RTH-24

Junction dose from gap error

D_j / D0 ≈ 1 + k Δg / P. Gap error times penumbra slope.

Reading speed

MatchingField matching

Governing equation

D_j/D_0=1+k\,\Delta g/P

$\Delta g \in \left[-8, 8\right]$

where

\Delta g: Gap error (mm)
P: Penumbra 80/20 (mm)
k: Slope factor (—)
D_j/D_0: Junction dose ratio (—)

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.

00:0 / 00:08

①

Governing law — red

D_j/D_0=1+k\,\Delta g/P

$\Delta g \in \left[-8, 8\right]$

$\Delta g = -8$ $D_j/D_0 = 0.2$

Along the curve

②

Domain of the variable — blue

\Delta g_{\min} = -8,\quad \Delta g_{\max} = 8

$\Delta g \in \left[-8, 8\right]$

$\Delta g = -8$ $\Delta g = -8$

Along the curve

③

Response curve — green

D_j/D_0=1+k\,\Delta g/P

$\Delta g \in \left[-8, 8\right]$

$\Delta g = -8$ $D_j/D_0 = 0.2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}D_j/D_0}{\mathrm{d}\Delta g}

$\Delta g \in \left[-8, 8\right]$

$\Delta g = -7.899$ $D_j/D_0^{\prime} = 0.1$

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-24 — Junction dose from gap error) is the form associated with Field matching. Working symbols: $\Delta g$ , $P$ , $k$ $\rightarrow$ $D_j/D_0$ . A 2 mm gap error on a 6 mm penumbra is a ~15–30 % junction miss. Half-beam blocks shrink this.

Purpose

Purpose: compute

D_j/D_0

from

\Delta g

P

k

in Radiotherapy via

D_j/D_0=1+k\,\Delta g/P

D_j / D0 ≈ 1 + k Δg / P. Gap error times penumbra slope. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\Delta g = 2.000\,\mathrm{mm}

P = 6.000\,\mathrm{mm}

k = 0.600\,\mathrm{—}

, the governing relation

D_j/D_0=1+k\,\Delta g/P

yields

D_j/D_0 = 1.200\,\mathrm{—}

. Two overlapping penumbras and a hot or cold junction. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Gap error \Delta g2 mmPenumbra 80/20 P6 mmSlope factor k0.6 —

Outputs

Junction dose ratio D_j/D_01.200 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Two overlapping penumbras and a hot or cold junction.

A 2 mm gap error on a 6 mm penumbra is a ~15–30 % junction miss. Half-beam blocks shrink this.

Reading speed

Watch on YouTube