPM SS
( ) cm
S E   

Range
Range
 Rt = average depth of penetration in the original
 Rt average depth of penetration in the original
particle direction
 R50 = range at 50% max dose
50 g
 Rp = practical or extrapolated range, intersection of
tangent @R50 with brems tail
50
©JVS: 2009 AAPM SS

Range-Energy
Relationships
 Incident energy
 Incident energy
0 50
2.33
E R

 Average energy at depth (Harder’s Formula)
1
o
p
depth
E E
R
 
 
 
 
©JVS: 2009 AAPM SS
 

Equilibrium Part 3:
CPE Revisited
CPE 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
 ( ) ( )
c
D x K x


TCPE
©JVS: 2009 AAPM SS

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