Electron Depth Dose Curves:

 

 

  1. Electron depth dose curves are characterized by a relatively high surface dose (compared to photon depth dose curves), a sharp falloff beyond the 80% isodose line, and a finite range.
  2. The most notable labels from above are:
  1. R100 - or dmax (the depth of maximum dose).
  2. D- which is the surface dose.
  3. R- which is the useful therapeutic range (usually the 80-90% isodose line).
  1. A handy rule of thumb for water is image014.
  1. R- is the practical range and is found by creating a line tangential to the steep portion of the %DD and the bremsstrahlung tail. The intersection of those lines is the practical range.
  1. a handy rule of thumb for water is image016.
  1. R50 - the depth where dose falls to 50% its maximum.

 

Electron %DD Curve Behavior:

 

 

  1. Electron %DD curves vary with energy and the following ideas are important to understand:
  1. Surface dose increases with energy.
  1. This is because, at higher energies, scatter is less likely and predominantly forward.  Therefore, the surface dose relative to the maximum dose is similar in high energy beams (in low energy beams there is more scatter and larger scattering angles involved causing the dose to build up more rapidly and to a greater degree).
  1. The slope of the falloff decreases with energy.
  1. This is due to the randomness of the electron paths as they travel through the body.  At higher energies, they have a longer path length and therefore more opportunity for their energy spectrum to spread out.
  1. Higher energy electron beams have a very large flat plateau that occurs due to the relative lack of buildup in high energy beams.
  2. As the energy of the electron beam increases, the amount of x-ray contamination increases due to the higher likelihood of bremsstrahlung interactions (proportional to energy).
  1. Electron %DD curves also vary with field size.  In general:

 

image019

 

  1. A smaller field size results in the depth of dmax shifting shallower and a decrease in the slope of the falloff (notice the practical range does not really change as the energy has not changed).

 

 

  1. %DD curves are relatively constant until the field size becomes small enough that lateral charged particle equilibrium is lost (see 2x2-10x10 cm2 above).
  1. When the field size is approximately equal to the practical range of the electrons, then the %DD is constant (e.g. for 12 Mev, R= 6.0 cm, and above 5.5x5.5 cm2 the %DD is almost constant).

 

 

  1. Another factor that has a major effect on electron %DD curves is the angle of incidence.
  1. An oblique angle will shift dmax shallower along with the 80% isodose curve depth (effective treatment depth).
  2. Notice that the range appears to increase at greater oblique angles.  This is due to electrons side scattering from parts of the beam that have not passed through much water due to the oblique angle.
  1. Measuring electron %DD curves:
  1. Using an ionization chamber you cannot directly measure a %DD curve.  Instead, you measure a percent ionization curve (%I). The reason for this is that for electrons, stopping power ratios for water to air vary with energy (or depth).  To recover a %DD curve we must use the following relationship, where (image005) is the restricted mass stopping power:

image022

  1. The reason for this is an effect called the polarization density effect which occurs in high energy electron beams.
  1. In a dense medium (water) when an electron interacts it creates ions.  Due to the high density of the medium, the created ions are also very dense.  These ions screen the incident electron’s electric field from interacting with distant particles and reduce the interaction rate.
  2. In a gas (air) the relatively low density means that the ionization track has a low density of ions, and, therefore, there is negligible screening of distant particles.
  3. When comparing the stopping power ratio of water to air the ratio is no longer constant.
  4. However, using a silicon diode (also a solid) the ratio remains relatively constant and, thus, instant %DD curve.
  1. Equivalent Square field sizes:

 

image024

 

  1. Equivalent square field sizes are defined as a square field that has the same %DD as the field in question.
  2. For electron fields, there is not a clear relationship as in photon fields.
  3. This brings us to an important point; it is always best to directly measure a cutout’s %DD and output as electrons do not behave as predictably as photons.
  1. At the very least a large table should be created for each machine such that cutout factors can be interpolated.

 

image025

 

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