Spatial Encoding I

Review of Contrast

How do you make a T2 image? Long TE, long TR.

Why?

Long TR => allows for full equilibration

Long TE => allows for contrast according to T2 differences

For T1 weighted images,

Use a short TR, tissues that recover quickly will have > signal than tissues with slower recovery because all that recovered longitudinal magnetization gets converted to transvers by the 90 pulse => contrast

Increase TE,

See contrast between tissues with different T2 decays.

Ratio of T2s between different tissues increase with time, but signal ends up decaying into noise.

The really important # is the contrast-to-noise ratio:

(Signal Tissue 1 - SI Tissue 2)/Noise

Contrast figure

TE

How do you know where SI comes from?

Trick: Subtle

Setup situation where B field strength depends on position => precession depends on position.

Ex: With a piano, you can tell whether someone hit a note at the far left or far right of the keyboard based on frequency.

Tissue at high-end field of magnet precesses at higher frequency than at lower locations.

So, look at SI strength at various frequencies

However, cannot do this 3-D. So, we need to do our frequency encoding different along each dimension.

3 steps:

1. Slice selection
2. Phase Encoding
3. Frequency encoding

J.B. Fourier Transformer

Shorter pendulum oscillates faster.

Can selectively excite by vibrating at appropriate frequency.

Works the same way.

Put gradient in B field, so intensity depends on position in linear manner.

Put RF at frequency to excite slice we want.

Determine slice thickness by range of frequencies selected and magnitude of gradient.

After RF pulse, spins in slice are in xy, spins out of slice are in z.

Oversimplification: edge effects.

Transmit RF pulse via 3-lobe thing while gradient is on for 2 msec.

Signal becomes strong, then starts to decay.

Starts out mostly in phase; they are all precessing at same rate.

In order to make the spins faster on left and right, put gradient along x-axis.

Get signal that decays in time, looks really confusing, but we analyze for its frequency content.

Do FT, then look at SI as function of frequency.

Get a shadow of his body.

Similar to doing x-ray w/ attenuation.

So, we got 2 dimensions, on from slice selection, the other from frequency encoding.

CAT scanner:

Get shadows at whole bunch of different projections => projection reconstruction. Prone to artifacts. Using back-projection, get image.

First MR was done this way. Except instead of rotating emitter, use gradients along x and y.

Have RF channel, x, y, z gradients, data acquisition channel.

To do selective excitation, turn gradient in z while transmit RF pulse for 3 msec.

Gradients are generally trapezoidal because of ramping time.

Rephase signal by putting gradient on z in opposite direction. Duration not as long though. Roughly 60 % of area. Generally tuned and found experimentally.

Turn on x-gradient when we listen to our signal.

Spins start to dephase, and signal goes to 0 very quickly.

To combat this, before sampling, turn on oppositely direction x-gradient so will rephase by center of x-gradient.

So will be strong during readout period. This way we catch the in-phase point.

This is called gradient echo.

T2 decay is going on. So this has to be going on for 10s of milliseconds.

What does TE mean? For us, time between RF and center of readout.

Remember, whenever there is a gradient is on, dephasing occurs. By using them strategically, we can make a gradient echo.

Abstract for now.

MR signal has a complex time domain. We sample by digitizing, making a table, an array, versus time.

Why complex? Gradient is on.

Only reason signal changes (ignoring T2) between 2 time points is because gradient is on between the 2 time points. Dephasing only occurs when gradient is on. Magnitude of signal goes down with increasing gradient.

If gradient is very steep, get cancellation points (handwave).

This doesn't depend on time between sample points. Just on the gradient activity between sample points which causes dephasing (ignoring T2). That is, it depends on the gradient-time product up until sampling. You can have time in between sampling points where there is no gradient activity, and can still sample normally.

Phase encoding is the same as frequency encoding except the gradient is pulsed.

Do an x gradient but no y, get SI depending on frequency.

When x gradient undone in gradient echo, SI not dependent on position.

At the center points in time along x-axis, frequency does not depend on x.

But at that same point in time, the frequency depends on the y position according to the pulsed gradient!

So the FFT of those points gives you the signal intensity with position along the y-axis.

Time between points does not matter, but the gradient time product.

In the end, Phase encoding = Frequency Encoding