IMG-13

Chemical shift

Δf = δ (γ/2π) B0. Water–fat is 3.5 ppm.

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MRIChemical shift

Governing equation

\Delta f=\delta\,(\gamma/2\pi)\,B_0

$B_0 \in \left[0.2, 7\right]$

where

\delta: Shift δ (ppm)
\gamma/2\pi: Gyromagnetic ratio (MHz/T)
B_0: Field (T)
\Delta f: Frequency shift (Hz)

The figure, part by part

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①

Governing law — red

\Delta f=\delta\,(\gamma/2\pi)\,B_0

$B_0 \in \left[0.2, 7\right]$

$B_0 = 0.2$ $\Delta f = 29.81$

Along the curve

②

Domain of the variable — blue

B_0_{\min} = 0.2,\quad B_0_{\max} = 7

$B_0 \in \left[0.2, 7\right]$

$B_0 = 0.2$ $B_0 = 0.2$

Along the curve

③

Response curve — green

\Delta f=\delta\,(\gamma/2\pi)\,B_0

$B_0 \in \left[0.2, 7\right]$

$B_0 = 0.2$ $\Delta f = 29.81$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta f}{\mathrm{d}B_0}

$B_0 \in \left[0.2, 7\right]$

$B_0 = 0.243$ $\Delta f^{\prime} = 149$

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-13 — Chemical shift) is the form associated with Chemical shift. Working symbols: $\delta$ , $\gamma/2\pi$ , $B_0$ $\rightarrow$ $\Delta f$ . At 1.5 T, water–fat Δf ≈ 224 Hz; at 3 T it doubles. Pixel-shift = Δf / BW_pixel.

Purpose

Purpose: compute

\Delta f

from

\delta

\gamma/2\pi

B_0

in Medical imaging via

\Delta f=\delta\,(\gamma/2\pi)\,B_0

Δf = δ (γ/2π) B0. Water–fat is 3.5 ppm. 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

\delta = 3.500\,\mathrm{ppm}

\gamma/2\pi = 42.580\,\mathrm{MHz/T}

B_0 = 1.500\,\mathrm{T}

, the governing relation

\Delta f=\delta\,(\gamma/2\pi)\,B_0

yields

\Delta f = 223.5\,\mathrm{Hz}

. Two spectral peaks a few ppm apart. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Shift δ \delta3.5 ppmGyromagnetic ratio \gamma/2\pi42.58 MHz/TField B_01.5 T

Outputs

Frequency shift \Delta f223.5 Hz

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Narration of this film

Two spectral peaks a few ppm apart.

At 1.5 T, water–fat Δf ≈ 224 Hz; at 3 T it doubles. Pixel-shift = Δf / BW_pixel.

Reading speed

Watch on YouTube