The nerve fiber layer of the human retina is made up of the retinal segments of ganglion cell axons. Its geometry can be described mathematically as a fibration of a 2D domain: a partition of a certain region into smooth curves. Here, we present a simple family of curves that closely models the observed geometry of the nerve fiber layer. For each retina, the pattern depends on 2 parameters, A and B: A computer program determines A and B for a given retina and the theory matches the retina with a standard deviation of Ϸ6 -8°. These particular curves turn out to be the curves that would be generated if the growing ganglion cell axon tip moved down a gradient toward a source of diffusible neuroattractant at the disk and away from a weaker macular diffusible repellant. Thus, this model provides morphological evidence that diffusible substances provide positional information to the embryonic ganglion cell axons in finding their way to the optic nerve head.diffusion ͉ embryology ͉ optic nerve ͉ retina T he human optic nerve consists of bundles of axons originating in the ganglion cells of the retina. These axons first traverse the retina in a typically unmyelinated layer called the nerve fiber layer (NFL), before converging at the optic disk and, subsequently, emerging from the globe in the optic nerve. Thus, the detailed anatomy of the optic nerve head depends crucially upon the axon paths in the NFL. (Fig. 1A) The NFL was first described in 1914 by Vogt (1). Because of its transparency, the NFL is difficult to visualize and was not photographed for another fifty years (2). An improved method for wide angle, conformal (angle-preserving) photography was later devised (3).The fascicles of the NFL have the following characteristics:Y Macula-avoiding. The ganglion cells are displaced radially from the macula and their axons radiate from the macula, so that no axons cross over the macula. Y Horizontal raphe. The direction of nerve fiber varies continuously throughout the retina except along the horizontal raphe, the ray originating at the macula directed away from the nerve. No fibers cross the raphe, which is a sort of part or watershed in the retinal fibration. Axons just superior to the raphe are directed superiorly, while neighboring fiber just inferior abruptly take the opposite direction. Y Noncrossing. When axons from distal cells pass over proximal fibers, they follow the same path as the more proximal fibers, but on a more inner retinal layer. Thus, the fibers passing over any point determine a unique direction (excluding, of course, the macula and horizontal raphe-the two areas without overlying fibers). Vogt's article (1) overlooked this noncrossing feature.Any theory of retinal pathfinding by embryonic ganglion cell axons should account for the three features detailed above. Crick (4) made plausible the proposal of Ramon y Cajal (5) that positional information in embryology is specified by gradients of ''morphogens,'' diffusible substances acting as attractants or repellants-in this case, for the growing gangl...

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