Comparative statistical analysis of the release kinetics models for nanoprecipitated drug delivery systems based on poly(lactic-co-glycolic acid)

Abstract

Poly(lactic-co-glycolic acid) is one of the most used polymers for drug delivery systems (DDSs). It shows excellent biocompatibility, biodegradability, and allows spatio-temporal control of the release of a drug by altering its chemistry. In spite of this, few formulations have reached the market. To characterize and optimize the drug release process, mathematical models offer a good alternative as they allow interpreting and predicting experimental findings, saving time and money. However, there is no general model that describes all types of drug release of polymeric DDSs. This study aims to perform a statistical comparison of several mathematical models commonly used in order to find which of them best describes the drug release profile from PLGA particles synthesized by nanoprecipitation method. For this purpose, 40 datasets extracted from scientific articles published since 2016 were collected. Each set was fitted by the models: order zero to fifth order polynomials, Korsmeyer-Peppas, Weibull and Hyperbolic Tangent Function. Some data sets had few observations that do not allow to apply statistic test, thus bootstrap resampling technique was performed. Statistic evidence showed that Hyperbolic Tangent Function model is the one that best fit most of the data.

Fig 1. Flow diagram for the screening procedure and selection criteria for the scientific articles chosen in this study.

Fig 2. Time-line of conventional empirical/semi-empirical models.

a. [82]; b. [83]; c. [84]; d. [85]; e. [79]; f. [81]; g. [86]; h. [50]; i. [76].

Fig 3. Diagram of the process for parameter estimation by Bootstrap resampling.

Fig 4. Average of R²—R²_a of the data sets fitted to the second to fifth order polynomials.

Fig 5. AIC / BIC vs. R² plots obtained from linear regression fitting (left) and AIC versus R2 obtained from Bootstrap fitting (right) for the zero-order (top) and first-order (bottom) mathematical models.

Fig 6. AIC / BIC vs R² plots obtained from linear regression fitting (left) and AIC vs R2 obtained from Bootstrap fitting (right) for the mathematical models of Korsmeyer-Peppas fitted to the entire release curve (top) and Korsmeyer-Peppas fitted to the first 60% of the release curve (bottom).

Fig 7. AIC / BIC vs R² plots obtained from linear regression fitting (left) and AIC vs R2 obtained from Bootstrap fitting (right) for the mathematical models of Weibull (top) and Hyperbolic Tangent Function (bottom).