01 Therapy

Gradient index

GI = PIV_{50%} / PIV. Lower is a sharper fall-off (SRS/SBRT).

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Simulation

Gradient index — 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{GI}=\frac{V_{50\%}}{V_{100\%}}=\frac{\mathrm{PIV}_{50}}{\mathrm{PIV}}

Variables

V_50% · 50% isodose volumecm³V_100% · Prescription isodose volumecm³

Results

GI
Gradient index
3

Explanation

\mathrm{GI}=\frac{V_{50\%}}{V_{100\%}}=\frac{\mathrm{PIV}_{50}}{\mathrm{PIV}}

What it means

Gradient index measures how fast dose falls outside the target — the quantity that predicts V12Gy in brain SRS and chest-wall dose in lung SBRT. A single-iso 6 MV VMAT SRS plan often lands at GI 3–4; a large target or a low-energy cone can exceed 5. CyberKnife / Gamma Knife with many entries do better (GI ~2.5–3). 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 the 50% isodose volume and the prescription isodose volume. GI < 3 is often the in-house goal for small SRS targets; quote it next to Paddick CI. Change one input and watch the curve and the simulation follow.

Symbols

V_50%50% isodose volume36 cm³
V_100%Prescription isodose volume12 cm³

Worked example

A typical case from the default values: V_50% = 36 cm³ (50% isodose volume); V_100% = 12 cm³ (Prescription isodose volume). Substituting into the relation gives GI = 3. These are teaching numbers — align them with your machine.

Typical values give

GI = 3

Where it comes from

The displayed formula is the working relation. GI = PIV_{50%} / PIV. Lower is a sharper fall-off (SRS/SBRT). Usual reference: Paddick & Lippitz 2006. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Paddick & Lippitz 2006

Assumptions & limits

Requires the 50% isodose to be a single contiguous volume; islands of 50% from a second iso inflate GI. Energy, penumbra, number of entries and modulation all affect it.

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. Requires the 50% isodose to be a single contiguous volume; islands of 50% from a second iso inflate GI. Energy, penumbra, number of entries and modulation all affect it.

Keep this

Name the SSD, energy, and field size with every PDD or TMR you quote. Requires the 50% isodose to be a single contiguous volume; islands of 50% from a second iso inflate GI. Energy, penumbra, number of entries and modulation all affect it.

In this specialty

Radiotherapy