TCP & NTCP

Tumor control probability (TCP) is a model estimate of the chance that a dose distribution controls a tumor. Normal tissue complication probability (NTCP) is the estimated chance that it causes a stated complication in an organ. Both rise with dose along an S-shaped (sigmoid) curve.

AAPM TG-166 describes the common forms:

• Poisson TCP. Most mechanistic TCP models assume the number of surviving tumor clonogens — cells able to regrow the tumor — follows a Poisson distribution, and that one surviving clonogen is enough for regrowth. TCP is then the probability that none survive: exp(−S × N).
• Empirical TCP. A sigmoid curve described by two parameters: D₅₀, the dose at which 50% of tumors are controlled, and the normalized dose-response gradient (γ), its steepness.
• Lyman-Kutcher-Burman (LKB) NTCP. A sigmoid curve described by TD₅₀ (where the curve sits on the dose axis) and m (its steepness), with a third parameter, n, for the size of the volume effect.

TG-166 also covers the equivalent uniform dose (EUD) and combined measures such as uncomplicated tumor control probability (UTCP) and the probability of complication-free tumor control (P+).

A DVH holds a whole curve for every structure; TCP and NTCP try to reduce it to one number each. The QUANTEC summary describes NTCP models as attempts to reduce complicated dosimetric and anatomic information to a single risk measure — and points out that familiar metrics such as the mean lung dose and the cord maximum are themselves simple models.

NTCP models also capture the volume effect: the tolerance dose rises as the irradiated volume falls, to a degree that depends on the tissue and the complication. TG-166 links this to organ structure:

• Parallel organs — such as lung, kidney and liver — where each functional subunit works fairly independently, so damage to a small region does not make the whole organ fail. Their response depends on how much of the organ is irradiated.
• Serial organs — such as the spinal cord, intestines and optic nerve — where losing one subunit can cause a complication. Their response depends on the hottest small region.

In the LKB model, a small n corresponds to a small volume effect (serial-like) and a large n to a large one. Constraint tables reflect the same idea: the UT Southwestern SBRT tables (Timmerman 2022) list serial tissues with a volume maximum and a maximum point dose, and parallel tissues with a critical volume — see Maximum Dose and Mean Dose.

Some planning systems calculate TCP, NTCP or EUD. TG-166's recommendations on using them:

1. Plan evaluation should, at present, be based on established dose-volume criteria. Biological metrics should be shown alongside physical ones (DVHs, minimum, maximum and mean dose), not instead of them.
2. Relative values can help choose between rival plans — provided users understand the range of applicability of the models and parameter values in their planning system.
3. Absolute TCP/NTCP values are not warranted as the main indicators of plan quality.
4. Review of the 3D dose distribution should always remain part of plan evaluation.

The numbers are only as good as the model and its parameters. TG-166 advises checking a model retrospectively against treatments known to be safe and effective in your practice, warns that published parameter sets carry significant risk if applied without following the practices used to generate them, and recommends using the LQ-equivalent dose in 2 Gy fractions (EQD2) rather than physical dose in TCP and NTCP calculations. For TCP, the tumor's α/β is itself uncertain — van Leeuwen and colleagues' review found large variation in published values.