for b-values that are sufficiently small so that the O ( b 3 ) terms of eqn (36) are negligible. As for DTI, the meaning of “sufficiently small” is, in general, sample dependent, but will typically include a larger range of b-values than for eqn (33) due to the inclusion of the higher order term. With this approximation, one can estimate both D and K by fitting to the diffusion-weighted signal intensity data with three or more b-values (since there are now 3 unknowns) in any given gradient direction. For exactly three b-values, b 1 , b 2 and b 3 , the closed-form expressions are ( 37 )

In order to localize this signal attenuation to get images of diffusion one has to combine the pulsed magnetic field gradient pulses used for MRI (aimed at localization of the signal, but those gradient pulses are too weak to produce a diffusion related attenuation) with additional "motion-probing" gradient pulses, according to the Stejskal and Tanner method. This combination is not trivial, as cross-terms arise between all gradient pulses. The equation set by Stejskal and Tanner then becomes inaccurate and the signal attenuation must be calculated, either analytically or numerically, integrating all gradient pulses present in the MRI sequence and their interactions. The result quickly becomes very complex given the many pulses present in the MRI sequence and, as a simplication, Le Bihan suggested to gather all the gradient terms in a "b factor" (which depends only on the acquisition parameters), so that the signal attenuation simply becomes: [1]

Although typical diffusion images have a spatial resolution of a few millimeters, they reflect events happening at the molecular level. As noted previously, when diffusing spins run into cellular constituents and membranes, the ADC value will be reduced when compared with diffusion in bulk water like cerebrospinal fluid (CSF). 24 Diffusion measurements become more complex when the structures restricting water diffusion have a structure themselves. For instance, axons restrict water diffusion perpendicular to their long axis, but not in the direction of the axon. This difference in magnitude of diffusion in different directions is referred to as diffusion anisotropy. What makes this more complex is that unless the axon is aligned with the imaging gradient, the reduction in signal will be seen in all 3 directions. When diffusion is to be measured in an anisotropic environment, diffusion tensor imaging is needed for a complete description.