ActiveAx_ADD: Toward non‐parametric and orientationally invariant axon diameter distribution mapping using PGSE

Abstract

Purpose Non‐invasive axon diameter distribution (ADD) mapping using diffusion MRI is an ill‐posed problem. Current ADD mapping methods require knowledge of axon orientation before performing the acquisition. Instead, ActiveAx uses a 3D sampling scheme to estimate the orientation from the signal, providing orientationally invariant estimates. The mean diameter is estimated instead of the distribution for the solution to be tractable. Here, we propose an extension (ActiveAxADD) that provides non‐parametric and orientationally invariant estimates of the whole distribution. Theory The accelerated microstructure imaging with convex optimization (AMICO) framework accelerates mean diameter estimation using a linear formulation combined with Tikhonov regularization to stabilize the solution. Here, we implement a new formulation (ActiveAxADD) that uses Laplacian regularization to provide robust estimates of the whole ADD. Methods The performance of ActiveAxADD was evaluated using Monte Carlo simulations on synthetic white matter samples mimicking axon distributions reported in histological studies. Results ActiveAxADD provided robust ADD reconstructions when considering the isolated intra‐axonal signal. However, our formulation inherited some common microstructure imaging limitations. When accounting for the extra axonal compartment, estimated ADDs showed spurious peaks and increased variability because of the difficulty of disentangling intra and extra axonal contributions. Conclusion Laplacian regularization solves the ill‐posedness regarding the intra axonal compartment. ActiveAxADD can potentially provide non‐parametric and orientationally invariant ADDs from isolated intra‐axonal signals. However, further work is required before ActiveAxADD can be applied to real data containing extra‐axonal contributions, as disentangling the 2 compartment appears to be an overlooked challenge that affects microstructure imaging methods in general.

Axon morphology is modulated by the local environment and impacts the non-invasive investigation of its structure-function relationship

“…This will be the case for all diffusion MRI models that assume a cylindrical axonal geometry and base the AD estimation on measurements perpendicular to the axon population, confirming the need to account for fiber dispersion effects 14,16,21,44 . Some studies implement biophysical models to account for axon dispersion or crossing axon effects 12,45 , but the intra-axonal MRI signal profile intermingles with that of the ECS, challenging a robust fitting 46 . We could not extract the ECS from our XNH data due to insufficient resolution and shrinkage caused by the tissue processing.…”

The variability of MR axon radii estimates in the human white matter

“…Diffusion‐weighted MRI (dMRI) is a particularly relevant neuroimaging modality to probe cellular features, far below the resolution of the imaging experiment (Alexander et al, 2010; Assaf Blumenfeld‐Katzir, Yovel, & Basser, 2008; Fan et al, 2020; Huang et al, 2020; McNab et al, 2013; Romascano et al, 2020; Sepehrband, Alexander, Kurniawan, Reutens, & Yang, 2016; Veraart et al, 2020). Indeed, dMRI is sensitive to a wide range of tissue microstructural parameters because the signal is sensitized to the micrometer length scale of the diffusion of water molecules (Tanner, 1979).…”

The variability of MR axon radii estimates in the human brain

“…Diffusion-weighted MRI (dMRI) is a particularly relevant neuroimaging modality to probe cellular features, far below the resolution of the imaging experiment (Assaf et al, 2008;Alexander et al, 2010;Romascano et al, 2020;McNab et al, 2013;Fan et al, 2020;Sepehrband et al, 2016b;Veraart et al, 2020;Huang et al, 2020). Indeed, dMRI is sensitive to a wide range of tissue microstructural parameters because the signal is sensitized to the micrometer length scale of the diffusion of water molecules (Tanner, 1979).…”