RTH-14

Off-axis ratio

OAR(x,d) = D(x,d)/D(0,d). The relative profile at depth d.

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ProfilesOAR

Governing equation

\mathrm{OAR}(x,d)=D(x,d)/D(0,d)

$D(x) \in \left[0.05, 8\right]$

where

D(x): Off-axis dose (Gy)
D(0): Central-axis dose (Gy)
OAR: Off-axis ratio (—)

The figure, part by part

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①

Governing law — red

\mathrm{OAR}(x,d)=D(x,d)/D(0,d)

$D(x) \in \left[0.05, 8\right]$

$D(x) = 0.05$ $OAR = 0.025$

Along the curve

②

Domain of the variable — blue

D(x)_{\min} = 0.05,\quad D(x)_{\max} = 8

$D(x) \in \left[0.05, 8\right]$

$D(x) = 0.05$ $D(x) = 0.05$

Along the curve

③

Response curve — green

\mathrm{OAR}(x,d)=D(x,d)/D(0,d)

$D(x) \in \left[0.05, 8\right]$

$D(x) = 0.05$ $OAR = 0.025$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}OAR}{\mathrm{d}D(x)}

$D(x) \in \left[0.05, 8\right]$

$D(x) = 0.1$ $OAR^{\prime} = 0.5$

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-14 — Off-axis ratio) is the form associated with OAR. Working symbols: $D(x)$ , $D(0)$ $\rightarrow$ $OAR$ . OARs are tabulated versus x and d for flattened and FFF beams. Horns grow with depth in FFF.

Purpose

Purpose: compute

OAR

from

D(x)

D(0)

in Radiotherapy via

\mathrm{OAR}(x,d)=D(x,d)/D(0,d)

OAR(x,d) = D(x,d)/D(0,d). The relative profile at depth d. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

D(x) = 1.920\,\mathrm{Gy}

D(0) = 2.000\,\mathrm{Gy}

, the governing relation

\mathrm{OAR}(x,d)=D(x,d)/D(0,d)

yields

OAR = 0.9600\,\mathrm{—}

. A profile normalised to CAX. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Off-axis dose D(x)1.92 GyCentral-axis dose D(0)2 Gy

Outputs

Off-axis ratio OAR0.9600 —

Reading speed

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Narration of this film

A profile normalised to CAX.

OARs are tabulated versus x and d for flattened and FFF beams. Horns grow with depth in FFF.

Reading speed

Watch on YouTube