2D or not 2D? Mapping the in-depth inclination of the collagen fibers of the corneoscleral shell

The collagen fibers of the corneoscleral shell play a central role in the eye mechanical behavior. Although it is well-known that these fibers form a complex three-dimensional interwoven structure, biomechanical and microstructural studies often assume that the fibers are aligned in-plane with the tissues. This is convenient as it removes the out-of-plane components and allows focusing on the 2D maps of in-plane fiber organization that are often quite complex. The simplification, however, risks missing potentially important aspects of the tissue architecture and mechanics. In the cornea, for instance, fibers with high in-depth inclination have been shown to be mechanically important. Outside the cornea, the in-depth fiber orientations have not been characterized, preventing a deeper understanding of their potential roles. Our goal was to characterize in-depth collagen fiber organization over the whole corneoscleral shell. Seven sheep whole-globe axial sections from eyes fixed at an IOP of 50 mmHg were imaged using polarized light microscopy to measure collagen fiber orientations and density. In-depth fiber orientation distributions and anisotropy (degree of fiber alignment) accounting for fiber density were quantified over the whole sclera and in 15 regions: central cornea, peripheral cornea, limbus, anterior equator, equator, posterior equator, posterior sclera and peripapillary sclera on both nasal and temporal sides. Orientation distributions were fitted using a combination of a uniform distribution and a sum of pi-periodic von Mises distributions, each with three parameters: primary orientation mu, fiber concentration factor k, and weighting factor a. To study the features of fibers that are not in-plane, i.e., fiber inclination, we quantified the percentage of inclined fibers and the range of inclination angles (half width at half maximum of inclination angle distribution). Our measurements showed that the fibers were not uniformly in-plane but exhibited instead a wide range of in-depth orientations, with fibers significantly more aligned in-plane in the anterior parts of the globe. We found that fitting the orientation distributions required between one and three pi-periodic von Mises distributions with different primary orientations and fiber concentration factors. Regions of the posterior globe, particularly on the temporal side, had a larger percentage of inclined fibers and a larger range of inclination angles than anterior and equatorial regions. Variations of orientation distributions and anisotropies may imply varying out-of-plane tissue mechanical properties around the eye globe. Out-of-plane fibers could indicate fiber interweaving, not necessarily long, inclined fibers. Effects of small-scale fiber undulations, or crimp, were minimized by using tissues from eyes at high IOPs. These fiber features also play a role in tissue stiffness and stability and are therefore also important experimental information.