RTH-20

Electron R50

R50 = E0 / 2.33. Depth of 50 % dose indexes the mean energy.

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ElectronsAAPM TG-25IAEA TRS-398

Governing equation

R_{50}=E_0/2.33

$E_0 \in \left[2, 30\right]$

where

E_0: Mean incident energy (MeV)
R_{50}: R50 (cm)

The figure, part by part

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①

Governing law — red

R_{50}=E_0/2.33

$E_0 \in \left[2, 30\right]$

$E_0 = 2$ $R_{50} = 0.858$

Along the curve

②

Domain of the variable — blue

E_0_{\min} = 2,\quad E_0_{\max} = 30

$E_0 \in \left[2, 30\right]$

$E_0 = 2$ $E_0 = 2$

Along the curve

③

Response curve — green

R_{50}=E_0/2.33

$E_0 \in \left[2, 30\right]$

$E_0 = 2$ $R_{50} = 0.858$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R_{50}}{\mathrm{d}E_0}

$E_0 \in \left[2, 30\right]$

$E_0 = 2.176$ $R_{50}^{\prime} = 0.429$

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-20 — Electron R50) is the form associated with AAPM TG-25 · IAEA TRS-398. Working symbols: $E_0$ $\rightarrow$ $R_{50}$ . AAPM: Ē0 = 2.33 R50. R50 is preferred over Rp for beam-quality specification.

Purpose

Purpose: compute

R_{50}

from

E_0

in Radiotherapy via

R_{50}=E_0/2.33

R50 = E0 / 2.33. Depth of 50 % dose indexes the mean energy. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E_0 = 12.000\,\mathrm{MeV}

, the governing relation

R_{50}=E_0/2.33

yields

R_{50} = 5.150\,\mathrm{cm}

. A PDD crossing 50 % at R50. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mean incident energy E_012 MeV

Outputs

R50 R_{50}5.150 cm

Reading speed

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Narration of this film

A PDD crossing 50 % at R50.

AAPM: Ē0 = 2.33 R50. R50 is preferred over Rp for beam-quality specification.

Reading speed

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