01 Therapy

Geometric penumbra

Source-size penumbra at depth from collimator distance.

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Simulation

Geometric penumbra — 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

P = s\cdot\frac{\mathrm{SSD}+d-\mathrm{SCD}}{\mathrm{SCD}}

Variables

s · Source diametermmSSD · SSDcmd · DepthcmSCD · Source-collimator distancecm

Results

P
Geometric penumbra
6mm

Explanation

P = s\cdot\frac{\mathrm{SSD}+d-\mathrm{SCD}}{\mathrm{SCD}}

What it means

Geometric penumbra is the region where the finite source is partially obscured by the collimator. It widens with source size and with distance beyond the collimator, and narrows if you push the jaws closer to the patient (larger SCD… actually smaller gap beyond SCD). 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

Enter source diameter s (≈ 3–7 mm for a linac target as seen through the primary collimator), SSD, depth, and source-to-collimator distance. Physical penumbra also includes lateral scatter and transmission — typically 4–8 mm (20–80%) at 10 cm for 6 MV. Change one input and watch the curve and the simulation follow.

Symbols

sSource diameter5 mm
SSDSSD100 cm
dDepth10 cm
SCDSource-collimator distance50 cm

Worked example

A typical case from the default values: s = 5 mm (Source diameter); SSD = 100 cm (SSD); d = 10 cm (Depth); SCD = 50 cm (Source-collimator distance). Substituting into the relation gives P = 6 mm. These are teaching numbers — align them with your machine.

Typical values give

P = 6mm

Where it comes from

The displayed formula is the working relation. Source-size penumbra at depth from collimator distance. Usual reference: Khan. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Khan

Assumptions & limits

Pure geometry. Transmission through jaws, extrafocal radiation, and phantom scatter add to the measured 20–80% penumbra.

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. Pure geometry. Transmission through jaws, extrafocal radiation, and phantom scatter add to the measured 20–80% penumbra.

Keep this

Name the SSD, energy, and field size with every PDD or TMR you quote. Pure geometry. Transmission through jaws, extrafocal radiation, and phantom scatter add to the measured 20–80% penumbra.

In this specialty

Radiotherapy