Transcript Physics of Radiotherapy - Phy428-528

Physics of Radiotherapy
Lecture II: Interaction of
Ionizing Radiation With Matter
Charge Particle Interaction
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Energetic charged particles interact with
matter by electrical forces and lose kinetic
energy via:
• Excitation
• Ionization
• Radiative losses (Bremsstrahlung Production)
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~ 70% of charged particle energy
deposition leads to non-ionizing excitation
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Specific Ionization
• Number of primary and secondary ion
pairs produced per unit length of
charged particle’s path is called specific
ionization
• Expressed in ion pairs (IP)/mm
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Increases with electrical charge of particle
(more for alpha as compare to electron)
Decreases with incident particle velocity
Linear Energy Transfer (Stopping
Power of The Medium)
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Amount of energy deposited per unit path
length (eV/cm) is called the linear energy
transfer (LET) and is also known as
stopping power of the medium
LET of a charged particle is proportional to
the square of the charge and inversely
proportional to its kinetic energy
High LET radiations (alpha particles,
protons, etc.) are more damaging to
tissue than low LET radiations (electrons,
gamma and x-rays)
Electron Interaction
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As an energetic electron traverses matter,
it undergoes
• Coulomb interactions with absorber atoms,
i.e., with:
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Atomic orbital electrons
Atomic nuclei
Through these collisions the electrons
may:
• Lose their kinetic energy (collision and
radiation loss).
• Change direction of motion (scattering).
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Energy losses are described by
stopping power (LET).
Scattering is described by angular
scattering power.
Collision between the incident
electron and an absorber atom may
be:
• Elastic
• Inelastic
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In elastic collision the incident electron is
deflected from its original path but no energy loss
occurs.
In an inelastic collision with orbital electron the
incident electron is deflected from its original
path and loses part of its kinetic energy
(collisional loss).
In an inelastic collision with nucleus the incident
electron is deflected from its original path and
loses part of its kinetic energy in the form of
bremsstrahlung (radiative loss)
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The energy loss by incident electron
through inelastic collisions is
described by the total linear stopping
power Stot which represents the
kinetic energy EK loss by the electron
per unit path length x:
Stot =dEK/dx MeV/cm
Mass Stopping Power
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Total mass stopping power is defined as
the linear stopping power divided by the
density of the absorbing medium.
It has two parts, collisional and radiative
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Electrons traversing an absorber lose their
kinetic energy through ionization collisions
and radiation collisions.
The rate of energy loss per gram and per
cm2 is called the mass stopping power and
it is a sum of two components:
• Mass collision stopping power
• Mass radiation stopping power
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The rate of energy loss for a therapy
electron beam in water and water-like
tissues, averaged over the electron’s
range, is about 2 MeV/cm.
Photon Interactions
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Probability
• “chance” of event happening
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can be mathematically expressed
example:
The probability of a woman experiencing
breast cancer in her lifetime is 1:9
• x-ray interactions are chance events
 relative predictions can be made
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• energy of the photons
• type of matter the x rays are passing through
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cannot predict how one photon will interact
Photon Interactions
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Probability of photon interaction
depends on
• Energy of Incident Photon
• The type of traversing matter
Photon Interactions
 Transmitted through matter (unchanged)
 Change direction with no energy loss
1.Classical Scattering (Coherent Scattering)
 Change direction and lose energy
2.Compton Scattering
 Deposit all energy in the matter
3.Photoelectric Effect
4.Pair Production
5.Photodisintegration
Classical Scattering
(Coherent or Elastic)
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Occurs at low energy (< 10 keV)
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Atom first excited by photon
Then releases (radiates) photon of same keV & l
New photon travels in different direction from original
photon but usually forward (small scatter angle)
Coherent Scattering is further classified as
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Rayleigh Scattering
• If interaction occurs with whole atom
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Thompson Scattering
• If interaction occurs with shell e-
Photoelectric Effect (Complete
absorption)
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The orbital electron is ejected from the
atom with kinetic energy
EK=hν-EB
• where EB is the binding energy of the orbital
electron.
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The ejected orbital electron is called a
photoelectron.
When the photon energy hν exceeds the
K-shell binding energy EB of the absorber
atom, the photoelectric effect is most
likely to occur with a K-shell electron in
comparison with higher shell electrons.
