Doeller et al wanted to test whether grid cells exist in humans, but being unable to just stick electrodes in people's heads, they made use of two useful facts about rat grid cells. First, the orientation of the grid is fixed in all the cells in each particular rat, although each cell prefers different locations, i.e. the "grids" are offset, but not rotated. Second, grid cells fire faster when the animal is walking or running in a direction which corresponds to "along the lines" of their brain's internal grid - especially when the movement is rapid.
So, if our brains do contain grid cells, our entorhinal cortex should be more active overall when we're moving along the lines of our grids, as opposed to across them. Bearing in mind that there are three axes, and that you could move either "forward" or "backward" along each one, that makes 6 directions, so the grid cell theory predicts that entorhinal cortex activity should correlate with direction of motion with "6-way directional symmetry", like this:
Doeller et al point out that they haven't directly proven the existence of grid cells in humans - in theory, these results could also indicate the presence of another type of cell which encodes direction with 6-way directional symmetry. But this is a great piece of research, and a nice example of using neuroimaging to test neurobiological theories, as opposed to just going hunting for blobs of activation without knowing what to look for, which I've criticized before.
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