fundamental question on spatial encoding

[jon1000]

Despite several textbooks, I am still unclear about one aspect of spatial encoding. I understand phase encoding. It is frequency encoding that is confusing me.

With frequency encoding I understand how temporal frequency of the emitted signal is directly related to spatial position along x, but what we plot in k space is not spatial position, rather it is spatial frequency. How do we get from multiple superimposed temporal frequencies and corresponding spatial positions, to spatial frequency?

Thanks. Jon.

[jon1000]

I've realized that there were a couple of previous questions/responses on this topic. I think they cleared it up for me. To confirm:

Frequency encoding is in fact almost the same as phase encoding in that it also relies on phase shift of one voxel relative to another voxel to get spatial frequency.

That is, the name "FREQUENCY encoding" is more a reflection that there is variation in frequency during readout while it is really the phase differences along the x axis that give spatial frequency -- if we only had frequency difference without the subsequent phase differences, we wouldn't get spatial frequency data.

Is that correct?

Thanks again.

[Dave Higgins]

Hi Jon,

This is a great question. It's about the nature of the data we acquire in MRI--which is not often considered in detail, I suspect.

For example. We have nice pictures on this website and others which show us what a single k-space data point represents: a wave in space--bright and dark fringes oscillating across the slice. Then we can understand that if we add all the waves which we derive from all acquired k-space data points, they add in all the right places and cancel in all the right places, to yield a picture of what was in the scanner--a head or a bottle--whatever.

So we interpret a k-space data value as a wave. Fine. But what was happening in the slice when we measured that point?

Think about what happens as we record, say, the central k-space line (no phase encoding). The first k-space point in the line is recorded (digitised). What does that point represent? As you correctly state, it's multiple signals from the whole slice all added together. But does the distribution of signal in the slice at that moment in time look like the wave which we deduce from that data point? It certainly does not! Take any k-space data point and see the wave it represents. Now think about the distribution of signal-emitting nuclei in the scanner. Were there nuclei in the corners of the slice? No! But we see that the spatial frequency (the wave) which we draw using that point puts some signal out there. What's going on!?

This is bending my mind. I'm going to have to think about it for a bit. Nice one Jon, for biting the bullet.

Dave