American Institute of Mathematical Sciences

Advanced
January  2009, 5(1): 127-140. doi: 10.3934/jimo.2009.5.127

An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume

Song Wang 1, and  Xia Lou 2,

1. 

School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009
2. 

Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA 6846, Australia

Received  September 2008 Revised  October 2008 Published  December 2008

In this paper we propose a new mathematical model based on optimal fitting for estimating effective diffusion coefficients of a drug from a delivery device of 2D disc geometry to an external finite volume. In this model, we assume that the diffusion process occurs within the boundary layer of the external fluid, while outside the layer the drug concentration is uniform because of the convection-domination. An analytical solution to the corresponding diffusion equation with appropriate initial and boundary conditions is derived using the technique of separation of variables. A formula for the ratio of the mass released in the time interval $[0,t]$ for any $t>0$ and the total mass released in infinite time is also obtained. Furthermore, we extend this model to one for problems with two different effective diffusion coefficients, in order to handle the phenomenon of 'initial burst'. The latter model contains more than one unknown parameter and thus an optimization process is proposed for determining the effective diffusion coefficient, critical time and width of the effective boundary layer. These models were tested using experimental data of the diffusion of prednisolone 2-hemisuccinate sodium salt from porous poly(2-hydroxyethylmethacrylate) hydrogel based discs. The numerical results show that the usefulness and accuracy of these models.
Keywords: controlled drug release., diffusion equation, optimization, Effective diffusion coefficient, optimum design.
Mathematics Subject Classification: Primary: 65M32, 76R50, 35C05; Secondary: 62K0.
Citation: Song Wang, Xia Lou. An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume. Journal of Industrial and Management Optimization, 2009, 5 (1) : 127-140. doi: 10.3934/jimo.2009.5.127
[1]

Shalela Mohd Mahali, Song Wang, Xia Lou. Determination of effective diffusion coefficients of drug delivery devices by a state observer approach. Discrete and Continuous Dynamical Systems - B, 2011, 16 (4) : 1119-1136. doi: 10.3934/dcdsb.2011.16.1119
[2]

Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reaction-diffusion patterns. Communications on Pure and Applied Analysis, 2012, 11 (1) : 189-207. doi: 10.3934/cpaa.2012.11.189
[3]

Shalela Mohd--Mahali, Song Wang, Xia Lou, Sungging Pintowantoro. Numerical methods for estimating effective diffusion coefficients of three-dimensional drug delivery systems. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 377-393. doi: 10.3934/naco.2012.2.377
[4]

Xin Li, Xingfu Zou. On a reaction-diffusion model for sterile insect release method with release on the boundary. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2509-2522. doi: 10.3934/dcdsb.2012.17.2509
[5]

Zhidong Zhang. An undetermined time-dependent coefficient in a fractional diffusion equation. Inverse Problems and Imaging, 2017, 11 (5) : 875-900. doi: 10.3934/ipi.2017041
[6]

Giovany M. Figueiredo, Tarcyana S. Figueiredo-Sousa, Cristian Morales-Rodrigo, Antonio Suárez. Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3689-3711. doi: 10.3934/dcdsb.2018311
[7]

Elena Beretta, Cecilia Cavaterra. Identifying a space dependent coefficient in a reaction-diffusion equation. Inverse Problems and Imaging, 2011, 5 (2) : 285-296. doi: 10.3934/ipi.2011.5.285
[8]

Qinghua Luo. Damped Klein-Gordon equation with variable diffusion coefficient. Communications on Pure and Applied Analysis, 2021, 20 (11) : 3959-3974. doi: 10.3934/cpaa.2021139
[9]

Zhi Lin, Katarína Boďová, Charles R. Doering. Models & measures of mixing & effective diffusion. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 259-274. doi: 10.3934/dcds.2010.28.259
[10]

Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami Radunskaya, Ian Tucker. Predicting the drug release kinetics of matrix tablets. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 261-277. doi: 10.3934/dcdsb.2009.12.261
[11]

Carlos Fresneda-Portillo. A new family of boundary-domain integral equations for the diffusion equation with variable coefficient in unbounded domains. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5097-5114. doi: 10.3934/cpaa.2020228
[12]

Zhi-Xue Zhao, Mapundi K. Banda, Bao-Zhu Guo. Boundary switch on/off control approach to simultaneous identification of diffusion coefficient and initial state for one-dimensional heat equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2533-2554. doi: 10.3934/dcdsb.2020021
[13]

Vladimir V. Chepyzhov, Mark I. Vishik. Trajectory attractor for reaction-diffusion system with diffusion coefficient vanishing in time. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1493-1509. doi: 10.3934/dcds.2010.27.1493
[14]

Zhenzhen Chen, Sze-Bi Hsu, Ya-Tang Yang. The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants. Communications on Pure and Applied Analysis, 2020, 19 (1) : 203-220. doi: 10.3934/cpaa.2020011
[15]

Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227-238. doi: 10.3934/mbe.2005.2.227
[16]

Bastian Harrach. Simultaneous determination of the diffusion and absorption coefficient from boundary data. Inverse Problems and Imaging, 2012, 6 (4) : 663-679. doi: 10.3934/ipi.2012.6.663
[17]

Laure Cardoulis, Michel Cristofol, Morgan Morancey. A stability result for the diffusion coefficient of the heat operator defined on an unbounded guide. Mathematical Control and Related Fields, 2021, 11 (4) : 965-985. doi: 10.3934/mcrf.2020054
[18]

Yunmei Chen, Weihong Guo, Qingguo Zeng, Yijun Liu. A nonstandard smoothing in reconstruction of apparent diffusion coefficient profiles from diffusion weighted images. Inverse Problems and Imaging, 2008, 2 (2) : 205-224. doi: 10.3934/ipi.2008.2.205
[19]

Elie Bretin, Imen Mekkaoui, Jérôme Pousin. Assessment of the effect of tissue motion in diffusion MRI: Derivation of new apparent diffusion coefficient formula. Inverse Problems and Imaging, 2018, 12 (1) : 125-152. doi: 10.3934/ipi.2018005
[20]

Thomas Frenzel, Matthias Liero. Effective diffusion in thin structures via generalized gradient systems and EDP-convergence. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 395-425. doi: 10.3934/dcdss.2020345

2021 Impact Factor: 1.411

Tools

Metrics

  • PDF downloads (70)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy