Parametric Probability Distribution Functions for Axon Diameters of Corpus Callosum.
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.
Centre for Advanced Imaging, The University of QueenslandBrisbane, QLD, Australia; Laboratory of Neuro Imaging, USC Mark and Mary Stevens Neuroimaging and Informatics Institute, Keck School of Medicine of USC, University of Southern CaliforniaLos Angeles, CA, USA.
Farshid
F
Sepehrband
Department of Computer Science, Centre for Medical Image Computing, University College London London, UK.
Daniel C
DC
Alexander
Laboratory of Neuro Imaging, USC Mark and Mary Stevens Neuroimaging and Informatics Institute, Keck School of Medicine of USC, University of Southern California Los Angeles, CA, USA.
Kristi A
KA
Clark
Centre for Advanced Imaging, The University of Queensland Brisbane, QLD, Australia.
Nyoman D
ND
Kurniawan
Centre for Advanced Imaging, The University of QueenslandBrisbane, QLD, Australia; Brainnetome Center, Institute of Automation, Chinese Academy of SciencesBeijing, China; Faculty of Information Engineering, Southwest University of Science and TechnologyMianyang, China.
Zhengyi
Z
Yang
Centre for Advanced Imaging, The University of Queensland Brisbane, QLD, Australia.
David C
DC
Reutens
axon diameter distribution; corpus callosum; electron microscopy; gamma distribution; generalized extreme value distribution; probability distribution function