In the brain's white matter, the signal travels along axons — long neuronal processes wrapped in an insulating myelin sheath. Water fills the space inside axons and outside, in the narrow gaps between fibers. Two MRI methods — diffusion (which tracks molecular motion) and relaxometry (which measures how quickly the signal decays)—are like two translators listening to the same conversation but hearing different things. Both pick up the impacts of water molecules against the walls, but they interpret them differently.
The authors derived closed-form formulas for these surface effects inside and outside myelinated cylinders. The key parameter is the volume fraction of fibers (VF). When VF exceeds a critical threshold (VF* = 1/(1+g), where g is the ratio of inner to outer surface relaxivity), the intracellular water dominates the signal. For healthy white matter, VF is indeed above this threshold, so the diffusion method at a clinical echo time of 80 ms overestimates the intra-axonal fraction by about 12%. The thinnest axons add to the confusion: their water relaxes so quickly that it falls into the myelin time window, and relaxometry attributes it to the myelin fraction, inflating the estimate by 0.33 percentage points. This error is small but systematic and depends on fiber packing density.
Thus, the same physics of wall collisions distorts two microstructural maps in different ways. For diffusion, it is a first-order error sensitive to packing; for relaxometry, it is a small structural correction that barely changes with primary demyelination and therefore shrinks in longitudinal studies. From now on, these distortions can not only be noticed but also predicted by a simple law.
In the white matter of a typical adult human, there are about 150,000 kilometers of axons — enough to wrap around the Earth's equator nearly four times.