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

• DOI: 10.1007/s10665-013-9669-y
• Publication Date: 2014-05-05T10:30:45Z
• Authors: Shalela Mohd Mahali; Song Wang; Xia Lou
• Keywords: Nonlinear least-squares method; Finite volume discretization; Effective diffusion coefficient; 0101 mathematics; Sink condition; 01 natural sciences; Controlled drug delivery; 510

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.