*3.3. In Vitro Release Test of DEX-Loaded LPNCs and Free DEX*

*3.3. In Vitro Release Test of DEX-Loaded LPNCs and Free DEX*  The release data of the free DEX and LPNCs can be seen in Figure 4. After 24 h, the DEX formulated in an ethanolic solution (FREE-DEX) was released at 100%, while the release of DEX loaded in LPNCs (LPNCs-DEX) was more sustained, due to diffusion The release data of the free DEX and LPNCs can be seen in Figure 4. After 24 h, the DEX formulated in an ethanolic solution (FREE-DEX) was released at 100%, while the release of DEX loaded in LPNCs (LPNCs-DEX) was more sustained, due to diffusion through the polymeric framework and the affinity of the active for the lipid cores of the particles. *Pharmaceutics* **2021**, *13*, x 11 of 21

through the polymeric framework and the affinity of the active for the lipid cores of the

**Figure 4.** Mean release data obtained from the DEX-loaded LPNCs and from the ethanolic solution of DEX (FREE-DEX) after 24 h of the in vitro release test. **Figure 4.** Mean release data obtained from the DEX-loaded LPNCs and from the ethanolic solution of DEX (FREE-DEX) after 24 h of the in vitro release test.

After adjusting the mean release data with the different mathematical models (see Table 6), it was observed that Weibull was the model that best fit (AIC 28.81) the experimental data in the case of LPNCs, and Korsmeyer–Peppas was the model that best fit (AIC After adjusting the mean release data with the different mathematical models (see Table 6), it was observed that Weibull was the model that best fit (AIC 28.81) the experimental data in the case of LPNCs, and Korsmeyer–Peppas was the model that best fit (AIC 44.86) in the case of DEX formulated in a hydroalcoholic solution.

44.86) in the case of DEX formulated in a hydroalcoholic solution. **Table 6.** Model selection and parameter estimation of the LPNCs-DEX and FREE-DEX. Bold type Once the mean release kinetic behavior was determined, the mean and standard deviation of the individual release data for free DEX and LPNCs-DEX were obtained, as reported in Table 7.

indicates the selected model, based on the lowest AIC. **Formulation Model AIC Parameters Value**  LPNCs-DEX First order 31.84 k (h<sup>−</sup>1) 0.128 Higuchi 39.98 kH (%h<sup>−</sup>1/2) 16.263 Korsmeyer–Peppas 39.13 kKP (%h<sup>−</sup>n) n 7.91 0.573 Although the Weibull equation is a non-mechanistic equation, Papadopoulou et al. [22] obtained a relationship between the shape parameter β and the release mechanism, in the same way as the power law equation (Korsmeyer–Peppas equation) does with the exponent n. In the case of LPNCs-DEX, the value of β was between 0.75 and 1, which corresponds to a combined release mechanism; that is, diffusion in a normal Euclidean substrate with the contribution of another release mechanism. This fact was confirmed by the *n* value (0.573)

First-order 68.51 k (h<sup>−</sup>1)

**Korsmeyer–Peppas 44.86 kKP (%h<sup>−</sup>n)** 

Weibull 47.43 <sup>β</sup>

Once the mean release kinetic behavior was determined, the mean and standard deviation of the individual release data for free DEX and LPNCs-DEX were obtained, as

**Table 7.** Individual modelling and parameters for the LPNCs and FREE DEX release data.

**Formulation Model Parameters Value** 

**β**

Fmax (%)

**n** 

Td (h)

Higuchi 71.60 kH (%h<sup>−</sup>1/2) 22.475

Td (h)

kKP (%h−n) n

**13.49 0.79** 

0.192 104.35

**42.78 0.271** 

0.698 3.21

0.82 ± 0.17 14.16 ± 4.11

42.39 ± 5.96 0.278 ± 0.034

LPNCs-DEX Weibull <sup>β</sup>

pas

FREE-DEX Korsmeyer–Pep-

FREE-DEX

reported in Table 7.

found for LPNCs reported in Table 6, corresponding to anomalous transport or a combined mechanism. Due to the hybrid nature of these nanoparticles, the active ingredient could be distributed both in the lipid core and the polymeric framework, resulting in an overlap of both release kinetics, such that anomalous transport would be observed. In the case of FREE-DEX, this study was below the limits set in the Korsmeyer–Peppas model (i.e., 0.43). However, Singhvi and Singh [32] reported that, although the value of n obtained was not in the range suggested in Korsmeyer–Peppas model, it also indicates a diffusion-controlled drug release mechanism. This fact could be confirmed by the Weibull model, which had an AIC value close to that of Korsmeyer–Peppas, where the β value for FREE-DEX was 0.698 (i.e., between 0.69 and 0.75), which would indicate the release as a normal diffusion mechanism dominated by the concentration difference without the contribution of other release mechanisms, unlike the case of LPNCs.


**Table 6.** Model selection and parameter estimation of the LPNCs-DEX and FREE-DEX. Bold type indicates the selected model, based on the lowest AIC.

**Table 7.** Individual modelling and parameters for the LPNCs and FREE DEX release data.

