Time-dependent diffusion in undulating structures: Impact on axon diameter estimation

TL;DR

This study investigates how undulating axonal trajectories affect diffusion MRI-based axon diameter estimation, revealing that ignoring undulations can lead to overestimations and misinterpretations of diffusion spectra.

Contribution

The paper introduces an undulating thin-fiber model to analyze the impact of axonal undulations on diffusion spectra, highlighting the importance of considering non-straight trajectories in axon diameter estimation.

Findings

Microscopic orientation dispersion mainly influences diffusion spectrum characteristics.

Ignoring undulations leads to overestimating axon diameter proportional to undulation amplitude.

High-frequency spectra differ between straight cylinders and undulating fibers, affecting interpretation.

Abstract

Diffusion MRI may enable non-invasive mapping of axonal microstructure. Most approaches infer axon diameters from effects of time-dependent diffusion on the diffusion-weighted MR signal by modelling axons as straight cylinders. Axons do not, however, run in straight trajectories and so far, the impact of the axonal trajectory on diameter estimation has not been systematically investigated. Here, we employ a toy-model of axons, which we refer to as undulating thin-fiber model, to analyze the impact of undulating trajectories on the diffusion-time dependence represented by the diffusion spectrum. We analyze the spectrum by its height (diffusivity at high frequencies), width (half width at half maximum), and low-frequency behavior (power law exponent). Results show that microscopic orientation dispersion of the thin-fibers is the main parameter that determines the characteristics of the diffusion spectra. Straight cylinders and undulating thin-fibers have virtually identical spectra at lower frequencies. If the straight-cylinder assumption is used to interpret data from undulating thin axons, the diameter is overestimated by an amount proportional to the undulation amplitude and the microscopic orientation dispersion. At high frequencies (short diffusion times), spectra from cylinders and undulating thin-fibers differ. The spectra from the undulating thin-fibers can also differ from that of cylinders by exhibiting power law behaviors with exponents below two. In conclusion, we argue that the non-straight nature of axonal trajectories should not be ignored when analyzing dMRI data and that careful experiments may enable separation of diffusion within straight cylinders and diffusion in undulating thin-fibers.