RTH-23

Skin gap for depth match

g = ½ L1 d/SSD1 + ½ L2 d/SSD2. Adjacent fields match at depth d.

Reading speed

MatchingKhan gap

Governing equation

g=\tfrac12 L_1 d/\mathrm{SSD}_1+\tfrac12 L_2 d/\mathrm{SSD}_2

$d \in \left[0.5, 20\right]$

where

L_1: Field length 1 (cm)
L_2: Field length 2 (cm)
d: Match depth (cm)
SSD_1: SSD 1 (cm)
SSD_2: SSD 2 (cm)
g: Skin gap (cm)

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

g=\tfrac12 L_1 d/\mathrm{SSD}_1+\tfrac12 L_2 d/\mathrm{SSD}_2

$d \in \left[0.5, 20\right]$

$d = 0.5$ $g = 0.09$

Along the curve

②

Domain of the variable — blue

d_{\min} = 0.5,\quad d_{\max} = 20

$d \in \left[0.5, 20\right]$

$d = 0.5$ $d = 0.5$

Along the curve

③

Response curve — green

g=\tfrac12 L_1 d/\mathrm{SSD}_1+\tfrac12 L_2 d/\mathrm{SSD}_2

$d \in \left[0.5, 20\right]$

$d = 0.5$ $g = 0.09$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}g}{\mathrm{d}d}

$d \in \left[0.5, 20\right]$

$d = 0.623$ $g^{\prime} = 0.18$

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-23 — Skin gap for depth match) is the form associated with Khan gap. Working symbols: $L_1$ , $L_2$ , $d$ , $SSD_1$ , $SSD_2$ $\rightarrow$ $g$ . Too small a gap hot-spots the junction; too large a gap cold-spots it. Couch rotation adds a hinge.

Purpose

Purpose: compute

g

from

L_1

L_2

d

SSD_1

SSD_2

in Radiotherapy via

g=\tfrac12 L_1 d/\mathrm{SSD}_1+\tfrac12 L_2 d/\mathrm{SSD}_2

g = ½ L1 d/SSD1 + ½ L2 d/SSD2. Adjacent fields match 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

L_1 = 20.000\,\mathrm{cm}

L_2 = 16.000\,\mathrm{cm}

d = 5.000\,\mathrm{cm}

SSD_1 = 100.000\,\mathrm{cm}

SSD_2 = 100.000\,\mathrm{cm}

, the governing relation

g=\tfrac12 L_1 d/\mathrm{SSD}_1+\tfrac12 L_2 d/\mathrm{SSD}_2

yields

g = 0.900\,\mathrm{cm}

. Two field edges and a skin gap. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Field length 1 L_120 cmField length 2 L_216 cmMatch depth d5 cmSSD 1 SSD_1100 cmSSD 2 SSD_2100 cm

Outputs

Skin gap g0.900 cm

Reading speed

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Narration of this film

Two field edges and a skin gap.

Too small a gap hot-spots the junction; too large a gap cold-spots it. Couch rotation adds a hinge.

Reading speed

Watch on YouTube