RTH-29

TCP snapshot (Poisson)

TCP = exp(−N0 S), S = e^{−αD−βD²}. Zero clonogens left.

Reading speed

RadiobiologyPoisson TCP

Governing equation

\mathrm{TCP}=\exp\!\left(-N_0 e^{-\alpha D-\beta D^{2}}\right)

where

N_0: Clonogens N0 (—)
\alpha: Linear α (1/Gy)
\beta: Quadratic β (1/Gy²)
D: Dose (Gy)
TCP: Control 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-29 — TCP snapshot (Poisson)) is the form associated with Poisson TCP. Working symbols: $N_0$ , $\alpha$ , $\beta$ , $D$ $\rightarrow$ $TCP$ . N0 is the initial clonogen number. A log-kill of 8–10 is a typical curative ambition.

Purpose

Purpose: compute

TCP

from

N_0

\alpha

\beta

D

in Radiotherapy via

\mathrm{TCP}=\exp\!\left(-N_0 e^{-\alpha D-\beta D^{2}}\right)

TCP = exp(−N0 S), S = e^{−αD−βD²}. Zero clonogens left. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

N_0 = 1.000e+7\,\mathrm{—}

\alpha = 0.300\,\mathrm{1/Gy}

\beta = 0.030\,\mathrm{1/Gy^{2}}

D = 60.000\,\mathrm{Gy}

, the governing relation

\mathrm{TCP}=\exp\!\left(-N_0 e^{-\alpha D-\beta D^{2}}\right)

yields

TCP = 1.0000\,\mathrm{—}

. A falling SF and a rising TCP sigmoid. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Clonogens N0 N_010000000 —Linear α \alpha0.3 1/GyQuadratic β \beta0.03 1/Gy²Dose D60 Gy

Outputs

Control probability TCP1.0000 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A falling SF and a rising TCP sigmoid.

N0 is the initial clonogen number. A log-kill of 8–10 is a typical curative ambition.

Reading speed

Watch on YouTube