Topical Problems of Fluid Mechanics


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Institute of Thermomechanics AS CR, v.v.i. CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics MIO Université du Sud Toulon Var - AMU - CNRS - IRD Czech Pilot centre ERCOFTAC
Modeling and Simulations of Drug Distribution in the Human Vitreous

S. Dörsam, E. Friedmann, J. Stein

Abstract:
We develop a mathematical model for the drug distribution in the vitreous body of a human eye. The drug is injected in the vitreous and used for the treatment of retinal diseases. For an optimal ffect the drug is supposed to stay as long as possible in a certain area. We model the distribution of the drug with anisotropic diffusion which include the effect of the collagen fibers which have a certain orientation in the vitreous body. In addition to the diffusion we include also the steady permeating ow of the aqueous humor and model it with the Darcy equation driven by a pressure drop. The simulations are performed with the Finite Element method. Therefore, the geometry of the vitreous and a grid is constructed. The discretization is realized by using the Crank-Nicolson scheme in time, the Raviart-Thomas elements for the velocity, discontinous zero-order elements for the pressure and Lagrange elements for the concentration. The position of injection is analyzed by introducing specific output functionals which measure the mean or relative amount of the drug in the vitreous and in the area of action. Our simulations show that the injections should be located in the center of the vitreous body for a more ffcient therapy.

Keywords:
anisotropic diffusion, darcy equations, finite elements, drug distribution, vitreous
Fulltext: PDF
DOI: https://doi.org/10.14311/TPFM.2017.013
In Proceedings Topical Problems of Fluid Mechanics 2017, Prague, 2017 Edited by David Šimurda and Tomáš Bodnár, pp. 95-102
ISBN 978-80-87012-61-1 (Print)
ISSN 2336-5781 (Print)
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