Welcome Contact Getting Started Site Map Project 1 2 3 4 5 6 7 8 9 10 11

# 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

### 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

## •     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.

### 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

### 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

### 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

• 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
 Welcome Contact Getting Started Site Map Project 1 2 3 4 5 6 7 8 9 10 11
 College of Engineering OSU Extended Campus Local 541-737-9204 Fax 541-737-2734 4943 The Valley Library Corvallis, OR 97331-4504