Mathematical Modelling of flow in Schlemm's canal and its influence on primary open angle glaucoma


Ismail, Zuhaila and Fitt, Alistair D. (2008) Mathematical Modelling of flow in Schlemm's canal and its influence on primary open angle glaucoma. In, Proceedings of the Second International Conference on Science and Technology: Application in Industry & Education 2008 (ICSTIE2008). Second International Conference on Science and Technology: Application in Industry & Education 2008 (ICSTIE2008) Pulau Pinang, Malaysia, Universiti Teknologi MARA, 1967-1973.

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Description/Abstract

POAG (Primary Open Angle Glaucoma) is a major cause of blindness. This normally occurs when the IOP (intraocular pressure) increases. High pressure can be caused by an imbalance in the production and drainage of fluid (aqueous humour, AH) in the eye. AH is continually being produced but sometimes cannot be drained because of improperly functioning drainage channels (trabecular meshwork, TM). A mathematical model is presented for the flow of AH through the TM and into the SC (canal of Schlemm) and to couple this flow in order to predict changes in IOP. The governing equations have been developed by using the lubrication theory limit of the Navier-Stokes equations. To close the model, Friedenwald’s law has been used to predict changes of IOP. Several different cases have been examined in the model, relating AH flow to changes in IOP for various submodels: (i) the permeability, k in Darcy’s law may be either constant or not constant; (ii) the TM may be deformable so that the general theory of a beam under axial load is applicable - a number of different subcases where either θ or λ, may be either large or small have been considered. However only the subcase θ is small has been discussed in this study by assuming the permeability, k is constant and the TM is deformable. This subcase has been solved by using the regular perturbation method. The results show that the IOP rises continually when θ is small and may cause blindness.

Item Type: Book Section
Keywords: poag, lubrication theory flow, friedenwald’s law, darcy’s law, beam bending theory
Subjects: R Medicine > RE Ophthalmology
R Medicine > RB Pathology
Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 67098
Date Deposited: 06 Aug 2009
Last Modified: 27 Mar 2014 18:48
URI: http://eprints.soton.ac.uk/id/eprint/67098

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