The development of retinal ganglion cells (RGC) was studied in the chick from stage 18 to adulthood. Our main objectives were to identify the retinal site where the first RGCs differentiate, to locate this site relative to the optically defined central retinal area, and to map the spatial arrangement of the RGC field at different stages in development. The eyes of the experimental animals were fixed and serially sectioned. The borders of RGC fields were determined from the presence of either ganglion cell perikarya or ganglion cell axons. In seven cases between stages 21 and 26, the borders of the RGC fields were confirmed electron microscopically. The serial sections together with the RGC fields were then reconstructed in three dimensions. The reconstructed retinae were projected onto a plane by using the radially equidistant polar azimuthal projection.



First, RGCs appear dorsal to the apex of the optic fissure. Ganglion cell development then initially spreads out symmetrically with respect to the optic fissure. However, from stage 29 on, the nasal half of the retina expands much more than the temporal half. This asymmetrical growth entails that the optic fissure is eventually located in the temporal half of the retina in the mature animal.



The RGC fields of the embryonic stages were superimposed on the retina of a visually active animal according to their real size and position. It turned out that the central retinal area was at least 2 mm away from the site where the first RGCs were generated. It is not before stage 28 that the prospective central retinal area is included into the expanding ganglion cell field. The fact that RGCs at the central retinal area are generated 2.5 days later than first RGCs near the apex of the optic fissure has important implications for the formation of the retinotectal projection. © 1993 Wiley-Liss, Inc.

Central retinal area is not the site where ganglion cells are generated first.

Sur les integrales premieres de certains feuilletages analytiques complexes

Section 1 deals with the notion of analytically branched coverings. The main theorem states that analytically branched coverings are normal complex spaces. Its proof makes use of L2-methods as developed by Hormander, and is sketched in § 2. In § 3 some applications are given, some of which are used in § 7.

Seminormal Complex Spaces

Set theoretic complex equivalence relations

Fibre cycles of holomorphic maps. I: Local flattening

A method of Stein [17] is generalized to construct in an explicit way complex bases of open holomorphic mappings, defined on normal complex analytic spaces. Using theorems concerning the existence of pushouts, we can sharpen a theorem of Wolffhardt ([22],§4) and generalize the above construction. As a consequence, we can prove for a big class of complex bases b:X→B, that the induced mapping π1(X)→π1(B) its surjective. We give a characterisation of locally simple and analytically locally simple analytic equivalence relations.

Zur Konstruktion komplexer Basen

The environment is represented in the brain by topographic maps. These maps and their interrelationship form a dominant feature in the brain, but unfortunately, they are often projected onto surfaces which are variously curved. It would be useful to be able to compare the topography on these surfaces quantitatively with the origin of the map. This comparison would be possible if the curved brain surfaces could be represented in planes. Therefore, it was necessary to develop a procedure for unfolding maps on convex structures like the retina and the optic tectum of the chick. For this purpose a unit sphere was constructed whose origin was close to the centre of gravity of the curved brain structure. The surface of this structure was then projected into the sphere. From its representation on the spherical surface it was unfolded into the plane using a polar azimuthal radially equidistant projection. Our method can safely be applied to convex structures only. However, it is not limited to the visual system. The mathematical procedure is formulated in such a way as to be easily implemented. It is exemplified by experiments on the optic tectum and the developing retina of the chick.

Burchard Kaup

Papers

Zur Konstruktion komplexer Basen

Projection of topographic maps from curved brain surfaces into a plane.