# Gamma Index

Class: NodeDoseGammaIndex Calculates the gamma index, first introduced by Low et al, between a reference and an evaluation dose distribution in 3D with sub-voxel accuracy according to the algorithm described by Wendling et al. It will only calculate the gamma index for reference voxels >0.

### Definition of the gamma index

The gamma index combines the dose difference and the distance difference into a dimensionless metric. In principle, this metric should be calculated for each reference point against all points in the evaluated dose distribution. The gamma statistic is calculated as

$\begin{equation} \Gamma(\textbf{r}_R,\textbf{r}_E) = \sqrt{\frac{\Delta r^2(\textbf{r}_R,\textbf{r}_E)}{\delta r^2} + \frac{\Delta D^2(\textbf{r}_R,\textbf{r}_E)}{\delta D^2}} \label{eq:sample} \end{equation}$

where $$\delta r$$ is the distance criterion (distance to agreement or DTA) and $$\delta D$$ is the dose difference criterion. The $$\gamma$$ is then taken as the minimum $$\Gamma$$ value over all evaluated points. If $$\gamma < 1$$, that point will pass. Standard values for $$\delta r$$ is 3 mm and $$\delta D$$ is 3%, and a standard value for accepting agreement between two distributions is usually that 97% of all evaluated points should pass.

## Inputs

#### Reference Dose

An image containing the dose matrix to be used as reference. This image is normally produced by importing a DICOM RT DOSE, or RD file.

Type: Image4DFloat, Required, Single

#### Evaluated Dose

An image containing the dose matrix to be evaluated. This image is normally produced by importing a DICOM RT DOSE, or RD file. It must have the same matrix size as the reference dose.

Type: Image4DFloat, Required, Single

A mask which specifies in which area the gamma index should be evaluated. It only applies to points in the evaluated dose. It must have the same matrix size as the reference dose.

Type: Image4DBool, Optional, Single

## Outputs

#### Map

A parameter map which contains the $$\gamma$$ values.

Type: Image4DFloat

#### Fail Map

A binary image which is True where $$\gamma > 1$$, i.e. failed points.

Type: Image4DBool

#### Evaluated Map

A binary image which is True for points that have been included in the evaluation.

Type: Image4DBool

#### Gamma Index

A table which contains information on the gamma evaluation, such as names of the evaluated distributions, the number of evaluated voxels and the gamma pass rate.

Type: DataCollection

## Settings

#### Sample Step Size(mm) Number

Determines the resolution of the evaluation, i.e. the accuracy of the interpolation. Recommended step size is at most 1/3 of the distance to agreement (DTA) and a fraction of the resolution of the voxel size. As an example, for a 1 mm DTA and voxel size of 2 mm, a step size of 0.25 mm would be suitable. Increasing resolution increases computation time.

#### Prescribed Dose(Gy) Number

The dose to which the dose criteria is related to if the option Use Local Dose Reference is not selected. I.e. if a 3% dose criterion is chosen and the prescribed dose is 10 Gy, the absolute dose difference criteria in the gamma calculations will be 0.3 Gy.

#### Use Local Dose Reference Boolean

If comparing the gamma distribution on a local level, i.e. not normalized to the prescribed dose, this option should be activated. This will check the dose difference at each individual sample point and normalize it to the dose level in the current reference voxel.

#### Dose Criteria(%) Number

Sets the dose criteria.

#### Distance Criteria(mm) Number

Sets the distance criteria, or distance to agreement.