Radiation%20Interactions

1
Radiation Interactions

• Robert Metzger, Ph.D.

2
Interactions with Matter

• Charged particles lose energy as they interact
  with the orbital electrons in matter by
  excitation and ionization, and/or radiative
  losses.
• Excitation occurs when the incident particle
  bumps an electron to a higher orbital in the
  absorbing medium.
• Ionization occurs when the transferred energy
  exceeds the binding energy of the electron and it
  is ejected. The ejected electron may then also
  produce further ionizations.

3
Specific Ionization

• The number of ion pairs produced per unit path
  length is the specific ionization.
• Alpha particles can produce as many as 7,000
  IP/mm. Electrons produce 50-100 IP/cm in air.
• LET is the product of the specific ionization and
  the average energy deposited per IP IP/cm x
  eV/IP.
• About 70 of electron energy loss leads to
  non-ionizing excitation.

4
Charged Particle Tracks

• e- follow tortuous paths through matter as the
  result of multiple Coulombic scattering processes
  
• An a2, due to its higher mass follows a more
  linear trajectory
• Path length actual distance the particle
  travels in matter
• Range effective linear penetration depth of the
  particle in matter
• Range path length

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p.34.
5
Bremsstrahlung

• Deceleration of an e- around a nucleus causes it
  to emit Electromagnetic radiation or
  bremsstrahlung (G.) breaking radiation
• Probability of bremsstrahlung emission ? Z2 Ratio
  of e- energy loss due to bremsstrahlung vs.
  excitation and ionization KEMeVZ/820
• Thus, for an 100 keV e- and tungsten (Z74) 1

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p.35.
6
Electromagnetic Radiation Interactions

• Raleigh Scattering Photon is scattered with no
  energy loss. Uncommon at diagnostic energies.
• Compton ScatteringPhoton strikes outer electron
  and ejects it, resulting in energy loss of photon
  and change of direction.
• Photoelectric Effect Photon is totally absorbed
  by K or L shell electron which is ejected.
• Pair Production High energy photon interaction.

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Rayleigh Scattering

• Excitation of the total complement of atomic
  electrons occurs as a result of interaction with
  the incident photon
• No ionization takes place
• No loss of E
• lt5 of interactions at diagnostic energies.

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 37.
8
Compton Scattering

• Dominant interaction of x-rays with soft tissue
  in the diagnostic range and beyond (approx. 30
  keV - 30MeV)
• Occurs between the photon and a free e- (outer
  shell e- considered free when Eg gtgt binding
  energy, Eb of the e- )
• Encounter results in ionization of the atom and
  probabilistic distribution of the incident photon
  E to that of the scattered photon and the ejected
  e-
• A probabilistic distribution determines the angle
  of deflection

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 38.
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Compton Scattering

• Compton interaction probability is dependent on
  the total no. of e- in the absorber vol. (e-/cm3
  e-/gm density)
• With the exception of 1H, e-/gm is fairly
  constant for organic materials (Z/A ? 0.5), thus
  the probability of Compton interaction
  proportional to material density (?)
• Conservation of energy and momentum yield the
  following equations
• Eo Esc Ee-
• , where
  mec2 511 keV

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Compton Scattering

• As incident E0 ? both photon and e- scattered in
  more forward direction
• At a given ? fraction of E transferred to the
  scattered photon decreases with ? E0
• For high energy photons most of the energy is
  transferred to the electron
• At diagnostic energies most energy to the
  scattered photon
• Max E to e- at ? of 180o max E scattered photon
  is 511 keV at ? of 90o

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 39.
11
Photoelectric Effect

• All E transferred to e- (ejected photoelectron)
  as kinetic energy (Ee) less the binding energy
  Ee E0 Eb
• Empty shell immediately filled with e- from
  outer orbitals resulting in the emission of
  characteristic x-rays (E? differences in Eb of
  orbitals), for example, Iodine EK 34 keV, EL
  5 keV, EM 0.6 keV

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 41.
12
Photoelectric Effect

• Eb ? Z2
• Photoe- and cation characteristic x-rays and/or
  Auger e-
• Probability of photoe- absorption ? Z3/E3 (Z
  atomic no.)

• Explains why contrast ? as higher energy x-rays
  are used in the imaging process
• Due to the absorption of the incident x-ray
  without scatter, maximum subject contrast arises
  with a photoe- effect interaction
• Increased probability of photoe- absorption just
  above the Eb of the inner shells cause
  discontinuities in the attenuation profiles
  (e.g., K-edge)

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Photoelectric Effect
c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 1st ed., p. 26.
14
Photoelectric Effect

• Edges become significant factors for higher Z
  materials as the Eb are in the diagnostic energy
  range
• Contrast agents barium (Ba, Z56) and iodine
  (I, Z53)
• Rare earth materials used for intensifying
  screens lanthanum (La, Z57) and gadolinium
  (Gd, Z64)
• Computed radiography (CR) and digital radiography
  (DR) acquisition europium (Eu, Z63) and cesium
  (Cs, Z55)
• Increased absorption probabilities improve
  subject contrast and quantum detective efficiency
  
