05 Biology
Logistic NTCP
NTCP = 1 / (1 + exp(−4 γ₅₀ (D − TD₅₀)/TD₅₀)).
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Simulation
Logistic NTCP — 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
NTCP
Normal-tissue complication probability
0.0923
NTCP
NTCP
9.23%
Curve
Explanation
What it means
A logistic NTCP is a sigmoid in dose: 50% complications at TD₅₀, with normalised slope γ₅₀ (percent response per percent dose at the 50% point). It is a lightweight stand-in for the Lyman-Kutcher-Burman model when you have a single equivalent uniform dose. 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
Example: myelopathy TD₅₀ ~ 70 Gy (EQD₂) with a steep γ₅₀. Keep NTCP in the few-percent range for serial organs. For partial-volume effects you need an EUD/n parameter this calculator does not include. Change one input and watch the curve and the simulation follow.
Symbols
- DDose50 Gy
- TD_50Tolerance dose 50%70 Gy
- γ_50Normalized slope at 50%2
Worked example
A typical case from the default values: D = 50 Gy (Dose); TD_50 = 70 Gy (Tolerance dose 50%); γ_50 = 2 (Normalized slope at 50%). Substituting into the relation gives NTCP = 0.0923; NTCP = 9.23 %. These are teaching numbers — align them with your machine.
Typical values give
- NTCP = 0.0923
- NTCP = 9.23%
Where it comes from
The displayed formula is the working relation. NTCP = 1 / (1 + exp(−4 γ₅₀ (D − TD₅₀)/TD₅₀)). Usual reference: Lyman / logistic approximation. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Lyman / logistic approximation
Assumptions & limits
Uniform organ dose, no volume effect (n=1 serial). Not a fitted LKB (m, n, TD₅₀) triple. Educational, not a protocol constraint.
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. Uniform organ dose, no volume effect (n=1 serial). Not a fitted LKB (m, n, TD₅₀) triple. Educational, not a protocol constraint.
Keep this
Always write α/β and the fraction size next to a BED or EQD2. Uniform organ dose, no volume effect (n=1 serial). Not a fitted LKB (m, n, TD₅₀) triple. Educational, not a protocol constraint.
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