The revolution in our understanding of white matter—which has only just begun—would never have been possible without diffusion tensor imaging. And diffusion tensor imaging, in turn, would never have been possible without the mathematical sciences. The mathematics is hidden in plain sight: in that mysterious word “tensor” in diffusion tensor imaging. A tensor is a mathematical concept, developed in the 19th century, that generalizes the notion of vectors. Tensors have proved useful in a number of areas of physics.

To explain what a tensor has to do with white matter in the brain, it helps to start with how MRI works. An MRI machine (see Figure 8) creates a strong magnetic field, which causes the protons in the body to rotate and line up in a predictable way. Most of these protons are actually hydrogen atoms in water molecules; thus MRI is especially sensitive to the water (or fluids) in your body. It is an excellent complement to traditional x-rays, which see the dense, hard structures in your body but are relatively blind to the soft tissues. One of the most informative parts of the body to image with MRI is the brain, because it is squishy and it uses a lot of blood.

By modulating or pulsing the magnetic field in various ways, doctors can tune the MRI scan to detect different kinds of tissue in the body. In particular, one technique allows them to measure the displacement of water molecules over a short period of time—displacements that are due not to blood flow but to random jitters of the molecules, called Brownian motion. Because Brownian motion underlies the process of diffusion, this technique measures what is called the “apparent diffusion coefficient” in a tiny cubic region of the brain.

Already this imaging capability has led to fundamental insights about normal and abnormal brains.

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8 / Magnetic resonance imaging (MRI is an important medical imaging technique that allows internal structures to be visualized. Image courtesy of the National Institutes of Health Clinical Center, Center for Interventional Oncology. /



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