title: An optimum principle predicts the distribution of axon diameters in normal white matter.
abstract: Many important functional properties affecting nerve conduction are influenced by axon diameter. It is also known that the axon diameter distribution (ADD) in normal nerve fascicles is heterogeneous and skewed. A recent attempt to model and explain the parametric form of these distributions was based on biomechanical principles. Here we explore a neurophysiologically-based hypothesis that the observed ADD can be obtained by optimizing the information flow through a fascicle subject to reasonable anatomical and metabolic constraints. Specifically, we use a variational framework to find an optimal distribution based on the fascicle's channel capacity and informative upper bound (IUB), subject to constraints of fixed available fascicle cross-sectional area and fixed number of axons, to derive two novel probability density functions, which we then compare to other previously used distributions. We show, using experimental histological data, that the distributions based on this optimum principle outperform other distributions. Moreover, the new distribution that optimizes the IUB is extremely robust in fitting ADD data obtained histologically, making it well-suited for use in MRI techniques to measure ADDs in vivo, e.g., AxCaliber MRI.
authors: Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland, United States of America. pajevic@nih.gov
authors: Sinisa
authors: S
authors: Pajevic
authors: Peter J
authors: PJ
authors: Basser
mesh_terms: D000465:Algorithms; D001369:Axons; D038524:Diffusion Magnetic Resonance Imaging; D009413:Nerve Fibers, Myelinated / Q000502:physiology*; D009900:Optic Nerve / Q000502:physiology*
references: J Neurosci. 2012 Jan 11;32(2):626-38
references: 22238098
references: J Physiol. 1951 Sep;115(1):101-22
references: 14889433
references: Magn Reson Med. 2008 Jun;59(6):1347-54
references: 18506799
references: Biophys J. 1967 Nov;7(6):797-826
references: 19210999
references: Neuroimage. 2008 May 1;40(4):1619-32
references: 18342541
references: Science. 1950 Aug 4;112(2901):143-4
references: 15442275
references: Proc Natl Acad Sci U S A. 2006 Mar 21;103(12):4723-8
references: 16537428
references: Proc Natl Acad Sci U S A. 2000 May 9;97(10):5621-6
references: 10792049
references: J Neurosci. 2008 Apr 9;28(15):4047-56
references: 18400904
references: Brain Res. 1992 Dec 11;598(1-2):143-53
references: 1486477
references: Eur Phys J E Soft Matter. 2009 Jul;29(3):337-44
references: 19579039
references: Biol Cybern. 1975 Sep 1;19(3):121-5
references: 1174580
references: J Neurophysiol. 1998 Mar;79(3):1219-29
references: 9497403
references: Trends Neurosci. 2008 Jul;31(7):361-70
references: 18538868
references: Science. 1951 Mar 16;113(2933):292-3
references: 14817273
references: BMC Neurosci. 2003 Aug 28;4:18
references: 12946281
references: Science. 2002 Oct 18;298(5593):556-62
references: 12386325
references: J Integr Neurosci. 2004 Jun;3(2):227-44
references: 15285056
references: Biol Cybern. 1975 Aug 8;19(2):61-7
references: 172162