Interaction of Radiation with Matter II

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Interaction of Radiation with Matter II
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Attenuation of X- and Gamma Rays

• Attenuation is the removal of photons from a beam
  of x- or gamma rays as it passes through matter
• Caused by both absorption and scattering of
  primary photons
• At low photon energies (lt26 keV), photoelectric
  effect dominates in soft tissue
• When higher energy photons interact with low Z
  materials, Compton scattering dominates
• Rayleigh scattering comprises about 10 of the
  interactions in mammography and 5 in chest
  radiography

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Attenuation in Soft Tissue (Z 7)
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Linear Attenuation Coefficient

• Fraction of photons removed from a monoenergetic
  beam of x- or gamma rays per unit thickness of
  material is called linear attenuation coefficient
  (?), typically expressed in cm-1
• Number of photons removed from the beam
  traversing a very small thickness ?x
• where n number removed from beam, and N
  number of photons incident on the material

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Linear Attenuation Coeff. (cont.)

• For monoenergetic beam of photons incident on
  either thick or thin slabs of material, an
  exponential relationship exists between number of
  incident photons (N0) and those transmitted (N)
  through thickness x without interaction

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Linear Attenuation Coeff. (cont.)

• Linear attenuation coefficient is the sum of
  individual linear attenuation coefficients for
  each type of interaction
• In diagnostic energy range, ? decreases with
  increasing energy except at absorption edges
  (e.g., K-edge)

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Attenuation in Soft Tissue (Z 7)
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Linear Attenuation Coeff. (cont.)

• For given thickness of material, probability of
  interaction depends on number of atoms the x- or
  gamma rays encounter per unit distance
• Density (?) of material affects this number
• Linear attenuation coefficient is proportional to
  the density of the material

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Linear Attenuation Data
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Mass Attenuation Coefficient

• For given thickness, probability of interaction
  is dependent on number of atoms per volume
• Dependency can be overcome by normalizing linear
  attenuation coefficient for density of material
• Mass attenuation coefficient usually expressed in
  units of cm2/g

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Mass Attenuation Coeff. (cont.)

• Mass attenuation coefficient is independent of
  density
• For a given photon energy
• In radiology, we usually compare regions of an
  image that correspond to irradiation of adjacent
  volumes of tissue
• Density, the mass contained within a given
  volume, plays an important role

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Radiograph of Ice Cubes in Water
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Mass Attenuation Coeff. (cont.)

• Using the mass attenuation coefficient to compute
  attenuation

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Half Value Layer

• Half value layer (HVL) defined as thickness of
  material required to reduce intensity of an x- or
  gamma-ray beam to one-half of its initial value
• An indirect measure of the photon energies (also
  referred to as quality) of a beam, when measured
  under conditions of good or narrow-beam geometry

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Narrow- and Broad-Beam Geometries
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Half Value Layer (cont.)

• For monoenergetic photons under narrow-beam
  geometry conditions, the probability of
  attenuation remains the same for each additional
  HVL thickness placed in the beam
• Relationship between ? and HVL
• HVL 0.693/ ?

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Effective Energy

• X-ray beams in radiology typically composed of a
  spectrum of energies (a polyenergetic beam)
• Determination of HVL in diagnostic radiology is a
  way of characterizing the hardness of the x-ray
  beam
• HVL, usually measured in mm of Al, can be
  converted to an effective energy
• Estimate of the penetration power of the x-ray
  beam, as if it were a monoenergetic beam

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Mean Free Path

• Range of a single photon in matter cannot be
  predicted
• Average distance traveled before interaction can
  be calculated from linear attenuation coefficient
  or the HVL of the beam
• Mean free path (MFP) of photon beam is

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Beam Hardening

• Lower energy photons of polyenergetic x-ray beam
  will preferentially be removed from beam while
  passing through matter
• Shift of x-ray spectrum to higher effective
  energies as beam traverses matter is called beam
  hardening
• Low-energy (soft) x-rays will not penetrate most
  tissues in the body their removal reduces
  patient exposure without affecting diagnostic
  quality of the exam

