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Mathematical model and simulation of retina and tectum opticum of lower vertebrates

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Abstract

The processing of information within the retino-tectal visual system of amphibians is decomposed into five major operational stages, three of them taking place in the retina and two in the optic tectum. The stages in the retina involve (i) a spatially local high-pass filtering in connection to the perception of moving objects, (ii) separation of the receptor activity into ON- and OFF-channels regarding the distinction of objects on both light and dark backgrounds, (iii) spatial integration via near excitation and far-reaching inhibition. Variation of the spatial range of excitation and inhibition allows to account for typical activities observed in a variety of classes of retina ganglion cells.

Mathematical description of the operations in the tectum opticum include (i) spatial summation of retinal output (mainly of class-2 and class-3 retina ganglion cells), and (ii) direct or indirect lateral inhibition between tectal cells. In the computer simulation, first the output of the mathematical retina model is computed which, then, is used as the input to the tectum model. The full spatio-temporal dynamics is taken into account.

The simulations show that different combinations of strength of lateral inhibition on the one side and the response properties of the retina ganglion cells on the other side determine the response properties of tectal cell types involved in object recognition.

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References

  1. an der Heiden, U. (1980). Analysis of Neural Networks. - Berlin, Heidelberg, New York: Springer.

    Google Scholar 

  2. an der Heiden, U. and Roth, G. (1983). Cooperative neural processes in amphibian visual prey recognition. In E. Basar, H. Flohr, H. Haken and A.J. Mandell, eds., Synergetics of the Brain. - Berlin, Heidelberg, New York, Tokio: Springer.

    Google Scholar 

  3. Cervantes-Perez, F., Lara, R. and Arbib, M.A. (1985). A neural model of interactions subserving prey-predator discrimination and size preference in anuran amphibia.- J. Theor. Biol. 113: 117–152.

    Google Scholar 

  4. Ewert, J.-P. (1968). Der Einfluss von Zwischenhirndefekten auf die Visuomotorik im Beute- und Fluchtverhalten der Erdröte (Bufo bufo L.) - Z. Vergl. Physiol. 61: 41–70,

    Google Scholar 

  5. Ewert, J.-P. (1972). Zentralnervöse Analyse und Verarbeitung visueller Sinnesreize. Naturwissenschaftliche Rundschau 25: 1–11.

    Google Scholar 

  6. Ewers, J.-P. (1976). The visual system of the toad: Behavioral and physiological studies on a pattern recognition system. In K.V. Kite, ed., The Amphibian Visual System, 141–202. - New York, San Francisco, London: Academic Press.

    Google Scholar 

  7. Ewert, J.-P. (1984). Tectal mechanisms that underlie preycatchinc and avoidance behaviors in toads. In H. Vanegas, ed., Comparative Neurology of the Optic Tectum, 247–416.- New York, London: Plenum Press.

    Google Scholar 

  8. Ewers, J.-P. and Hock, F.J. (1972). Movement sensitive neurons in the toad's retina. Exp. Brain Res. 16: 41–59.

    Google Scholar 

  9. Ewert, J.-P. and von Seelen, W. (1974). Neurobiologie und Systemtheorie eines visuellen Muster-Erkennungsmechanismus bei Kröten. - Biol. Cybern. 14: 167–183.

    Google Scholar 

  10. Ewert, J.-P. and von Wietersheim, A. (1974), Musterauswertung lurch Tectum- und Thalamus/Praetectum-Neurone im visuellen System der Kröte (Bufo bufo L.). - J. Comp. Physiol. 92: 131–148.

    Google Scholar 

  11. Ewers, J.-P., Burghagen, H. and Schürg-Pfeiffer, E. (1983). Neuroethological analysis of the innate releasing mechanism for prey catching in toads. In J.-P. Ewert, R.R. Capranica and D. Ingle, eds., Advances in Vertebrate Neuroethology. NATO ASI Ser. Vol. 56, 413–475. - New York, London: Plenum Press.

    Google Scholar 

  12. Finkenstadt, T. and Ewert, J.-P. (1983a). Processing of area dimensions of visual key stimuli by tectal neurons in Salamandra salamandra. - J. Comp. Physiol. 153: 85–98.

    Google Scholar 

  13. Finkenstädt, T. and Ewert, J.-P. (1983b). Visual pattern discrimination through interactions of neural networks: A combined electrical brain stimulation, brain lesion, and extracellular recording study in Salamandra Salamandra. - J. Comp. Physiol. 153: 99–110.

    Google Scholar 

  14. Grüsser, O.-J. and Grüsser-Cornehls, U, (1968). Neurophysologische Grundlagen visueller angeborener Auslösemechanismen beim Frosch. - Z. Vergl. Physiol. 59: 1–24.

    Google Scholar 

  15. Grüsser, O.-J. and Grüsser-Cornehls, U. (1970). Die Neurophysiologie visuell gesteuerter Verhaltensweisen bei Anuren. - Verh. Dtsch. Zool. Ges. 64: 201–218.

    Google Scholar 

  16. Grüsser, O.-J. and Grüsser-Cornehls, U. (1976). Neurophysiology of the anuran visual system. In R. Llinas and. W. Precht, eds., Frog Neurobiology, 297–385. - Berlin, Heidelberg, New York: Springer.

    Google Scholar 

  17. Grüsser, O.-J., Grüsser-Cornehls, U. and Licker, M.D. (1968). Further studies on the velocity function of movement-detecting class-2 neurons in the frog retina.- Vision Res. 8: 1173–1185.

