05 Biology
SBRT / hypofraction EQD2 check
EQD2 = D (d + α/β) / (2 + α/β) applied to a high d, with a warning when d > 2 α/β.
Listen
Listen · English
Simulation
SBRT / hypofraction EQD2 check — 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
EQD2
2 Gy equivalent
130Gy
BED
Biologically effective dose
216.6667Gy
2 α/β
Approx. LQ-L threshold
6Gy
- d > 2 α/β: LQ is outside its comfort zone — compare with LQ-L.
Explanation
What it means
The same EQD2 algebra as the dedicated calculator, flagged for the SBRT regime where its assumptions creak. Late-tissue α/β = 3 Gy: 10 Gy × 5 = 50 Gy physical → EQD2 = 130 Gy — a number that should make you reach for LQ-L or at least a second model. Tumour α/β = 10: the same course is EQD2 = 75 Gy, closer to a 2 Gy-equivalent radical dose. Always quote α/β with the number. 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 n, d, α/β. Read EQD2, BED, and whether d exceeds 2 α/β (LQ-L territory). Presets: 54/3 (lung), 50/5 (lung), 27/3 (prostate SBRT 9 Gy × 3), 20/1 (palliative). Change one input and watch the curve and the simulation follow.
Symbols
- nFractions5
- dDose per fraction10 Gy
- α/βAlpha/beta3 Gy
Worked example
A typical case from the default values: n = 5 (Fractions); d = 10 Gy (Dose per fraction); α/β = 3 Gy (Alpha/beta). Substituting into the relation gives EQD2 = 130 Gy; BED = 216.6667 Gy; 2 α/β = 6 Gy. These are teaching numbers — align them with your machine.
Typical values give
- EQD2 = 130Gy
- BED = 216.6667Gy
- 2 α/β = 6Gy
Where it comes from
The displayed formula is the working relation. EQD2 = D (d + α/β) / (2 + α/β) applied to a high d, with a warning when d > 2 α/β. Usual reference: Withers / Joiner / AAPM TG-101. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Withers / Joiner / AAPM TG-101
Assumptions & limits
No time factor (repopulation is a small term over 1–2 weeks of SBRT, a large one over 7 weeks of 2 Gy). No heterogeneity, no immune / vascular SBRT hypotheses. Compare with the LQ-L calculator before quoting 100+ Gy EQD2 of late tissue as if it were 2 Gy data.
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 (repopulation is a small term over 1–2 weeks of SBRT, a large one over 7 weeks of 2 Gy). No heterogeneity, no immune / vascular SBRT hypotheses. Compare with the LQ-L calculator before quoting 100+ Gy EQD2 of late tissue as if it were 2 Gy data.
Keep this
Always write α/β and the fraction size next to a BED or EQD2. No time factor (repopulation is a small term over 1–2 weeks of SBRT, a large one over 7 weeks of 2 Gy). No heterogeneity, no immune / vascular SBRT hypotheses. Compare with the LQ-L calculator before quoting 100+ Gy EQD2 of late tissue as if it were 2 Gy data.
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