Mechanics and spiral formation in the rat cornea

Abstract

During the maturation of some mammals such as mice and rats, corneal epithelial cells tend to develop into patterns such as spirals over time. A better understanding of these patterns can help to understand how the organ develops and may give insight into some of the diseases affecting corneal development. In this paper, a framework for explaining the development of the epithelial cells forming spiral patterns due to the effect of tensile and shear strains is proposed. Using chimeric animals, made by combining embryonic cells from genetically distinguishable strains, we can observe the development of patterns in the cornea. Aggregates of cell progeny from one strain or the other called patches form as organs and tissue develop. The boundaries of these patches are fitted with logarithmic spirals on confocal images of adult rat corneas. To compare with observed patterns, we develop a three-dimensional large strain finite element model for the rat cornea under intraocular pressure to examine the strain distribution on the cornea surface. The model includes the effects of oriented and dispersed fibrils families throughout the cornea and a nearly incompressible matrix. Tracing the directions of critical strain vectors on the cornea surface leads to spiral-like curves that are compared to the observed logarithmic spirals. Good agreement between the observed and numerical curves supports the proposed assumption that shear and tensile strains facilitate sliding of epithelial cells to develop spiral patterns.

Comparative Anatomy of the Mammalian Corneal Subbasal Nerve Plexus

“…The mechanisms that govern the formation and maintenance of whorl-like arrangements of SNFs remain poorly understood. According to the XYZ hypothesis of corneal epithelial renewal,52 basal epithelial cells near the corneoscleral limbus divide and migrate centripetally in a whorl-like fashion toward the corneal apex in response to chemotropic guidance, electromagnetic cues, population pressures, and preferential desquamation of central epithelial cells 53–61. As the basal epithelial cells slide continuously toward the corneal apex, SNFs lodged within narrow intercellular spaces between adjacent columns of migrating cells or sequestered within cytoplasmic infoldings of these cells6,7,62 are pulled along and guided into analogous curvilinear patterns 30,63.…”

Self-organized centripetal movement of corneal epithelium in the absence of external cues

“…Our simulation model shows that centripetal migration in the corneal epithelium can be explained through population pressure forces, without the need to invoke signals mediated by soluble morphogens, extracellular matrix molecules, neurons or biophysical cues. However, it does not rule out a role for those signals in mediating proliferative and migratory responses to conditions such as chronic inflammation, wound healing and intraocular pressure 2 6 15 21 26 27 28 . During homeostasis, the location of the stem cells within the limbus, together with the limited replicative capacity of TACs and the mobility of epithelial cells in response to pressure, is sufficient to produce both centripetal migration and cohesive self-organization of clonal lineages into sectors.…”

Trilinear Hexahedra with Integral-Averaged Volumes for Nearly Incompressible Nonlinear Deformation

“…In the final example, the incompressible behavior of a three-dimensional mouse cornea subjected to pressure loading is studied by means of standard and B methods. Biological tissues are prime examples of nearly incompressible media, and the current approach has been applied with good results in [30] [31]. An intraocular pressure of 1.73 kPa is applied to the posterior side of the cornea.…”