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Monday, July 11, 2011

Physics for understanding fMRI artifacts: Part Seven

Magnetic field gradients and one-dimensional MRI

Now that you have a basic understanding of the Fourier transform and some of the practical matters that arise from digital signals, it's time to look at a basic imaging pulse sequence and even make some simple images. We're going to use frequency encoding only for the time being, and for now we're going to make one-dimensional images (also called profiles) so that we can introduce an alternative form of timing diagram to represent a pulse sequence.

A magnetic field gradient alters the local resonance frequency

When a sample is placed into the magnet, all the protons (1-H nuclei) resonate at a near-identical frequency. At 3 T that resonance frequency is approximately 123 MHz, as given by the Larmor equation. If we then impose a magnetic field gradient across the sample - your subject's head, say - instead of having the same resonance frequency uniformly across the brain, there will now be a linear dependence in space (see Note 1):

In a real image we might consider 64 different positions along x. These would define the voxels in one (in-plane) dimension of the image. But for the time being we'll consider just three points in the x direction: the central point, and one point either side.

At the center of the magnet the gradient has no net effect, so the resonance frequency at that point is still 123 MHz. We call this point the null crossing, because all three linear gradients, X, Y and Z, are engineered to have no effect here. (See Note 2.) And to keep things symmetric, the gradient null crossing is placed in the geometric center of the magnet - the isocenter - because that's where the main magnetic field has been engineered to be most homogeneous, and we want to do all our imaging in that location to get the best scanner performance.