RTH-11

Output factor

S_{c,p}(s) = 1 + m log(s/10). Relative output versus 10 cm square.

Reading speed

OutputKhan Sc,p

Governing equation

S_{c,p}(s)=1+m\log(s/10)

$s \in \left[2, 40\right]$

where

s: Equivalent square (cm)
m: Slope m (—)
S_{c,p}: Output factor (—)

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.

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①

Governing law — red

S_{c,p}(s)=1+m\log(s/10)

$s \in \left[2, 40\right]$

$s = 2$ $S_{c,p} = 0.952$

Along the curve

②

Domain of the variable — blue

s_{\min} = 2,\quad s_{\max} = 40

$s \in \left[2, 40\right]$

$s = 2$ $s = 2$

Along the curve

③

Response curve — green

S_{c,p}(s)=1+m\log(s/10)

$s \in \left[2, 40\right]$

$s = 2$ $S_{c,p} = 0.952$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S_{c,p}}{\mathrm{d}s}

$s \in \left[2, 40\right]$

$s = 2.239$ $S_{c,p}^{\prime} = 0.013$

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-11 — Output factor) is the form associated with Khan Sc,p. Working symbols: $s$ , $m$ $\rightarrow$ $S_{c,p}$ . Head scatter Sc and phantom scatter Sp multiply. Collimator backscatter sits in Sc.

Purpose

Purpose: compute

S_{c,p}

from

s

m

in Radiotherapy via

S_{c,p}(s)=1+m\log(s/10)

S_{c,p}(s) = 1 + m log(s/10). Relative output versus 10 cm square. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

s = 12.000\,\mathrm{cm}

m = 0.030\,\mathrm{—}

, the governing relation

S_{c,p}(s)=1+m\log(s/10)

yields

S_{c,p} = 1.0055\,\mathrm{—}

. A family of square fields, an output curve. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Equivalent square s12 cmSlope m m0.03 —

Outputs

Output factor S_{c,p}1.0055 —

Reading speed

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Narration of this film

A family of square fields, an output curve.

Head scatter Sc and phantom scatter Sp multiply. Collimator backscatter sits in Sc.

Reading speed

Watch on YouTube