Tuesday, November 1, 2011

Physics for understanding fMRI artifacts: Part Twelve

Apologies for the lengthy delay getting this post out. New academic year, teaching, talks, etc. etc. Anyway, I hope that this opus will be the final post in the background physics series for the time being. I reserve the right to append further posts down the road, but with this post I hope you will be in a position to understand the origins of artifacts in real (EPI-based) fMRI data. So, after today we'll change tacks and start reviewing what "good" data should look like. First things first though. Time to put all your k-space knowledge to good use, and review the pulse sequence that the majority of us use for fMRI.


The Echo Planar Imaging (EPI) pulse sequence

In Part Ten we looked at a pulse sequence and its corresponding k-space representation for a gradient-recalled echo (GRE) imaging method. That sequence used conventional, or spin warp, phase encoding to produce the second spatial dimension of the final image. A single row of the k-space matrix was acquired per RF excitation, with successive rows of (frequency-encoded) k-space being sampled after stepping down (or up) in the 2D k-space plane following each new RF pulse.

One feature of the spin warp imaging scheme should have been relatively obvious: it's slow. Frequency encoding along kx is fast but stepping through all the ky (the phase-encoded) values is some two orders of magnitude slower, resulting in an imaging speed from tens of seconds (low resolution) to minutes (high resolution). That's not the sort of speed we need if we are to follow blood dynamics associated with neural events.

Instead of acquiring a single row of k-space per RF excitation - a process that is always going to be limited by the recovery time to allow the spins to relax via T1 processes - we need a way to acquire multiple k-space rows per excitation, in a sort of "magnetization recycling" scheme. Ideally, we would be able to recycle the magnetization so much that we could acquire an entire stack of 2D planes (slices) in just a handful of seconds. That's what echo planar imaging (EPI) achieves.

Gradient echo EPI pulse sequence

The objective with the EPI sequence, as for the GRE (spin warp) imaging sequence we saw in Part Ten, is to completely sample the plane of 2D k-space. That objective is unchanged. All we're going to do differently is sample the k-space plane with improved temporal efficiency. Then, once we have completed the plane we can apply a 2D FT to recover the desired image. Pretty simple, eh?

As before, sampling (data readout) need only happen along the rows of the k-space matrix, i.e. along kx. So we need a way to hop between the rows quickly, spending as much time as possible reading out signals under the frequency encoding gradients, Gx, and as little time as possible getting ready to sample the next row. EPI is the original recycled pulse sequence, so I'll color the readout gradient echoes in green:

The first four (and a half) gradient echoes in a gradient echo EPI pulse sequence.

To keep things simple I've omitted slice selection and indicated a 90 degree RF excitation; this could of course be any flip angle in practice. (See Note 1.) I've also shown just the first four (and a half) gradient echoes in the echo train. The full sequence repeats as many times as there are phase-encoded rows in the k-space matrix. A typical EPI sequence for fMRI might use 64 gradient echoes, corresponding to 63 little blue triangles in the train shown in the figure above. But for the example k-space plane below, the k-space grid is 16x16 so assume for the time being that the full echo train would consist of 15 little blue triangles separating eight positive Gx gradient periods and eight negative Gx gradient periods.