01 Therapy

Photon dmax versus energy

Teaching rule: dmax (cm) ≈ 0.25 E(MV) for flattening-filter beams, clamped 0.5–5 cm.

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Simulation

Photon dmax versus energy — Change the numbers; the scene follows.

Where it works

Linear accelerator

Isocenter

At isocenter, on the central axis through the patient (or a phantom in the same place).

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Formula

d_{\max}\approx 0.25\,E_{\mathrm{MV}}\ \mathrm{cm}\quad (6\,\mathrm{MV}:1.5\,\mathrm{cm};\ 18\,\mathrm{MV}:3.3\,\mathrm{cm})

Variables

E · Nominal energyMV

Results

dmax_rule
0.25 E rule
1.5cm
dmax_typ
Typical clinical value
1.5cm

Explanation

d_{\max}\approx 0.25\,E_{\mathrm{MV}}\ \mathrm{cm}\quad (6\,\mathrm{MV}:1.5\,\mathrm{cm};\ 18\,\mathrm{MV}:3.3\,\mathrm{cm})

What it means

Build-up depth increases with energy because the first collision electrons are thrown further forward. Clinical numbers every trainee memorizes: Co-60 0.5 cm, 6 MV 1.5 cm, 10 MV 2.5 cm, 18 MV 3.3 cm. FFF beams have slightly shallower dmax (more contamination). Field size, SSD and a tray all pull dmax up (contamination) or down. This is a working relation in Radiotherapy.

Where it is used

Clinically it sits on the Linear accelerator — Isocenter. At isocenter, on the central axis through the patient (or a phantom in the same place). 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 nominal MV. The rule is linear and will not hit 18 MV’s 3.3 cm exactly (0.25×18=4.5 — so the calculator also reports the textbook tabulated estimate). Use tabulated dmax for MU, never this rule. Change one input and watch the curve and the simulation follow.

Symbols

ENominal energy6 MV

Worked example

A typical case from the default values: E = 6 MV (Nominal energy). Substituting into the relation gives dmax_rule = 1.5 cm; dmax_typ = 1.5 cm. These are teaching numbers — align them with your machine.

Typical values give

dmax_rule = 1.5cm
dmax_typ = 1.5cm

Where it comes from

The displayed formula is the working relation. Teaching rule: dmax (cm) ≈ 0.25 E(MV) for flattening-filter beams, clamped 0.5–5 cm. Usual reference: Khan (empirical). Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Khan (empirical)

Assumptions & limits

Mnemonic only. Real dmax is measured during commissioning and shifts with field size (electron contamination). Electrons have a completely different dmax (≈ E/6 cm of water) — see the electron range-rules calculator.

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. Mnemonic only. Real dmax is measured during commissioning and shifts with field size (electron contamination). Electrons have a completely different dmax (≈ E/6 cm of water) — see the electron range-rules calculator.

Keep this

Name the SSD, energy, and field size with every PDD or TMR you quote. Mnemonic only. Real dmax is measured during commissioning and shifts with field size (electron contamination). Electrons have a completely different dmax (≈ E/6 cm of water) — see the electron range-rules calculator.

In this specialty

Radiotherapy