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Mechanisms of self-organization for the collagen fibril lattice in the human cornea
Mechanisms of self-organization for the collagen fibril lattice in the human cornea Peter M. Pinsky Department of Mechanical Engineering, Stanford University, Stanford, CA E-mail: pinsky@stanford.edu Computational biomechanical modeling of the human cornea has many potential benefits, including prediction of clinical outcomes to various surgical procedures which involve removing tissue, adding tissue or implants, or otherwise modifying tissue properties. Progress has been made in modeling the principal structural component of corneal tissue, namely the stromal lamellae (or fibers). However, the bulk properties of the tissue have not received as much consideration and modeling has most often proceeded based on an ungrounded assumption of incompressible or nearly-incompressible elastic behavior. The corneal stroma is a highly hydrated polyelectrolyte gel that generates strong osmotic pressure. As a result the stroma is hydrophilic – it wants to suck in water and swell. In the living cornea, this swelling must be opposed or our corneas would self-destruct. The agent used to control hydration in the living cornea is active ion transport across the corneal endothelium. This reduces tissue osmotic pressure and provides hydration control. The ex vivo tissue lacks this mechanisms and freely swells. The bulk properties of the tissue are dictated by the energy cost of changing hydration and can be modeled by treating the cornea as a polyelectrolyte gel consisting of a mixture of fluid, solid and ionic phases. In this talk, an energy-based approach is described in which the free energy of the polyelectrolyte gel over a unit cell is decomposed into various components which characterize the behavior of the tissue under general deformations. To account for active ion transport across the endothelium, a modified Boltzmann ion distribution is introduced into the energy framework. In this way, the hydration, swelling and bulk properties of ex vivo and in vivo corneas can be predicted. The transparency of the human cornea depends on the regular lattice arrangement of the collagen fibrils which are assembled in parallel arrays with short-range order. This regular lattice-like arrangement produces interference effects from scattered light that underlie the transparency of the tissue. The mechanism by which the fibrils are maintained in this lattice has been the subject of some study and controversy. It will be proposed in this talk that local gradients in osmotic pressure provide a highly effective means of keeping the collagen fibrils separated and the tissue transparent. Thus mechanics allows us to appreciate how the cornea “manipulates” osmotic pressure to meet its remarkable functionality. The collagen fibril lattice and linear glycosaminoglycan (GAG) chains of the human cornea; some GAGs form fibril coatings while others occupy the interfibrillar fluid – both producing specialized charge distributions.
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Mechanisms of self-organization for the collagen fibril lattice in the human cornea
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