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

• 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.
Mathematics Subject Classification: Primary: 65M32, 76R50, 35C05; Secondary: 62K05.

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