07 MRI
Chemical-shift pixels
Water–fat shift in pixels = Δf / (BW / N_x).
Listen
Listen · English
Simulation
Chemical-shift pixels — Change the numbers; the scene follows.
Where it works
MRI scanner
Patient in bore
In the tissue inside the bore — relaxation, fat/water, contrast, flow, magic angle.
Open this machineFormula
Variables
Results
Δf
Frequency offset
223.5Hz
n
Shift in pixels
1.1445px
BW/px
Bandwidth per pixel
195.3Hz/px
Explanation
What it means
The water–fat spatial misregistration in the readout direction equals Δf divided by Hz/pixel. Low bandwidth / high field / high matrix all worsen the India-ink and fat-shift artefacts. This is a working relation in MRI physics.
Where it is used
Clinically it sits on the MRI scanner — Patient in bore. In the tissue inside the bore — relaxation, fat/water, contrast, flow, magic angle. MRI physics lives in the magnet, the gradient, and the voxel: Larmor, Ernst, diffusion, and SAR. These relations decide whether a sequence is possible, safe, and worth the time.
MRI scanner · Open this machineHow to use it
At 1.5 T, 3.5 ppm, 256 matrix, 50 kHz → ~1.1 pixels. At 3 T it doubles. Swap phase/frequency if the shift overlays a lesion; or raise BW. Change one input and watch the curve and the simulation follow.
Symbols
- δChemical shift3.5 ppm
- B₀Field1.5 T
- N_xReadout matrix256
- BWTotal receiver bandwidth50 kHz
- γ/2πGyromagnetic ratio42.577 MHz/T
Worked example
A typical case from the default values: δ = 3.5 ppm (Chemical shift); B₀ = 1.5 T (Field); N_x = 256 (Readout matrix); BW = 50 kHz (Total receiver bandwidth); γ/2π = 42.577 MHz/T (Gyromagnetic ratio). Substituting into the relation gives Δf = 223.5 Hz; n = 1.1445 px; BW/px = 195.3 Hz/px. These are teaching numbers — align them with your machine.
Typical values give
- Δf = 223.5Hz
- n = 1.1445px
- BW/px = 195.3Hz/px
Where it comes from
The displayed formula is the working relation. Water–fat shift in pixels = Δf / (BW / N_x). Usual reference: McRobbie. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: McRobbie
Assumptions & limits
Readout-direction only (or EPI blips). Fat saturation / Dixon aim to remove the second peak rather than live with the shift.
Pitfalls
γ for ¹H is not γ for ¹³C. Ernst angle needs the true T1 at that field, not a 1.5 T table used at 3 T. SAR scales with B₀² and flip² — a 3 T copy of a 1.5 T protocol is not automatically legal. Readout-direction only (or EPI blips). Fat saturation / Dixon aim to remove the second peak rather than live with the shift.
Keep this
Name the nucleus and the field before you quote a Larmor frequency. Readout-direction only (or EPI blips). Fat saturation / Dixon aim to remove the second peak rather than live with the shift.
In this specialty