# EUD

Class: NodeEquivalentUniformDose

Calculates the equivalent uniform dose (EUD), tumor control probability (TCP) and normal tissue complication probability (NTCP) to volumes, which can be used for quantitatively comparing and reporting inhomogeneous dose distributions based on radiobiological effect. The EUD parameter summarizes the 3D dose distribution in a volume to a dose “which, when distributed uniformely across the target volume, cases the survival of the same number of clonogens”, as described by Niemierko.

EUD is calculated as follows:

$$$EUD = \left(\sum_i{v_i D_i^a}\right)^{1/a} \label{eq:1}$$$

where $$v_i$$ is the fractional organ volume recieving a dose $$D_i$$ and $$a$$ is a tissue specific parameter that describes the volume effect. TCP is calculated as

$$$TCP = \frac{1}{1 + \left(\frac{TCD_{50}}{EUD}\right)^{4\gamma50}} \label{eq:2}$$$

where $$\gamma_{50}$$ describes the slope of the dose-response curve. $$TCD_{50}$$ is the dose to control 50% of the tumors. NTCP is calculated as

$$$NTCP = \frac{1}{1 + \left(\frac{TD_{50}}{EUD}\right)^{4\gamma50}} \label{eq:3}$$$

where $$TD_{50}$$ is the tissue tolerance dose, i.e. the dose that causes normal tissue complication in 50% of cases.

## Inputs

#### Dose

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

Type: Image4DFloat, Required, Single

#### Volume(s)

Mask(s) containing the structures for which to calculate the EUD. Must have the same matrix size as the dose.

Type: Image4DBool, Required, Multiple

## Outputs

#### EUD

A table containing information on the dose and structures evaluated as well as the EUD, normal tissue complication probability (NTCP) and and tumor control probability (TCP).

Type: DataCollection

## Settings

The values of these settings can be found in literature, for example in this reference by Emami.

### EUD

#### a Number

Tissue specific parameter that describes volume effect.

### NTCP/TCP

#### γ50 Number

Slope of the dose-response curve.

#### TD50 Number

The tissue tolerance dose, i.e. the dose that causes normal tissue complication in 50% of cases.

#### TCD50 Number

The dose of radiation that locally controls 50% of tumors.

## References

1. "Reporting and analyzing dose distributions: A concept of equivalent uniform dose", Medical Physics, 1996, Andrzej Niemierko.