RTH-06

Inverse-square monitor units

MU = D / (Ḋ_cal (SCD/r)²). Calibration output scaled by inverse square.

Reading speed

Monitor unitsKhan MU

Governing equation

\mathrm{MU}=\dfrac{D}{\dot D_{\mathrm{cal}}(\mathrm{SCD}/r)^{2}}

$r \in \left[80, 140\right]$

where

D: Prescribed dose (Gy)
\dot D_{cal}: Calibration output (Gy/MU)
SCD: Calibration distance (cm)
r: Source to point (cm)
MU: Monitor units (MU)

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

\mathrm{MU}=\dfrac{D}{\dot D_{\mathrm{cal}}(\mathrm{SCD}/r)^{2}}

$r \in \left[80, 140\right]$

$r = 80$ $MU = 128$

Along the curve

②

Domain of the variable — blue

r_{\min} = 80,\quad r_{\max} = 140

$r \in \left[80, 140\right]$

$r = 80$ $r = 80$

Along the curve

③

Response curve — green

\mathrm{MU}=\dfrac{D}{\dot D_{\mathrm{cal}}(\mathrm{SCD}/r)^{2}}

$r \in \left[80, 140\right]$

$r = 80$ $MU = 128$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}MU}{\mathrm{d}r}

$r \in \left[80, 140\right]$

$r = 80.38$ $MU^{\prime} = 3.215$

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-06 — Inverse-square monitor units) is the form associated with Khan MU. Working symbols: $D$ , $\dot D_{cal}$ , $SCD$ , $r$ $\rightarrow$ $MU$ . SCD is the source-to-calibration distance. r is the source-to-point distance in the treatment geometry.

Purpose

Purpose: compute

MU

from

D

\dot D_{cal}

SCD

r

in Radiotherapy via

\mathrm{MU}=\dfrac{D}{\dot D_{\mathrm{cal}}(\mathrm{SCD}/r)^{2}}

MU = D / (Ḋ_cal (SCD/r)²). Calibration output scaled by inverse square. 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 = 2.000\,\mathrm{Gy}

\dot D_{cal} = 0.010\,\mathrm{Gy/MU}

SCD = 100.000\,\mathrm{cm}

r = 110.000\,\mathrm{cm}

, the governing relation

\mathrm{MU}=\dfrac{D}{\dot D_{\mathrm{cal}}(\mathrm{SCD}/r)^{2}}

yields

MU = 242.0\,\mathrm{MU}

. A linac, a phantom, an MU counter. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Prescribed dose D2 GyCalibration output \dot D_{cal}0.01 Gy/MUCalibration distance SCD100 cmSource to point r110 cm

Outputs

Monitor units MU242.0 MU

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A linac, a phantom, an MU counter.

SCD is the source-to-calibration distance. r is the source-to-point distance in the treatment geometry.

Reading speed

Watch on YouTube