Mesoscopic structure of neuronal tracts from time-dependent diffusion

Abstract

Interpreting brain diffusion MRI measurements in terms of neuronal structure at a micrometer level is an exciting unresolved problem. Here we consider diffusion transverse to a bundle of fibers, and show theoretically, as well as using Monte Carlo simulations and measurements in a phantom made of parallel fibers mimicking axons, that the time dependent diffusion coefficient approaches its macroscopic limit slowly, in a (lnt)/t fashion. The logarithmic singularity arises due to short range disorder in the fiber packing. We identify short range disorder in axonal fibers based on histological data from the splenium, and argue that the time dependent contribution to the overall diffusion coefficient from the extra-axonal water dominates that of the intra-axonal water. This dominance may explain the bias in measuring axon diameters in clinical settings. The short range disorder is also reflected in the linear frequency dependence of the diffusion coefficient measured with oscillating gradients, in agreement with recent experiments. Our results relate the measured diffusion to the mesoscopic structure of neuronal tissue, uncovering the sensitivity of diffusion metrics to axonal arrangement within a fiber tract, and providing an alternative interpretation of axonal diameter mapping techniques.

Machine Learning Based Compartment Models with Permeability for White Matter Microstructure Imaging

“…The approach, as used here, also neatly avoids the need for any analytical model of tortuous extra-cellular diffusion for which only approximations are available (Burcaw et al, 2015). Given that these compartment models tend to overestimate key microstructure parameters such as the axon diameter , including the effects of these intractable parameters not only gives us clinically useful parameters, but may also improve the estimation of other microstructure indices.…”

Improving the Realism of White Matter Numerical Phantoms: A Step toward a Better Understanding of the Influence of Structural Disorders in Diffusion MRI

“…Some OGSE studies have reported that, at frequencies below 400 Hz, the OG-measured extra-axonal diffusivity transverse to axons in white matter is linearly dependent on the frequency of the employed OGSE sequence [2], whereas state-of-the art multi-compartment models of white matter relying on PGSE or OGSE sequences usually assume a Gaussian diffusion in the extra-axonal space [3][4][5][6]. A theoretical explanation was given in Burcaw et al [7], where the observed frequency-dependence is interpreted as resulting from the extra-axonal 2D short-range disorder of axonal packings in the plane transverse to white matter fibers.…”

“…where t is the diffusion time, ω is the dual frequency and t c represents the time to diffuse across the correlation length l c of the packing geometry (l c closely follows the mean external radius r ext of the axon packing [7,8]). Similar to recent models accounting for extra-axonal time-dependence in the case of single diffusion encoding sequences [9], a multi-compartment model for cosine OGSE sequences was proposed in Ginsburger et al [10] which added a frequency-dependent term in the extra-axonal diffusion tensor perpendicular diffusivity based on Equation (2), showing a significant improvement of the model fit quality.…”

“…An empirical law A ∼ l 2 c relating A to the correlation length l c was given in Burcaw et al [7] and Fieremans et al [8] but is not sufficient to catch the complexity of the scaling coefficient A. The value of A is a measure of the strength of the structural disorder [7,11], thus related to the geometrical properties characterizing the spatial organization of white matter at various scales. A possible approach to decipher the complex relationship between A and white matter features is to perform Monte-Carlo simulations of the diffusion process in diffusing media with increasing level of structural disorder.…”

Multi-Spherical Diffusion MRI: Exploring Diffusion Time Using Signal Sparsity

“…Recent literature is increasingly emphasizing the need for such a representation, where accounting for the diffusion time dependence of the extra-axonal diffusion signal [1,2] has already resulted in a more accurate estimation of the axon density and diameter [3]. To measure the four-dimensional dMRI signal it is necessary to go beyond a multi-shell q-space acquisition -which only varies gradient strength and direction -and also vary the diffusion time.…”