Chemical shift · in-phase / opposed-phase · Dixon

Adding Rotating Vectors

Two chemical species in one voxel, turning at two different rates. Their sum beats in and out of phase, and where you sit in that beat decides what the voxel looks like.

Fat and water in one voxel at 3 T.

species A (water) species B (fat) sum

B is redrawn from the tip of A, so the red sum closes the triangle. The faint curve is the path the sum's tip has traced.

Signal magnitude against echo time. The dashed lines are the perfectly in-phase sum (A+B) and the perfectly opposed sum (|A−B|).

The two species

A: frequency offset Water is conventionally put on resonance, at 0 Hz.

B: frequency offset Fat sits 3.4 ppm below water: −217 Hz at 1.5 T, −434 Hz at 3 T.

A: amount Fraction of the voxel that is water.

B: amount Fraction of the voxel that is fat.

Playback speed Simulated milliseconds per second. Real fat and water beat far too fast to watch.

Draw B from the tip of A Path of the sum

Δf434 Hz

phase difference0°

|sum|1.000

first opposed-phase TE--

first in-phase TE--

t0.00 ms

What this figure is for

A voxel almost never contains one substance. Protons in fat are shielded by their surrounding electrons, so they feel a slightly smaller field and precess about 3.4 ppm slower than protons in water. Two vectors, two rates, one sum, and the sum depends on when you choose to measure it.

Δf = 3.4 ppm × f₀ | TE_opposed = 1/(2Δf) | TE_in = 1/Δf

The beat is the whole point. At TE = 0 the two species add. Half a beat later they subtract. The readouts give both times for the current Δf, and the dashed lines on the plot give both amplitudes. At 3 T the first opposed-phase echo lands at about 1.15 ms and the first in-phase echo at about 2.3 ms, which is why those two numbers appear on abdominal protocols.
Chemical-shift imaging falls out of this. Take one image at each TE and you can solve for the two species separately: (in + opposed)/2 is water, (in − opposed)/2 is fat. That is two-point Dixon, and it is why an adrenal adenoma or a fatty liver darkens on the opposed-phase image.
Amount matters. Set both amounts equal and the opposed-phase signal goes to zero: a voxel that is half fat and half water cancels completely. Make one species dominant and the dip becomes shallow. The India-ink outline around organs is this cancellation happening in the voxels that straddle a fat-water boundary.
Set Δf to zero and the beating stops: the sum is just A+B forever. Everything interesting here comes from the difference in frequency, not from the frequencies themselves, which is exactly why the rotating frame is a legitimate place to work.

Try this in class: switch between the 1.5 T and 3 T presets and watch the beat period halve. Chemical shift in hertz scales with field strength, which is why chemical-shift artifacts get worse, and Dixon echo times get shorter, as you go up in field.