To appear in ‘Ninth International Conference on Artificial Neural Networks’, September 1999. 1 Modelling retinal mosaic development with dendritic outgrowth and lateral cell movement Stephen J. Eglen Arjen van Ooyen Institute for Adaptive and Neural Computation Netherlands Institute for Brain Research Division of Informatics, Univ. of Edinburgh Meibergdreef 33, 1105 AZ Amsterdam Scotland EH8 9LW The Netherlands stephen@anc.ed.ac.uk A.van.Ooyen@nih.knaw.nl Abstract Retinal cells are regularly spaced across the retina and form mosaic-like patterns. The devel- opmental processes involved in producing such mosaics are unclear, although recent evidence suggests that lateral movement of cells may be involved [1]. In this paper, we extend a model of neurite outgrowth [2] to allow cells to move as well as to change their dendritic extent. Start- ing from random initial positions, cells reor- ganise into regular mosaics. The network can also dynamically adapt to either increases or decreases in network size during development. Our results support the hypothesis that local cell movement produced by local dendritic interac- tions can generate regular mosaics. 1 Introduction A common property of retinal cells is that they are regularly spaced in neural tissue. This reg- ular arrangement ensures that the visual field is processed efficiently and with complete cov- erage. Many different classes of retinal cells, including cone photoreceptors, horizontal cells and ganglion cells, are all regularly arranged [3]. How do such mosaics arise during de- velopment — are newborn cells positioned im- mediately in a regular fashion across the sur- face, or do they gradually self-organise from some unordered state? Two lines of recent evi- dence favours the argument that cells reorganise during development to produce mosaics. First, staining of cholinergic amacrine cells in the rat showed that during migration the cells have no spatial ordering, but then later become regularly spaced within their destination layer [4]. Sec- ond, labelling of retinal progenitor cells showed that it is common for certain classes of retinal cells to be tangentially dispersed from their col- umn of origin [1]. Hence it is suggested that lateral cell movement contributes to establish- ing the regularity of these mosaics. The forces controlling such tangential cell movement however are still unknown. We sug- gest that this lateral movement could be the re- sult of repulsive forces between cells. Such re- pulsive forces were hypothesised as a mecha- nism for creating mosaics: “identical nerve cells show repulsive action towards each other and an originally random pattern disentangles itself” [3, p457]. 1.1 Previous work Previous theoretical work on retinal mosaics has focused mainly on describing the final mosaic pattern rather than on how the mosaics develop. Two rules have been devised for generating mo- saic patterns [5]. In the first, the disturbed trian- gular lattice rule, cells were initially positioned in a regular hexagonal mosaic and then each cell moved to some random position within a fixed- width radius. By superimposing two indepen- dent mosaics generated using this rule, on- and off-centre ganglion cell mosaics could be simu- lated [6]. In the second rule, the soft disk parking rule, cells were sequentially positioned onto the sur- face. A tentative position for a new cell was selected at random. The probability of keeping the new cell was a function of distance to its nearest neighbour, following a Boltzmann-like distribution. This rule produced a closer match to horizontal cell mosaics in turtles than the dis- turbed triangular lattice rule [5]. A simpler ver-