RTH-27

Gradient index

GI = V50% / V100%. How fast the dose falls outside the target.

Reading speed

Plan qualityPaddick GI

Governing equation

\mathrm{GI}=V_{50\%}/V_{100\%}

$V_{50\%} \in \left[0.5, 200\right]$

where

V_{50\%}: 50 % isodose volume (cm³)
V_{100\%}: 100 % isodose volume (cm³)
GI: Gradient index (—)

The figure, part by part

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①

Governing law — red

\mathrm{GI}=V_{50\%}/V_{100\%}

$V_{50\%} \in \left[0.5, 200\right]$

$V_{50\%} = 0.5$ $GI = 0.083$

Along the curve

②

Domain of the variable — blue

V_{50\%}_{\min} = 0.5,\quad V_{50\%}_{\max} = 200

$V_{50\%} \in \left[0.5, 200\right]$

$V_{50\%} = 0.5$ $V_{50\%} = 0.5$

Along the curve

③

Response curve — green

\mathrm{GI}=V_{50\%}/V_{100\%}

$V_{50\%} \in \left[0.5, 200\right]$

$V_{50\%} = 0.5$ $GI = 0.083$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}GI}{\mathrm{d}V_{50\%}}

$V_{50\%} \in \left[0.5, 200\right]$

$V_{50\%} = 1.755$ $GI^{\prime} = 0.167$

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-27 — Gradient index) is the form associated with Paddick GI. Working symbols: $V_{50\%}$ , $V_{100\%}$ $\rightarrow$ $GI$ . SRS wants GI ≲ 3. A small GI is a tight fall-off and spare of the brain.

Purpose

Purpose: compute

GI

from

V_{50\%}

V_{100\%}

in Radiotherapy via

\mathrm{GI}=V_{50\%}/V_{100\%}

GI = V50% / V100%. How fast the dose falls outside the target. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V_{50\%} = 18.000\,\mathrm{cm^{3}}

V_{100\%} = 6.000\,\mathrm{cm^{3}}

, the governing relation

\mathrm{GI}=V_{50\%}/V_{100\%}

yields

GI = 3.000\,\mathrm{—}

. Two isodose clouds, a volume ratio. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

50 % isodose volume V_{50\%}18 cm³100 % isodose volume V_{100\%}6 cm³

Outputs

Gradient index GI3.000 —

Reading speed

Watch on YouTube

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Narration of this film

Two isodose clouds, a volume ratio.

SRS wants GI ≲ 3. A small GI is a tight fall-off and spare of the brain.

Reading speed

Watch on YouTube