PUBLIC LIBRARY / CALCULATOR

BED and EQD2

Explores BED and EQD2 using the linear-quadratic model with an explicitly selected α/β ratio. The mathematical result establishes neither clinical equivalence nor a radiotherapy plan.

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Check the population, units and version. The result shows the formula or classification; it does not make an automatic treatment decision.

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Method · Limits of application

Fowler 1989/2010; linear-quadratic model without time corrections

Mathematical model without repopulation, incomplete repair, recovery or plan summation. α/β is a selected assumption; the result does not establish clinical equivalence or a radiotherapy plan.

Conditions of use

Check the conditions of application before calculating. The result presents the documented formula or criteria; it does not establish a diagnosis or prescription.

Scope of this implementation

Mathematical model without repopulation, incomplete repair, recovery or plan summation. α/β is a selected assumption; the result does not establish clinical equivalence or a radiotherapy plan.

Parameters in this edition

Dose per fraction (d) · Gy
Number of fractions (n) · fractions
Tissue α/β ratio

Sources and documentation

Method version

Fowler 1989/2010; linear-quadratic model without time corrections

Formula and criteria

BED = n × d × (1 + d/(α/β)); EQD2 = BED/(1 + 2/(α/β)).

Population and limitations

Mathematical model without repopulation, incomplete repair, recovery or plan summation. α/β is a selected assumption; the result does not establish clinical equivalence or a radiotherapy plan.

Synthetic cases checked (3)

Synthetic cases for checking the implementation, with no patient data.

Case 1

reference-001

Inputs

Dose per fraction (d): 2 Gy
Number of fractions (n): 30 fractions
Tissue α/β ratio: 10 Gy · tumors in general and acutely responding tissues

{
  "dose": 2,
  "n": 30,
  "ab": "10"
}

Expected result

{
  "dose": 60,
  "bed": 72,
  "eqd2": 60
}

Actual result

{
  "dose": 60,
  "bed": 72,
  "eqd2": 60
}

Case 2

reference-002

Inputs

Dose per fraction (d): 4 Gy
Number of fractions (n): 5 fractions
Tissue α/β ratio: 3 Gy · late-responding tissues (usual value)

{
  "dose": 4,
  "n": 5,
  "ab": "3"
}

Expected result

{
  "dose": 20,
  "bed": 46.666666666666664,
  "eqd2": 28
}

Actual result

{
  "dose": 20,
  "bed": 46.66666666666666,
  "eqd2": 27.999999999999996
}

Case 3

reference-003

Inputs

Dose per fraction (d): 6 Gy
Number of fractions (n): 1 fractions
Tissue α/β ratio: 1.5 Gy · prostate cancer

{
  "dose": 6,
  "n": 1,
  "ab": "1.5"
}

Expected result

{
  "dose": 6,
  "bed": 30,
  "eqd2": 12.857142857142858
}

Actual result

{
  "dose": 6,
  "bed": 30,
  "eqd2": 12.85714285714286
}

Source for the active edition

eviQ · BED/EQD2 · version 3

Additional reading and history

Identifier: bed-e-eqd2

Original clinical content: Brazilian Portuguese.

Code and reproducibility

This tool’s code on GitHub

Download code and tests

Sources, version and reproduction instructions

README

Local installation

Code license: Apache-2.0

Guidelines and conditions

This repository’s license applies to the code. Third-party instruments, questionnaires, data and models remain subject to their owners’ conditions.

The code tests are technical checks. Clinical approval and professional translation review are recorded separately.

Relationship with cancer research

Specific oncological application

A biological dose model in radiotherapy. Comparing fractionation schedules requires tissue parameters, model assumptions and specialist review.

Applications: Pharmacology · Adverse effects and safety

Rare tumors

EQD2 with α/β=3 Gy was used to compare SBRT schedules in a retrospective series of 46 patients with sarcoma, most of whom had metastatic disease (Stragliotto et al., 2012). The local calculation supports radiobiological comparison within the linear-quadratic model when the number of fractions and uniform dose are known; it does not reproduce 3D/DVH/EUD planning, organ tolerance, or treatment decisions.

DOI: 10.1007/s12032-012-0256-2