# Diffusion Primer

Diffusion weighted imaging is a classic MR technique that estimates the amount of diffusion (mainly the Brownian motion of water) in a particular direction. Modern diffusion imaging methods acquire data in multiple directions (See Huettel et al. Figure 5.17).

##  Diffusion

The free diffusion (self-diffusion) of water is about 3 um^2 per ms at body temperature. The rate of diffusion is tightly coupled to temperature (e.g., see Krynicki, Green & Sawyer (1978). Pressure and temperature dependence of self-diffusion in water. Faraday Discuss. Chem. Soc., 66, 199 - 208 and the mrDiffusion function models/dtiSelfDiffusionOfWater.m). Le Bihan even proposed imaging local variations in brain temperature using diffusion.

There are various gradient sequences for measuring diffusion. The classic citation is Stejskal and Tanner, 1964, in which they worked out how to optimize a sequence to measure diffusion through sequential application of equal and opposite gradients. Anything that moves around during the time the gradients are applied will not be 'reset'. This idea is clear and simple to explain. More modern imaging methods use variants that improve SNR but are more annoying to explain (See Huettel around Fig 5.19b).

Diffusion in the brain is anisotropic - diffusion is impeded by cell membranes, and probably by smaller structures within cells.

In a diffusion weighted image, the intensity of the image is negatively related to the amount of the diffusion. The more the water diffused within a voxel, the darker that voxel will appear in the diffusion weighted image.

##  Diffusion tensor

Diffusion tensor imaging (DTI) is a method proposed by Basser, Mattiello and LeBihan (1984) to measure at least 6 well-chosen diffusion directions and then fit a 3d Gaussian model to the measurements (the diffusion tensor). Then, diffusion in any direction (including those that weren't measured) can be estimated from the model. In general, Basser's group at the NIH is a great example of how a national lab should work, and represents a real bargain for the American taxpayers.

There are three spatial resolutions to consider in DTI. One is the length-scale of the diffusion of the water itself; this is on the order of ~10um given the typical diffusion times in DTI sequences. The second is the sampling of the voxels for reading out the bulk change in the signal; this is typically on the order of 2-5mm. The third is how finely we measure different diffusion directions; this is on the order of 6 to 100s of different directions.

Diffusion imaging isn't just for white matter- it can also reveal the gray matter pyramidal cell axons running perpendicular to the cortical surface (Dâ€™Arceuil, H.E., Grant, E., de Crespigny, A.J. 2005. High Resolution DTI of Fixed Human Brain Specimens. ISMRM Workshop on Methods for Quantitative Diffusion MRI of Human Brain, Lake Louise, AB).