IMG-30

Frequency-encode shift

Δf = (γ/2π) Gx x. Position becomes a frequency under the readout gradient.

Reading speed

MRIFrequency encode

Governing equation

\Delta f=(\gamma/2\pi)G_x x

where

G_x: Readout gradient (mT/m)
x: Offset from isocentre (mm)
\Delta f: Frequency offset (kHz)

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-30 — Frequency-encode shift) is the form associated with Frequency encode. Working symbols: $G_x$ , $x$ $\rightarrow$ $\Delta f$ . FOV in the readout direction is BW / (γ G). Stronger G shrinks FOV and pixel size.

Purpose

Purpose: compute

\Delta f

from

G_x

x

in Medical imaging via

\Delta f=(\gamma/2\pi)G_x x

Δf = (γ/2π) Gx x. Position becomes a frequency under the readout gradient. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

G_x = 10.000\,\mathrm{mT/m}

x = 60.000\,\mathrm{mm}

, the governing relation

\Delta f=(\gamma/2\pi)G_x x

yields

\Delta f = 25.548\,\mathrm{kHz}

. A gradient ramp painting frequency onto x. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Readout gradient G_x10 mT/mOffset from isocentre x60 mm

Outputs

Frequency offset \Delta f25.548 kHz

Reading speed

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Narration of this film

A gradient ramp painting frequency onto x.

FOV in the readout direction is BW / (γ G). Stronger G shrinks FOV and pixel size.

Reading speed

Watch on YouTube