07 MRI
Pixel and voxel size
FOV over matrix, plus voxel volume.
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Simulation
Pixel and voxel size — Change the numbers; the scene follows.
Where it works
MRI scanner
Gradient coils
In the gradient coils — slice thickness, FOV, diffusion encoding, voxel size.
Open this machineFormula
Variables
Results
Δx
Pixel x
0.9375mm
Δy
Pixel y
0.9375mm
V
Voxel volume
3.5156mm³
Explanation
What it means
Pixel size is FOV/matrix in each in-plane direction; voxel volume multiplies by slice thickness. Small voxels buy resolution and cost SNR (see relative SNR). This is a working relation in MRI physics.
Where it is used
Clinically it sits on the MRI scanner — Gradient coils. In the gradient coils — slice thickness, FOV, diffusion encoding, voxel size. 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
A 240 mm FOV on 256² is 0.94 mm pixels. Rectangular FOV (smaller N_y) is a time-saving trick that enlarges Δy unless you keep pixel size constant. Change one input and watch the curve and the simulation follow.
Symbols
- FOV_xField of view x240 mm
- N_xMatrix x256
- FOV_yField of view y240 mm
- N_yMatrix y256
- ΔzSlice thickness4 mm
Worked example
A typical case from the default values: FOV_x = 240 mm (Field of view x); N_x = 256 (Matrix x); FOV_y = 240 mm (Field of view y); N_y = 256 (Matrix y); Δz = 4 mm (Slice thickness). Substituting into the relation gives Δx = 0.9375 mm; Δy = 0.9375 mm; V = 3.5156 mm³. These are teaching numbers — align them with your machine.
Typical values give
- Δx = 0.9375mm
- Δy = 0.9375mm
- V = 3.5156mm³
Where it comes from
The displayed formula is the working relation. FOV over matrix, plus voxel volume. Usual reference: McRobbie. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: McRobbie
Assumptions & limits
Nominal pixel size ignores interpolation, zero-fill and the true PSF (T2 decay during readout). Partial-volume averages over the voxel.
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. Nominal pixel size ignores interpolation, zero-fill and the true PSF (T2 decay during readout). Partial-volume averages over the voxel.
Keep this
Name the nucleus and the field before you quote a Larmor frequency. Nominal pixel size ignores interpolation, zero-fill and the true PSF (T2 decay during readout). Partial-volume averages over the voxel.
In this specialty