# Equivalent Uniform Dose

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

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

Type: Image, List, Required, Single

#### Volume(s)

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

Type: Mask, List, Required, Single

## Outputs

#### Output

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: Table

## Settings

#### Volume Effect (a) [1] Float

Tissue specific parameter that describes volume effect. The volume effect in refers to the relationship between the size of the tumor and the amount of radiation needed to effectively treat it. Larger tumors require higher doses of radiation to achieve an equivalent level of cell killing as smaller tumors, leading to an increase in the risk of side effects to healthy tissue.

#### Dose-Reponse Slope (γ50) [1] Float

Slope of the dose-response curve. The dose-response slope measures the relationship between radiation dose and the level of cell killing in a tumor. A steeper slope means the tumor is more sensitive to radiation and less radiation is needed for the same level of cell killing, while a flatter slope means the opposite.

#### Tissue Tolerance Dose (TD50) [Gy] Float

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

#### Tumor Control Dose (TCD50) [Gy] Float

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

#### Merge Tables Boolean

If output produces a list, merge the list into one table.

## References

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

Keywords: EUD, TCP, NTCP, equivalent uniform dose, normal tissue complication probablity, tumor control