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 radiativeloss
energy, but excluding energy passed from one charged particle
to another
Quantities to Describe a Radiation Beam
 Fluence
 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 = 10^{14 }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, 7.307.06 = 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 (ChargedParticle) 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
Isotope 
Maximum Dose Septh (mm in Tissue) 
Beam Attenuation (% of original beam) 
^{137}Cs 
2 
1 
^{60}Co 
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
 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
