This paper studies the electrostatic contribution to the elasticity of corneal stroma using the Poisson-Boltzmann (PB) equation. Corneal stroma is a transparent connective tissue consisting of regularly organized collagen fibrils and proteoglycans (PGs) within an aqueous matrix. The cornea proteoglycan decorin is crucial for the regulation of collagen fibril diameters and their spacings. Decorin is the simplest small leucine-rich PG and is made up of a core protein and a glycosaminoglycan (GAG) side chain. Under physiological pH conditions, GAG molecules are completely ionized and become negatively charged. Their repulsive electrostatic interaction, mediated by free ions inside the bath, controls collagen interfibril spacings and contributes to corneal stiffness. In order to quantify the electrostatic contribution of GAGs to the elastic properties of the cornea, we define a unit cell in which GAGs are represented as cylindrical rods with a fixed charge density. The unit cell is deformed affinely and the electrical potential and free ion distribution inside the unit cell are obtained from the solution of the nonlinear PB equation. Having the potential and charge distribution, the changes in electrostatic free energy due to the deformation gives the electrostatic elastic moduli.
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The Contribution of Proteoglycans on the Mechanical Properties of the Corneal Stroma
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Hatami-Marbini, H, & Pinsky, PM. "The Contribution of Proteoglycans on the Mechanical Properties of the Corneal Stroma." Proceedings of the ASME 2010 First Global Congress on NanoEngineering for Medicine and Biology. ASME 2010 First Global Congress on NanoEngineering for Medicine and Biology. Houston, Texas, USA. February 7–10, 2010. pp. 299-300. ASME. https://doi.org/10.1115/NEMB2010-13175
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