Relating Extracellular Diffusivity to Cell Size Distribution and Packing Density as Applied to White Matter

Dmitry S. Novikov¹, Els Fieremans¹

Tissues are often viewed as tight packings of practically impermeable cells. While the intra- and extracellular water fractions can be determined using a straightforward biexponential fit, quantifying the cell size distribution and packing geometry with low-q diffusion metrics has been a notoriously hard problem. We develop a novel analytical approach for relating the diffusivity in the extra-axonal space to the volume fraction of axons and their size heterogeneity that agrees with Monte Carlo simulations. Our formalism quantitatively distinguishes between demyelination and axonal loss in the diffusion coefficient of the extra-axonal space transverse to the fibers.