I. Jordanov and L.C. Jain (Eds.): Innovations in Intelligent Machines -3, SCI 442, pp. 69–87. springerlink.com © Springer-Verlag Berlin Heidelberg 2013 Chapter 5 The Reproduction of the Physiological Behaviour of the Axon of Nervous Cells by Means of Finite Element Models Simona Elia and Patrizia Lamberti Dept. of Electronic and Computer Engineering, University of Salerno, Italy {selia,plamberti}@unisa.it 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. Keywords: Axon, Neuron, Hodgkin-Huxley equations, FEM. Introduction Computational modelling and analysis in biology and medicine have received major attention in recent years in order to understand, analyze and predict the complex