01 Therapy

Field size at depth

Geometric projection of a surface field to depth d.

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Simulation

Field size at depth — Change the numbers; the scene follows.

Where it works

Linear accelerator

Collimator / MLC

At the jaws / MLC: field size on the collimator sets equivalent square, penumbra, and Sc,p.

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Formula

s(d)=s_0\frac{\mathrm{SSD}+d}{\mathrm{SSD}}=s_{\mathrm{iso}}\frac{\mathrm{SAD}+d-\mathrm{SAD}_{\mathrm{iso}}}{\mathrm{SAD}}

Variables

s₀ · Surface field sizecmSSD · Source-to-surface distancecmd · Depthcm

Results

s(d)
Field size at depth
11cm
s_iso
Size at isocenter if SAD=SSD
10cm

Curve

Explanation

s(d)=s_0\frac{\mathrm{SSD}+d}{\mathrm{SSD}}=s_{\mathrm{iso}}\frac{\mathrm{SAD}+d-\mathrm{SAD}_{\mathrm{iso}}}{\mathrm{SAD}}

What it means

Photon field size grows linearly with distance from the source. At depth d the side is s₀ (SSD+d)/SSD. This projected size is what you use for scatter (Sp, TMR) lookups, not the surface size. This is a working relation in Radiotherapy.

Where it is used

Clinically it sits on the Linear accelerator — Collimator / MLC. At the jaws / MLC: field size on the collimator sets equivalent square, penumbra, and Sc,p. 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

A 10×10 field at SSD 100 is 11×11 at 10 cm depth. For SAD setups replace SSD by SAD and s₀ by the isocentre size. Change one input and watch the curve and the simulation follow.

Symbols

s₀Surface field size10 cm
SSDSource-to-surface distance100 cm
dDepth10 cm

Worked example

A typical case from the default values: s₀ = 10 cm (Surface field size); SSD = 100 cm (Source-to-surface distance); d = 10 cm (Depth). Substituting into the relation gives s(d) = 11 cm; s_iso = 10 cm. These are teaching numbers — align them with your machine.

Typical values give

s(d) = 11cm
s_iso = 10cm

Where it comes from

The displayed formula is the working relation. Geometric projection of a surface field to depth d. Usual reference: Khan. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Khan

Assumptions & limits

Geometric projection only. Jaw/MLC transmission, penumbra and divergence of each leaf are not included.

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. Geometric projection only. Jaw/MLC transmission, penumbra and divergence of each leaf are not included.

Keep this

Name the SSD, energy, and field size with every PDD or TMR you quote. Geometric projection only. Jaw/MLC transmission, penumbra and divergence of each leaf are not included.

In this specialty

Radiotherapy