Quantitative mapping of the per-axon diffusion coefficients in brain white matter.

Enrico Kaden,Frithjof Kruggel,Daniel C Alexander

doi:10.1002/mrm.25734

Enrico Kaden, Frithjof Kruggel + Show 1 more

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https://doi.org/10.1002/mrm.25734

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Abstract

PurposeThis article presents a simple method for estimating the effective diffusion coefficients parallel and perpendicular to the axons unconfounded by the intravoxel fiber orientation distribution. We also call these parameters the per‐axon or microscopic diffusion coefficients.Theory and MethodsDiffusion MR imaging is used to probe the underlying tissue material. The key observation is that for a fixed b‐value the spherical mean of the diffusion signal over the gradient directions does not depend on the axon orientation distribution. By exploiting this invariance property, we propose a simple, fast, and robust estimator of the per‐axon diffusion coefficients, which we refer to as the spherical mean technique.ResultsWe demonstrate quantitative maps of the axon‐scale diffusion process, which has factored out the effects due to fiber dispersion and crossing, in human brain white matter. These microscopic diffusion coefficients are estimated in vivo using a widely available off‐the‐shelf pulse sequence featuring multiple b‐shells and high‐angular gradient resolution.ConclusionThe estimation of the per‐axon diffusion coefficients is essential for the accurate recovery of the fiber orientation distribution. In addition, the spherical mean technique enables us to discriminate microscopic tissue features from fiber dispersion, which potentially improves the sensitivity and/or specificity to various neurological conditions. Magn Reson Med, 2015. Magn Reson Med 75:1752–1763, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.

Highlights

The method we propose to quantify the per-axon diffusion process and call the spherical mean technique (SMT) is based on the insight that for a fixed b-value the spherical mean of the diffusion signal over the gradient directions does not depend on the fiber orientation distribution
SMT requires at least two non-zero diffusion weighting factors for the quantification of the per-axon diffusion coefficients lk and l?
For our simulation experiments the per-axon diffusion coefficients are set to lk 1⁄4 2:5 and l? 1⁄4 0:1 mm2=ms

Summary

Introduction

The measured signal is sensitive to tissue properties in the range of few micrometers, such as the axon caliber, the degree of myelination, and the interaxonal space, averaged over a large population of microenvironments with potentially complex orientation distribution. The transcallosal fibers do link homotopic brain regions, and heterotopic cortical areas, do not run parallel to each other, leading to complex orientation distributions [6]. The presence of axon undulation, which is supposed to cope with mechanical tension such as pulsation, in other brain regions with eye movement and locomotion [7], gives rise to significant orientation dispersion, whose potential effect on the diffusion signal was recently demonstrated in a simulation study [8]. The callosal fibers may be arched on the millimeter voxel scale, in many instances apparent in the midsagittal plane

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