07 MRI
In-phase / opposed-phase TE
TE_in = n/Δf and TE_out = (n+½)/Δf for water–fat.
Listen
Listen · English
Simulation
In-phase / opposed-phase TE — 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
TE_in
In phase
4.4737ms
TE_out
Opposed phase
6.7105ms
Explanation
What it means
Water and fat go in and out of phase every 1/Δf. At 1.5 T (Δf ≈ 224 Hz) opposed-phase TE ≈ 2.3 ms and in-phase ≈ 4.5 ms; at 3 T the times halve. Opposed-phase images show India-ink at fat–water borders and are used to detect intracellular fat. 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
Enter B₀ and the order n (n=1 is the first in-phase after 0). Dual-echo Dixon uses one in and one opposed echo. Change one input and watch the curve and the simulation follow.
Symbols
- B₀Field1.5 T
- δChemical shift3.5 ppm
- nOrder n1
- γ/2πGyromagnetic ratio42.577 MHz/T
Worked example
A typical case from the default values: B₀ = 1.5 T (Field); δ = 3.5 ppm (Chemical shift); n = 1 (Order n); γ/2π = 42.577 MHz/T (Gyromagnetic ratio). Substituting into the relation gives Δf = 223.5 Hz; TE_in = 4.4737 ms; TE_out = 6.7105 ms. These are teaching numbers — align them with your machine.
Typical values give
- Δf = 223.5Hz
- TE_in = 4.4737ms
- TE_out = 6.7105ms
Where it comes from
The displayed formula is the working relation. TE_in = n/Δf and TE_out = (n+½)/Δf for water–fat. Usual reference: Hashemi / McRobbie. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Hashemi / McRobbie
Assumptions & limits
Uses a single 3.5 ppm fat peak. Multi-peak fat models shift the ‘perfect’ TE slightly. T2* decay between echoes is ignored here.
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. Uses a single 3.5 ppm fat peak. Multi-peak fat models shift the ‘perfect’ TE slightly. T2* decay between echoes is ignored here.
Keep this
Name the nucleus and the field before you quote a Larmor frequency. Uses a single 3.5 ppm fat peak. Multi-peak fat models shift the ‘perfect’ TE slightly. T2* decay between echoes is ignored here.
In this specialty