Interaction of Radiation with Matter II

1
Interaction of Radiation with Matter II
2
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

3
Attenuation in Soft Tissue (Z 7)
4
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

5
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

6
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)

7
Attenuation in Soft Tissue (Z 7)
8
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

9
Linear Attenuation Data
10
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

11
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

12
Radiograph of Ice Cubes in Water
13
Mass Attenuation Coeff. (cont.)

• Using the mass attenuation coefficient to compute
  attenuation

14
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

15
Narrow- and Broad-Beam Geometries
16
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/ ?

17
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

18
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

19
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

20
Beam Hardening
21
Fluence

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

22
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

23
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)

24
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

25
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

26
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 (?tr/?) ratio for 20-keV photons in
  tissue is 0.68 reduces to 0.18 for 50-keV photons

27
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

28
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

29
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

30
Calculation of Dose

• Dose in any material is given by
• where

31
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)

32
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

33
Roentgen-to-Rad Conversion Factors
34
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)

35
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

36
Imparted Energy

• Total amount of energy deposited in matter
  product of the dose and the mass over which the
  energy is imparted (unit Joule)
• Example
• Assume each 1-cm slice of a head CT scan delivers
  30 mGy dose to the tissue in the slice. If the
  scan covers 15 cm, the dose to the irradiated
  volume (ignoring scatter from adjacent slices) is
  still 30 mGy
• Imparted energy is approximately 15 times that of
  a single scan slice

37
Equivalent Dose

• Not all types of radiation cause the same
  biologic damage per unit dose
• A radiation weighting factor (wR) established by
  ICRP to modify the dose to reflect effectiveness
  of the type of radiation in producing biologic
  damage
• Equivalent dose H D wR
• SI unit for equivalent dose is the sievert (Sv)
• Traditional unit is the rem (1 Sv 100 rem)

38
Radiation Weighting Factors (wR)
39
Sources of Additional Information

• Canadian Nuclear Safety Commission
• http//www.nuclearsafety.gc.ca
• International Commission on Radiation Protection
  (ICRP)
• http//www.icrp.org