05 Biology
Biologically effective dose
BED for comparing fractionation schedules.
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Simulation
Biologically effective dose — Change the numbers; the scene follows.
Where it works
Linear accelerator
Isocenter
In the treated volume — tumour and OARs at isocenter, after the dose has been delivered.
Open this machineFormula
Typical values
Variables
Results
D
Physical dose
60Gy
BED
Biologically effective dose
72Gy
Curve
Explanation
What it means
Biologically effective dose BED = nd (1 + d/(α/β)) is the LQ dose that would produce the same log cell kill if given in infinitely small fractions. It lets you compare 2 Gy × 30 with 2.67 Gy × 20 on one scale. This is a working relation in Radiobiology.
Where it is used
Clinically it sits on the Linear accelerator — Isocenter. In the treated volume — tumour and OARs at isocenter, after the dose has been delivered. Radiobiology sits between the prescription and the organ-at-risk: LQ, BED, EQD2, and why 2 Gy is not 2 Gy if the fraction size changed. Use it to compare regimens, not to invent one.
Linear accelerator · Open this machineHow to use it
Always state α/β with the BED (BED₁₀ vs BED₃). A prostate SBRT 7.25 Gy × 5 is a large BED₁.₅ and a much smaller BED₁₀ — late tissues ‘see’ more effect. Change one input and watch the curve and the simulation follow.
Symbols
- nNumber of fractions30
- dDose per fraction2 Gy
- α/βAlpha/beta10 Gy
Worked example
A typical case from the default values: n = 30 (Number of fractions); d = 2 Gy (Dose per fraction); α/β = 10 Gy (Alpha/beta). Substituting into the relation gives D = 60 Gy; BED = 72 Gy. These are teaching numbers — align them with your machine.
Typical values give
- D = 60Gy
- BED = 72Gy
Where it comes from
The displayed formula is the working relation. BED for comparing fractionation schedules. Usual reference: Fowler, 1989. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Fowler, 1989
Assumptions & limits
No time factor (see BED with time), no incomplete repair (see g-factor). EQD2 is often easier to quote to physicians than raw BED.
Pitfalls
α/β is a model parameter, not a measured organ. BED from incomplete repair or a changed overall time is not the simple n·d·(1+d/(α/β)). Never EQD2 a stereotactic dose with an α/β you did not state. No time factor (see BED with time), no incomplete repair (see g-factor). EQD2 is often easier to quote to physicians than raw BED.
Keep this
Always write α/β and the fraction size next to a BED or EQD2. No time factor (see BED with time), no incomplete repair (see g-factor). EQD2 is often easier to quote to physicians than raw BED.
In this specialty