Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals

Abstract

In this study, we investigated the release kinetic of fluorescein from colloidal liquid crystals made from monoglyceride and different non-ionic surfactants. The crystals were physicochemically characterized and the release experiments were carried out under the sink conditions, while mathematical models were described as extrapolations from solutions of the diffusion equation, in different initial and boundary conditions imposed by pharmaceutical formulations. The diffusion equation was solved using Laplace and Fourier transformed functions for release kinetics from infinite reservoirs in a semi-infinite medium. Solutions represents a general square root law and can be applied for the release kinetic of fluorescein from lyotropic colloidal liquid crystals. Akaike, Schwartz, and Imbimbo criteria were used to establish the appropriate mathematical model and the hierarchy of the performances of different models applied to the release experiments. The Fisher statistic test was applied to obtain the significance of differences among mathematical models. Differences of mathematical criteria demonstrated that small or no significant statistic differences were carried out between the various applied models and colloidal formulations. Phenomenological models were preferred over the empirical and semi-empirical ones. The general square root model shows that the diffusion-controlled release of fluorescein is the mathematical models extrapolated for lyotropic colloidal liquid crystals.

Keywords: drug delivery systems; lyotropic colloidal liquid crystals; mathematical models; release kinetic; release profile; square root laws.

Figure 1

Release kinetic of fluorescein through lyotropic colloidal liquid crystal formulations. Lines and symbols, if not shown, are merged or filled in with those of other formulations. Data are the average of three different experiments ± standard deviation. Error bar if not shown is within the symbol.

Figure 2

Release kinetic of fluorescein from the lyotropic colloidal liquid crystal formulation 1, according to the following mathematical models: (a) Linear regression; (b) Higuchi; (c) Siepman–Peppas; (d) Noyes-Whitney; (e) Weibul. Data represented by the average of three different measurements. Error bars if not shown are within the symbols.

Figure 3

Evaluation of the release profile of fluorescein from the monoglyceride colloidal liquid crystal formulation 2, using the following mathematical models: (a) Linear regression; (b) Higuchi; (c) Siepman–Peppas; (d) Noyes–Whitney; and (e) Weibull. Data represented the average of three different measurements. Error bars, if not shown, are within the symbols.

Figure 4

Evaluation of the release profile of fluorescein from the lyotropic colloidal liquid crystal formulation 3, using the following mathematical models: (a) Linear regression; (b) Higuchi; (c) Siepman–Peppas; (d) Noyes–Whitney; and (e) Weibull. Data represented the average of three different measurements. Error bars, if not shown, are within the symbols.

Figure 5

Evaluation of the release profile of fluorescein from lyotropic colloidal liquid crystal formulation 4, using the following mathematical models: (a) Linear regression; (b) Higuchi; (c) Siepman–Peppas; (d) Noyes–Whitney; and (e) Weibull. Data represents the average of three different measurements ± standard deviation. Error bars, if not shown, are within the symbols.

Figure 6

Evaluation of the release profile of fluorescein by lyotropic colloidal liquid crystal formulation 5, using the following mathematical models: (a) Linear regression; (b) Higuchi; (c) Siepman–Peppas; (d) Noyes–Whitney; and (e) Weibull. Data represents the average of three different measurements ± standard deviation. Error bars, if not shown, are within the symbols.