# Biologically Effective Dose (BED) Calculator

Determines the biologically effective dose (BED) and the equivalent dose (EQD2) for cancer radiotherapy.

Refer to the text below the tool for more information about the formulas used and appropriate α/β ratios.

The Biologically Effective Dose (BED) is a measure of the true biological dose delivered by a particular combination of dose per fraction and total dose to a particular tissue characterized by a specific α/β ratio and is commonly used for isoeffective dose calculations.

Biologically equivalent doses are calculated in 2-Gy equivalents using the EQD_{2} equation. An equivalent total dose in 2-Gy fractions (EQD_{2}) can be found for any BED by dividing it by the RE for 2-Gy fractions, using the appropriate α/β ratio.

### Formulas

`BED = Total dose x (1 + (Fraction dose / αβ))`

Or, alternatively, if there is a known dose rate factor:

`BED = Total dose x (1 + ((Dose rate factor x Fraction dose) / αβ))`

`EQD₂ = Total dose x ((Fraction dose + αβ) / (2 + αβ))`

## Send Us Your Feedback

**Steps on how to print your input & results:**

1. Fill in the calculator/tool with your values and/or your answer choices and press Calculate.

2. Then you can click on the Print button to open a PDF in a separate window with the inputs and results. You can further save the PDF or print it.

Please note that once you have closed the PDF you need to click on the Calculate button before you try opening it again, otherwise the input and/or results may not appear in the pdf.

## BED and EQD_{2} Explained

The Biologically Effective Dose (BED) is a measure of the true biological dose delivered by a particular combination of dose per fraction and total dose to a particular tissue characterized by a specific α/β ratio and is commonly used for isoeffective dose calculations.

Biologically equivalent doses are calculated in 2-Gy equivalents using the EQD_{2} equation. An equivalent total dose in 2-Gy fractions (EQD_{2}) can be found for any BED by dividing it by the RE for 2-Gy fractions, using the appropriate α/β ratio.

The variables used are:

- Irradiation duration – can be less than a few minutes or more than a few minutes. In case of the former, a slowly delivered fraction may reduce side-effects. If this option is selected, a dose rate factor is required (indicated the repairability of a cell).
- α/β ratio – is the measure of tissue radiation sensitivity, where the higher the ratio, the greater the tissue sensitivity.
- Fraction dose – indicates the dose received during single irradiation (most commonly measured in grays Gy).
- Total dose – indicates the sum of all doses received.

The formulas used, based on the linear dependence of cell’s survival, are:

`BED = Total dose x (1 + (Fraction dose / αβ))`

Or, alternatively, if there is a known dose rate factor:

`BED = Total dose x (1 + ((Dose rate factor x Fraction dose) / αβ))`

`EQD₂ = Total dose x ((Fraction dose + αβ) / (2 + αβ))`

The BED and EQD_{2} allows comparison between different fractionation regimens. The concept of biologically effective dose is useful for quantifying treatment expectations, with the caveat that careful interpretation of modelling results is required before clinical decisions are made. Correct use of BED calculations often involves the collaboration with other patient parameters.

An α/β ratio of 10 is typically used for early-responding tissues and tumors whilst an α/β ratio of 3 is often used for late-responding tissues, such as normal tissue.

Where the fraction dose is being altered and it there is a risk that normal tissue tolerance may be compromised, calculations should include two or more α/β ratio values.

The following tables can be used for the α/β ratio for tissues:

Early reactions |
Late reactions |
||||

Skin, desquamation Erythema |
8.6 - 12.5 | Spinal cord, cervical Spinal cord, lumbar |
1.5 - 3.0 2.3 - 4.9 |
Subcutis, fibrosis | 1.7 |

Jejunum | 6.0 - 10.7 | Colon, weight loss | 3.1 - 5.0 | Breast | 3.1 - 3.4 |

Colon | 9 - 13 | Kidney (animal studies) | 0.5 - 4.3 | Nerve, optic neuropathy Nerve, brachial plexopathy |
1.6 2 - 3.5 |

Testis | 12 - 13 | Lung, pneumonitis Lung, fibrosis |
4.0 3.1 |
Bowel | 3.9 - 4.3 |

Tumor bed | 5.6 - 6.8 | Bladder, frequency capacity | 5 - 10 | Head and Neck, various | 3.5 - 4.0 |

Oral mucosa, mucositis | 8 - 15 | Skin, vasculature | 2.6 - 2.8 | Supraglottic larynx Oral Cavity + oropharynx |
3.8 0.8 |

The following tables can be used for the α/β ratio for tumors:

Tumor |
α / β |

Head and Neck, various | 10.5 |

Larynx | 14.5 |

Vocal cord | 13 |

Buccal mucosa | 6.6 |

Tonsil | 7.2 |

Nasopharynx | 16 |

Skin | 8.5 |

Prostate | 1.1 |

Breast | 4.6 |

Oesophagus | 4.9 |

Melanoma | 0.6 |

Liposarcoma | 0.4 |

## References

Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989; 62(740):679-694.

Jones B, Dale RG, Deehan C, Hopkins KI, Morgan DA. The role of biologically effective dose (BED) in clinical oncology. Clin Oncol (R Coll Radiol). 2001; 13(2):71-81.

Fowler JF. 21 years of biologically effective dose. Br J Radiol. 2010; 83(991):554-68.

Lee SP, Leu MY, Smathers JB, McBride WH, Parker RG, Withers HR. Biologically effective dose distribution based on the linear quadratic model and its clinical relevance. Int J Radiat Oncol Biol Phys. 1995; 33(2):375-389.

Kuperman VY, Spradlin GS. Effect of variable dose rate on biologically effective dose. Int J Radiat Biol. 2013; 89(11):889-897.

Joiner MC, Kogel A. Basic Clinical Radiobiology Fourth Edition. Abingdon, Oxon: CRC Press; 2009.

Specialty: Oncology

Abbreviation: BED

Article By: Denise Nedea

Published On: July 6, 2020 · 12:00 AM

Last Checked: July 6, 2020

Next Review: July 6, 2025