05 Biology
Tumour control probability
Poisson model: TCP = exp(−N₀ S).
Listen
Listen · English
Simulation
Tumour control probability — 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
TCP
Tumour control probability
0.90484
TCP
Tumour control probability
90.48%
Curve
Explanation
What it means
Poisson TCP = exp(−N₀ S) is the probability that zero clonogens survive. If N₀ S = 1 (on average one survivor), TCP = 37%. The curve is a steep sigmoid once you plot vs dose through S(d). 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
N₀ ~ 10⁶–10⁸ for many tumours. Pair with the LQ survival calculator to turn a schedule into S then TCP. Population TCP is shallower because of heterogeneity (σ of radiosensitivity). Change one input and watch the curve and the simulation follow.
Symbols
- N₀Clonogen number1.0000e+7
- SSurviving fraction1.0000e-8
Worked example
A typical case from the default values: N₀ = 1.0000e+7 (Clonogen number); S = 1.0000e-8 (Surviving fraction). Substituting into the relation gives TCP = 0.90484; TCP = 90.48 %. These are teaching numbers — align them with your machine.
Typical values give
- TCP = 0.90484
- TCP = 90.48%
Where it comes from
The displayed formula is the working relation. Poisson model: TCP = exp(−N₀ S). Usual reference: Webb / Nahum. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Webb / Nahum
Assumptions & limits
Identical cells, no hypoxia, no inter-patient spread. Lyman-Kutcher-Burman and logistic models are used for NTCP; this Poisson form is the classic TCP sketch.
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. Identical cells, no hypoxia, no inter-patient spread. Lyman-Kutcher-Burman and logistic models are used for NTCP; this Poisson form is the classic TCP sketch.
Keep this
N₀ is the number of clonogens, S is surviving fraction after treatment.
In this specialty