9.2 - Electron Beam Dose Distribution

In a similar way to photon beams, electron beams may be represented with depth dose charts, beam profiles, and isodose charts.

## Central Axis Depth Dose

The typical features of an electron depth dose chart are shown below.

In general, electron beams demonstrate:

• A high surface dose relative to photon beams
• A broad ‘effective dose’ region
• A linear fall off in dose at depth
• A bremsstrahlung tail due to generation of photons from inelastic 'collisions' with nuclei

R90 is the point beyond which dose is less than 90% of the maximum. R50 is the point of 50% dose, and is useful in describing the quality of the electron beam. Rp is the potential range, the maximum range obtained by electrons incident on the surface.

### Comparison of depth dose values

Electrons lose energy constantly as they pass through a medium, and their rate of energy loss and amount of scattering is dependent on their energy. For lower energy electrons, lateral scattering happens shortly after they enter the tissue. This leads to a relatively rapid loss of energy, with a significant 'peak' of energy loss at zmax relative to the surface dose. Higher energy electron beams tend to undergo minimal scattering near the surface and continue onwards, losing their energy over a greater distance. This leads to significantly broader region of dose distribution, and zmax is not significantly greater than the surface dose. The final outcome of these interactions is that high energy electrons have a high surface dose relative to low energy electrons.

Beam 6 MeV 9 MeV 12 MeV 16 MeV 20 MeV Surface Dose Pre-max 90% zmax Post-max 90% R50 R10 75% 0.8 cm 1.5 cm 2 cm 2.5 cm 3 cm 83% 1 cm 2 cm 3 cm 3.5 cm 4.5 cm 88% 0.5 cm 3 cm 4 cm 5 cm 6 cm 94 % N/A 3.5 cm 5 cm 6.5 cm 8 cm 95% N/A 2.3 cm 6 cm 8.5 cm 10.5 cm

### Formula for determining depth dose figures

This is useful for exams.

#### Surface Dose

This only works in my department. There are five energies. In order, assign them a value of $2^{3-n}$ where n is in order of energies. This value is x.

(1)
$$x=2^{3-n}$$
(2)
\begin{align} \text{Surface Dose} = 100 - {E \times x} \end{align}

This gives a vague approximation of surface doses, eg (for 9 MeV where $x = 2^{3-2} = 2^1 = 2$

(3)
\begin{align} \text{Surface Dose} = 100 - {9 \times 2} = 82% \end{align}

#### zmax

zmax usually occurs at a depth of $\frac{E}{4}$

#### Post-max R90

R90 usually occurs at a depth of $\frac{E}{3}$

#### R50

R50 is a bit tricker; it occurs at a depth of $\frac{\frac{E}{3} + \frac{E}{2}}{2}$.
This is the average distance between R90 and R10

#### R10

R10 occurs at a depth of $\frac{E}{2}$
Beyond R10, the curve is relatively flat, the bremsstrahlung tail.

## Beam Profile

The beam profile is a chart of the off-axis ratios for the beam along a line perpendicular to the beam direction at a particular depth. It allows determination of beam symmetry and beam flatness.

## Isodose Charts

Electron isodose charts are constructed in the same way as photon charts but have significantly different features. There are several major differences with electron beams when compared to photons:

• The isodose curves for 20% of dose and below tend to bulge outwards, if beam energy is over 10 MeV. This is due to increased lateral range of electrons when they possess a higher starting energy.
• The isodose curves for 80% of dose and above in beams over 15 MeV show lateral constriction - the isodose lines trend towards the central axis due to loss of electronic equilibrium. This has a similar cause to the bulging of low energy isodose lines - there is increased lateral scatter of electrons at higher energies due to their increased range.
• There is rapid loss of dose after the R90 is reached for all beams

The penumbra is defined by the ICRU as the region that lies between the 20 and 80% isodose lines, at a depth of R85 / 2, where R85 is the depth beyond zmax where the percentage depth dose is 85%. The penumbra is typically broader than for a photon beam, mostly due to lateral scatter of high energy electrons.