RTH-28

NTCP snapshot (Lyman)

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

Reading speed

RadiobiologyLyman–Kutcher–Burman

Governing equation

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

$D \in \left[5, 90\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

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

$D \in \left[5, 90\right]$

$D = 5$ $NTCP = 3.8\times 10^{-10}$

Along the curve

②

Domain of the variable — blue

D_{\min} = 5,\quad D_{\max} = 90

$D \in \left[5, 90\right]$

$D = 5$ $D = 5$

Along the curve

③

Response curve — green

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

$D \in \left[5, 90\right]$

$D = 5$ $NTCP = 3.8\times 10^{-10}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}NTCP}{\mathrm{d}D}

$D \in \left[5, 90\right]$

$D = 5.535$ $NTCP^{\prime} = 3.5\times 10^{-10}$

Along the curve

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

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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