Abstract
This paper describes 3D Finite Element modelling solutions for a segment of a nervous cell axon, which take into account the non linear and time varying dynamics of the membrane surrounding it in order to reproduce its physiological behaviour, in terms of Action Potentials (AP) elicitation and its temperature dependence. The axial-symmetry of the system is exploited in order to conduct a more efficient analysis. A combination of the so called Hodgkin-Huxley equations modelling the dynamics of the membrane voltage-controlled ionic channels, together with the Maxwell equations in Electro Quasi-Static approximation, describing the electromagnetic behaviour of each medium, is tackled in a numerical procedure implemented in a commercial Finite Elements multiphysical environment. The usefulness of Finite Elements in order to have interesting quantitative responses (field shape and axon physiological behaviour) is investigated. Two different models are presented here. One exploits the typical thin layer approximation for the axon membrane, proving to be useful when the field solution inside the membrane domain is not a matter of interest. Its performances are compared with the other model, which is introduced in order to obtain a more realistic representation of the studied system: the axon membrane is here realized with a non-linear active medium (exploiting its equivalent electric conductivity) allowing the reproduction of the electric potential also inside the membrane. The passive electrotonic nature of the membrane and the elicitation of an AP in presence of different stimuli are computed and the results are in keeping with the predicted ones. Finally the AP temperature dependences and the propagation effect are reproduced by using the corresponding “best” numerical model, i.e. the coarse one without membrane for the temperature, the more detailed with membrane for the propagation, leading to a trade off between the computational effort and the objective of the analysis. The models open a wide range of applications and extensions in order to understand the true behaviour of a complete neuron.
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References
Finn, W., LoPresti, P.: The Handbook of Neuroprosthetic Methods. CRC Press (2003)
Talelea, S., Gaynor, P.: Non-linear time domain model of electropermeabilization: Response of a single cell to an arbitrary applied electric field. Journal of Electrostatics 65, 775–784 (2007)
Koch, C., Segev, I.: Methods in Neuronal Modeling: From Synapses to Networks. MIT Press, Cambridge (1989)
Ying, Z., et al.: Micro-stimulator Design for Visual Prosthesis based on Optic Nerve Stimulation. In: International Symposium on Biophotonics, Nanophotonics and Metamaterials, pp. 139–142 (2006)
Berger, et al.: Brain-Implantable Biomimetic Electronics as Neural Prosthetics. In: Proceedings of the 1st International IEEE EMBS Conference on Neural Engineering, Capri Island, Italy, March 20-22 (2003)
Daniel, J., et al.: Chronic Intraneural Electrical Stimulation For Prosthetic Sensory Feedback. In: Proceedings of the 1st International IEEE EMBS Conference on Neural Engineering, Capri Island, Italy, March 20-22 (2003)
Moulin, C., et al.: A New 3-D Finite-Element Model Based on Thin-Film Approximation for Microelectrode Array Recording of Extracellular Action Potential. IEEE Transactions on Biomedical Engineering 55(2), 683–692 (2008)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)
McIntyre, C.C., Grill, W.M.: Microstimulation of spinal motoneurons: a model study. In: Proceedings of the 19th International Conference - IEEE/EMBS, Chicago, IL, USA, October 30-November 2 (1997)
Woo, J., Miller, C.A., Abbas, P.J.: Biophysical Model of an Auditory Nerve Fiber With a Novel Adaptation Component. IEEE Transactions on Biomedical Engineering 56(9), 2177–2180 (2009)
Greenberg, R.J., Velte, T.J., Humayun, M.S., Scarlatis, G.N., de Juan Jr., E.: A Computational Model of Electrical Stimulation of the Retinal Ganglion Cell. IEEE Transactions on Biomedical Engineering 46(5), 505–514 (1999)
Tupsie, S., Isaramongkolrak, A., Paolaor, P.: Analysis of Electromagnetic Field Effects Using FEM for Transmission Lines Transposition. World Academy of Science, Engineering and Technology 53, 870–874 (2009)
Holt, G.R., Koch, C.: Electrical Interactions via the Extracellular Potential Near Cell Bodies. Journal of Computational Neuroscience 6(2), 169–184 (1999)
Stickler, Y., Martinek, J., Rattay, F.: Modeling Needle Stimulation of Denervated Muscle Fibers: Voltage–Distance Relations and Fiber Polarization Effects. IEEE Transactions on Biomedical Engineering 56(10), 2396–2403 (2009)
Hodgkin, A.L., Katz, B.: The effect of temperature on the electrical activity of the giant axon of the squid. J. Physiol. 109, 240–249 (1949)
Keynes, R.D.: The ionic movements during nervous activity. J. Physiol. 114, 119–150 (1951)
Huxley, A.F.: Ion movements during nerve activity. Annals of the New York Academy of Sciences 81, 221–246 (1959)
COMSOL Multiphysics 3.2 Reference Manual, Thin Film Resistance application example
Izhikevich, E.M.: Which Model to Use for Cortical Spiking Neurons? IEEE Transaction on Neuronal Networks 15(5), 1063–1070 (2004)
Moulin, C.: Contribution à l’étude et à la réalisation d’un système électronique de mesure et excitation de tissu nerveux à matrices de microélectrodes. Thèse Institut National des Sciences Appliquées de Lyon, p. 163 (2006)
Rattay, F.: Electrical Nerve Stimulation: Theory, Experiments and Applications. Springer (August 2001) ISBN: 321182247X
Malmivuo, Plonsey, R.: Bioelectromagnetism. Principles and Applications of Bioelectric and Biomagnetic Fields. Oxford University Press (1995)
Taglietti, Casella, C.: Elementi di fisiologia e biofisica della cellula. La goliardica Pavese Editore, Italy (1997)
Rattay, F.: Analysis of the electrical excitation of CNS neurons. IEEE Transaction on Biomedical Engineering 45(6), 766–772 (1998)
Elia, S., Lamberti, P., Tucci, V.: A Finite Element Model for The Axon of Nervous Cells. In: COMSOL Europe Conference 2009, October 14-16, pp. 1–7 (2009) ISBN/ISSN: 978-0-9825697-0-2
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Elia, S., Lamberti, P. (2013). The Reproduction of the Physiological Behaviour of the Axon of Nervous Cells by Means of Finite Element Models. In: Jordanov, I., Jain, L.C. (eds) Innovations in Intelligent Machines -3. Studies in Computational Intelligence, vol 442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32177-1_5
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