This work focuses on the mathematical analysis of the controlled release of a standardized extract of A. chica from chitosan/alginate (C/A) membranes, which can be used for the treatment of skin lesions. Four different types of C/A membranes were tested: a dense membrane (CA), a dense and flexible membrane (CAS), a porous membrane (CAP) and a porous and flexible membrane (CAPS). The Arrabidae chica extract release profiles were obtained experimentally in vitro using PBS at 37 °C and pH 7. Experimental data of release kinetics were analyzed using five classical models from the literature: Zero Order, First Order, Higuchi, Korsmeyer–Peppas and Weibull functions. Results for the Korsmeyer–Peppas model showed that the release of A. chica extract from four membrane formulations was by a diffusion through a partially swollen matrix and through a water filled network mesh; however, the Weibull model suggested that non-porous membranes (CA and CAS) had fractal geometry and that porous membranes (CAP and CAPS) have highly disorganized structures. Nevertheless, by applying an explicit optimization method that employs a cost function to determine the model parameters that best fit to experimental data, the results indicated that the Weibull model showed the best simulation for the release profiles from the four membranes: CA, CAS and CAP presented Fickian diffusion through a polymeric matrix of fractal geometry, and only the CAPS membrane showed a highly disordered matrix. The use of this cost function optimization had the significant advantage of higher fitting sensitivity.

Breast cancer ranks among the most commonly diagnosed cancers worldwide and bears the highest mortality rate. As an integral component of cancer treatment, mastectomy entails the complete removal of the affected breast. Typically, breast reconstruction, involving the use of silicone implants (augmentation mammaplasty), is employed to address the aftermath of mastectomy. To mitigate postoperative risks associated with mammaplasty, such as capsular contracture or bacterial infections, the functionalization of breast implants with coatings of cyclodextrin polymers as drug delivery systems represents an excellent alternative. In this context, our work focuses on the application of a mathematical model for simulating drug release from breast implants coated with cyclodextrin polymers. The proposed model considers a unidirectional diffusion process following Fick’s second law, which was solved using the orthogonal collocation method, a numerical technique employed to approximate solutions for ordinary and partial differential equations. We conducted simulations to obtain release profiles for three therapeutic molecules: pirfenidone, used for preventing capsular contracture; rose Bengal, an anticancer agent; and the antimicrobial peptide KR-12. Furthermore, we calculated the diffusion profiles of these drugs through the cyclodextrin polymers, determining parameters related to diffusivity, solute solid–liquid partition coefficients, and the Sherwood number. Finally, integrating these parameters in COMSOL multiphysics simulations, the unidirectional diffusion mathematical model was validated.

In many countries, whey from the dairy industry is an abundant waste that generates an important environmental impact. Alternative processes to use the whey and minimize the environmental impact are needed. This work considered six formulations with different ammonium sulfate and L-phenylalanine (L-Phe) concentrations to produce bioethanol in sweet whey fermentation by Kluyveromyces marxianus. The results showed a maximum bioethanol concentration equal to 25.13 ± 0.37 g L⁻¹ (p < 0.05) for formulation F6, with 1 g L⁻¹ of L-Phe and 1.350 g L⁻¹ of ammonium sulfate (96 h). For these conditions, the chemical oxygen demand removal percentage (CODR%) was 67%. The maximum CODR% obtained was 97.5% for formulation F3 (1 g L⁻¹ of L-Phe) at 96 h; however, a significant decrease in bioethanol concentration (14.33 ± 2.58 g L⁻¹) was observed. On the other hand, for formulation, F3, at 48 h of fermentation time, a bioethanol concentration of 23.71 ± 1.26 g L⁻¹ was observed, with 76.5% CODR%. Based on these results, we suggest that the best conditions to obtain a significant bioethanol concentration and CODR% value are those used on the configuration F3 at 48 h.