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• W2103001484 abstract "Journal of Integrative NeuroscienceVol. 03, No. 02, pp. 227-244 (2004) Research ReportsNo AccessSCALING LAWS FOR MYELINATED AXONS DERIVED FROM AN ELECTROTONIC CORE-CONDUCTOR MODELPETER J. BASSERPETER J. BASSERNational Institutes of Health, 13 South Drive, Bldg. 13, Rm. 3W16, Bethesda, MD 20892-5772, USA Search for more papers by this author https://doi.org/10.1142/S0219635204000427Cited by:19 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractA macroscopic cable equation, which describes the passive linear (electrotonic) response of a myelinated axon, was previously derived from a segmented cable equation using Keller's two-space homogenization method [Basser, PJ, Med. and Biol. Comput., 1993, Vol. 31, pp. S87–S92]. Here we use the space and length constants of this averaged cable equation to predict classical scaling laws that govern relationships among the inner and outer diameters of the axon's myelin sheath and the distance separating adjacent nodes of Ranvier. These laws are derived by maximizing the characteristic speed of an electrical disturbance along the axon, i.e., the ratio of the characteristic length and the characteristic time constants of the macroscopic cable, subject to the constraint that the nodal width is constant. Using this result, it is also possible to show that all myelinated axons are equally fault tolerant. No free parameters were used in this analysis; all variables and physical constants used in these calculations were taken from published experimental data.Keywords:Scalingaxonmyelincablemodelequationtwo-space methodhomogenization References W. A. H. Rushton, J. Physiol. (London) 115, 101 (1951). Crossref, Google ScholarR. FitzHugh, Biological Engineering, ed. H. 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Systematic review, qualitative assessment, and meta-analysis of studies validating microstructural imaging with myelin histologyAlberto Lazari and Ilona Lipp1 Apr 2021 | NeuroImage, Vol. 230Neural selectivity, efficiency, and dose equivalence in deep brain stimulation through pulse width tuning and segmented electrodesCollin J. Anderson, Daria Nesterovich Anderson, Stefan M. Pulst, Christopher R. Butson and Alan D. Dorval1 Jul 2020 | Brain Stimulation, Vol. 13, No. 4Individual variations of the human corticospinal tract and its hand-related motor fibers using diffusion MRI tractographyKyriakos Dalamagkas, Magdalini Tsintou, Yogesh Rathi, Lauren J. O’Donnell and Ofer Pasternak et al.8 January 2019 | Brain Imaging and Behavior, Vol. 14, No. 3Optimizing selective stimulation of peripheral nerves with arrays of coils or surface electrodes using a linear peripheral nerve stimulation metricMathias Davids, Bastien Guérin, Valerie Klein, Martin Schmelz and Lothar R Schad et al.14 January 2020 | Journal of Neural Engineering, Vol. 17, No. 1Material Characterization and Bioanalysis of Hybrid Scaffolds of Carbon Nanomaterial and Polymer NanofibersMadhulika Srikanth, Ramazan Asmatulu, Kim Cluff and Li Yao8 March 2019 | ACS Omega, Vol. 4, No. 3Regulation of myelin structure and conduction velocity by perinodal astrocytesDipankar J. Dutta, Dong Ho Woo, Philip R. Lee, Sinisa Pajevic and Olena Bukalo et al.29 October 2018 | Proceedings of the National Academy of Sciences, Vol. 115, No. 46Simulated auditory nerve axon demyelination alters sensitivity and response timing to extracellular stimulationJesse M. Resnick, Gabrielle E. O'Brien and Jay T. Rubinstein1 Apr 2018 | Hearing Research, Vol. 361Predicting Magnetostimulation Thresholds in the Peripheral Nervous System using Realistic Body ModelsMathias Davids, Bastien Guérin, Matthias Malzacher, Lothar R. Schad and Lawrence L. Wald13 July 2017 | Scientific Reports, Vol. 7, No. 1From wearable robotics to quantifiable outcomes: In vivo imaging biomarkers to accelerate the translation of new interventions in neurorehabilitationKyriakos Dalamagkas and Magdalini Tsintou1 Nov 2017Mapping temporo-parietal and temporo-occipital cortico-cortical connections of the human middle longitudinal fascicle in subject-specific, probabilistic, and stereotaxic Talairach spacesNikos Makris, A. Zhu, G. M. Papadimitriou, P. Mouradian and I. Ng et al.6 October 2016 | Brain Imaging and Behavior, Vol. 11, No. 5Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusionLipeng Ning, Evren Özarslan, Carl-Fredrik Westin and Yogesh Rathi1 Feb 2017 | NeuroImage, Vol. 146Variability and anatomical specificity of the orbitofrontothalamic fibers of passage in the ventral capsule/ventral striatum (VC/VS): precision care for patient-specific tractography-guided targeting of deep brain stimulation (DBS) in obsessive compulsive disorder (OCD)Nikolaos Makris, Yogesh Rathi, Palig Mouradian, Giorgio Bonmassar and George Papadimitriou et al.30 October 2015 | Brain Imaging and Behavior, Vol. 10, No. 4Evolution of rapid nerve conductionAnn M. Castelfranco and Daniel K. Hartline1 Jun 2016 | Brain Research, Vol. 1641Human middle longitudinal fascicle: segregation and behavioral-clinical implications of two distinct fiber connections linking temporal pole and superior temporal gyrus with the angular gyrus or superior parietal lobule using multi-tensor tractographyN. Makris, M. G. Preti, D. Wassermann, Y. Rathi and G. M. Papadimitriou et al.18 May 2013 | Brain Imaging and Behavior, Vol. 7, No. 3Human middle longitudinal fascicle: variations in patterns of anatomical connectionsN. Makris, M. G. Preti, T. Asami, P. Pelavin and B. Campbell et al.11 July 2012 | Brain Structure and Function, Vol. 218, No. 4An Optimum Principle Predicts the Distribution of Axon Diameters in Normal White MatterSinisa Pajevic, Peter J. Basser and Christian Beaulieu28 January 2013 | PLoS ONE, Vol. 8, No. 1Stochastic Population Model for Electrical Stimulation of the Auditory NerveN.S. Imennov and J.T. Rubinstein1 Oct 2009 | IEEE Transactions on Biomedical Engineering, Vol. 56, No. 10Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fieldsP C Miranda, L Correia, R Salvador and P J Basser3 September 2007 | Physics in Medicine and Biology, Vol. 52, No. 18The Role of Tissue Heterogeneity in Neural Stimulation by Applied Electric FieldsPedro C. Miranda, Ludovic Correia, Ricardo Salvador and Peter J. Basser1 Aug 2007 Recommended Vol. 03, No. 02 Metrics History Received 29 February 2004 Accepted 24 April 2004 KeywordsScalingaxonmyelincablemodelequationtwo-space methodhomogenizationPDF download" @default.
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