RTH-25

Homogeneity index

HI = (D2% − D98%)/D50%. Zero is a perfectly flat PTV.

Reading speed

Plan qualityICRU 83

Governing equation

\mathrm{HI}=(D_{2\%}-D_{98\%})/D_{50\%}

$D_{2\%} \in \left[20, 90\right]$

where

D_{2\%}: D2% (Gy)
D_{98\%}: D98% (Gy)
D_{50\%}: D50% (Gy)
HI: Homogeneity index (—)

The figure, part by part

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①

Governing law — red

\mathrm{HI}=(D_{2\%}-D_{98\%})/D_{50\%}

$D_{2\%} \in \left[20, 90\right]$

$D_{2\%} = 20$ $HI = -0.617$

Along the curve

②

Domain of the variable — blue

D_{2\%}_{\min} = 20,\quad D_{2\%}_{\max} = 90

$D_{2\%} \in \left[20, 90\right]$

$D_{2\%} = 20$ $D_{2\%} = 20$

Along the curve

③

Response curve — green

\mathrm{HI}=(D_{2\%}-D_{98\%})/D_{50\%}

$D_{2\%} \in \left[20, 90\right]$

$D_{2\%} = 20$ $HI = -0.617$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}HI}{\mathrm{d}D_{2\%}}

$D_{2\%} \in \left[20, 90\right]$

$D_{2\%} = 20.44$ $HI^{\prime} = 0.017$

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-25 — Homogeneity index) is the form associated with ICRU 83. Working symbols: $D_{2\%}$ , $D_{98\%}$ , $D_{50\%}$ $\rightarrow$ $HI$ . ICRU 83 dropped the 95–107 % window for a report of D98, D50, D2. HI captures the spread.

Purpose

Purpose: compute

HI

from

D_{2\%}

D_{98\%}

D_{50\%}

in Radiotherapy via

\mathrm{HI}=(D_{2\%}-D_{98\%})/D_{50\%}

HI = (D2% − D98%)/D50%. Zero is a perfectly flat PTV. 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_{2\%} = 63.000\,\mathrm{Gy}

D_{98\%} = 57.000\,\mathrm{Gy}

D_{50\%} = 60.000\,\mathrm{Gy}

, the governing relation

\mathrm{HI}=(D_{2\%}-D_{98\%})/D_{50\%}

yields

HI = 0.100\,\mathrm{—}

. A DVH, three dose ticks, an HI bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

D2% D_{2\%}63 GyD98% D_{98\%}57 GyD50% D_{50\%}60 Gy

Outputs

Homogeneity index HI0.100 —

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Narration of this film

A DVH, three dose ticks, an HI bar.

ICRU 83 dropped the 95–107 % window for a report of D98, D50, D2. HI captures the spread.

Reading speed

Watch on YouTube