Interpreting spatial encoding in MRI
Selecting a slice plane and spatially encoding each voxel involves the use of magnetic field gradients. Magnetic field intensity varies regularly along the gradient application axis. Each gradient is characterized by its strength (greater or lesser field variation for the same unit of distance), direction and the moment and time of application. The slice selection gradient modifies the precession frequency of the protons such that an RF pulse with the same frequency will cause them to shift (resonance). The slice selection gradient is simultaneously applied to all the RF pulses. Through the intermediary of the slice selection gradient, RF pulse frequency corresponds to selectivity in space. RF pulse bandwith and waveform determine slice thickness and profile.
Each phase encoding step acts as a kind of sieve letting through regularly spaced horizontal signals. This filter is sensitive to the vertical spatial distribution of the signals in the slice plane. The greater the phase difference, the thinner and finer the filter. In the absence of phase encoding, the signal will come from the whole slice. This is why multiple phase encoding steps are needed to acquire enough data to reconstruct the image. By analyzing the signals obtained with hundreds of different profiles, corresponding to as many fine combs, an image can be reconstructed (not only composed of horizontal bands, but of more complex contours).
To carry out the different phase encoding steps, the gradient is applied with different, regularly incremented values. It is bipolar, that is to say gradients are used with positive and negative values that are symmetrical to 0. In terms of the « filter size » range, a bipolar gradient is equivalent to a gradient that is only positive, for instance, and of the same absolute variation amplitude. However this requires positive amplitudes that are twice as high (causing greater dephasing and a poorer quality signal).
Frequency encoding can be interpreted in the same way, in the horizontal direction. When the frequency-encoding gradient is applied, the signal is digitized at regular intervals in time. Each signal sample corresponds to a given accumulation of the gradient effect on the whole splice signal: the longer the time, the longer the effect of the gradient on the spins, and the greater their phase modification. We see the same filter effect, sensitive to spatial distribution in the horizontal direction (the direction in which the gradient is applied). To obtain the equivalent of a bipolar effect, a frequency encoding gradient half-lobe is applied but in the opposite direction (dephasing lobe) prior to signal recording.
All the signals from the same slice are recorded in k-space then processed to form an image of the slice plane.
While frequency spatial encoding only takes a few milliseconds of signal reading, phase spatial encoding involves repeating the imaging sequence. In a classic spin echo sequence, a single phase encoding step is performed during each repetition time (TR). As TR values can be of up to 3 seconds, phase encoding is therefore much longer than frequency encoding.