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Topic 5 - Dose Units

Radiation Dosimetry

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Dosimetry Overview

  • Units
  • Specific Gamma-Ray Emission
  • Beta Radiation
  • Internally Deposited Radionuclides
  • Neutrons


  • Dosimetry attempts to quantitatively relate specific radiation measurements to chemical/biological changes that could be produced
  • Essential for quantifying biological changes as a function of radiation received
  • For comparing experiments
  • For other purposes
  • Radiation interaction
    • Produces ionized and excited atoms and molecules
    • Secondary electrons
      • Produce additional ionizations and excitations
      • Finally all energies are expended.
    • Initial electronic transitions rapid (<10-15s)
    • Represent the initial physical perturbations from which all effects evolve.
  • So, ionization and energy absorption are the starting point for radiation dosimetry

Quantities and Units

  • Absorbed Dose
    • Primary physical standard in dosimetry
    • Defined as energy absorbed per unit mass from any kind of ionizing radiation in any target.
  • SI Unit of absorbed dose,
    • Called the gray (Gy)
    • 1 Gy = 1 J kg-1
  • Historical (older) term
    • rad, (100 erg g-1)
  • 1 Gy = 107 erg/103g = 104 erg/g = 100 rad
  • Exposure
    • Defined for X and gamma radiation
      • In terms of ionization of air
      • Old unit called “roentgen” (R)
      • Initially defined in 1928, current definition is:
      • 1 R º 2.58 x 10-4C kg-1 of air, exactly
    • Applies only to electromagnetic radiation; the charge and mass refer only to air.

Roentgen - original definition

  • Amount of radiation that produced 1 esu of charge in 1 cm3 of air at STP
    • 1 esu = 3.335 x 10-10C
    • diagram


    • At STP air has a density of 0.001293 g cm-3
    • 1 kg of air has a volume of 7.734 x 105 cm3
  • 1 R = 3.335 x 10-10 C cm-3 of air
  • How much energy is absorbed in air from 1R?

Absorbed Dose and Exposure

  • What is the absorbed dose in air when the exposure is 1 R?
    • Need to know W for air
      • 33.7 eV/ip = 33.7 J/C.
    • 1 R º 2.58 x 10-4C/kg x 33.7 J/C = 8.8 x 10-3 J kg-1
  • This equals 8.8 x 10-3 Gy (0.88 rad)
    • Similar calculations show that 1R would produce a dose of 9.5 x10-3 Gy (=0.95 rad) in soft tissue.
      • Why is there a difference between air and tissue???
    • This is why one can say that 1 R ~ 1 rad in tissue.

Exposure Measurement - Free Air Chamber

  • Feasible to measure exposure at radiation energies between few keV and several MeV
  • Definitive measure is by laboratory device known as free air chamber
  • X-ray beam enters through a portal and interacts with cylindrical column of air defined by entry diaphragm
  • Ions created in defined space are measured

Parallel Plate Free-air Ionization Chambers


Free Air Chamber

  • Photons enter chamber and interact with fixed quantity of air
    • PE, CS
  • Ions from air collected by plates
  • Lead lined (shielded)
  • Electric fields are kept perpendicular to plates by guard rings and guard wires
    • Guard wires assure uniform potential drop across plates
  • Field intensity is ~ 100 V/cm
  • Collect ions prior to recombination
  • Voltage low enough so no secondary ionizations
  • Current flow is measured
  • All energy of primary electrons must be deposited in sensitive volume of air for meter to work properly
  • What if all primary electrons are not collected in sensitive volume?
  • If equal number coming in from outside of sensitive volume as is going out: Electronic Equilibrium

Electronic Equilibrium

  • For every electron which escapes the sensitive volume, another electron of equal energy enters the sensitive volume and deposits energy in the detector 
  • A layer of air between entrance port of free air chamber and the sensitive volume can provide enough air so that electronic equilibrium is attained

Free-Air Ionization Chamber

Free-Air Ionization Chamber

Wide-Angle Free Air Chamber (WAFAC)

  • NIST primary standard for low-energy photon-emitting brachytherapy sources such as 125I.
    • Variable volume, circular free-air chamber,
    • Symmetrical about the beam axis, with lines of force parallel to the beam axis.
    • 80 mm diam. Tungsten aperture (not visible at right) chamber used to define the beam.
    • 3 electrodes: polarizing, middle, and collecting electrode (farthest from the source and left in the picture) about 150 mm in diameter.
    • Chamber volume varied from ~75 cm3 to 804 cm3 by changing middle electrode from 11 mm to 152 mm.

