01 Therapy

Equivalent uniform dose (Niemierko)

EUD = (Σ v_i D_i^a)^{1/a}. For a single hot/cold volume: EUD = D v^{1/a}.

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Simulation

Equivalent uniform dose (Niemierko) — 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

\mathrm{EUD}=\left(\sum_i v_i D_i^{a}\right)^{1/a}=D\,v^{1/a}\ \ (D=0\ \mathrm{elsewhere})

Typical values

Variables

D · Partial-volume doseGyv · Volume fractiona · Niemierko exponent

Results

gEUD
Generalised EUD
20Gy

Explanation

\mathrm{EUD}=\left(\sum_i v_i D_i^{a}\right)^{1/a}=D\,v^{1/a}\ \ (D=0\ \mathrm{elsewhere})

What it means

Niemierko’s generalised EUD compresses a DVH into the uniform dose that would cause the same biological effect. The exponent a is large and negative for tumours (cold-spot sensitive, a ≈ −10), near 1 for parallel organs (mean dose, a ≈ 1), and large positive for serial organs (hot-spot sensitive, a ≈ 16 for cord). gEUD is the input to many TCP/NTCP models. 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.

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How to use it

This form is a single-bin DVH: fraction v of the organ receives dose D and the rest 0. Enter a from a published fit (parotid a≈1, cord a≈16, tumour a≈−10). For a uniform whole-organ dose, v=1 and EUD=D. Change one input and watch the curve and the simulation follow.

Symbols

DPartial-volume dose40 Gy
vVolume fraction0.5
aNiemierko exponent1

Worked example

A typical case from the default values: D = 40 Gy (Partial-volume dose); v = 0.5 (Volume fraction); a = 1 (Niemierko exponent). Substituting into the relation gives gEUD = 20 Gy. These are teaching numbers — align them with your machine.

Typical values give

gEUD = 20Gy

Where it comes from

The displayed formula is the working relation. EUD = (Σ v_i D_i^a)^{1/a}. For a single hot/cold volume: EUD = D v^{1/a}. Usual reference: Niemierko, Med Phys 1999. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Niemierko, Med Phys 1999

Assumptions & limits

One-bin approximation. A real DVH needs the sum over all bins (export from TPS). a is tissue- and endpoint-specific and poorly known. Not a substitute for a full LKB/TCP calculation.

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. One-bin approximation. A real DVH needs the sum over all bins (export from TPS). a is tissue- and endpoint-specific and poorly known. Not a substitute for a full LKB/TCP calculation.

Keep this

Name the SSD, energy, and field size with every PDD or TMR you quote. One-bin approximation. A real DVH needs the sum over all bins (export from TPS). a is tissue- and endpoint-specific and poorly known. Not a substitute for a full LKB/TCP calculation.

In this specialty

Radiotherapy