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Modeling and simulating the nerve axon as a thin-film microstrip

Published online by Cambridge University Press:  12 December 2012

A. Dueñas Jiménez*
Affiliation:
Departamento de Electrónica, CUCEI, Universidad de Guadalajara, Av. Revolución No. 1500, Guadalajara, Jalisco, 44430, México. Phone: 52 33 1378 5900, Ext. 7726
R. Magallanes Gómez
Affiliation:
Departamento de Ciencias Computacionales e Ingenierías, CUVALLES, Universidad de Guadalajara, Av. Revolución No. 1500, Guadalajara, Jalisco, 44430, México
J.M. Dueñas Jiménez
Affiliation:
Departamento de Neurociencias, CUCS, Universidad de Guadalajara, Av. Revolución No. 1500, Guadalajara, Jalisco, 44430, México
S.H. Dueñas Jiménez
Affiliation:
Departamento de Neurociencias, CUCS, Universidad de Guadalajara, Av. Revolución No. 1500, Guadalajara, Jalisco, 44430, México
*
Corresponding author:A. Dueñas Jiménez Email: [email protected]

Abstract

Since Hodgkin and Huxley described the nerve axon as a cable (H–H model), many efforts have been made to find more approximated transmission line models representing the nerve axon. This paper describes a simple model that represents the nerve axon in two parts: the internodal space as a lossy thin-film microstrip line and the node of Ranvier as an active complex load. The complex load terminating the transmission line is given by the variable impedance of a tunnel diode. First, the internodal space is circuitally analyzed and electromagnetically simulated as a lossy thin-film microstrip line terminated on a complex fixed load. The transmission line circuit theory, the two-port network analysis, and a two-dimensional finite difference time domain method are used for such a task by forcing a strip subatomic metallization. Then, the transfer function of the internodal space, cascaded with the node of Ranvier, is equated to the transfer function of a transmission line section that includes a tunnel diode. This procedure is carried out in order to obtain the diode's variable impedance. The diode was introduced by Nagumo, Arimoto, and Yoshizawa for simulating the nerve axon as an active transmission line. The active transmission line is represented by the FitzHugh simplified H–H model known as the Bonhoeffer–van der Pol model.

Type
Research Papers
Copyright
Copyright © Cambridge University Press and the European Microwave Association 2012

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References

[1]Hodgkin, L.; Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 117 (1952), 500544.Google Scholar
[2]FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophysical J., 1 (1961), 445466.Google Scholar
[3]Nagumo, J.; Arimoto, S.; Yoshizawa, S.: An active pulse transmission line simulating nerve axon. Proc. IRE, 50 (1962), 20612070.CrossRefGoogle Scholar
[4]Ferrero Corral, J.M.; Saiz, F.J.; Ferrero, J.M. Jr.: Analytical derivation of the internodal transfer function in myelinated fibers, in 15th Annual Int. Conf. IEEE/EMBS, San Diego, USA, 1993.Google Scholar
[5]Ferrero Corral, J.M.; Ferrero y de Loma-Osorio, J.M.; Saiz Rodríguez, F.J.; Arnau Vives, A.: Bioelectrónica: Señales Bioeléctricas, Universidad Politécnica de Valencia, Valencia, 1993.Google Scholar
[6]Plonsey, R.; Barr, R.C.: Bioelectricity: A Quantitative Approach, Springer, New York, 2007.Google Scholar
[7]Collin, R.E.: Foundations for Microwave Engineering, John Wiley and Sons Inc., New York, 2001.Google Scholar
[8]Schnieder, F.; Heinrich, W.: Model of thin-film microstrip line for circuit design. IEEE Trans. Microw. Theory Tech., 49 (2001), 104110.Google Scholar
[9]Llamas-Garro, I.; Lancaster, M.J.; Hall, P.S.: Air-filled square coaxial transmission line and its use in microwave filters. IEE Proc. Microw. Antennas Propag., 152 (2005), 155159.Google Scholar
[10]Reid, J.R.; Marsh, E.D.; Webster, R.T.; Micromachined rectangular-coaxial transmission lines. IEEE Trans. Microw. Theory Tech., 54 (2006), 34333442.Google Scholar
[11]Dueñas Jiménez, A.: 2-D Electromagnetic Simulation of Passive Microstrip Circuits, CRC Press – A Taylor and Francis Company, Boca Raton, Florida, 2009.Google Scholar
[12]Villapecellín-Cid, M.M.; Roa, L.M.; Reina-Tosina, J.: Transverse magnetic waves in myelinated nerves, in 23rd Annual Int. Conf. IEEE/EMBS, Istanbul, Turkey, 2001.Google Scholar
[13]Villapecellín-Cid, M.M.; Roa, L.; Reina-Tosina, J.: Ranvier nodes impedance match with internodal transmission lines of myelinated axons, in 25th Annual Int. Conf. IEEE/EMBS, Cancun, México, 2003.Google Scholar
[14]Rosenthal, J.J.C.; Bezanilla, F.: Seasonal variation in conduction velocity of action potentials in squid giant axons. Biol. Bull., 199 (2000), 135143.Google Scholar
[15]Van der Pol, B.: On relaxation oscillations. Phil. Mag., 2 (1926), 978.Google Scholar
[16]Bonhoeffer, K.F.: Activation of passive iron as a model for the excitation of nerve. J. Gen. Physiol., 32 (1948), 69.Google Scholar
[17]Sze, S.M.: Physics of Semiconductor Devices, John Wiley and Sons, New York, 1981.Google Scholar
[18]Hirasuna, B.; Busdeicker, D.: Analog Behavioral Modeling Using PSpice, Application Note, Cadence Design Systems Inc., USA, 2004.Google Scholar
[19]Huybrechs, D.: On the Fourier extension of nonperiodic functions. SIAM J. Numer. Anal., 47 (2010), 43264355.Google Scholar
[20]Cárdenas, C.M.F.; Jiménez, A.D.: Influence of measured scattering parameters on the convolution simulation of non-linear loaded high-speed microstrip interconnects. Prog. Electromagn. Res. M., 19 (2011), 7790.Google Scholar
[21]Pozar, D.M.: Microwave Engineering, John Wiley and Sons, Inc., New York, 1998.Google Scholar