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Spatially-Dependent Model for Rods and Cones in the Retina



Daniel M. Anderson, Danielle Brager, Anthony J. Kearsley


We develop a mathematical model for photoreceptors in the retina. We focus on rod and cone outer segment dynamics and interactions with a nutrient source associated with the retinal pigment epithelium cells. Rod and cone densities (number per unit area of retinal surface) are known to have significant spatial dependence in the retina with cones located primarily near the fovea and the rods located primarily away from the fovea. Our model accounts for this spatial dependence of the rod and cone photoreceptor density as well as for the possibility of nutrient diffusion. We present equilibrium and dynamic solutions, discuss their relation to existing models, and estimate model parameters through comparisons with available experimental measurements of both spatial and temporal photoreceptor characteristics. Our model compares well with existing data on spatially-dependent regrowth of photoreceptor outer segments in the macular region of Rhesus Monkeys. Our predictions are also consistent with existing data on the spatial dependence of photoreceptor outer segment length near the fovea in healthy human subjects. We focus primarily on the healthy eye but our model could be the basis for future efforts designed to explore various retinal pathologies, eye-related injuries, and treatments of these conditions.
Bulletin of Mathematical Biology


Mathematical Model, Retina, Cone, Rod, fovea


Anderson, D. , Brager, D. and Kearsley, A. (2023), Spatially-Dependent Model for Rods and Cones in the Retina, Bulletin of Mathematical Biology, [online],, (Accessed April 23, 2024)
Created December 14, 2023, Updated March 27, 2024