IMG-15

k-space step Δk

Δk = 1/FOV = γ G τ / 2π. The sample spacing that sets FOV.

Reading speed

MRIk-space

Governing equation

\Delta k=1/\mathrm{FOV}

$FOV \in \left[80, 500\right]$

where

FOV: Field of view (mm)
\Delta k: k-space step (1/mm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta k=1/\mathrm{FOV}

$FOV \in \left[80, 500\right]$

$FOV = 80$ $\Delta k = 0.013$

Along the curve

②

Domain of the variable — blue

FOV_{\min} = 80,\quad FOV_{\max} = 500

$FOV \in \left[80, 500\right]$

$FOV = 80$ $FOV = 80$

Along the curve

③

Response curve — green

\Delta k=1/\mathrm{FOV}

$FOV \in \left[80, 500\right]$

$FOV = 80$ $\Delta k = 0.013$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta k}{\mathrm{d}FOV}

$FOV \in \left[80, 500\right]$

$FOV = 82.64$ $\Delta k^{\prime} = -1.47\times 10^{-4}$

Along the curve

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-15 — k-space step Δk) is the form associated with k-space. Working symbols: $FOV$ $\rightarrow$ $\Delta k$ . FOV wrap occurs when Δk is coarser than 1/FOV. Pixel size is 1/(N Δk).

Purpose

Purpose: compute

\Delta k

from

FOV

in Medical imaging via

\Delta k=1/\mathrm{FOV}

Δk = 1/FOV = γ G τ / 2π. The sample spacing that sets FOV. 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

FOV = 240.000\,\mathrm{mm}

, the governing relation

\Delta k=1/\mathrm{FOV}

yields

\Delta k = 0.00417\,\mathrm{1/mm}

. A k-space raster whose pitch is Δk. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Field of view FOV240 mm

Outputs

k-space step \Delta k0.00417 1/mm

Reading speed

Watch on YouTube

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Narration of this film

A k-space raster whose pitch is Δk.

FOV wrap occurs when Δk is coarser than 1/FOV. Pixel size is 1/(N Δk).

Reading speed

Watch on YouTube