Mathematical models for estimating effective diffusion parameters of spherical drug delivery devices

Mathematical modeling of drug delivery is of increasing academic and industrial importance in manyaspects. In this paper, we propose an optimization approach for the estimation of the parameters characterizing the diffusion process of a drug from a spherical porous polymer device to an external finite volume. The approach is based on a nonlinear least-squares method and a novel mathematical model which takes into consideration both boundary layer effect and initial burst phenomenon. Ananalytical solution to the model is derived and a formula for the ratio of the mass released in a given time interval and the total mass released in infinite time is also obtained. The approach has been tested using experimental data of the diffusion of prednisolone 21-hemisuccinate sodium saltfrom spherical devices made of porous poly(2-hydroxyethyl methacrylate) hydrogels. The effectiveness and accuracy of the method are well demonstrated by the numerical results. The model was used to determine the diffusion parameters including the effective diffusion coefficient of the drug from a series of devices that vary in both the porous structure and the drug loading levels. The computed diffusion parameters are discussed in relation to the physical properties of the devices

Model demonstrates functional purpose of the nasal cycle

Background: Despite the occurrence of the nasal cycle being well documented, the functional purpose of this phenomenon is not well understood. This investigation seeks to better understand the physiological objective of the nasal cycle in terms of airway health through the use of a computational nasal air-conditioning model. Method: A new state-variable heat and water mass transfer model is developed to predict airway surface liquid (ASL) hydration status within each nasal airway. Nasal geometry, based on in-vivo magnetic resonance imaging (MRI) data is used to apportion inter-nasal air flow. Results: The results demonstrate that the airway conducting the majority of the airflow also experiences a degree of ASL dehydration, as a consequence of undertaking the bulk of the heat and water mass transfer duties. In contrast, the reduced air conditioning demand within the other airway allows its ASL layer to remain sufficiently hydrated so as to support continuous mucociliary clearance. Conclusions: It is quantitatively demonstrated in this work how the nasal cycle enables the upper airway to accommodate the contrasting roles of air conditioning and the removal of entrapped contaminants through fluctuation in airflow partitioning between each airway