RTH-15

SAD versus SSD conversion

D_SAD / D_SSD = ((SSD+d)/SAD)². Inverse-square between the two setups.

Reading speed

GeometrySAD/SSD

Governing equation

\dfrac{D_{\mathrm{SAD}}}{D_{\mathrm{SSD}}}=\left(\dfrac{\mathrm{SSD}+d}{\mathrm{SAD}}\right)^{2}

$d \in \left[0.5, 30\right]$

where

D_{SSD}: SSD dose (Gy)
SSD: SSD (cm)
d: Depth (cm)
SAD: SAD (cm)
D_{SAD}: SAD dose (Gy)

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

\dfrac{D_{\mathrm{SAD}}}{D_{\mathrm{SSD}}}=\left(\dfrac{\mathrm{SSD}+d}{\mathrm{SAD}}\right)^{2}

$d \in \left[0.5, 30\right]$

$d = 0.5$ $D_{SAD} = 2.02$

Along the curve

②

Domain of the variable — blue

d_{\min} = 0.5,\quad d_{\max} = 30

$d \in \left[0.5, 30\right]$

$d = 0.5$ $d = 0.5$

Along the curve

③

Response curve — green

\dfrac{D_{\mathrm{SAD}}}{D_{\mathrm{SSD}}}=\left(\dfrac{\mathrm{SSD}+d}{\mathrm{SAD}}\right)^{2}

$d \in \left[0.5, 30\right]$

$d = 0.5$ $D_{SAD} = 2.02$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}D_{SAD}}{\mathrm{d}d}

$d \in \left[0.5, 30\right]$

$d = 0.686$ $D_{SAD}^{\prime} = 0.04$

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-15 — SAD versus SSD conversion) is the form associated with SAD/SSD. Working symbols: $D_{SSD}$ , $SSD$ , $d$ , $SAD$ $\rightarrow$ $D_{SAD}$ . Isocentric SAD keeps the source-to-point distance fixed; SSD does not. Scatter factors still differ.

Purpose

Purpose: compute

D_{SAD}

from

D_{SSD}

SSD

d

SAD

in Radiotherapy via

\dfrac{D_{\mathrm{SAD}}}{D_{\mathrm{SSD}}}=\left(\dfrac{\mathrm{SSD}+d}{\mathrm{SAD}}\right)^{2}

D_SAD / D_SSD = ((SSD+d)/SAD)². Inverse-square between the two setups. 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_{SSD} = 2.000\,\mathrm{Gy}

SSD = 100.000\,\mathrm{cm}

d = 10.000\,\mathrm{cm}

SAD = 100.000\,\mathrm{cm}

, the governing relation

\dfrac{D_{\mathrm{SAD}}}{D_{\mathrm{SSD}}}=\left(\dfrac{\mathrm{SSD}+d}{\mathrm{SAD}}\right)^{2}

yields

D_{SAD} = 2.420\,\mathrm{Gy}

. A couch, two geometries, two inverse-square spheres. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

SSD dose D_{SSD}2 GySSD SSD100 cmDepth d10 cmSAD SAD100 cm

Outputs

SAD dose D_{SAD}2.420 Gy

Reading speed

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Narration of this film

A couch, two geometries, two inverse-square spheres.

Isocentric SAD keeps the source-to-point distance fixed; SSD does not. Scatter factors still differ.

Reading speed

Watch on YouTube