Measuring Exposure

  • Free air chamber practical only as laboratory device
  • Portable instrument needed

Exposure Measurement: Air Wall Chamber

diagram: Air Wall Chamber
  • Practical alternative to free-air chamber
  • Built as a capacitor
    • Central anode, insulated from rest of chamber
    • Given an initial charge
    • When exposed to photons, 20 electrons neutralize charge & lower potential between anode and wall
    • Change in potential difference is proportional to total ionization (and therefore exposure)
  • Better for field use than the Free Air Chamber
  • Simulates compressing air into a small volume by using ‘air equivalent’ material
    • X-ray absorption properties similar to that of air
  • Walls must be thick enough to generate enough primary electrons
  • Walls must be thin enough so that primary radiation is not shielded
  • Ideal air wall chambers have only primary electrons ionizing the air in the sensitive volume
  • Ideal wall thickness is almost energy independent over a range from 200 keV to almost 2 MeV (See figure 6.4)
  • Greater than 3 MeV primary electrons have long range
  • Impractical to build air wall chamber of sufficient size
    • When walls are made thick enough to generate primary electrons, radiation is attenuated significantly
    • Radiation intensity will no longer be constant
    • Primary electrons not produced uniformly
    • No electronic equilibrium

Exposure-Dose Relationship

  • Exposure
    • measures charge produced in a mass of air
    • C/kg
  • Absorbed dose
    • Measures energy absorbed per mass
    • J/kg
  • How to relate measurement in air to absorbed dose in something besides air?
  • Energy absorption in air ¹ energy absorption in tissue
  • Dose in air ¹ dose in tissue
  • 1 R = 87.7 ergs/gair = 95 ergs/gtissue
  • 1 rad = 100 ergs/gtissue
  • For regulatory purposes, frequently 1 R is assumed to be equal to 1 rad
  • Conversion can be done if required

Exposure to Dose Conversion

  • Equation 6.12
  •  mm = Energy absorption coefficient for tissue
  •  ma = Energy absorption coefficient for air
  •  rm = Tissue density
  •  ra = Air density

Bragg-Grey Theory

  • How to measure absorbed dose?
  • The best way would be calorimetry...but not very practical.  Instead, absorbed dose is measured by:
    • measuring ionization
    • use of correction factors
    • calculating (approximating) dose
  • This is done with BRAGG-GREY CAVITY THEORY

Measurement of Absorbed Dose

  • Bragg-Gray principle relates ionization measurements in a gas to absorbed dose in some material.
  • Consider a gas in a walled enclosure irradiated by photons:
  • Photons interact in cavity and wall
    • Chose wall material that has similar radiation absorption properties as tissue (e.g., Z)
    • Cavity is very small
      • (doesn’t change angular and velocity distributions of 20 electrons)
    • Electronic equilibrium” exists in cavity
      • (# e- stopping = # e- starting in cavity)
      • requires wall thickness > range of 2o e
  • Ionizations in the gas
  • Can measure the charge liberated. 
  • If you know the energy required to ionize the gas,equation
  • Then the dose to the gas is:
  • where,
    • Q = coulombs of charge liberated
    • W = average ionization energy for the gas
    • m = kg of gas in the cavity
  • Example: A cavity filled with (1 cm3) air at STP is exposed to a radiation field that liberates 3.336X10-10 C.  What is the dose to the air?
  • At STP:

  • Know the dose to the gas. 
    • What about the dose to the medium surrounding it?
  • Assume our cavity is really small...small enough that it does not disrupt the electron spectrum.
  • Wall thickness must be as great as range as secondary charged particles (not too great to attenuate beam)
  • Then energy absorbed per unit mass of wall is related to that absorbed per unit mass of gas by: equation
  • Note - this special case is where the wall and gas are the same type of material
  • Dw is the dose to the wall
  • Dg is the dose to the gas
  • Nq is the number of ions produced in the gas
  • W is eV required to produce and ion pair
  • m is the mass of gas in the cavity
  • If gas and wall don’t have same atomic composition, a slight modification is required: equation
  • where Sg,w are the mass stopping powers of the wall and the gas
  • the cavity and gas pressure must be small


  • 1 cm3 of air in a block of carbon is exposed to 60Co γ
    • Q=3X10-8 C is produced. 
  • What is the absorbed dose to the carbon?
  • equation
  • Mean mass stopping power ratio for 60Co γ in carbon relative to air (Table 6.1) = 1.009
  • This equation allows us to measure the ionizations in a gas and relate it to dose to the medium. 
  • If neutrons are present, the wall must be at least as thick as the maximum energy range of any secondary charged recoil nuclei produced by the nuclear interactions.
  • Chambers that meet these conditions can be used to measure absorbed dose to the medium
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