In vitro determination of drug diffusion coefficients in viscous media using pulsatile microdialysis: Theory and method development

Drug diffusion in a biological environment is a fundamental process in pharmaceutical science. It has been a historically difficult task to study such processes because of the lack of a suitable technology that can provide in situ information. In fact, it is not possible to determine diffusion coefficients using currently available methods in many systems (for instance, in viscous, multiphase and polymer-containing media). Pulsatile microdialysis (PMD) is a recently developed technology that can be used to characterize the diffusion process in such systems. The goal of this work was to optimize the PMD technology for the purpose of determining drug diffusion coefficients, and to assess the quality of the resulting diffusion coefficients by determining if they follow certain classically known relationships, especially with regard to temperature and medium viscosity. (This is necessary because, for many of these systems, no diffusion coefficient data are available for direct comparison.);The method optimization of PMD was a theory guided process. A mathematical model for the PMD diffusion processes was set up based on Fick's Laws of diffusion in cylindrical coordinates, and the resulting equations were solved with the appropriate initial and boundary conditions. Equations were then derived to determine basic transport parameters, such as diffusion and permeability coefficients, from mass uptake data obtained through PMD experiments. It was found that the calculation of diffusion coefficients required accurately determining the volume of the probe window VW and a mathematical parameter lambda, which is a property of the probe and not the materials or temperature. Prior to this work, VW was calculated based on data supplied by the probe manufacturer, but these data were determined in a dry state and not accurate enough for this work. Therefore, experimental methods were developed to determine VW in the wet state. As long as the surface properties of the probe remain constant, lambda should not change. From the mathematical and experimental developments, it was found that once a probe is calibrated for VW and lambda, it can be used to determine the diffusion coefficient of a drug in the dialysate by a simple two parameter fit of the PMD data.;In this work, the resulting mathematical equations were numerically implemented and evaluated for data analysis. Because the solutions to the governing model equations were in the form of infinite series, significant attention was given to the details of the data analysis calculations. One area of focus was to reduce the amount of calculation required without jeopardizing accuracy of the results. This was done by analyzing how many terms were needed in infinite series. It was found that, in most of the cases, the first three exponential terms were sufficient to ensure accurate calculations.;The application of PMD to the determination of diffusion coefficients was tested by investigating the diffusion of ibuprofen in water, Tween 40 plus water systems, and aqueous solutions of polyethylene glycol (PEG) at different temperatures. The ibuprofen diffusion coefficients were determined from PMD data and the viscosities of the media were measured using a viscometer, and the results were related using the Arrhenius relationship and the Stokes-Einstein equation. This was important because no methods are available to determine diffusion coefficients in some of the systems, so it was not possible to compare the diffusion coefficients obtained from some of the systems with previously published data. A linear Arrhenius relationship of diffusion coefficient versus reciprocal of temperature was found in water and PEG media. The resistance to diffusion is only due to the molecular interaction between the drug molecules and the solvent and PEG molecules in the media. A nonlinear Arrhenius plot was found for the diffusion coefficient of ibuprofen in the TweenRTM 40 solutions. The resistant of this diffusion process was from more than one source. One possible source could be the interactions between ibuprofen and the micelles formed by Tween 40. Stokes-Einstein plots were made for ibuprofen in water and Tween-40 in water media. The resulting ibuprofen molecular radius from water was very close to that was found in the literature, but the radius calculated using results from Tween 40 plus water systems was found to be ten times larger. This was explained by the existence of micelles in the Tween 40 plus water systems, which affected the diffusion processes by increasing the tortuosity.;Experimental approaches to determine the solubility in messy, viscous, and multiphase media were studied. The ibuprofen solubility was measured using a continuous flow microdialysis technique (CFMD) and a PMD method for microemulsion dispersions in water. The results were comparable.;In conclusion, the PMD experimental method was optimized for the purpose of determining drug diffusion coefficients in media for which other methods are not suitable. This included the identification and development of necessary probe calibration procedures, extending the mathematical theory and optimizing the numerical implementation of the resulting equations for data analysis.