    Google Scholar 

  18. Grüsser-Cornehls, U. (1984). The neurophysiology of the amphibian optic tectum. In H. Vanegas, ed., Comparative Neurology of the Optic Tectum, 211–245. New York, London: Plenum Press.

    Google Scholar 

  19. Grüsser-Cornehls, U. and Himstedt, W. (1973). Responses of retinal and tectal neurons of the salamander (Salamandra salamandra L.) to moving visual stimuli. - Brain Behav. Evol. 7: 145–168.

    Google Scholar 

  20. Grüsser-Cornehls, U. and Himstedt, W. (1976). The urodele visual system. In K.V. Fite, ed., The Amphibian Visual System. A Multidisciplinary Approach, 203–266. - London, New York: Academic Press.

    Google Scholar 

  21. Herrick, C.J. (1948). The Brain of the Tiger Salamander Ambystoma tigrinum. - Chicago, IL: Univ. Chicago Press.

    Google Scholar 

  22. Himstedt, W. and Roth, G. (1980). Neuronal responses in the tectum opticum of Salamandra to visual prey stimuli. - J. Comp. Physiol. 135: 251–257.

    Google Scholar 

  23. Ingle, D.J. (1973). Two visual systems in the frog. Science 181: 1053–1055.

    Google Scholar 

  24. Ingle, D.J. (1980). Some effects of pretectum lesions on the frog's detection of stationary objects. - Behav. Brain Res. 1: 139–163.

    Google Scholar 

  25. Ingle, D.J. (1983). Brain mechanisms of visual localization by frogs and toads. In J.-P. Ewert, R.R. Capranica and D.J. Ingle, eds., Advances in Vertebrate Neuroethology. NATO ASI Series, Vol. 56, 177–226. - New York, London: Plenum Press.

    Google Scholar 

  26. Lara, R. and Arbib, M.A. (1985). A model of the neural mechanisms responsible for pattern recognition and stimulus specific habituation in toads. - Biol. Cybern. 51: 223–237.

    Google Scholar 

  27. Levine, M-W. and Shefner, I.M. (1977). Variability in ganglion cell firing patterns: Implications for separate “on” and “off” processes. - Vision Res. 17: 765–776.

    Google Scholar 

  28. Manteuffel, G. (1985). Monocular and binocular optic inputs to salamander pretectal neurons: An intracellular recording and HRP-labelling study. - Brain Behav. Evol. 27: 1–10.

    Google Scholar 

  29. Pfeiffer, E. (1975). Musterauswertung lurch retinale Ganglienzellen beim Frosch (Rana esculenta L.). - Diplomarbeit, Universität Darmstadt.

    Google Scholar 

  30. Roth, G. (1978). The role of stimulus movement patterns in the prey catching behavior of Hydromantes genei (Amphibia, Plethodontidae). - J. Comp. Physiol. 123: 261–264.

    Google Scholar 

  31. Roth, G. (1982a). Responses in the optic tectum of the salamander Hydromantes italicus to moving prey stimuli. Exp. Brain Res. 45: 386–392.

    Google Scholar 

  32. Roth, G. (1982b). Beuteerkennungsmechanismen im Tectum opticum von Amphibian - eine vergleichende Untersuchung. Funkt. Biol. Med. 1: 90–98.

    Google Scholar 

  33. Roth, G. (1986). Neural mechanisms of prey recognition: An example in amphibians. In M.E. Feder and G.V. Lauder, eds., Predator-Prey Relationships, 42–68. - Chicago, London: Univ. Chicago Press.

    Google Scholar 

  34. Roth, G. (1987). Visual Behavior in Salamanders. - Berlin, Heidelberg, New York, Tokyo: Springer.

    Google Scholar 

  35. Roth, G. and Jordan, J.-P. (1982). Response characteristics and stratification of tectal neurons in the toad Bufo bufo (L.). - Exp. Brain Res. 45: 393–398.

    Google Scholar 

  36. Schürg-Pfeiffer, E. and Ewert, J.-P. (1981). Investigations of neurons involved in the analysis of gestalt prey features in the frog Rana temporaria. - J. Comp. Physiol. 141: 139–152.

    Google Scholar 

  37. Székely, G. and Lázár, G. (1976). Cellular and synaptic architecture of the optic tectum. In R. Llinas and W. Precht, eds., Frog Neurobiology, 407–434. - Berlin, Heidelberg, New York: Springer.

    Google Scholar 

  38. Varjú, D. (1978). Excitatory and inhibitory processes giving rise to the delayed response in the retinal ganglion cell of the frog. In R. Heim and G. Palm, eds., Theoretical Approaches to Complex Systems. - Berlin, Heidelberg, New York: Springer.

    Google Scholar 

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Authors and Affiliations

  1. Fakultät für Naturwissenschaften, Universität Witten/Herdecke, Stockumer Str. 10, D-5810, Witten, Fed. Rep. Germany

    U. an der Heiden

  2. Fachbereich 2/Biologie, Universität Bremen, D-2800, Bremen 33, Fed. Rep. Germany

    G. Roth

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  1. U. an der Heiden
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Supported by the Deutsche Forschungsgemeinschaft.

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an der Heiden, U., Roth, G. Mathematical model and simulation of retina and tectum opticum of lower vertebrates. Acta Biotheor 36, 179–212 (1987). https://doi.org/10.1007/BF00052064

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  • DOI: https://doi.org/10.1007/BF00052064

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