A tension-based morphogenesis model of retinal fovea development

Wrinkling morphogeneses of organs broadly fall into two categories: those in which the thickness oscillations of the slower-growing substrate are in phase with thickness oscillations of the faster-growing film, and those in which these oscillations are out of phase. Morphogenesis of the retinal fovea may fall into the latter category, where considerations of elastic bilayer instabilities fail to explain observed phase relationships between the photoreceptive outer nuclear and ganglionic layers. Prior work has shown that tension-based morphogenesis (TBM) models that incorporate system–spanning radial glial fibers can produce out of phase behavior in two dimensions. Here, we extend this TBM modeling framework to three dimensions and to the concave geometry of the developing retina. With a spatially localized growth term motivated by observations of ganglion cell mounding, the governing equation for the ganglion cell layer thickness becomes an inhomogeneous variable-coefficient spherical Helmholtz equation. In some parameter regimes, solutions reproduce the observed phase relationship as well as foveal pit-like morphologies. Our modeling results will be compared with data on foveal formation across species with the aim of better understanding biomechanics relevant to normal and pathological eye development.