Parametric Probability Distribution Functions for Axon Diameters of Corpus Callosum.

Farshid Sepehrband,David C Reutens,Daniel C Alexander,Kristi A Clark,Zhengyi Yang,Nyoman D Kurniawan

doi:10.3389/fnana.2016.00059

Abstract

Axon diameter is an important neuroanatomical characteristic of the nervous system that alters in the course of neurological disorders such as multiple sclerosis. Axon diameters vary, even within a fiber bundle, and are not normally distributed. An accurate distribution function is therefore beneficial, either to describe axon diameters that are obtained from a direct measurement technique (e.g., microscopy), or to infer them indirectly (e.g., using diffusion-weighted MRI). The gamma distribution is a common choice for this purpose (particularly for the inferential approach) because it resembles the distribution profile of measured axon diameters which has been consistently shown to be non-negative and right-skewed. In this study we compared a wide range of parametric probability distribution functions against empirical data obtained from electron microscopy images. We observed that the gamma distribution fails to accurately describe the main characteristics of the axon diameter distribution, such as location and scale of the mode and the profile of distribution tails. We also found that the generalized extreme value distribution consistently fitted the measured distribution better than other distribution functions. This suggests that there may be distinct subpopulations of axons in the corpus callosum, each with their own distribution profiles. In addition, we observed that several other distributions outperformed the gamma distribution, yet had the same number of unknown parameters; these were the inverse Gaussian, log normal, log logistic and Birnbaum-Saunders distributions.

Highlights

Axon diameter is an important structural characteristic of tissue in the central nervous system
Axon diameter correlates with conduction velocity, is affected by some neurological disorders, such as multiple sclerosis and autism, and changes during development (Ritchie, 1982; Piven et al, 1997; Bauman and Kemper, 2005; Hughes, 2006; Kunz et al, 2014)
We investigated the optimum probability distribution function for describing axons of corpus callosum

Summary

Introduction

Axon diameter is an important structural characteristic of tissue in the central nervous system. The gamma distribution is the most common probability distribution function used for this purpose It has two parameters, shape and scale, and broadly reflects the shape of the axon diameter distribution, which has been consistently observed to be right-skewed and heavy-tailed (i.e., an asymmetric distribution, in which the right tail of the distribution is much longer than the left tail). Pajevic and Basser (2013) argued, from neurophysiological perspective, that this skewed profile optimizes information transfer and capacity along bundles of axons. They reported optimum distributions, based on parameters describing the fiber’s ability to transmit information, that outperform the gamma distribution, in practical applications such as AxCaliber (Assaf et al, 2008)

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Conclusion