05 Biology
α/β from two isoeffective schedules
If two schedules are isoeffective, α/β = (D₁ d₁ − D₂ d₂)/(D₂ − D₁).
Listen
Listen · English
Simulation
α/β from two isoeffective schedules — 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
α/β
Alpha/beta
3Gy
Explanation
What it means
Two isoeffective schedules fix α/β: α/β = (D₁ d₁ − D₂ d₂)/(D₂ − D₁). This is how historical fraction-size trials estimated tissue α/β (and why prostate estimates sit near 1.5 Gy). 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
Enter total doses and fraction sizes that were judged isoeffective (same TCP or same late grade). If D₁ = D₂ the ratio is undefined — you need different fraction sizes. Change one input and watch the curve and the simulation follow.
Symbols
- D₁Total dose 160 Gy
- d₁Fraction 12 Gy
- D₂Total dose 250 Gy
- d₂Fraction 23 Gy
Worked example
A typical case from the default values: D₁ = 60 Gy (Total dose 1); d₁ = 2 Gy (Fraction 1); D₂ = 50 Gy (Total dose 2); d₂ = 3 Gy (Fraction 2). Substituting into the relation gives α/β = 3 Gy. These are teaching numbers — align them with your machine.
Typical values give
- α/β = 3Gy
Where it comes from
The displayed formula is the working relation. If two schedules are isoeffective, α/β = (D₁ d₁ − D₂ d₂)/(D₂ − D₁). Usual reference: Fowler / Thames. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Fowler / Thames
Assumptions & limits
Assumes true isoeffect, same overall time, and LQ validity in both dose-per-fraction regimes. Noise in clinical isoeffect data is large — quote confidence intervals in papers, not here.
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. Assumes true isoeffect, same overall time, and LQ validity in both dose-per-fraction regimes. Noise in clinical isoeffect data is large — quote confidence intervals in papers, not here.
Keep this
Always write α/β and the fraction size next to a BED or EQD2. Assumes true isoeffect, same overall time, and LQ validity in both dose-per-fraction regimes. Noise in clinical isoeffect data is large — quote confidence intervals in papers, not here.
In this specialty