Linear-quadratic survival, BED, and EQD2 — how a 2-gray fraction and a 8-gray fraction stop being comparable until you convert.
For Clinical oncologists · planning physicists·8 min
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You will be able to
01Sketch SF = exp(−αD − βD²) and point to α/β.
02Convert a schedule to BED and to EQD2.
03Say why late tissue hates large fractions.
Chapter 01
A bend in survival
Log surviving fraction is linear plus quadratic in dose. Alpha is the linear kill — more important in tumours with high α/β. Beta is the bend — late normal tissue, low α/β, feels the square term. That is why a single 8-gray fraction is not four times a 2-gray fraction for the cord.
α/β is not a tumour marker. It is a fractionation sensitivity.
Simulation
Survival fraction — LQ model — Change the numbers; the scene follows.
Variables
S = 4.1614e-10
SF=e−αD−βD2
Keep thisα/β is not a tumour marker. It is a fractionation sensitivity.
BED is total dose times one plus dose-per-fraction over α/β. It lets 3-gray times 13 talk to 2-gray times 30. EQD2 rewrites the same schedule as 2-gray fractions. Pick the α/β of the tissue you care about. Using tumour α/β on a late-tissue question is a category error.
Simulation
Biologically effective dose — Change the numbers; the scene follows.
EQD2 is the BED of your schedule divided by one plus two over α/β. Constraints in protocols are often EQD2. A SABR 10 times 5 is a different sentence in tumour α/β = 10 and in cord α/β = 3. Compute both before you shrug.
Simulation
Equivalent dose in 2 Gy fractions — Change the numbers; the scene follows.
Variables
EQD₂ = 60 Gy
Keep thisTwo tissues, two conversions. One number is not enough.