05 Biology
Logistic TCP
TCP = 1 / (1 + exp(−4 γ₅₀ (D − TCD₅₀)/TCD₅₀)). Population dose–response.
Listen
Listen · English
Simulation
Logistic TCP — 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
0.7374
TCP
TCP
73.74%
Curve
Explanation
What it means
A logistic (or probit) of dose is how empirical tumour-control series are fit when you do not want to commit to a clonogen number. TCD₅₀ is the dose that controls 50% of tumours; γ₅₀ is the normalised slope at that point (typical 1.5–3). It is the tumour-side twin of the logistic NTCP already in the library. Poisson TCP (the other calculator) is more mechanistic but needs N₀ and α. 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 D, TCD₅₀ and γ₅₀. A node-positive H&N series might have TCD₅₀ = 62 Gy, γ₅₀ = 2. Read TCP and the steepness in % per % dose. Change one input and watch the curve and the simulation follow.
Symbols
- DDose70 Gy
- TCD_5050% control dose62 Gy
- γ_50Normalised slope2
Worked example
A typical case from the default values: D = 70 Gy (Dose); TCD_50 = 62 Gy (50% control dose); γ_50 = 2 (Normalised slope). Substituting into the relation gives TCP = 0.7374; TCP = 73.74 %. These are teaching numbers — align them with your machine.
Typical values give
- TCP = 0.7374
- TCP = 73.74%
Where it comes from
The displayed formula is the working relation. TCP = 1 / (1 + exp(−4 γ₅₀ (D − TCD₅₀)/TCD₅₀)). Population dose–response. Usual reference: Brahme / Okunieff. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Brahme / Okunieff
Assumptions & limits
Population, not an individual. Homogeneous dose, no time factor, no hypoxia distribution. γ₅₀ already includes inter-patient heterogeneity; do not also smear D.
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. Population, not an individual. Homogeneous dose, no time factor, no hypoxia distribution. γ₅₀ already includes inter-patient heterogeneity; do not also smear D.
Keep this
Always write α/β and the fraction size next to a BED or EQD2. Population, not an individual. Homogeneous dose, no time factor, no hypoxia distribution. γ₅₀ already includes inter-patient heterogeneity; do not also smear D.
In this specialty