*3.4. Model Fitting: Kinetic Drug Release Mechanisms*

The experimental release data were fitted to different kinetic models to better understand the release profiles: Higuchi, Korsmeyer–Peppas, Kim, Peppas–Sahlin, zero order, and first order. This point is highly recommended since mathematical modeling could help to understand the further in vivo performance of the formulations [96]. Fitting parameters of all the models using the first 10 h data and 72 h data are listed in Table S1, Supplementary Materials section. The AIC was used as a comparative of the goodness of fit (also listed in Table S1, Supplementary Materials section). In general, the Korsmeyer–Peppas model presented the lowest AIC values, indicating an accurate fitting, for almost all formulations. However, in certain cases (T1d 10 h, T2c 72 h, E1 72 h and S), the first order was the best model. The Kim model is a modification of the Korsmeyer–Peppas one that considers a possible burst effect. This burst effect (represented by parameter "b") was neglected by the fitting, and the results of both models match. Burst release effect of drugs is frequently related to "dose dumping", an event to avoid in a controlled release system that was demonstrated not to happen in our prototypes [97,98].

The main difference between the first order model and the Korsmeyer–Peppas one is the mechanisms underlying the release process. First order only reflects a passive diffusion, while Korsmeyer–Peppas also considers other effects, such as relaxation or matrix erosion. Contrary to what was expected for ultraflexible vesicles, the Korsmeyer– Peppas model was more suitable for most of the cases, pointing out that they present a mixed release mechanism. It seems that relaxation has a stronger influence during the first steps and gets diluted during longer sampling times, in favor of passive diffusion. This behavior can be deduced from the values of the release exponent "n", which presents intermediate values (0.5–0.85) when the initial 10 h data are fitted and low values (<0.5) when 72 h data are included. Finally, the *R* <sup>2</sup> values from both models are also listed in Table S2 (Supplementary Materials section). We could observe from their analysis that the models used are suitable for explaining the release process (they account for >90% of the experimental data variation) [57,58].
