Commenced in January 2007
Paper Count: 30743
Modeling the Saltatory Conduction in Myelinated Axons by Order Reduction
Abstract:The saltatory conduction is the way the action potential is transmitted along a myelinated axon. The potential diffuses along the myelinated compartments and it is regenerated in the Ranvier nodes due to the ion channels allowing the flow across the membrane. For an efficient simulation of populations of neurons, it is important to use reduced order models both for myelinated compartments and for Ranvier nodes and to have control over their accuracy and inner parameters. The paper presents a reduced order model of this neural system which allows an efficient simulation method for the saltatory conduction in myelinated axons. This model is obtained by concatenating reduced order linear models of 1D myelinated compartments and nonlinear 0D models of Ranvier nodes. The models for the myelinated compartments are selected from a series of spatially distributed models developed and hierarchized according to their modeling errors. The extracted model described by a nonlinear PDE of hyperbolic type is able to reproduce the saltatory conduction with acceptable accuracy and takes into account the finite propagation speed of potential. Finally, this model is again reduced in order to make it suitable for the inclusion in large-scale neural circuits.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1474279Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 393
 R. Barbulescu, D. Ioan and J. Ciurea, Simple 1D models for neuro-signals transmission along axons, 2016 International Conference and Exposition on Electrical and Power Engineering (EPE), 2016: 313-319.
 A. Huxley and R.!Stampeli, Evidence for saltatory conduction in peripheral myelinated nerve fibres, The Journal of physiology 108(3), 1949: 315-339.
 R. FitzHugh, Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber, Biophysical journal 2.1, 1962: 11.
 I. Tasaki, Physiology and Electrochemistry of Nerve Fibers, Academic Press, New York, 1982.
 R. FitzHugh, Mathematical models of excitation and propagation in nerve, . Chapter 1 (pp. 185 in H.P. Schwan, ed. Biological Engineering, McGrawHill Book Co., N.Y.), 1969.
 F. Rattay et al., Impact of morphometry, myelinization and synaptic current strength on spike conduction in human and cat spiral ganglion neurons, PloS one 8.11, 2013: e79256.
 A. M. Brown and M. Hamann, Computational modeling of the effects of auditory nerve dysmyelination, Frontiers in neuroanatomy 8, 2014.
 J. P. Keener and J. Sneyd, Mathematical physiology., Vol.1, New York: Springer, 1998, 2nd ed., 2009.
 J. M. Bower and D. Beeman, The Book of GENESIS: Exploring Realistic Neural Models with the GEneralNEuralSImulation System, Second edition, Springer-Verlag, New York, 1998.
 N. T. Carnevale and M. L. Hines, The NEURON book., Cambridge University Press, 2006.
 D. Ioan, R. Barbulescu, L. M. Silveira and G. Ciuprina, Reduced Order Models of Myelinated Axonal Compartments, 2018, under review.
 B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting, IEEE Transactions on power delivery 14(3), 1999: 1052-1061.
 D. Ioan and I. Munteanu, Missing link rediscovered: The electromagnetic circuit element concept, JSAEM Studies in Applied Electromagnetics and Mechanics 8, 1999: 302-320.
 G. Ciuprina et al., Parameterized model order reduction, Coupled Multiscale Simulation and Optimization in Nanoelectronics. Springer, Berlin, Heidelberg, 2015: 267-359.
 B. Frankenhaeuser and A. F. Huxley, The action potential in the myelinated nerve fibre of Xenopuslaevis as computed on the basis of voltage clamp data, The Journal of Physiology 171.2, 1964: 302.
 E. M. Izhikevich, Simple model of spiking neurons, IEEE Transactions on neural networks 14.6, 2003: 1569-1572.
 A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of physiology, 117(4), 1952: 500-44.
 M. C. Ford et al., Tuning of Ranvier node and internode properties in myelinated axons to adjust action potential timing, Nature communications 6, 2015: 8073.
 S. Grissmer, Properties of potassium and sodium channels in frog internode, J Physiol, vol. 381, 1986:119-34.
 N. A. Angel, Equivalent circuit implementation of demyelinated human neuron in spice, Master’s Thesis, 2011.