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Meta 2010 & FEM 2010 – Rome, 13-15 December 2010 Finite Element model of charge transport across ionic channels S. Coco and A. Laudani (1) University of Catania, DIEES Catania, Italy – e-mail: alaudani@diees.unict.it, coco@diees.unict.it The exchange of signals between living cells takes place mainly through the cellular membrane, which represents a selective permeable barrier between the cell and extracellular environment. Among interesting substances, ions are of paramount importance, since activation of several critical signaling pathways and a number of cellular functions depend on ionic concentrations (especially Ca++ and K+). The flow of ions across cell membranes takes place through membrane channels, which are typical hydrophobic regions having a size of the order of few Å, where the membrane lipid bilayer exhibits ’openings’ [1]. The simulation of the mechanism of ion flow across ionic channels is a very complicated task, mainly for the lack of accurate descriptions of channel structure, the difficulty of modeling the behaviour of the proteic chains constituting the channel walls, the very high number of atoms, the very short time scale of the involved dynamical phenomena, etc. Several attempts have been made to build coherent representations of ion flow across ionic channels, in accordance with experimental measurements. In literature the most investigated approaches are Molecular Dynamic (MD), Brownian Dynamic (BD), Langevin- Lorentz-Poisson (LLP) particle model, and Poisson-Nernst-Planck (PNP) [2-4]. In this paper a 3-D Finite Element (FE) model of charge transport across ionic channel membrane is presented. The use of irregular FE mesh allows us to model the 3-D channel geometry with a lower number of degree of freedom with respect to FD. The problem is solved by a FE discretization and by an appositely developed iterative scheme. The model allows us to obtain an accurate description of ion flow across the cell membrane. The results are globally summarized by the computed I/V characteristic relationship, in which the ionic current flowing through the channel is shown as a function of the membrane voltage. References [1] B. Hille, Ionic Channels of Excitable Membranes, Sunderland, MA: Sinauer, 1992. [2] Salvatore Coco, Daniela S. M. Gazzo, Antonino Laudani, Giuseppe Pollicino, “3-D Finite Element Poisson-Nernst-Planck model for the analysis of ion transport across ionic channels”, IEEE trans. on Magnetics, 43, 1461-1464, 2007. [3] M. E. Oliveri, S. Coco, D. S. M. Gazzo, A. Laudani and G. Pollicino, “3-D FE particle based model of ion transport across ionic channels”, Scientific Computing in Electrical Engineering, Mathematics in Industry, Springer-Verlag, 9, 2006 [4] S. Aboud, D. Marreiro, M.Saraniti, and R. Eisenberg, “A poisson p3m force field scheme for particle-based simulations of ionic liquids,” Journal of Computational Electronics, vol. 3, pp. 117– 133, 2004. 30
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010 Transient Model of the Human Upper Limb Under Surface Electrical Stimulation Simone Tricarico, Michela Goffredo, Maurizio Schmid, Silvia Conforto, Filiberto Bilotti, Tommaso D’Alessio, Lucio Vegni “Roma Tre” University, Department of Applied Electronics Rome, Italy – E-mail: stricarico@uniroma3.it In this contribution, we propose an accurate phantom model of the human upper limb based on the volume conductor approximation [1,2]. The model implements a simplified anatomical representation of the arm where the involved tissues are stacked in a multilayered cylindrical geometry (see Figure 1a). Each tissue has been characterized by proper electrical and geometrical properties. We applied the model to successfully derive the electromagnetic field distribution induced inside the arm by the excitation of an array of electrodes fed by a generic current pattern (Figure 1b). We used, then, a finite integration based time domain commercial solver [3] to evaluate the passive electromagnetic response of the structure to the given stimulation. Following a classical two-step analysis [4], the model may thus effectively provide a set of reliable electric parameters, such as current density values, which can be used by active models to predict nerve fibers behavior. b) b) Figure 1 – a) Cylindrical model of the human upper limb. b) magnitude of current density distribution exited by an array of electrodes inside the arm at a given time instant. References [1] T.A. Kuiken, N.S. Stoykov, M. Popović, M. Lowery and A. Taflove, “Finite element modeling of electromagnetic signal propagation in a phantom arm,” IEEE Trans. Neural. Syst. Rehabil. Eng., 9, 346–354, 2001 [2] A. Kuhn, T. Keller, M. Lawrence and M. Morari, “A model for transcutaneous current stimulation: simulations and experiments,” Med. Biol. Eng. Comput., 47, 279–289, 2009 [3] CST Design Studio TM 2009, www.cst.com [4] A. Kuhn and T. Keller, “A 3D transient model for transcutaneous functional electrical stimulation,” Proc. of 10th Annual Conference of the International FES Society, Montreal, Canada, July 2005 31
Page 1 and 2: Meta 2010 & FEM 2010 - Rome, 13-15
Page 3 and 4: Meta 2010 - Committees Chairmen Met
Page 7 and 8: Meta 2010 Foreword Ladies and Gentl
Page 9 and 10: FEM 2010 Foreword Ladies and Gentle
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Abstracts - Dipartimento di Elettronica Applicata

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