Hodgkin-Huxley model has been reframed to incorporate the physical parameters of fluid inside the axon. The reframed model comprises of set of partial differential equations containing the physical parameters: density, mass fraction of sodium, potassium and chlorine ions, longitudinal diffusivity of ions and rate of additions of ions along with the temperature. Obtained conduction velocity of at a temperature of 18.5 degree celcius and conduction velocity dependency on temperature within the range 5 to 25 degree celcius are two important results that strongly validate the proposed model. The behavior of all the physical parameters has been characterized with respect to the action potential. Action potential conduction velocity along with axoplasmic fluid viscosity has been characterized with respect to different temperatures. Longitudinal diffusivity of ions is also quantified.
ChapmanR.A., Dependence on temperature of the conduction velocity of the action potential of the squid giant axon, Nature213(5081) (1967), 1143–1144. doi:10.1038/2131143a0.
4.
ChhabraR.P. and RichardsonJ.F., Non-Newtonian Flow and Applied Rheology: Engineering Applications, Butterworth-Heinemann, 2011.
5.
CiarletP.G., Numerical Methods for Non-Newtonian Fluids, Volume 16: Special Volume, 1st edn, North Holland, Amsterdam, 2011. ISBN 978-0-444-53047-9.
6.
ColeK.S., Permeability and impermeability of cell membranes for ions, Cold Spring Harb Symp Quant Biol8 (1940), 110–122. doi:10.1101/SQB.1940.008.01.013.
7.
ColeK.S. and MichaelisE.M., Surface forces of fertilized Arbacia eggs, J. Cell. Comp. Physiol.2(1) (1932), 121–126. doi:10.1002/jcp.1030020110.
8.
El KhatibN., A fluid-structure interaction model of the cell membrane deformation: Formation of a filopodium, Mathematical Modelling of Natural Phenomena9(1) (2014), 27–38. doi:10.1051/mmnp/20149103.
9.
ForrestM.D., Can the thermodynamic Hodgkin–Huxley model of voltage-dependent conductance extrapolate for temperature?, Computation2(2) (2014), 47–60. doi:10.3390/computation2020047.
10.
GerstnerW. and KistlerW.M., Spiking Neuron Models: Single Neurons, Populations, Plasticity, 1st edn, Cambridge University Press, Cambridge, U.K.; New York, 2002. ISBN 978-0-521-89079-3.
11.
GilbertD.S., Axoplasm chemical composition in Myxicola and solubility properties of its structural proteins, J Physiol253(1) (1975), 303–319. doi:10.1113/jphysiol.1975.sp011191.
12.
HilleB., Ion Channels of Excitable Membranes, 3rd edn, Sinauer Associates, Sunderland, Mass, 2001. ISBN 978-0-87893-321-1.
13.
HodgkinA.L. and HuxleyA.F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J Physiol117(4) (1952), 500–544. doi:10.1113/jphysiol.1952.sp004764.
14.
HodgkinA.L. and KeynesR.D., The mobility and diffusion coefficient of potassium in giant axons from Sepia, The Journal of Physiology119(4) (1953), 513–528. doi:10.1113/jphysiol.1953.sp004863.
15.
JavidS., RezaeiA. and KaramiG., A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem, Journal of the Mechanical Behavior of Biomedical Materials30 (2014), 290–299. doi:10.1016/j.jmbbm.2013.11.010.
16.
KoechlinB.A., On the chemical composition of the axoplasm of squid giant nerve fibers with particular reference to its ion pattern, J Biophys Biochem Cytol1(6) (1955), 511–529. doi:10.1083/jcb.1.6.511.
17.
NoelA.C., GuoH.Y., MandicaM. and HuD.L., Frogs use a viscoelastic tongue and non-Newtonian saliva to catch prey, Journal of The Royal Society Interface14(127) (2017), 20160764. doi:10.1098/rsif.2016.0764.
18.
OferN. and ShefiO., Axonal geometry as a tool for modulating firing patterns, Applied Mathematical Modelling40(4) (2016), 3175–3184. doi:10.1016/j.apm.2015.10.017.
19.
RashidiM.M., YangZ., AwaisM., NawazM. and HayatT., Generalized magnetic field effects in Burgers’ nanofluid model, PLOS ONE12(1) (2017), e0168923. doi:10.1371/journal.pone.0168923.
20.
RoquemoreW.M. and KattaV.R., Role of flow visualization in the development of UNICORN, J Vis2(3–4) (2000), 257–272. doi:10.1007/BF03181442.
21.
RoselliR.J. and DillerK.R., Biotransport: Principles and Applications, Springer Science & Business Media, 2011. ISBN 978-1-4419-8119-6.
22.
RubinsonK.A. and BakerP.F., The flow properties of axoplasm in a defined chemical environment: influence of anions and calcium, Proceedings of the Royal Society of London B: Biological Sciences205(1160) (1979), 323–345. doi:10.1098/rspb.1979.0068.
23.
SalmonE.D., SaxtonW.M., LeslieR.J., KarowM.L. and McIntoshJ.R., Diffusion coefficient of fluorescein-labeled tubulin in the cytoplasm of embryonic cells of a sea urchin: Video image analysis of fluorescence redistribution after photobleaching, J. Cell Biol.99(6) (1984), 2157–2164. doi:10.1083/jcb.99.6.2157.
24.
SamsonE., MarchandJ. and SnyderK.A., Calculation of ionic diffusion coefficients on the basis of migration test results, Mat. Struct.36(3) (2003), 156–165. doi:10.1007/BF02479554.
25.
SterrattD.GrahamB.GilliesA. and WillshawD., Principles of Computational Modelling in Neuroscience, Cambridge University Press, Cambridge, 2011.
26.
TasakiI., SingerI. and WatanabeA., Cation interdiffusion in squid giant axons, The Journal of General Physiology50(4) (1967), 989–1007. doi:10.1085/jgp.50.4.989.
27.
XiangZ.X., LiuG.Z., TangC.X. and YanL.X., A model of ion transport processes along and across the neuronal membrane, Journal of Integrative Neuroscience16(1) (2017), 33–55. doi:10.3233/JIN-160002.
