Mathematical modeling of drug release from swellable polymeric nanoparticles

Abstract

This study aims to provide a comparative mathematical analysis of drug release from swellable polymeric delivery systems to find a general model applicable to multi-mechanistic release. Drug release data from various swellable polymeric nanoparticles extracted from the literatures were applied to the eight conventional models. Coefficient of determination (R 2 ) and absolute percent error (E%) were calculated for each set as well as the overall error (OE), the number of error (NE) and the akaike information criterion (AIC) for all sets. The model has the highest R 2 and the number of the error, as well as both the lowest overall error (OE) and the akaike information criterion, was considered as the best one. Among the models Weibull (W) model produced R 2 and OE values of 0.93 and 8.79, respectively. Also, the AIC value and the number of errors less than 5% for the model was -34.93 and 46.15% of a total number of data sets respectively. Mathematical modeling of drug release from a carrier is often attempted to recognize the main determinants of the drug release rate from the carrier with the final goal of the identification of the ideal set of conditions leading to the desired release profile in vivo.

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

“…In addition, zero-order behavior can be observed in materials capable of swelling [ 129 ], yet due to complicated bulk erosion and surface erosion and diffusion processes, most studies on the sustained release of hydrophilic drugs have failed to achieve a release profile that conforms to zero-order kinetics for a prolonged time [ 130 ]. This conclusion was verified in this study, in which the data sets had a biphasic behavior far from zero-order according to the low values of R 2 and R 2 a and the high averages of the calculated AIC and BIC [ 131 ]. Likewise, the results obtained showed rejection of the first-order model for all data sets, demonstrating that the data sets do not follow a model that is dependent on the initial drug concentration [ 78 , 132 ].…”

“…The empirical Weibull model is an expression that tries to find a linear relationship between the logarithm of drug release and the logarithm of time [ 136 ]. Despite not having a kinetic nature, nor parameters physically related to the release phenomena, the ability of the logarithmic form to dampen the abrupt changes in drug concentration rate over time as they pass from one phase to another, has allowed this model to be successfully applied in several release studies [ 58 , 131 , 135 , 137 , 138 ]. In this study, the Weibull equation was able to fit 12 data sets adequately according to the R 2 and R 2 adjusted, however, when studying the value of AIC and BIC, the model failed to have the best fit in any of the sets, probably because as an empirical model, its predictive power is poor [ 58 , 62 , 137 ].…”

“…Equally, the values of AIC and BIC were more positive compared to the mathematical models. Since AIC and BIC are a measure of goodness-of-fit conditional on the number of parameters used in the model, this result is congruent, and indicates the inability of the expressions to predict the future behavior of the system [ 131 , 145 ]. Pourtalebi Jahromi and collaborators (2020) used the second degree polynomial equation in their analysis of the release kinetics from nanoparticles, obtaining results similar to those of this study [ 58 ].…”

Overcoming the Limits of Flash Nanoprecipitation: Effective Loading of Hydrophilic Drug into Polymeric Nanoparticles with Controlled Structure

“…The caffeine concentration was determined by UV spectrophotometry. Caffeine cumulative release data were collected and fitted by 5 models, i.e., (i) Zero-Order; (ii) First-Order; (iii) Higuchi; (iv) Hixon-Crowell; and (v) Baker-Lonsdale model [48,49]. The regressions were carried out by interpolating the data until the asymptote in the cumulative release curve was reached.…”

Insight into oral amphiphilic cyclodextrin nanoparticles for colorectal cancer: comprehensive mathematical model of drug release kinetic studies and antitumoral efficacy in 3D spheroid colon tumors

“…“β” ≤ 0.75 indicates Fickian diffusion, while 0.75 < “β” < 1 indicates a complex mechanism (Fickian diffusion and controlled release). For values of “β” higher than 1, it was demonstrated that the drug transport follows a complex release mechanism [ 35 , 47 – 48 ]. The “β” value for the Weibull model was calculated as 0.493 and 0.401 for the 6-O-capro-β-CD and CS-(6-O-capro-β-CD) NPs, respectively.…”