Diffusion MRI Diffusion Primer Peter J. Basser, Ph.D. Section on Tissue Biophysics & Biomimetics, NICHD National Institutes of Health, Bethesda, MD, USA pjbasser@helix.nih.gov 1. What is Diffusion? Diffusion is one of several “transport processes” that occur in nature. A distinguishing feature of diffusion is that it results in mixing or mass transport without requiring bulk motion. Thus, diffusion should not be confused with convection or dispersion, which are other transport mechanisms that use bulk motion to move particles from one place to another. 2. Gedanken Experiment Paul Berg’s book “Random Walks in Biology” (1), describes a useful thought experiment that illustrates the diffusion phenomenon. Imagine carefully introducing a drop of colored fluorescent dye into a jar of water. Initially, the dye remains concentrated at the point of release, but over time, it spreads radially, in a spherically symmetric distribution. This mixing process is taking place without stirring or other “convective” processes. 3. Underlying Physical Process This diffusive mixing results solely from collisions between molecules in liquids and gases. Another interesting feature of diffusion is that it occurs even in thermodynamic equilibrium. For example, it can occur in a jar of water kept at a constant temperature and pressure. This is quite remarkable, because the classical picture of diffusion, expressed in Fick’s First Law (2,3) was that, particles, like heat, flow from regions of high concentration to low concentation. When these gradients vanished, however, there was no net flux. There were many who held that diffusion stopped at this point. While the net flux vanishes, however, there are still diffusive fluxes nonetheless, however they cancel each other. 4. Brownian Motion Robert Brown is credited with being the first one to discover random motions of pollen grains while studying them through his microscope (4). It wasn’t until Einstein revisited this phenomenon in the early 20 th century that a coherent description of diffusion emerged, identifying the diffusion coefficient in Fick’s law and the variance of the particle displacement distribution that describes the migration of particles in “Brownian motion”. 5. Einstein’s insights into the diffusion process Einstein was able to derive an explicit relationship between the mean-squared displacement of a particle and the classical diffusion coefficient (5,6). Langevin improved Einstein’s description of diffusion for ultra-short timescales in which there are few molecular collisions. 1