Estimation of effective diffusion coefficients of drug delivery devices in a flow-through system
We present a numerical approach to estimating the effective diffusion coefficients of drug diffusion from a device into a container with a source and sink condition due to a fluid flowing through the system at a constant rate. In this approach we first formulate this estimation problem as a continuo...
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Published in | Journal of engineering mathematics Vol. 87; no. 1; pp. 139 - 152 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Netherlands
01.08.2014
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ISSN | 0022-0833 1573-2703 |
DOI | 10.1007/s10665-013-9669-y |
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Abstract | We present a numerical approach to estimating the effective diffusion coefficients of drug diffusion from a device into a container with a source and sink condition due to a fluid flowing through the system at a constant rate. In this approach we first formulate this estimation problem as a continuous, nonlinear, least-squares problem subject to a set of constraints containing a partial differential equation system. The nonlinear optimization problem is then discretized by applying a finite volume scheme in space and an implicit time-stepping scheme to the equation system, yielding a finite-dimensional, nonlinear, least-squares problem. An algorithm is proposed for the resulting finite-dimensional, constrained, nonlinear optimization problem. Numerical results using experimental data are presented to demonstrate the usefulness and accuracy of the method. |
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AbstractList | We present a numerical approach to estimating the effective diffusion coefficients of drug diffusion from a device into a container with a source and sink condition due to a fluid flowing through the system at a constant rate. In this approach we first formulate this estimation problem as a continuous, nonlinear, least-squares problem subject to a set of constraints containing a partial differential equation system. The nonlinear optimization problem is then discretized by applying a finite volume scheme in space and an implicit time-stepping scheme to the equation system, yielding a finite-dimensional, nonlinear, least-squares problem. An algorithm is proposed for the resulting finite-dimensional, constrained, nonlinear optimization problem. Numerical results using experimental data are presented to demonstrate the usefulness and accuracy of the method. |
Author | Lou, Xia Wang, Song Mohd Mahali, Shalela |
Author_xml | – sequence: 1 givenname: Shalela surname: Mohd Mahali fullname: Mohd Mahali, Shalela email: shalela@umt.edu.my organization: Department of Mathematics, Universiti Malaysia Terengganu – sequence: 2 givenname: Song surname: Wang fullname: Wang, Song organization: School of Mathematics & Statistics, University of Western Australia – sequence: 3 givenname: Xia surname: Lou fullname: Lou, Xia organization: Department of Chemical Engineering, Curtin University |
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Cites_doi | 10.1016/j.camwa.2005.11.035 10.1080/10556789508805614 10.1016/j.amc.2004.03.003 10.1021/ci9604652 10.1016/S0168-3659(96)01482-4 10.1080/10556789708805655 10.1007/978-3-540-77974-2 10.1007/s00214-009-0649-2 10.1006/jcph.1994.1178 10.1007/s11081-008-9069-8 10.1016/j.ijpharm.2008.09.004 10.1016/0022-1694(87)90207-1 10.1016/j.ijpharm.2010.08.043 10.1093/imanum/14.2.257 10.1016/j.camwa.2006.07.004 10.1016/j.biomaterials.2004.01.058 10.3934/jimo.2009.5.127 10.1090/qam/10666 10.1006/jcph.1999.6358 10.1016/j.ejps.2004.11.007 10.1016/j.cma.2008.07.019 10.1137/0111030 10.1002/apj.62 |
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Keywords | Finite volume discretization Controlled drug delivery Effective diffusion coefficient Nonlinear least-squares method Sink condition |
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Comput20051621219122610.1016/j.amc.2004.03.0031063.650992113964 – reference: FarrugiaCAFlow-through dissolution testing: a comparison with stirred beaker methodsChronic Illn200261719 – reference: LouXMunroSWangSDrug release characteristics of phase separation PHEMA sponge materialsBiomaterials2004255071508010.1016/j.biomaterials.2004.01.058 – reference: SiepmannJSiepmannFMathematical modeling of drug deliveryInt J Pharm200836432834310.1016/j.ijpharm.2008.09.004 – reference: LouXWangSTanSYMathematics-aided quantitative analysis of diffusion characteristics of PHEMA sponge hydrogelsAsia Pac J Chem Eng2007260961710.1002/apj.62 – reference: HelblingIMIbarraJCDLunaJACabreraMIGrauRJAModeling of dispersed-drug delivery from planar polymeric systems: optimizing analytical solutionsInt J Pharm201040013113710.1016/j.ijpharm.2010.08.043 – reference: ZuninoPD’AngeloCPetriniLVergaraCCapelliCMigliavaccaFNumerical simulation of drug eluting coronary stents: mechanics, fluid dynamics and drug releaseComput Methods Appl Mech Eng2009198363336442009CMAME.198.3633Z10.1016/j.cma.2008.07.0191229.761222571827 – reference: MillerJJHWangSA new non-conforming Petrov–Galerkin finite element method with triangular elements for a singularly perturbed advection–diffusion problemIMA J Numer Anal19941425727610.1093/imanum/14.2.2570806.651111268995 – reference: Jean-Marie G, Jean-Louis R (2006) A review of dissolution tests with the flow through method – reference: ColesCMurioDParameter estimation for a drying system in a porous mediumComput Math Appl2006511519152810.1016/j.camwa.2005.11.0351135.760502237648 – reference: VibekeHSBettyLPHenningGKAnetteMIn vivo in vitro correlations for poorly soluble drug, Danazol, using the flow-through dissolution method with biorelevant dissolution mediaEur J Pharm Sci20052430531310.1016/j.ejps.2004.11.007 – reference: MarquardtDWAn algorithm for least squares estimation of nonlinear parametersSIAM J Appl Math19631143144110.1137/01110300112.10505153071 – 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SubjectTerms | Algorithms Applications of Mathematics Computational Mathematics and Numerical Analysis Devices Diffusion coefficient Least squares method Mathematical analysis Mathematical and Computational Engineering Mathematical Modeling and Industrial Mathematics Mathematical models Mathematics Mathematics and Statistics Nonlinearity Optimization Theoretical and Applied Mechanics |
Title | Estimation of effective diffusion coefficients of drug delivery devices in a flow-through system |
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