Past Event: Oden Institute Seminar

Tties of the Human Cornea: From Molecular to Macroscopic Scale Models

Peter M. Pinsky, Department of Mechanical Engineering, Stanford University

Abstract

The highly organized microstructure of the corneal stroma make it an ideal tissue for a multiscale modeling approach where various mechanical attributes are characterized at different length scales. The bulk and swelling properties of the tissue are best understood when viewing the tissue as a reinforced electrolyte gel involving molecular-scale interactions between collagen fibrils, proteoglycans (PGs) and the mobile ions in the interfibrillar space. We use the 3-d lattice arrangement of collagen fibrils and a heterogeneous distribution of PGs corresponding to a dense coating of PGs on the fibrils, to create a unit cell model based on the free energy of the system. Free energy contributions arise from electrostatic, entropic elastic and molecular mixing sources. The model is solved numerically and employed to explain stromal swelling pressure, bulk stiffness, and the origin of forces which are responsible for the maintenance of the collagen fibril lattice – a necessary condition for transparency of the tissue. The tensile properties of the cornea arise entirely from the fibrillar collagen and are effectively described at the macroscopic level using a continuum model. While the anisotropy of the collagen spatial arrangement viewed over the corneal surface is now well mapped and appreciated, what has not been so well studied is the role of the full 3-d collagen architecture. Recent imaging has revealed that the cornea features lamellae interweaving whereby these “fibers” follow trajectories that take them diving through the corneal thickness with profiles that are depth-dependent. A hyperelastic model, based on measured angular probability distributions, is described and combined with the swelling pressure/bulk property model to arrive at a finite element model for the tissue. Experimental studies on corneal transverse shear stiffness are used for model validation.