RTH-08

Clarkson sector scatter

S = (1/n) Σ SAR(r_i). Irregular-field scatter by circular sectors.

Reading speed

ScatterClarkson 1941

Governing equation

S=\dfrac1n\sum_{i=1}^{n}\mathrm{SAR}(r_i)

$SAR_1 \in \left[0, 25\right]$

where

SAR_1: SAR sector 1 (%)
SAR_2: SAR sector 2 (%)
SAR_3: SAR sector 3 (%)
SAR_4: SAR sector 4 (%)
S: Mean scatter (%)

The figure, part by part

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①

Governing law — red

S=\dfrac1n\sum_{i=1}^{n}\mathrm{SAR}(r_i)

$SAR_1 \in \left[0, 25\right]$

$SAR_1 = 0$ $S = 5.75$

Along the curve

②

Domain of the variable — blue

SAR_1_{\min} = 0,\quad SAR_1_{\max} = 25

$SAR_1 \in \left[0, 25\right]$

$SAR_1 = 0$ $SAR_1 = 0$

Along the curve

③

Response curve — green

S=\dfrac1n\sum_{i=1}^{n}\mathrm{SAR}(r_i)

$SAR_1 \in \left[0, 25\right]$

$SAR_1 = 0$ $S = 5.75$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S}{\mathrm{d}SAR_1}

$SAR_1 \in \left[0, 25\right]$

$SAR_1 = 0.157$ $S^{\prime} = 0.25$

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-08 — Clarkson sector scatter) is the form associated with Clarkson 1941. Working symbols: $SAR_1$ , $SAR_2$ , $SAR_3$ , $SAR_4$ $\rightarrow$ $S$ . Each sector of opening Δφ sees a circular field of radius r(θ). Average the SAR table.

Purpose

Purpose: compute

S

from

SAR_1

SAR_2

SAR_3

SAR_4

in Radiotherapy via

S=\dfrac1n\sum_{i=1}^{n}\mathrm{SAR}(r_i)

S = (1/n) Σ SAR(r_i). Irregular-field scatter by circular sectors. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

SAR_1 = 8.000\,\mathrm{%}

SAR_2 = 6.000\,\mathrm{%}

SAR_3 = 10.000\,\mathrm{%}

SAR_4 = 7.000\,\mathrm{%}

, the governing relation

S=\dfrac1n\sum_{i=1}^{n}\mathrm{SAR}(r_i)

yields

S = 7.75\,\mathrm{%}

. An irregular outline split into pizza slices. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

SAR sector 1 SAR_18 %SAR sector 2 SAR_26 %SAR sector 3 SAR_310 %SAR sector 4 SAR_47 %

Outputs

Mean scatter S7.75 %

Reading speed

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Narration of this film

An irregular outline split into pizza slices.

Each sector of opening Δφ sees a circular field of radius r(θ). Average the SAR table.

Reading speed

Watch on YouTube