Determination of effective diffusion coefficients of drug delivery devices by a state observer approach

Pages: 1119 - 1136, Volume 16, Issue 4, November 2011

doi:10.3934/dcdsb.2011.16.1119       Abstract        References        Full Text (532.9K)       Related Articles

Shalela Mohd Mahali - School of Mathematics & Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia (email)
Song Wang - School of Mathematics & Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia (email)
Xia Lou - Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA 6846, Australia (email)

Abstract: In this paper we present a state observer approach for the estimation of effective diffusion coefficients of a drug delivery device. In this approach, we construct estimators for the unknown effective diffusion coefficients characterizing the diffusion process of a drug release device using a combination of state observers from the area of adaptive control and the drug diffusion models developed recently by us. We show that the constructed systems are asymptotically stable and the estimators converge to the exact diffusion coefficients. An algorithm is proposed to recursively compute the estimators using a given time series of a release profile of a device. To demonstrate the efficiency and usefulness of this approach, numerical experiments have been performed using experimentally observed drug release profiles of polymeric spherical devices. The numerical results show that the present approach is about 9 times faster than the conventional least squares method when applied to the test problems.

Keywords:  State observer, estimator, diffusion coefficient, optimization, drug delivery.
Mathematics Subject Classification:  Primary: 49N45; Secondary: 93C45.

Received: October 2010;      Revised: February 2011;      Published: August 2011.

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