Proceedings of the Conference on Differential and Difference Equations (Aug 1-5, 2005, Melbourne, FL, USA), Eds. R.P. Agarwal and K. Perera, Hindawi, ISBN 977-5945-380, pp. 721--732, 2006
This paper reports a mathematical model and finite-element simulation of the dynamic piezoelectricity in human cornea including the effect of dehydration and stress generated due to incision and bacterial growth. A constitutive model is proposed for the numerical characterization of cornea based on the available experimental data. The constitutive model is then employed to derive the conservation law for the dynamic piezoelectricity supplemented by the time-dependent equation for the electromagnetic field. The resulting system of partial differential equations is solved numerically with finite-element methodology. Numerical results presented here demonstrate promising applications of the developed model in aiding refractive surgery and a better understanding of regenerative processes in cornea.
Keywords: mathematical biology; anisotropic structures; human tissues; dynamics; cornea; sclera; surgical procedures; collagen fibrils