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The exciting thing is that within the last five years or so people have figure out how to use magnetic resonance imaging (MRI) to measure the diffusion tensor in living tissue, such as the brain. The brain is an interesting thing to study because it has a varity of anisotropies. At the surface of the brain, there's the gray matter, which is isotropic. More inside the brain, there's the white matter, where the axons are organized into "white matter fiber tracts", which are anisotropic. We can see those characteristics in actual measured MRI data such as this. This (left) is a matrix of images, where each image shows one component of the diffusion tensor across a full two-dimensional slice of the data. We can pick this spot (red circle) in the gray matter; here's the matrix; and here's the corresponding ellipsoid- its basically a sphere, which makes sense since we know that gray matter is isotropic. Here's a spot in the white matter (green circle) in a region called the corpus collosum, which is the bridge between the two halves of the brain. Here's the corresponding matrix, and you can see from the ellipsoid that the region is very linearly anisotropic. Finally, just to point out that all sorts of anistropy happen in measured brain data, here's another point in the white matter (blue circle), the corresponding matrix, and the ellipsoid, which indicates planar anistropy.