Analytical Models for Transient Responses in the Retina

  • Gabriel de Blasio
  • Arminda Moreno-Díaz
  • Roberto Moreno-Díaz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5601)

Abstract

We propose analytical models for slow potentials transients as they are recorded at different layers of the retina, but mostly as they are integrated to produce ganglion cells outputs. First, two possible pathways from photoreceptors to bipolars and to ganglia are formulated, their formal equivalence being shown for quasi-linear behaviour. Secondly, a linear oscillator analytical model is introduced which is shown also to be equivalent to the first under certain circumstances. Finally, local instantaneous nonlinearities are introduced in the models. Tunning their parameters, the models are very versatile in describing the different neurophysiological situations and responses.

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References

  1. 1.
    Hodgkin, A., Huxley, A.: A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve. Journal of Physiology 117, 500–544 (1952)CrossRefGoogle Scholar
  2. 2.
    Hoppensteadt, F.C.: An Introduction to the Mathematics of Neurons. Cambridge University Press, Cambridge (1997)MATHGoogle Scholar
  3. 3.
    Moreno-Díaz, R., de Blasio, G., Moreno-Díaz, A.: A Framework for Modelling Competitive and Cooperative Computation. In: Ricciardi, L.M., Buonocuore, A., Pirozzi, E. (eds.) Retinal Processing, In Collective Dynamics: Topics on Competition and Cooperation in the Biosciences. American Institute of Physics, pp. 88–97 (2008)Google Scholar
  4. 4.
    Moreno-Díaz, R., Moreno-Díaz, A., de Blasio, G.: Local Space-time Systems Simulation of Linear and Non-linear Retinal Processes. In: Quesada, A., Rodríguez-Rodríguez, J.C., Moreno-Díaz Jr., R., Moreno-Díaz, R. (eds.) 12th International Workshop on Computer Aided Systems Theory, EUROCAST 2009, pp. 9–12 (2009)Google Scholar
  5. 5.
    Guttman, R., Feldman, L., Jacobsson, E.: Frequency Entrainment of Squid Axon Membrane. J. Membrane Biol. 56, 9–18 (1980)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gabriel de Blasio
    • 1
  • Arminda Moreno-Díaz
    • 2
  • Roberto Moreno-Díaz
    • 1
  1. 1.Instituto Universitario de Ciencias y Tecnologías CibernéticasUniversidad de Las Palmas de Gran CanariaSpain
  2. 2.School of Computer ScienceMadrid Technical UniversitySpain

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