Photoelectric Effect
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Electrons in higher energy shells
cascade down to fill energy void of
inner shell
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Characteristic radiation
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Photoelectric interaction probability
• inversely proportional to cube of photon
energy
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low energy event
• proportional to cube of atomic number
P.E ~ Z3/E3
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More likely with inner (higher) shells
• tightly bound electrons
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Interaction much more likely for
• low energy photons
• high atomic number elements
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Photon Energy Threshold
• binding energy of orbital electron
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binding energy depends on
• atomic number
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higher for increasing atomic number
• shell
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lower for higher (outer) shells
most likely to occur when photon energy &
electron binding energy are nearly the
same
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Photoelectric interactions decrease
with increasing photon energy BUT
• When photon energies just reaches binding
energy of next (inner) shell, photoelectric
interaction now possible with that shell
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shell offers new candidate target electrons
Causes step increases in interaction
probability as photon energy exceeds
shell binding energies
Interaction
Probability
L-shell
interactions
possible
L-shell
binding
energy
K-shell
binding
energy
Photon Energy
K-shell
interactions
possible
Compton Scattering
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Source of virtually all scattered radiation
Process
• incident photon (relatively high energy)
interacts with free (loosely bound) electron
• some energy transferred to recoil electron
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electron liberated from atom (ionization)
• emerging photon has
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less energy than incident
new direction
Electron out
(recoil electron)
Photon out
Photon in
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What is a “free” electron?
• low binding energy
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outer shells for high Z materials
all shells for low Z materials
Electron out
(recoil electron)
Photon in
Photon out
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Incident photon energy split between
electron & emerging photon
Fraction of energy carried by
emerging photon depends on
• incident photon energy
• angle of deflection
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similar principle to
billiard ball collision
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higher incident energy = less photon
deflection
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high energy (1MeV) photons primarily scatter forward
diagnostic energy photons scatter fairly uniformly
• forward & backward
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at diagnostic energy photons lose very little energy
during Compton Scattering
At therapy energy level, photons lose most of energy
through Compton scattering
• higher deflection = less energy retained
-
Electron out
(recoil electron)
deflection
angle
Photon in
Photon out
l ' l 
 Ee max
h
1  cos  
me c
2
 hf
1  2
λ’ is wavelength of scattered photon and λ
is the wavelength of incident photon
(Ee)Max is maximum energy transfer to
recoil electron and α=hf/mec2 (rest mass
energy of electron
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Interaction Probability is
• independent of atomic number (except
for hydrogen)
• Proportional to electron density
(electrons/gram)
• fairly equal for all elements except
hydrogen (~ double)
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Interaction Probability
• decreases with increasing photon
energy
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decrease much less pronounced than for
photoelectric effect
Interaction
Probability
Compton
Photoelectric
Photon Energy
Pair Production (Complete absorption)
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Exist at high photon energy
• Ei > 1.022 MeV
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(e- rest mass energy = .511 MeV)
Photon interacts with nuclear force field
• uses 1.022 MeV to produce pair of electron like
particles
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e+ (positron) & e- (negatron)
Photon ceases to exist
E = 1.022 MeV + Ee+KE + Ee-KE
Photon Interaction Probabilities
100
Pair Production
Photoelectric
Z
COMPTON
10
0.01
0.1
1.0
Energy (MeV)
10
100
Linear Attenuation Coefficient
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The most important parameter used for
characterization of x-ray or gamma ray
penetration into absorbing media is the linear
attenuation coefficient μ
The linear attenuation coefficient depends upon:
• Energy of the photon beam
• Atomic number Z of the absorber
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The linear attenuation coefficient may be
described as the probability per unit path length
that a photon will have an interaction with the
absorber
This interaction may be any one of the
interactions discussed so for (PE,CS PP etc.)
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For collimated beam of monoenergetic photons, the intensity of
photon beam after passing through
thickness x of some homogenous
medium is
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Several thicknesses of special interest are
defined as parameters for mono-energetic
photon beam characterization in narrow
beam geometry:
• Half-value layer (HVL1 or x1/2)
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Absorber thickness that attenuates the original
intensity to 50%.
• Mean free path (MFP )
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Absorber thickness which attenuates the beam
intensity to 1/e = 36.8%.
• Tenth-value layer (TVL or x1/10)
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Absorber thickness which attenuates the beam
intensity to 10%.
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In medical physics photon interactions fall
into four groups:
• Interactions of major importance
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Photoelectric effect
Compton scattering by free electron
Pair production (including triplet production)
• Interactions of moderate importance
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Rayleigh scattering
Thomson scattering by free electron
• Interactions of minor importance
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Photonuclear reactions
• Negligible interactions
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Thomson and Compton scattering by the nucleus
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For a given hν and Z:
• Linear attenuation coefficient μ is sum
of all interaction probabilities, mostly
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μ = PE Cross-section + Scattering Crosssection + PP Cross-section