RTH-28

NTCP snapshot (Lyman)

NTCP = Φ((D − TD50)/(m TD50)). Probit of a uniform organ dose.

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RadiobiologyLyman–Kutcher–Burman

Governing equation

\mathrm{NTCP}=\Phi\!\left(\dfrac{D-TD_{50}}{m\,TD_{50}}\right)

where

D: Equivalent uniform dose (Gy)
TD_{50}: TD50 (Gy)
m: Slope m (—)
NTCP: Complication probability (—)

Lecture brief

Historical brief

The linear-quadratic model, BED, tissue-maximum ratio and Clarkson scatter turned radiotherapy into fraction arithmetic. MU calculation on these sheets is that clinical closed form. This sheet (RTH-28 — NTCP snapshot (Lyman)) is the form associated with Lyman–Kutcher–Burman. Working symbols: $D$ , $TD_{50}$ , $m$ $\rightarrow$ $NTCP$ . m is the slope; n (not shown) is the volume exponent via the Kutcher–Burman gEUD reduction.

Purpose

Purpose: compute

NTCP

from

D

TD_{50}

m

in Radiotherapy via

\mathrm{NTCP}=\Phi\!\left(\dfrac{D-TD_{50}}{m\,TD_{50}}\right)

NTCP = Φ((D − TD50)/(m TD50)). Probit of a uniform organ dose. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

D = 50.000\,\mathrm{Gy}

TD_{50} = 65.000\,\mathrm{Gy}

m = 0.150\,\mathrm{—}

, the governing relation

\mathrm{NTCP}=\Phi\!\left(\dfrac{D-TD_{50}}{m\,TD_{50}}\right)

yields

NTCP = 0.0620\,\mathrm{—}

. A sigmoid of complication versus dose. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Equivalent uniform dose D50 GyTD50 TD_{50}65 GySlope m m0.15 —

Outputs

Complication probability NTCP0.0620 —

Reading speed

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Narration of this film

A sigmoid of complication versus dose.

m is the slope; n (not shown) is the volume exponent via the Kutcher–Burman gEUD reduction.

Reading speed

Watch on YouTube