Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview
SIAM-AMS Proceedings Volume 13 1981
Differential Equations for the Development of Topological Nerve Fibre Projections
CH. VON DER MALSBURG AND D. J. WILLSHAWWe are concerned with the period in vertebrate ontogenesis when the nerve cell layer of the eye, the retina, develops output cells, ganglion cells. Each of these puts out an axon which grows over the surface of the retina and through the optic stalk into the optic pathway to the brain, where it establishes connexions, synapses, with cells of the developing nervous system. In lower vertebrates, such as frog, toad or fish, which are the animals that have been most studied, the main central target structure is the optic tectum. The initial connexions made by the optic nerve fibres are, in some cases, quite haphazard. After some time, however, a final configuration is reached in which there is an ordered map of retina onto tectum. Such maps are called retinotopic. The problem that has been studied in this field for several decades is: how do the fibres manage to find their proper termination area? A large number of experiments has been performed to gather constraints for possible theories. Many of these are reviewed in [1], [2].This intensive work on the problem of retinotopy has been motivated by the hope of having a paradigm problem which is both conceptually very simple and provides insight into the way in which specific patterns of nerve connexions are constructed in the brain during ontogenesis and possibly also during learning.Now that many different theories have been formulated for the problem of retinotopy, a certain consensus is emerging for what might be the important ingredients. At least two mechanisms seem to be acting in cooperation.
a. A local fibre ordering mechanism ensures that each retinal fibre preferentially establishes synapses at those places on the tectal surface where other fibres coming from the same retinal region have their synapses.
b. A global mechanism provides just enough information to specify the orientation of the final mapping between retina and tectum.

1980 Mathematics Subject Classification. Primary 92A09, 34H05.

© 1981 American Mathematical Society

-39-

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