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Front. Phys. | doi: 10.3389/fphy.2018.00017

Influence of the size and curvedness of neural projections on the orientationally averaged diffusion MR signal

  • 1Department of Biomedical Engineering, Linköping University, Sweden
  • 2Department of Mathematics, Linköping University, Sweden
  • 3Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, United States

Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, $\bar{E}(q)\propto q^{-1}$, where $q$ is the wavenumber determined by the parameters of the pulsed field gradient measurements. \revisn{One particular study by McKinnon \etal.\ \cite{McKinnon17} reports}
a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements.
\revisn{We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the $q^{-1}$ decay, while such decay is robust when narrow gradient pulses are used.}
Thus, \revisn{in clinical acquisitions}, the lack of such a decay for a fibrous specimen \revisn{can be seen as} indicative of fibers that are \revisn{curved}. We note that the above discussion is valid for an intermediate range of $q$-values as the true asymptotic behavior of the signal decay is characterized by the Debye-Porod law, which suggests the dependence $\bar{E}(q)\propto q^{-4}$ at very large $q$-values.
This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.

Keywords: Diffusion, Magnetic resonance, Anisotropy, Stejskal-Tanner, curvature, Curvilinear, power-law, Powder

Received: 29 Sep 2017; Accepted: 09 Feb 2018.

Edited by:

Julien Valette, Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA), France

Reviewed by:

Sune N. Jespersen, Aarhus University, Denmark
Gernot Reishofer, Medizinische Universität Graz, Austria
Silvia Capuani, Consiglio Nazionale Delle Ricerche (CNR), Italy  

Copyright: © 2018 Özarslan, Yolcu, Herberthson, Knutsson and Westin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: PhD. Evren Özarslan, Linköping University, Department of Biomedical Engineering, Linköping, Sweden,