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Fluence

• Number of photons (or particles) passing through
  unit cross-sectional area is called fluence
  (expressed in units of cm-2)

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Flux

• Fluence rate (e.g., rate at which photons or
  particles pass through a unit area per unit time)
  is called flux (units of cm-2 sec-1)
• Useful in areas where photon beam is on for
  extended periods of time, such as fluoroscopy

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Energy Fluence

• Amount of energy passing through a unit
  cross-sectional area is called the energy
  fluence. For monoenergetic beam of photons
• Units of ? are energy per unit area (e.g., keV
  per cm2)

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Kerma

• A beam of indirectly ionizing radiation (e.g., x-
  or gamma rays or neutrons) deposits energy in a
  medium in a two-stage process
• Energy carried by photons (or particles) is
  transformed into kinetic energy of charged
  particles (such as electrons)
• Directly ionizing charged particles deposit their
  energy in the medium by excitation and ionization

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Kerma (cont.)

• Kerma (K) is an acronym for kinetic energy
  released in matter
• Defined as the kinetic energy transferred to
  charged particles by indirectly ionizing
  radiation
• For x- and gamma rays, kerma can be calculated
  from the mass energy transfer coefficient of the
  material and the energy fluence

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Mass Energy Transfer Coefficient

• Mass energy transfer coefficient is the mass
  attenuation coefficient multiplied by the
  fraction of energy of the interacting photons
  that is transferred to charged particles as
  kinetic energy
• Symbol
• Will always be less than the mass attenuation
  coefficient (ratio for 20-keV photons in tissue
  is 0.68 reduces to 0.18 for 50-keV photons)

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Calculation of Kerma

• For monoenergetic photon beams with energy
  fluence ? and energy E, the kerma K is given by
• SI units of energy fluence are J/m2, of mass
  energy transfer coefficient are m2/kg, and of
  kerma are J/kg

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Absorbed Dose

• Absorbed dose (D) is defined as the energy (?E)
  deposited by ionizing radiation per unit mass of
  material (?m)
• Absorbed dose is defined for all types of
  ionizing radiation
• SI unit of absorbed dose is the gray (Gy), equal
  to 1 J/kg. US units 1 rad 10 mGy

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Mass Energy Absorption Coefficient

• Mass energy transfer coefficient describes the
  fraction of the mass attenuation coefficient that
  gives rise to initial kinetic energy of electrons
  in a small volume of absorber
• These electrons may subsequently produce
  bremsstrahlung radiation, which can escape the
  small volume of interest
• The mass energy absorption coefficient is
  slightly smaller than the mass energy transfer
  coefficient

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Calculation of Dose

• Dose in any material is given by
• where

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Exposure

• The amount of electrical charge (?Q) produced by
  ionizing EM radiation per mass (?m) of air is
  called exposure (X)
• Units of charge per mass (e.g., C/kg).
• Historical unit of exposure is the roentgen (1 R
  2.58 x 10-4 C/kg exactly)

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Exposure (cont.)

• Exposure is a useful quantity because ionization
  can be directly measured with standard air-filled
  radiation detectors, and the effective atomic
  numbers of air and soft tissue are approximately
  the same
• Only applies to interaction of ionizing photons
  in air
• Relationship exists between amount of ionization
  in air and absorbed dose in rads for a given
  photon energy and absorber

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Roentgen-to-Rad Conversion Factors
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Exposure (cont.)

• Exposure can be calculated from the dose to air
• W is the average energy deposited per ion pair in
  air, approximately constant as a function of
  energy (W 33.97 J/C)

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Exposure (cont.)

• W is the conversion factor between exposure in
  air and dose in air
• In terms of the traditional unit of exposure, the
  roentgen, the dose to air is