About mathematical modeling of glaucoma

Abstract

Glaucomaisoneofthemostdangerous eyediseases.Therearetwoconceptsofitsdevelopment:mechanical andischemic.This workisdevoted to theischemic concept according to which the main reasonfor adisease is considered blood circulation violation in vessels of an optic nerve. In this article as vessels of an optic nerve the thin-walled cylindrical tubes loaded by internal and external pressure are considered. On the basis of the linear solution geometrically nonlinear model of a vessel of an optic nerveis constructed.Expressionsfordisplacement and stresses aredetermined.Physically and geometrically nonlinear model of a vessel of an optic nerve is constructed. On the basis of the received results the following conclusions are drawn: 1) To growth of intraocular pressure there is a lengthening of vessels of an optic nerve; 2) Decrease of internal diameter of vessel of an optic nerve connected with increase in a difference between intraocular pressure and pressure in a vessel can cause a delay of aksoplazmatic current and lead to collapse in astroglial tissue. These facts promote extension of excavation of a disk of an optic nerve.

Keywords:

theory of elasticity, geometrically nonlinearity, physically and geometrically nonlinearity, stresses, deformations, displacements, glaucoma, ischemic concept, vessels of an optic nerve