• At photon E ltlt 50 keV, the photoelectric effect
  plays an important role in imaging soft tissue,
  amplifying small differences in tissues of
  slightly different Z, thus improving subject
  contrast (e.g., in mammography)

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Pair Production

• Conversion of mass to E occurs upon the
  interaction of a high E photon (gt 1.02 MeV rest
  mass of e- 511 keV) in the vicinity of a heavy
  nucleus
• Creates a negatron (ß-) - positron (ß) pair
• The ß annihilates with an e- to create two 511
  keV photons separated at an ? of 180o

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 44.
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Radiation Interactions
WHICH ISHIGH kVp CHEST RADIOGRAPH AND WHICH IS
LOW kVp CHEST RADIOGRAPH ?
A
B
17
Compton vs Photoelectric
WHICH ISLOW kVp BONE RADIOGRAPHAND WHICH
ISHIGH kVp BONE RADIOGRAPH ?
A
B
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Linear Attenuation Coef

• Cross section is a measure of the probability
  (apparent area) of interaction ?(E) measured
  in barns (10-24 cm2)
• Interaction probability can also be expressed in
  terms of the thickness of the material linear
  attenuation coefficient ?(E) cm-1 Z e-
  /atom Navg atoms/mole 1/A moles/gm ?
  gm/cm3 ?(E) cm2/e-
• ?(E) ? as E ?, e.g., for soft tissue
• ?(30 keV) 0.35 cm-1 and ?(100 keV) 0.16 cm-1
• ?(E) fractional number of photons removed
  (attenuated) from the beam by absorption or
  scattering
• Multiply by 100 to get removed from the beam/cm

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Attenuation Coefficient

• An exponential relationship between the incident
  radiation intensity (I0) and the transmitted
  intensity (I) with respect to thickness
• I(E) I0(E) e-?(E)x
• ?total(E) ?PE(E) ?CS(E) ?RS(E) ?PP(E)
• At low x-ray E ?PE(E) dominates and ?(E) ? Z3/E3
  
• At high x-ray E ?CS(E) dominates and ?(E) ? ?
• Only at very-high E (gt 1MeV) does ?PP(E)
  contribute

• The value of ?(E) is dependent on the phase
  state
• ?water vapor ltlt ?ice lt ?water

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Attenuation Coefficient
c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 46.
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Mass Attenuation Coef

• Mass attenuation coefficient ?m(E) cm2/g
  normalization for ? ?m(E) ?(E)/?Independent of
  phase state (?) and represents the fractional
  number of photons attenuated per gram of material
  
• I(E) I0(E) e-?m(E)?x
• Represent thickness as g/cm2 - the effective
  thickness of 1 cm2 of material weighing a
  specified amount (?x)

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Half Value Layer

• Thickness of material required to reduce the
  intensity of the incident beam by ½
• ½ e-?(E)HVL or HVL 0.693/?(E)
• Units of HVL expressed in mm Al for a Dx x-ray
  beam
• For a monoenergetic incident photon beam (i.e.,
  that from a synchrotron), the HVL is easily
  calculated
• Remember for any function where dN/dx ? N which
  upon integrating provides an exponential function
  (e.g., I(E) I0(E) ekw ), the doubling (or
  halving) dimension w is given by 69.3/k (e.g.,
  3.5 CD doubles in 20 yr)
• For each HVL, I ? by ½ 5 HVL ? I/I0 100/32
  3.1

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Mean Free Path

• Mean free path (avg. path length of x-ray) 1/?
  HVL/0.693
• Beam hardening
• The Bremsstrahlung process produces a wide
  spectrum of energies, resulting in a
  polyenergetic (polychromatic) x-ray beam
• As lower E photons have a greater attenuation
  coefficient, they are preferentially removed from
  the beam
• Thus the mean energy of the resulting beam is
  shifted to higher E

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 1st ed., p. 281.
24
Effective Energy

• The effective (avg.) E of an x-ray beam is ? to ½
  the peak value (kVp) and gives rise to an ?eff,
  the ?(E) that would be measured if the x-ray beam
  were monoenergetic at the effective E
• Homogeneity coefficient 1st HVL/2nd HVL
• A summary description of the x-ray beam
  polychromaticity
• HVL1 lt HVL2 lt HVLn so the homogeneity
  coefficient lt 1

c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 43.
c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 45.
25
Shielding

• I BI0 e-?x
• I is the Intensity in shielded area
• I0 is the unattenuated intensity
• B is the buildup factor
• ? is the attenuation coefficient
• X is the shield thickness

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Shielding

• The buildup factor is the ratio of scattered
  photons that scatter back into the beam.
• Since the photoelectric effect dominates at
  diagnostic x-ray energies, the buildup factor is
  1.0.
• Therefore lead aprons work well in diagnostic
  x-ray, but not in Nuclear Medicine (140 keV
  gammas)
• Buildup must be considered for PET.