OSU Extended Campus Oregon State University
official course number and title
jump over navigation bar
Welcome Contact Getting Started Site Map Project 1 2 3 4 5 6 7 8 9 10 11

Topic 5 - Dose Units


link to previous page in the series link to next page in the series
  • “Sum of the initial kinetic energies per unit mass of all charged particles produced by the radiation”
    • This is regardless of where the energy is deposited
    • Bremsstrahlung photons are not counted, whether they escape or not
    • Annihilation radiation is not counted, regardless of fate of annihilation photons
      • Initial positron, if primary ionizing particle, is counted

Energy Transfer - A Two Stage Process - Kerma and Absorbed Dose


Correction/Clarification on Kerma

  • Etr is just the kinetic energy received by charged particles in a specified volume V, regardless of where or how they spend the energy
  • Kerma is the expectation value of the energy transferred to charged particles per unit mass at a point of interest, including radiative-loss energy, but excluding energy passed from one charged particle to another

Quantities to Describe a Radiation Beam

  • Fluence
    • # photons/area
    • F = dN/da
  • Energy fluence
    • Energy / area
    • Y = dN hn/da
  • Fluence rate
    • # photons/(time area)
    • f = dF/dt
  • Energy fluence rate
  • Energy / (time area)
  • y= dY/dt

Relationship of Kerma to Photon Fluence

     > is attenuation coefficient

     is density

    • gives the number of photon interactions that take place per unit mass of material.
  • m is attenuation coefficient
  • r is density
  • For a spectrum of energies that can be described by dΦ(hv) /d hv, then:

Calculating Kerma

  • Given incident on a block of carbon
    • 10 MeV photons
    • F = 1014 m-2
  • What is kerma?

  • Kerma is easy to calculate - but very difficult to measure!

Relating Kerma & Absorbed Dose

  • Kerma
    • a measure of  kinetic energy transferred at a point in space.
  • Absorbed dose is more “interesting”.
    • Energy is transferred in the medium
    • not all is retained there. 
    • absorbed dose is the energy retained in the medium brought about by the ionizations along the track of the charged particle.
  • Kerma and Absorbed Dose do not take place at the same location

Calculating Absorbed Dose

  • dEab is the mean energy “imparted” by the ionizing radiation into a mass, dm. 
    • Mass should be sufficiently small so that it the absorbed dose is defined at a point, but not so small that statistical fluctuations become important
  • From the previous example, dEtr = 7.3 MeV
    • fraction of 10 MeV photon energy transferred to the medium.
  • A smaller amount is absorbed along the electron track: dEab = 7.06MeV
  • dEtr- dEab
    • The difference, 7.30-7.06 = 0.24 MeV, is bremsstrahlung.
  • What is the path length of the 7.3 MeV electron in C?
    • Estimate from graphs or tables of electron ranges,
    • ~ 4.2 g cm-2.
    • Divide by the density of carbon
    • Path length: 1.9 cm. 

Dose and Kerma

Important Relationship

  • Relate absorbed dose in air to exposure:
    • assuming CPE (electronic equilibrium)

Electronic (Charged-Particle) Equilibrium

  • The transfer of energy (kerma) occurs upstream from the absorbed dose. 
    • Kerma can be easily calculated from fluence
    • Absorbed dose cannot.  Why?
    • Kerma remains constant       
    • Absorbed takes time to build up as upstream electrons increase:

No Attenuation of Photon Beam, Φ Constant

diagram: No Attenuation of Photon Beam
  • arrow Number of electron tracks set in motion by photon interaction
    • Φ constant with depth (small # interactions)
    • Same # electrons set in motion in each square
    • i.e., interactions per volume constant through target

Absorbed Dose and Kerma


Beam Unattenuated

  • Same number of photon tracks set in motion in each square
    • e.g., square D is traversed by 400 tracks
    • ionization in D is the same as total ionization started in A
    • absorbed dose is proportional to ionization produced in each saure
    • dose reaches a maximum at R (range of 2o)
    • kerma constant with depth, equals absorbed dose beyond R

Absorbed Dose and Kerma


Attenuation of Photon Beam

  • Beam attenuation,
  • Φ decreases with depth. 
  • Dose increases to a maximum (at maximum range of particle) overshoots then tracks kerma.

Attenuation of Photons in Tissue

Isotope Maximum Dose Septh (mm in Tissue) Beam Attenuation (% of original beam)
137Cs 2 1
60Co 5 2
6 MV 15 6
  • CPE will generally exist in a uniform medium at a point more than the maximum range for the secondary charged particles from the boundary of the medium

Relating Energy Fluence and Exposure

diagram: radioactive beam incident
  • Radioactive beam incident on an area
    • What is relationship  between energy fluence and exposure at point p?
      • Assume small mass of air at p
      • The dose at p is: D= F(m/r)Eab= Y (mab/r)
    • Can relate to R as:
      • 1 R = 0.00873 J/kg, then
      • Y/X = 0.00873 J/ ((mab/r)kg R)
      • Complicated variation of energy absorption coefficient for air and energy of beam

Relating photon fluence to exposure

  • Relationship between energy fluence and photon fluence:
    • F = dN/da
    • Y= dN hn/da
    • So, Y= F hn, and

Specific Gamma Ray Emission

  • G = Specific Gamma Ray Constant
  • Has been calculated for many gamma ray emitting isotopes
  • Can ‘easily’ be calculated
  • Where do the numbers come from?

Specific Gamma Ray Constant

  • Assumes that the absorption of photons in air is constant over a large range
  • See Figure 5.18 in text (p. 148) or Table 5.3 (p. 149)
  • Absorption is almost constant from 60 keV to almost 2 MeV
  • Assumes photons isotropic, no ‘buildup’
  • Eliminates many constants for ease of calculation
  • 3.5 ´ 10-3 m-1 linear absorption coefficient
  • Combine terms
  • Thus, 0.5 is the value of all of the constants combined
  • Equation 6.18 can then be written
  • G = 0.5 S fi ´ Ei
  • Remember this is only useful for photons
  • Some values are listed on page 187
  link to previous page in the series link to next page in the series
Welcome Contact Getting Started Site Map Project 1 2 3 4 5 6 7 8 9 10 11