05 Biology
Isoeffect dose (Withers)
Change fraction size at constant BED: D₂ = D₁ (d₁+α/β)/(d₂+α/β).
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Simulation
Isoeffect dose (Withers) — 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
Variables
Results
D₂
Isoeffective total dose
56.8272Gy
n₂
Number of fractions
21.28
Explanation
What it means
Withers’ isoeffect: if BED is held constant, total dose scales as D₂ = D₁ (d₁+α/β)/(d₂+α/β). Changing from 2 Gy to 3 Gy fractions reduces the total dose more for late tissues (low α/β) than for tumours (high α/β). 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
Classic example: 60 Gy / 2 Gy → at 3 Gy/fx and α/β=10, D₂ = 60×12/13 ≈ 55.4 Gy (about 18–19 fractions). Recalculate with α/β=3 for cord. Change one input and watch the curve and the simulation follow.
Symbols
- D₁Original total dose60 Gy
- d₁Original fraction size2 Gy
- d₂New fraction size2.67 Gy
- α/βAlpha/beta10 Gy
Worked example
A typical case from the default values: D₁ = 60 Gy (Original total dose); d₁ = 2 Gy (Original fraction size); d₂ = 2.67 Gy (New fraction size); α/β = 10 Gy (Alpha/beta). Substituting into the relation gives D₂ = 56.8272 Gy; n₂ = 21.28. These are teaching numbers — align them with your machine.
Typical values give
- D₂ = 56.8272Gy
- n₂ = 21.28
Where it comes from
The displayed formula is the working relation. Change fraction size at constant BED: D₂ = D₁ (d₁+α/β)/(d₂+α/β). Usual reference: Withers / Fowler. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Withers / Fowler
Assumptions & limits
No time factor. Incomplete repair if fractions are closer than ~6 h is ignored (see g-factor).
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. Incomplete repair if fractions are closer than ~6 h is ignored (see g-factor).
Keep this
Always write α/β and the fraction size next to a BED or EQD2. No time factor. Incomplete repair if fractions are closer than ~6 h is ignored (see g-factor).
In this specialty