RTH-05

Percentage depth dose

PDD = 100 e^{−μ(d−dm)} ((SSD+dm)/(SSD+d))². Inverse-square plus attenuation.

Reading speed

Beam dataBJR Suppl. 25

Governing equation

\mathrm{PDD}=100\,e^{-\mu(d-d_m)}\left(\dfrac{\mathrm{SSD}+d_m}{\mathrm{SSD}+d}\right)^{2}

$d \in \left[0.5, 40\right]$

where

\mu: Attenuation μ (1/cm)
d: Depth (cm)
d_m: dmax (cm)
SSD: SSD (cm)
PDD: Percentage depth dose (%)

The figure, part by part

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①

Governing law — red

\mathrm{PDD}=100\,e^{-\mu(d-d_m)}\left(\dfrac{\mathrm{SSD}+d_m}{\mathrm{SSD}+d}\right)^{2}

$d \in \left[0.5, 40\right]$

$d = 0.5$ $PDD = 107.2$

Along the curve

②

Domain of the variable — blue

d_{\min} = 0.5,\quad d_{\max} = 40

$d \in \left[0.5, 40\right]$

$d = 0.5$ $d = 0.5$

Along the curve

③

Response curve — green

\mathrm{PDD}=100\,e^{-\mu(d-d_m)}\left(\dfrac{\mathrm{SSD}+d_m}{\mathrm{SSD}+d}\right)^{2}

$d \in \left[0.5, 40\right]$

$d = 0.5$ $PDD = 107.2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}PDD}{\mathrm{d}d}

$d \in \left[0.5, 40\right]$

$d = 0.748$ $PDD^{\prime} = -7.362$

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-05 — Percentage depth dose) is the form associated with BJR Suppl. 25. Working symbols: $\mu$ , $d$ , $d_m$ , $SSD$ $\rightarrow$ $PDD$ . SSD setups quote PDD. Mayneord's F converts PDD between SSDs.

Purpose

Purpose: compute

PDD

from

\mu

d

d_m

SSD

in Radiotherapy via

\mathrm{PDD}=100\,e^{-\mu(d-d_m)}\left(\dfrac{\mathrm{SSD}+d_m}{\mathrm{SSD}+d}\right)^{2}

PDD = 100 e^{−μ(d−dm)} ((SSD+dm)/(SSD+d))². Inverse-square plus attenuation. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu = 0.050\,\mathrm{1/cm}

d = 10.000\,\mathrm{cm}

d_m = 1.500\,\mathrm{cm}

SSD = 100.000\,\mathrm{cm}

, the governing relation

\mathrm{PDD}=100\,e^{-\mu(d-d_m)}\left(\dfrac{\mathrm{SSD}+d_m}{\mathrm{SSD}+d}\right)^{2}

yields

PDD = 55.66\,\mathrm{%}

. A fading PDD curve past dmax. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Attenuation μ \mu0.05 1/cmDepth d10 cmdmax d_m1.5 cmSSD SSD100 cm

Outputs

Percentage depth dose PDD55.66 %

Reading speed

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Narration of this film

A fading PDD curve past dmax.

SSD setups quote PDD. Mayneord's F converts PDD between SSDs.

Reading speed

Watch on YouTube