*2.6. In Vitro Release Tests of the DEX-Loaded LPNCs*

In vitro release of DEX from the LPNCs was studied using vertical Franz cells (Vidrafoc, Barcelona, Spain) with a 12 mL receptor compartment and an effective diffusion area of 1.54 cm<sup>2</sup> . A mixture of ethanol and purified water (50:50) was used as receptor medium (RM), at 32 ◦C and stirred at 500 rpm, to keep the sink conditions throughout the experiment. A total of 0.6 g of LPNCs was applied in the donor compartment, corresponding to 60 mg of DEX. The membrane used was a dialysis membrane (Spectrum Chemical, New Brunswick, NJ, USA) with pore diameter of 12–14 kDa.

Aliquots of 300 µL were taken at certain times (1, 2, 3, 4, 5, 21, 22, 23, and 24 h) and injected into the HPLC with the method described in Section 2.5, to quantify the amount of DEX that had diffused through the membrane.

Kinetic modelling of the release data was studied with the DD-solver [20] Excel Add-on, using a non-linear approach. Model selection was based on the lowest Akaike Information Criteria (AIC), reflecting the lowest deviation of the model with respect to the empirical data [21]. Firstly, the mean release values were adjusted to the model described in Table 2, to obtain the mean population behavior. Then, individual data were adjusted, according to the model selected. The mean and standard deviation of the parameters were reported.

**Table 2.** Different kinetic models and equations tested.


In Table 2, F is the fraction of active released at time *t*, *Fmax* is the maximum fraction of active released (i.e., at infinite time), K<sup>1</sup> is the first-order constant, *K<sup>H</sup>* is the Higuchi constant, *KKP* is the Korsmeyer–Peppas constant (related to the structural and geometric character of the drug release matrix), *n* is the diffusional exponent indicating the drugrelease mechanism (if *n* is less than 0.43, then a Fickian diffusion release mechanism is implied; if *n* is between 0.43 and 0.85, then the release mechanism follows an anomalous transport mechanism), T<sup>d</sup> represents the time at which 63.2% of the drug is released, and β is the Weibull shape parameter. For values of β lower than 0.75, the release follows a Fickian diffusion, either in Euclidian (0.69 < β < 0.75) or fractal (β < 0.69) space. Values of β in the range of 0.75–1.0 indicate a combined mechanism, which is frequently encountered in release studies [22,23].
