8.6 - Photon Beam Calculations

There are numerous factors which can be used to calculate photon beam dose distributions.

## Percent Depth Dose

Percent Depth Dose is the ratio of dose at a point on the central axis (P) relative to the point of maximum dose (zmax). (1)
\begin{align} PDD = \frac{D_P}{D_{z_{max}}} \end{align}

### Use of PDD

The PDD allows monitor units to be calculated when the point of calculation is not zmax.

## Off Axis Ratio

The OAR is the ratio of the dose at a point (Q) relative a point on the central axis at the same depth (P). (2)
\begin{align} OAR = \frac{D_Q}{D_P} \end{align}

### Use of the OAR

The OAR is used for for calculation of dose at points away from the central axis.

## Peak Scatter Factor (PSF) and Back Scatter Factor (BSF)

The peak scatter factor (PSF) is the the ratio of dose at a point P' (a point in air, surrounded by enough buildup to reach electronic equilibrium) compared with point P, located at the point of maximum dose in a phantom (zmax, at depth z cm). Point P' and point P are the same distance from the source (SSD + z cm). (3)
\begin{align} \text{PSF} = \frac{D_P}{D_{P'}} \end{align}

The peak scatter factor determines the ratio of dose at zmax that is due to scatter from other parts of the beam.

A special case of the PSF occurs for kilovoltage beams at zmax - which for these beams is located on the surface. All scattered radiation reaching this point has been backscattered (undergone at least a 180o turn), and therefore the PSF for kilovoltage beams is known as the *backscatter factor*. ## Tissue Air Ratio (TAR)

The TAR is used for isocentric techniques. It describes the ratio of dose at the isocentre in two situations:

• When the isocentre is submerged in depth x in water (point P)
• When the isocentre is in air (point P')

The TAR is affected by the field size and beam energy as well as the depth x. (4)
\begin{align} TAR (z) = \frac{D_{P}}{D_{P'}} \end{align}

The TAR is useful for low megavoltage beams. The buildup cap required for an ionisation chamber to detect the dose from higher energy megavoltage beams is excessive and not accurate.

### Use of the TAR

The TAR is used in isocentric techniques when the point of dose calculation is always the same distance from the source. It eliminates the need for an SSD measurement as the TAR is constant for most SSDs used in radiotherapy treatment. It is not used for modern linear accelerators due to concerns with buidup in the air measurement.

## Tissue Phantom Ratio (TPR) and Tissue Maximum Ratio (TMR)

### Tissue Phantom Ratio (TPR)

The TPR is similar to the TAR, except that it is the ratio of dose at the isocentre:

• When the isocentre is submerged in depth x in water (point P)
• When the isocentre is submerged in depth y in water (point P') (5)
\begin{align} TPR = \frac{D_{P}}{D_{P'}} \end{align}

This has the advantage of giving accurate measurements for high energy photon beams as there is sufficient buildup of dose in water.

### Tissue Maximum Ratio (TMR)

The TMR is a special case of the TPR, where the depth y used for the comparison is at the depth of maximum dose zmax (depth z). (6)
\begin{align} TMR = \frac{D_{P}}{D_{z_{max}}} \end{align}

### Use of the TPR/TMR

The tissue phantom and tissue maximum ratios are used for high energy photon beams. They allow correction of monitor units/treatment time to account for change in dose at depths other than the reference used. They have an advantage over percentage depth dose measurements which are also dependent on source surface distance.

## Scatter Air Ratio (SAR)

The scatter air ratio is the difference between two tissue air ratios:

• The TAR with a field size of A cm, at a depth of x cm in water
• The TAR with a field size of 0 cm, at a depth of x cm in water (7)
\begin{align} SAR = TAR({x,A \text{ cm}}) - TAR({x,0 \text{ cm}}) \end{align}

### Use of the Scatter Air Ratio

The SAR is a useful in determining how much of the dose at a point on the central axis is due to dose scattered from lateral parts of the beam.