Ram Avtar

Modeling the drug transport in the anterior segment of the eye

PURPOSE The aim of the present work is the development of a simple mathematical model for the time course concentration profile of topically administered drugs in the anterior chamber aqueous humor and investigation of the effects of various model parameters on the aqueous humor concentration of lipophilic and hydrophilic drugs. METHOD A simple pharmacokinetic model for the transient drug transport in the anterior segment has been developed by using the conservation of mass in the precorneal tear film, Ficks law of diffusion and Michaelis-Menten kinetics of drug metabolism in cornea, and the conservation of mass in the anterior chamber. An analytical solution describing the drug concentration in the anterior chamber has been obtained. RESULT The model predicts that an increase in the drug metabolic (consumption) rate in the corneal epithelium reduces the drug concentration in the anterior chamber for both lipophilic and hydrophilic molecules. A decrease in the clearance rate and distribution volume of the drug in the anterior chamber raises the aqueous humor concentration significantly. It is also observed that decay rate of drug concentration in the anterior chamber is higher for lipophilic molecules than that for hydrophilic molecules. CONCLUSION The bioavailability of drugs applied topically to the eye may be improved by a rise in the precorneal tear volume, diffusion coefficient in corneal epithelium and distribution coefficient across the endothelium anterior chamber interface, and by reducing the drug metabolism, drug clearance rate and distribution volume in anterior chamber.

Aqueous outflow in Schlemm’s canal

Abstract A mathematical model is presented for the flow of aqueous humor in Schlemm’s canal in the eye. Schlemm’s canal is modelled as a porous compliant channel that is held open by the trabecular mesh work. The inner wall of canal is porous and aqueous humour percolate through it in the canal. The aqueous humour percolating along the canal segment before reaching a collector channel. The model introduces in a canal-segment between two collector channels as a elliptical cross-sectional and circular cross-sectional tubes. Aqueous fluid pressure and flow profiles in the proposed model are drawn and the effects of important parameter on these profiles are brought out and discussed.

Modelling the flow of aqueous humor in anterior chamber of the eye

A simple mathematical model for the natural convectional flow of aqueous humor in the anterior chamber of a human eye is developed. The model treats the flow as viscosity dominated due to its low Reynolds number and driven by buoyancy affects because of the temperature gradient (though small but significant) across the anterior chamber. The model incorporates Beavers and Joseph slip flow condition and the convection boundary condition at porous posterior surface of the cornea. The expressions for the temperature and velocity profiles in the anterior chamber as well as for the stream function are obtained. The computational results are presented through graphs and the effects of model parameters: the convection heat transfer coefficient, the thermal conductivity and the slip parameter on the velocity and temperature distributions also have been shown and discussed.

Modelling aqueous humor outflow through trabecular meshwork

Abstract A simple model of aqueous outflow through the trabecular meshwork in eye has been developed. The model considers the meshwork as an annular cylindrical ring with uniform thickness of homogenous, isotropic, viscoelastic material, swollen with continuously percolating aqueous humor through it. It incorporates a strain-dependent permeability function into Darcy’s law which is coupled to the force balance for the bulk material. A simple analytical expression relating aqueous flux to pressure differential is developed which shows how strain-dependent permeability can lead to reduction in hydraulic conductivity (aqueous outflow facility) with increasing intraocular pressure (IOP) as observed in experiments by ophthalmologists. Analytical expressions for the displacement, fluid pressure and dilatation in the trabecular meshwork have been obtained.

Modelling the transmural transport of oxygen to the retina

Oxygen transport from retinal capillaries to retinal tissue is studied by use of a Krogh-type cylinder model. The retinal tissue is represented as an array of uniformly cylinders with capillaries along the axes. The model introduces the transmural transport of oxygen from the retinal capillaries to its surrounding (retinal) tissue in a hypoxia environment. Computational results for concentration distribution in the retinal tissue are presented through graphs and the effects of important model parameters: intraocular pressure, capillary wall permeability coefficient, capillary wall pressure gradient constant on the oxygen concentration distribution are depicted and discussed.