RTH-31

Incomplete-repair G-factor

G = 2(μT − 1 + e^{−μT})/(μT)². Lea–Catcheside for a pulse of length T.

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RadiobiologyLea–Catcheside

Governing equation

G=\dfrac{2(\mu T-1+e^{-\mu T})}{(\mu T)^{2}}

where

\mu: Repair constant μ (1/h)
T: Exposure duration (h)
G: Lea–Catcheside G (—)

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-31 — Incomplete-repair G-factor) is the form associated with Lea–Catcheside. Working symbols: $\mu$ , $T$ $\rightarrow$ $G$ . μ = ln2 / T½ of repair. G→1 for an instant dose, G→0 for a very protracted one.

Purpose

Purpose: compute

G

from

\mu

T

in Radiotherapy via

G=\dfrac{2(\mu T-1+e^{-\mu T})}{(\mu T)^{2}}

G = 2(μT − 1 + e^{−μT})/(μT)². Lea–Catcheside for a pulse of length T. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu = 0.500\,\mathrm{1/h}

T = 0.250\,\mathrm{h}

, the governing relation

G=\dfrac{2(\mu T-1+e^{-\mu T})}{(\mu T)^{2}}

yields

G = 0.9596\,\mathrm{—}

. A finite beam-on, a fading damage pool. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Repair constant μ \mu0.5 1/hExposure duration T0.25 h

Outputs

Lea–Catcheside G G0.9596 —

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Narration of this film

A finite beam-on, a fading damage pool.

μ = ln2 / T½ of repair. G→1 for an instant dose, G→0 for a very protracted one.

Reading speed

Watch on YouTube