01 Therapy

Effective SSD (electrons)

Output versus air gap using the effective-SSD inverse square.

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Simulation

Effective SSD (electrons) — Change the numbers; the scene follows.

Where it works

Linear accelerator

Treatment couch

On the couch: changing SSD versus SAD is a setup change, not a new beam model.

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Formula

\dot{D}(g)=\dot{D}_0\left(\frac{f+d_{\max}}{f+d_{\max}+g}\right)^2

Variables

Ḋ₀ · Output at zero gapcGy/MUf · Effective SSDcmdₘₐₓ · Depth of dose maxcmg · Air gapcm

Results

Ḋ
Output with gap
0.8743cGy/MU
F
Inverse-square factor
0.8743

Curve

Explanation

\dot{D}(g)=\dot{D}_0\left(\frac{f+d_{\max}}{f+d_{\max}+g}\right)^2

What it means

Electron output does not follow the photon inverse square from the virtual source because of scatter in the cone. An effective SSD (often 50–90 cm) is fitted so that output versus air gap g behaves as [(f+dmax)/(f+dmax+g)]². This is a working relation in Radiotherapy.

Where it is used

Clinically it sits on the Linear accelerator — Treatment couch. On the couch: changing SSD versus SAD is a setup change, not a new beam model. Radiotherapy equations sit at the console and in the bunker: output, depth dose, equivalent square, and the monitor units that treat the patient. Hand-calc them beside the TPS, never instead of a commissioned plan.

Linear accelerator · Open this machine

How to use it

Measure output at gaps 0, 5, 10 cm, fit f, then use this calculator at the clinical gap (bolus, irregular surface). Ḋ drops faster than a 100 cm photon inverse square. Change one input and watch the curve and the simulation follow.

Symbols

Ḋ₀Output at zero gap1 cGy/MU
fEffective SSD70 cm
dₘₐₓDepth of dose max2 cm
gAir gap5 cm

Worked example

A typical case from the default values: Ḋ₀ = 1 cGy/MU (Output at zero gap); f = 70 cm (Effective SSD); dₘₐₓ = 2 cm (Depth of dose max); g = 5 cm (Air gap). Substituting into the relation gives Ḋ = 0.8743 cGy/MU; F = 0.8743. These are teaching numbers — align them with your machine.

Typical values give

Ḋ = 0.8743cGy/MU
F = 0.8743

Where it comes from

The displayed formula is the working relation. Output versus air gap using the effective-SSD inverse square. Usual reference: Khan / AAPM TG-25. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Khan / AAPM TG-25

Assumptions & limits

Valid near the fitted energy, cone, and gap range. Cutouts and large obliquity need extra output factors.

Pitfalls

Never mix PDD from one SSD with TMR from another without converting. Field size at the surface is not the size at isocentre. A hand MU is a check, not a treatment. Valid near the fitted energy, cone, and gap range. Cutouts and large obliquity need extra output factors.

Keep this

Name the SSD, energy, and field size with every PDD or TMR you quote. Valid near the fitted energy, cone, and gap range. Cutouts and large obliquity need extra output factors.

In this specialty

Radiotherapy