05 Biology
Surviving fraction at 2 Gy (SF2)
SF2 = exp(−2α − 4β). A common in-vitro radiosensitivity index.
Listen
Listen · English
Simulation
Surviving fraction at 2 Gy (SF2) — 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
SF2
Surviving fraction at 2 Gy
0.48675
α/β
Ratio
10Gy
Explanation
What it means
SF2 is surviving fraction after a single 2 Gy dose, a standard in-vitro radiosensitivity index: SF2 = e^{−2α−4β}. Typical tumour SF2 is 0.4–0.6; more sensitive lines sit lower. 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
Plug in α and β from a survival fit. SF2 correlates (imperfectly) with clinical radioresponsiveness. Change one input and watch the curve and the simulation follow.
Symbols
- αLinear coefficient0.3 Gy⁻¹
- βQuadratic coefficient0.03 Gy⁻²
Worked example
A typical case from the default values: α = 0.3 Gy⁻¹ (Linear coefficient); β = 0.03 Gy⁻² (Quadratic coefficient). Substituting into the relation gives SF2 = 0.48675; α/β = 10 Gy. These are teaching numbers — align them with your machine.
Typical values give
- SF2 = 0.48675
- α/β = 10Gy
Where it comes from
The displayed formula is the working relation. SF2 = exp(−2α − 4β). A common in-vitro radiosensitivity index. Usual reference: Hall & Giaccia. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Hall & Giaccia
Assumptions & limits
In-vitro, oxic, single dose. Does not include repair, reassortment, repopulation or reoxygenation of the 4 Rs.
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. In-vitro, oxic, single dose. Does not include repair, reassortment, repopulation or reoxygenation of the 4 Rs.
Keep this
Always write α/β and the fraction size next to a BED or EQD2. In-vitro, oxic, single dose. Does not include repair, reassortment, repopulation or reoxygenation of the 4 Rs.
In this specialty