Estimation of effective diffusion coefficients of drug delivery devices in a flow-through system

• Published in: Journal of engineering mathematics Vol. 87; no. 1; pp. 139 - 152
• Main Authors: Mohd Mahali, Shalela, Wang, Song, Lou, Xia
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2014
• Subjects: 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; Finite volume discretization; Controlled drug delivery; Effective diffusion coefficient; Nonlinear least-squares method; Sink condition
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-013-9669-y

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.