Figure 1.

Measurement of the “self-diffusion” coefficient with magnetic resonance. (A) Self-diffusion is a special case of diffusion that describes the relentless motion of microscopic particles in a substance. Such motion is random—it can be described by a “Gaussian” distribution whose width determines how far particles travel on average after some time; the important thing to remember is that only time, the “diffusion time,” and the “self-diffusion coefficient,” D, modulate this width. (B) Illustration of a magnetic resonance pulse sequence that is sensitive to self-diffusion: (i) an “excitation pulse” gives some energy to water protons; (ii) then the first “gradient” encodes where they are; (iii) and some (diffusion) time later, a second gradient decodes their position by giving them a “signal penalty” according to how far they have moved away from their original position; (iv) as a result of this penalty, protons that have moved furthest, return the least signal. The overall signal attenuation is a function of D and the gradient characteristics—i.e., intensity (G), duration (t_G) and diffusion time (t_D)—usually conglomerated into a single term known as the “b-value.” (C) Visual representation of the linear fit required to quantify D using two signals: a diffusion weighted measurement (i.e., with a non-zero b-value), S, that must be normalized by a measurement without diffusion weighting, S₀ (also often called b₀); D can be inferred as the “negative” of the slope.