Topic 5 - Dose Units

Kerma

• “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

• E_tr 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

• dE_ab 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, dE_tr = 7.3 MeV
  • fraction of 10 MeV photon energy transferred to the medium.
• A smaller amount is absorbed along the electron track: dE_ab = 7.06MeV
• dE_tr- dE_ab
  • 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

• 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 2^o)
  • 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

• 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

• 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)E_ab= Y (m_ab/r)
  • Can relate to R as:
    • 1 R = 0.00873 J/kg, then
    • Y/X = 0.00873 J/ ((m_ab/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 f_i ´ E_i
• Remember this is only useful for photons
• Some values are listed on page 187