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Educational radiobiology tool for clinicians and trainees. BED and EQD2 are model outputs, not measured biological doses or tissue-tolerance limits. The workbench uses the standard linear-quadratic (LQ) formalism for equal fractions and makes its assumptions visible.

BED / EQD2 Workbench

Calculate first. Then understand what the number means — and what it does not mean.

Local calculation No patient data transmitted v0.1
Explanation level The calculation is identical; only the amount of explanation changes.

1. What are you comparing?

Enter up to three equal-fraction courses. All courses use the same α/β so they can be compared for the same biological endpoint.

Input
Important: α/β is a model parameter, not a fixed physical constant. Presets are conveniences for teaching/comparison and must not replace a tissue-, tumour- and endpoint-appropriate value.
2 Gyused for EQD2
EQD2 uses 2 Gy per fraction because conventional radiotherapy historically made 2 Gy a useful reference. It is a convention, not a special biological dose at which nature changes behaviour.
Standard LQequal fractions
No repopulation correction, incomplete-repair correction, dose-rate correction or spatial dose accumulation is included in v0.1.
Course Aprimary comparison
Course Bcomparison
Course C

2. Results

The arithmetic is exact for the entered formula and inputs. The biological interpretation is not.

LQ model
Clinical equivalence is not established by equal BED or equal EQD2. Fraction size, tissue volume, spatial dose distribution, treatment interval, repair/repopulation, technique, patient selection and clinical evidence can all matter.

3. Why does fraction size matter?

The shortest route from physical dose to BED.

Concept
1

Start with physical dose

An absorbed dose of 1 gray (Gy) means 1 joule of radiation energy absorbed per kilogram of matter. If 2 Gy is delivered on 30 separate days, the physical total is 60 Gy.

That number alone does not describe the biological effect. Tissue has time between fractions to repair some radiation injury, and different tissues respond differently to fraction size.

2

Describe radiation survival with a simple model

The linear-quadratic model writes the logarithm of cell survival as:

−ln(S) = αD + βD²

αD is the component that grows in proportion to dose. βD² grows with the square of dose, so it becomes relatively more important as the dose per fraction increases.

This is a model of response. α and β summarize observed radiobiological behaviour; they are not little physical objects inside a cell.

3

What is α/β?

The α/β ratio is the dose at which the linear and quadratic contributions are equal:

αD = βD² → D = α/β

A lower α/β means the modeled effect changes more strongly with fraction size. A higher α/β means fraction size has less leverage within the model.

4

From the LQ model to BED

For n equal fractions of d Gy, the standard LQ expression can be rearranged into:

BED = n·d × (1 + d/(α/β))

Because total physical dose is n·d, BED is essentially the physical dose multiplied by a fraction-size weighting term. Larger fractions increase that weighting, especially when α/β is small.

5

What does EQD2 ask?

EQD2 answers a reference question:

What total dose, if delivered in 2-Gy fractions, would have the same BED according to this model?
EQD2 = BED / (1 + 2/(α/β))

It is useful because schedules with different fraction sizes can then be placed on the same familiar 2-Gy-fraction reference scale.

4. Why can “same BED” give different clinical outcomes?

Because BED deliberately compresses a complicated treatment into a small radiobiological model.

Interpretation

What BED captures

  • Total physical dose
  • Number of equal fractions
  • Dose per fraction
  • The selected α/β assumption

What simple BED does not capture

  • Spatial dose distribution and irradiated volume
  • Heterogeneous dose inside an SBRT/SRS target
  • Overall treatment time and tumour repopulation
  • Incomplete repair between closely spaced fractions
  • Reoxygenation and redistribution between fractions
  • Patient selection, systemic therapy and competing risks
  • Whether the LQ high-dose extrapolation is the best description of that clinical setting
Endpoint matters. Local control is more directly related to local radiation effect than overall survival. OS can change because of metastatic disease, systemic treatment, salvage treatment and competing mortality even when local tumour effect is identical.

5. Cumulative / reirradiation view

A scalar EQD2 sum can be useful, but it is not a substitute for spatial dose accumulation.

Advanced
Advanced: model an assumed recovery of the previous course
There is no universal “X% recovery after Y months” rule that is valid for every organ, endpoint and clinical situation. Leave this off unless you have a justified external assumption.
Cumulative EQD2 is a modelled dose summary, not a tolerance limit. In reirradiation, anatomy, spatial overlap, interval, prior toxicity, organ subvolume and uncertainty in dose mapping remain essential.

6. Sources and model boundaries

The Workbench teaches where its assumptions come from rather than hiding them.

Sources
Fowler 2010BED foundations and LQ-based fractionation comparisons HyTEC overview 2021High-dose-per-fraction clinical context and normal-tissue evidence Brenner 2008Argument for LQ use at large fraction sizes; illustrates the high-dose modelling debate ESTRO–EORTC 2022Reirradiation definition, reporting and clinical decision framework ESTRO Reirradiation Focus Group 2026Cumulative-dose evaluation, dose mapping, equieffective rescaling and uncertainty
About the warning thresholds used here: the Workbench uses ≤6, >6–10 and >10 Gy/fraction as a deliberately conservative teaching display. These are not biological cliffs and are not presented as universal validation cut-offs. Published authors differ on how far standard LQ extrapolation remains clinically useful at large fraction sizes.