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Physics Facts - Gradient echoes

Gradient of what ? Echo how ? Confused by MRI terminology ? Hallmarq's Nick Bolas explains

(Gradient) Echo Beach - Far away in time  [1]

Magnetic resonance, in the hands of physicists and chemists, normally starts with the sample in a magnet that has been carefully adjusted to have a highly uniform magnetic field.  In a process known as shimming (originally done with small metal plates, and now generally aided with electric currents passing through specially wound coils) the variation in magnetic field across the sample is reduced to a few parts per million (ppm).  When excited by a transmit pulse the nuclei then all resonate close to the same frequency, and their oscillation continues, ringing like a bell, for some time while gradually fading away.  Such an MR signal is termed a free induction decay (FID).

A highly uniform field is perfect for chemists, who can then use the very small changes in the field experienced by the nuclei inside molecules, due to the surrounding electron clouds (chemical shift), to learn about their chemical structure.

MRI requires the exact opposite, a deliberately non-uniform field to encode the position of the nuclei by their resonant frequency. But - if you just apply a field gradient across the sample, pulse and collect, you will only get a short dull thud[2] of a signal that fades almost instantly to nothing, as the radio waves from one part of the sample destructively interfere with those from another.  No signal - no MRI.

The simplest way to recover the signal is the gradient echo.  A field gradient is applied, left on for a few milliseconds, and then reversed.  Nuclei which initially precessed faster than average now resonate more slowly, while the initial laggards speed up.  As the nuclei resynchronise so the detectable signal gradually builds up, reaches a peak, and fades away again - a gradient echo.

Figure 1.  The basic gradient echo pulse sequence.  Slice select and phase encode gradients are not shown

The signal appears while the gradient is still turned on, and so is made of a mixture of frequencies coming from nuclei in different places, experiencing different magnetic fields.  The frequencies can be disentangled using a Fourier Transform once the electrical signal has been digitised and computerised.  Because this gradient is turned on during the signal acquisition it is termed the read gradient.

The peak of the echo occurs when the area under the first gradient lobe (a) is equal to the area under the first part of the second lobe (b).  The (phase encode) gradient used to encode position in a second, orthogonal direction is often applied at the same time as the first lobe of the read gradient.

The time between the RF pulse and the echo (TE) can be varied, so long the gradient lobes are balanced, but as it gets longer so more of the nuclei will fail to resynchronise and so the signal will become weaker.  The relationship between the echo time TE and the signal strength defines the relaxation time T2*.  A more heavily T2* weighted image is collected with a longer echo time, when more of the short T2* components will have faded away, leaving only the longer T2* components to give a signal and thus an image.

Reversing the gradient will only cause the nuclei to resynchronise if it is the only reason that the magnetic field changes.  But often it isn't: for example due to diffusion into a different part of the gradient, or diffusion into a region influenced by a nearby iron atom. So T2* is shorter than the T2 seen in a spin-echo pulse sequence (for another day).

One advantage of the gradient echo sequence is that it can be very fast.  Spin echoes are limited in speed by spin physics, but a gradient echo can essentially be as fast as the scanner can make it.  The key factors are the gradient ramp time (system specifications may give slew rate instead) and the maximum gradient strength.  A strong gradient will increase the frequency difference between adjacent pixels, and therefore reduce the data collection time needed to distinguish between them.

In high performance MRI systems there is a practical limit on gradient strength and speed when the induced electrical voltage caused by the rapidly changing magnetic field stimulates the patients peripheral nerves, especially around the head and neck.

It is not necessary, indeed normally not desirable, for the initial RF pulse to flip the nuclear spins through a full 90º.  With a small flip angle most of the sample magnetisation will remain along the direction of the main magnetic field, and be available for the next pulse to excite.  A very rapid succession of small pulses can be used, in combination with fast gradients, to collect an entire image in a few ms (the fast low-angle shot "FLASH" sequence).

Eventually though there will be no unsampled magnetisation left, until it recovers at a rate determined by the relaxation time constant T1.  There is therefore a relationship between flip angle, T1, and the rate at which pulses are applied (given by the interval TR between repetitions).  At very small flip angles not much magnetisation is tipped, so even with a slow T1 recovery there is enough to give a signal.  Conversely with a large flip angle only those nuclei with a relatively fast T1 recovery will return to give more signal unless TR is long, while slow T1 nuclei will saturate and remain dark in the image.  The balance of flip angle (α) and repetition time TR determines the T1 weighting of the image, with large flip angles and shorter TR times making the overall image more heavily T1 weighted.

[1] Echo Beach - Martha and the Muffins 1980

[2] In the days of analog electronics the signal inside the receiver electronics really could be amplified and connected to a loudspeaker, and the change from a ring to a thud clearly heard.