07 MRI

Velocity encoding VENC

VENC = π / (γ m₁) is the velocity that produces a π phase shift.

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Simulation

Velocity encoding VENC — 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.

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Formula

\mathrm{VENC}=\pi/(\gamma m_1),\quad \phi=\pi\,v/\mathrm{VENC}

Variables

VENC · Velocity encodingcm/sv · Velocitycm/s

Results

φ
Phase
1.6755rad
φ
Phase
96°
n
Alias wraps
0.5333

Explanation

\mathrm{VENC}=\pi/(\gamma m_1),\quad \phi=\pi\,v/\mathrm{VENC}

What it means

Phase-contrast MRI encodes velocity in the phase of the voxel by a bipolar gradient of first moment m₁. VENC is the velocity that wraps phase to π (and then aliases). Set VENC just above the peak expected speed: too low aliases (wrong direction / speed), too high wastes dynamic range (noisy velocity). Aorta ~150 cm/s, carotids ~80, venous ~20, CSF ~5–10. 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.

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How to use it

Enter VENC (cm/s) and the true velocity (cm/s). Read the phase in radians and degrees, and a flag if |v| > VENC (alias). Inverse: enter m₁ if you have the gradient waveform. Change one input and watch the curve and the simulation follow.

Symbols

VENCVelocity encoding150 cm/s
vVelocity80 cm/s

Worked example

A typical case from the default values: VENC = 150 cm/s (Velocity encoding); v = 80 cm/s (Velocity). Substituting into the relation gives φ = 1.6755 rad; φ = 96 °; n = 0.5333. These are teaching numbers — align them with your machine.

Typical values give

φ = 1.6755rad
φ = 96°
n = 0.5333

Where it comes from

The displayed formula is the working relation. VENC = π / (γ m₁) is the velocity that produces a π phase shift. Usual reference: Pelc / McRobbie. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Pelc / McRobbie

Assumptions & limits

First-moment encoding only, through-plane. Acceleration (second moment) and eddy-current offsets are the main residual errors. Background-phase subtraction from a static ROI is mandatory.

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. First-moment encoding only, through-plane. Acceleration (second moment) and eddy-current offsets are the main residual errors. Background-phase subtraction from a static ROI is mandatory.

Keep this

Name the nucleus and the field before you quote a Larmor frequency. First-moment encoding only, through-plane. Acceleration (second moment) and eddy-current offsets are the main residual errors. Background-phase subtraction from a static ROI is mandatory.

In this specialty

MRI physics