RTH-01

Linear–quadratic survival

S = e^{−αD−βD²}. Cell-survival LQ model.

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RadiobiologyLQFowler

Governing equation

S=e^{-\alpha D-\beta D^{2}}

where

\alpha: Linear α (1/Gy)
\beta: Quadratic β (1/Gy²)
D: Dose (Gy)
S: Surviving fraction (—)

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-01 — Linear–quadratic survival) is the form associated with LQ · Fowler. Working symbols: $\alpha$ , $\beta$ , $D$ $\rightarrow$ $S$ . α tracks single-hit lethal events; β tracks two-hit repairable damage. α/β is high for early tissue.

Purpose

Purpose: compute

S

from

\alpha

\beta

D

in Radiotherapy via

S=e^{-\alpha D-\beta D^{2}}

S = e^{−αD−βD²}. Cell-survival LQ model. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

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

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

D = 2.000\,\mathrm{Gy}

, the governing relation

S=e^{-\alpha D-\beta D^{2}}

yields

S = 0.4868\,\mathrm{—}

. A survival curve with a shoulder then a steep tail. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Linear α \alpha0.3 1/GyQuadratic β \beta0.03 1/Gy²Dose D2 Gy

Outputs

Surviving fraction S0.4868 —

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Narration of this film

A survival curve with a shoulder then a steep tail.

α tracks single-hit lethal events; β tracks two-hit repairable damage. α/β is high for early tissue.

Reading speed

Watch on YouTube